Towards Self-Driving Vehicles

**3**

**Chapter 1**

*Marian Găiceanu*

Science and New Technologies.

significant injuries for the other 600.

and Romania (97) the highest rate.

**2. Motivation**

**1. Introduction**

Introductory Chapter: European

Union towards Self-Driving Car

Europa, follows the Wim van de CAMP Euro-parliamentary initiative [1, 2], adopting *On the road to automated mobility: An EU strategy for mobility of the future*, Brussels, 2018. The communication includes the automated and connected mobility for all kinds of transport fields: underwater, water surface, on ground and underground, or by air. The main advantages of adopting Driverless vehicles are as follows: reducing transport costs, increased mobility access (by elder people or with disabilities), sharing mobility, increased safety transport and comfort, more efficient urban planning. For long term, the EU Vision Zero (2050) concept was introduced, which means no road fatalities. The EU regulatory framework has in view the deployment of interoperable Cooperative Intelligent Transport Systems. The ethical side in EU is equal in worth with the automated mobility, as in worldwide. The driverless vehicle should be safety, socially responsible (to respect the freedom of human choice and the human dignity), efficiently, and environmentally friendly. All these aspects are coordinated and investigated by the European Artificial Intelligence (AI) Alliance. The European AI Alliance born in 2018 with the main target: AI implementation in Europe taking into account the ethics rules in

One sight over the causes of death statistics in the European Union (EU) shows that the accident occurrences take the second place (most were male population).

As it is depicted in **Figure 2**, the number of railway accidents in EU27 decreases from 2249 (2010) to 1506 (2019). These accidents cause a total of 802 fatalities, and

The number of road accident fatalities per million inhabitants was 50.5 in the EU in 2016. Sweden and the United Kingdom recorded the lowest rate, Bulgaria (99)

Taking into consideration the statistics result from **Figures 2** and **3**, one dramatic

remark can be concluded that the accident fatalities on the road, railway, or by extrapolating on sea/undersea, or by air could be avoided if the human factor can be replaced. Therefore, the European Parliament [7] takes emergent measures [1, 2] to

avoid in the near future the accidents in the transport area.

Human error [3] is the most cause (95%) in road accidents (**Figure 1**).

Pathway. M2M Era

#### **Chapter 1**

## Introductory Chapter: European Union towards Self-Driving Car Pathway. M2M Era

*Marian Găiceanu*

#### **1. Introduction**

Europa, follows the Wim van de CAMP Euro-parliamentary initiative [1, 2], adopting *On the road to automated mobility: An EU strategy for mobility of the future*, Brussels, 2018. The communication includes the automated and connected mobility for all kinds of transport fields: underwater, water surface, on ground and underground, or by air. The main advantages of adopting Driverless vehicles are as follows: reducing transport costs, increased mobility access (by elder people or with disabilities), sharing mobility, increased safety transport and comfort, more efficient urban planning. For long term, the EU Vision Zero (2050) concept was introduced, which means no road fatalities. The EU regulatory framework has in view the deployment of interoperable Cooperative Intelligent Transport Systems.

The ethical side in EU is equal in worth with the automated mobility, as in worldwide. The driverless vehicle should be safety, socially responsible (to respect the freedom of human choice and the human dignity), efficiently, and environmentally friendly. All these aspects are coordinated and investigated by the European Artificial Intelligence (AI) Alliance. The European AI Alliance born in 2018 with the main target: AI implementation in Europe taking into account the ethics rules in Science and New Technologies.

#### **2. Motivation**

One sight over the causes of death statistics in the European Union (EU) shows that the accident occurrences take the second place (most were male population). Human error [3] is the most cause (95%) in road accidents (**Figure 1**).

As it is depicted in **Figure 2**, the number of railway accidents in EU27 decreases from 2249 (2010) to 1506 (2019). These accidents cause a total of 802 fatalities, and significant injuries for the other 600.

The number of road accident fatalities per million inhabitants was 50.5 in the EU in 2016. Sweden and the United Kingdom recorded the lowest rate, Bulgaria (99) and Romania (97) the highest rate.

Taking into consideration the statistics result from **Figures 2** and **3**, one dramatic remark can be concluded that the accident fatalities on the road, railway, or by extrapolating on sea/undersea, or by air could be avoided if the human factor can be replaced. Therefore, the European Parliament [7] takes emergent measures [1, 2] to avoid in the near future the accidents in the transport area.

**Figure 1.** *Causes of death — Standardised death rate, EU-27, 2016, (per 100 000 inhabitants). Source: Eurostat [4].*

**5**

**Figure 5.**

*Introductory Chapter: European Union towards Self-Driving Car Pathway. M2M Era*

The main investment of the EU27 Companies in research and development (R&D) is in transport (automobiles) field [10]. The second investment sector is in

The first two sectors are strong related to the green vehicles development. The

One key factor of developing is the investment in R&D. In Europe, by benchmarking EU Industry Innovation Performance, there is a step forward in the last years, the 5,6% of R&D rising only in one year, 2019, while in the rest of the world by 8,9% [11]. This demonstrates the high rate of investment in R&D in Europe

*Top. World top 2500 R&D investors. Down: Left number of companies by country; right: Companies by main* 

self-driving cars development is facilitated by both telecommunication infrastructure development and adopting of artificial intelligence strategy by the most countries. Cybersecurity, safety, and ethical rules should be inside of the regulatory

*DOI: http://dx.doi.org/10.5772/intechopen.97358*

ICT, followed by health sector (**Figure 4**).

*The accidents fatalities in road traffic per million inhabitants in 2016 [6].*

frameworks of self-driving car developing.

(**Figure 5**).

**Figure 4.**

*industrial sector of activity [10, 11].*

*R&D investment rate in Europe (2019) [12].*

**Figure 3.**

#### **Figure 2.**

*Statistics of major railway accidents between 2010 and 2019, in EU27 [5].*

The exponentially rise of the self-driving market is expected [8]. The main benefits of this trends is new jobs creation, involving the economic growth with safer roads, increased comfort, and more accessibility [9]. Moreover, the non-polluted self-driving cars implies a protection of the environment [9].

The challenges of introducing self-driving cars are in the field of legislation, ethics, cyber-security, maps creation, weather conditions, infrastructure technology, artificial intelligence adoption strategy by each EU country.

*Introductory Chapter: European Union towards Self-Driving Car Pathway. M2M Era DOI: http://dx.doi.org/10.5772/intechopen.97358*

**Figure 3.**

*Self-Driving Vehicles and Enabling Technologies*

**4**

**Figure 2.**

**Figure 1.**

The exponentially rise of the self-driving market is expected [8]. The main benefits of this trends is new jobs creation, involving the economic growth with safer roads, increased comfort, and more accessibility [9]. Moreover, the non-polluted

The challenges of introducing self-driving cars are in the field of legislation, ethics, cyber-security, maps creation, weather conditions, infrastructure technology,

*Causes of death — Standardised death rate, EU-27, 2016, (per 100 000 inhabitants). Source: Eurostat [4].*

self-driving cars implies a protection of the environment [9].

*Statistics of major railway accidents between 2010 and 2019, in EU27 [5].*

artificial intelligence adoption strategy by each EU country.

The main investment of the EU27 Companies in research and development (R&D) is in transport (automobiles) field [10]. The second investment sector is in ICT, followed by health sector (**Figure 4**).

The first two sectors are strong related to the green vehicles development. The self-driving cars development is facilitated by both telecommunication infrastructure development and adopting of artificial intelligence strategy by the most countries. Cybersecurity, safety, and ethical rules should be inside of the regulatory frameworks of self-driving car developing.

One key factor of developing is the investment in R&D. In Europe, by benchmarking EU Industry Innovation Performance, there is a step forward in the last years, the 5,6% of R&D rising only in one year, 2019, while in the rest of the world by 8,9% [11]. This demonstrates the high rate of investment in R&D in Europe (**Figure 5**).

#### **Figure 4.**

*Top. World top 2500 R&D investors. Down: Left number of companies by country; right: Companies by main industrial sector of activity [10, 11].*

**Figure 5.** *R&D investment rate in Europe (2019) [12].*

**Figure 6.**

*The sector hierarchy in Europe of the R&D investment [12].*

#### **Figure 7.** *The country hierarchy in Europe of the R&D investment [12].*

By analysing the above-mentioned **Figures 5**–**7**, the main conclusion is the fast-accelerating rate by the R&D investors in vehicle development sector in EU countries.

#### **3. Enabled actions and advanced technologies**

The grow-up of the driverless-vehicles is enabled by the on-going research project on the ecosystem (smart cities) and in the transport field.

The H2020 pilot research projects are the main catalysators towards Self-driving car Pathway. AUTOmated driving Progressed by Internet Of Things (AUTOPILOT) [13] is an open source platform for IoT vehicle (containing three main ingredients: vehicles, road infrastructure, and the IoT objects). The main objective includes the self-driving safety. Additional services are investigated (self-parking, terrain mapping or vehicle-sharing).

At the same time, the already open source IoT experimental platforms represent one important tool to test the new IoT technologies before integrating in the real world. Different M2M architectures, cyber physical systems (IoT-A), standards (for example oneM2M) and open platforms (UniversAAL, FIWARE) can be exploited by the pilot projects [14].

**7**

*Introductory Chapter: European Union towards Self-Driving Car Pathway. M2M Era*

Commission and Infrastructure Association (5G IA), the private side [19].

network by an 5G-based system architecture and new V3X services.

The pioneer project 5GCAR: Fifth Generation Communication Automotive Research and innovation [15–17] has in view connectivity and testing of V2X

The future generation communication infrastructure and connectivity standards will be handled by the 5G Public Private Partnership (5G PPP) [18], in the framework of The European Union Program for Research and Innovation, Horizon 2020 program. The Public Private Partnership is formed by the European

There are ambitious objectives to take care of 5G infrastructure development, and Key Performance Indicators (KPI) to be reach, including 1000 times higher wireless data volume than of 2010, large access (10 to 100 times more connected devices) to low-cost applications and services with a high reliable (End-to-End latency of <1 ms; 10 times to 100 times higher typical user data rate), secure Internet with low energy consumption (10 times lower energy consumption) [20]. ENabling SafE Multi-Brand pLatooning (ENSEMBLE) for Europe large scale research project has in view the multi-brand truck platooning in real world of the Europe traffic to ensure a safety road, low fuel consumption [21]. One of the project outcomes will be the standardisation of the communication protocols between the trucks platoon, in which each truck is followed by the other by respecting the traffic

The safe distance is mentioned from the preceding vehicle to lead vehicle by

According to European Commission Decision 2008/671 (named '5.9 GHz ITS Decision') there is specified for the safety-used communication technologies in Intelligent Transport Systems (ITS) the availability of the 5875–5905 MHz spectrum

In 2016 European Commission adopted European Strategy on Cooperative Intelligent Transport Systems (C-ITS), rising cooperative, connected and automated mobility (CCAM) [24]. In order to develop C-ITS services, the European Commission has in view to strength of the relationship between the investments and regulatory frameworks. The outcomes of the large pilot projects in intelligent transport will enable the specific standards within C-ITS. In USA, Society of

Automotive Engineers (SAE) introduce the level of driving automation in 2014 [25],

The cooperative driving of the self-driving vehicles is the next level of full automation. The new called Cooperative Driving Automation standard was introduced by the SAE on May 2020 through the SAEJ3216 standard. This standard is based to the predecessor SAE J3016 which stipulates the six levels of driving technologies

This new standard, J3216, defines the progress of cooperative control, from A to

The self-driving vehicles should include both e-safety systems and vehicle safety communications. The e-safety systems comprise at least: Advanced driverassistance systems (ADAS), automatic emergency braking systems, forward and reverse collision warning (FCW, RCW) system, adaptive cruise control, lane-

D classes, enabling machine to machine (M2M) communication systems.

One year later, on 21st of May 2020, SAE International comes with the new standard, SAE J3216: Taxonomy and Definitions for Terms Related to Cooperative

**4. Cooperative intelligent transport systems. Towards M2M**

Driving Automation for On-Road Motor Vehicles [27].

*DOI: http://dx.doi.org/10.5772/intechopen.97358*

rules (speed, distance, traffic signs) [22].

using radar or/and laser sensor systems.

use for IS applications in the EU [23].

and updated in 2019 [26].

keeping technology [28–30].

(from 0 to 5).

#### *Introductory Chapter: European Union towards Self-Driving Car Pathway. M2M Era DOI: http://dx.doi.org/10.5772/intechopen.97358*

The pioneer project 5GCAR: Fifth Generation Communication Automotive Research and innovation [15–17] has in view connectivity and testing of V2X network by an 5G-based system architecture and new V3X services.

The future generation communication infrastructure and connectivity standards will be handled by the 5G Public Private Partnership (5G PPP) [18], in the framework of The European Union Program for Research and Innovation, Horizon 2020 program. The Public Private Partnership is formed by the European Commission and Infrastructure Association (5G IA), the private side [19].

There are ambitious objectives to take care of 5G infrastructure development, and Key Performance Indicators (KPI) to be reach, including 1000 times higher wireless data volume than of 2010, large access (10 to 100 times more connected devices) to low-cost applications and services with a high reliable (End-to-End latency of <1 ms; 10 times to 100 times higher typical user data rate), secure Internet with low energy consumption (10 times lower energy consumption) [20].

ENabling SafE Multi-Brand pLatooning (ENSEMBLE) for Europe large scale research project has in view the multi-brand truck platooning in real world of the Europe traffic to ensure a safety road, low fuel consumption [21]. One of the project outcomes will be the standardisation of the communication protocols between the trucks platoon, in which each truck is followed by the other by respecting the traffic rules (speed, distance, traffic signs) [22].

The safe distance is mentioned from the preceding vehicle to lead vehicle by using radar or/and laser sensor systems.

According to European Commission Decision 2008/671 (named '5.9 GHz ITS Decision') there is specified for the safety-used communication technologies in Intelligent Transport Systems (ITS) the availability of the 5875–5905 MHz spectrum use for IS applications in the EU [23].

#### **4. Cooperative intelligent transport systems. Towards M2M**

In 2016 European Commission adopted European Strategy on Cooperative Intelligent Transport Systems (C-ITS), rising cooperative, connected and automated mobility (CCAM) [24]. In order to develop C-ITS services, the European Commission has in view to strength of the relationship between the investments and regulatory frameworks. The outcomes of the large pilot projects in intelligent transport will enable the specific standards within C-ITS. In USA, Society of Automotive Engineers (SAE) introduce the level of driving automation in 2014 [25], and updated in 2019 [26].

One year later, on 21st of May 2020, SAE International comes with the new standard, SAE J3216: Taxonomy and Definitions for Terms Related to Cooperative Driving Automation for On-Road Motor Vehicles [27].

The cooperative driving of the self-driving vehicles is the next level of full automation. The new called Cooperative Driving Automation standard was introduced by the SAE on May 2020 through the SAEJ3216 standard. This standard is based to the predecessor SAE J3016 which stipulates the six levels of driving technologies (from 0 to 5).

This new standard, J3216, defines the progress of cooperative control, from A to D classes, enabling machine to machine (M2M) communication systems.

The self-driving vehicles should include both e-safety systems and vehicle safety communications. The e-safety systems comprise at least: Advanced driverassistance systems (ADAS), automatic emergency braking systems, forward and reverse collision warning (FCW, RCW) system, adaptive cruise control, lanekeeping technology [28–30].

*Self-Driving Vehicles and Enabling Technologies*

*The sector hierarchy in Europe of the R&D investment [12].*

**6**

**Figure 7.**

**Figure 6.**

countries.

ping or vehicle-sharing).

by the pilot projects [14].

*The country hierarchy in Europe of the R&D investment [12].*

**3. Enabled actions and advanced technologies**

project on the ecosystem (smart cities) and in the transport field.

By analysing the above-mentioned **Figures 5**–**7**, the main conclusion is the fast-accelerating rate by the R&D investors in vehicle development sector in EU

The grow-up of the driverless-vehicles is enabled by the on-going research

The H2020 pilot research projects are the main catalysators towards Self-driving car Pathway. AUTOmated driving Progressed by Internet Of Things (AUTOPILOT) [13] is an open source platform for IoT vehicle (containing three main ingredients: vehicles, road infrastructure, and the IoT objects). The main objective includes the self-driving safety. Additional services are investigated (self-parking, terrain map-

At the same time, the already open source IoT experimental platforms represent one important tool to test the new IoT technologies before integrating in the real world. Different M2M architectures, cyber physical systems (IoT-A), standards (for example oneM2M) and open platforms (UniversAAL, FIWARE) can be exploited

#### **Figure 8.** *The 3 trucks platoon formation [21].*

The safety of the vehicle communications becomes a critical safety point. This is a complex task due to the diversity aspects: ethical, legislative framework, technology, governance. The solutions to this task are offered by the cybersecurity and data protection rules [31].

Practically, the J3216 standard improves the level of full automation by facilitating the car road traffic in platoon formation, as in **Figure 8**. This concept is named by SAE as Cooperative Driving Automation (CDA).

Connected eco-driving concept is based on the V2I real time communication to advice the drivers about the traffic congestion or other infrastructure conditions [32, 33].

### **5. Conclusion**

The content of this chapter is structured within 4 Sections. The first Section, there is an Introduction in the European initiative of self-driving technology. The Second Section includes the main motivation of enabling such technologies, the Vision Zero accident fatalities. The third Section, Enabled Actions and Advanced Technologies, includes the main catalysators of implementing self-driving car: the H2020 pilot research projects. The last Section, "*Cooperative Intelligent Transport Systems. Towards M2M*", presents both the promoted EU tools, i.e., cooperative, connected and automated mobility (CCAM), and USA tools, SAEJ3216 standard, to enable self-driving car pathway towards M2M level.

#### **Acknowledgements**

The project leading to this application has received funding from the Research Fund for Coal and Steel under grant agreement No 899469.

### **Author details**

Marian Găiceanu Integrated Energy Conversion Systems and Advanced Control of Complex Processes Research Center, Dunarea de Jos University of Galati, Romania

\*Address all correspondence to: marian.gaiceanu@ugal.ro

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**9**

2021-03-17].

[Accessed: 2021-03-17]

[11] https://iri.jrc.ec.europa.eu/ scoreboard/2020-eu-industrial-rd-

*Introductory Chapter: European Union towards Self-Driving Car Pathway. M2M Era*

investment-scoreboard#dialognode-5706 [Accessed: 2021-03-17]

[12] https://iri.jrc.ec.europa.eu/rd\_ monitoring [Accessed: 2021-03-17]

[13] https://cordis.europa.eu/project/ id/731993 [Accessed: 2021-03-17]

[15] https://cordis.europa.eu/project/ id/731993 [Accessed: 2021-03-18]

[16] https://cordis.europa.eu/project/ id/761510/reporting [Accessed:

[17] https://5gcar.eu [Accessed:

[18] https://5g-ppp.eu [Accessed:

[19] https://5g-ia.eu [Accessed:

[20] https://5g-ppp.eu/kpis/ [Accessed:

[21] https://platooningensemble.eu/

[22] https://ec.europa.eu/inea/en/ horizon-2020/projects/h2020 transport/automated-road-transport/ ensemble [Accessed: 2021-03-18]

[23] https://eur-lex.europa.eu/legalcontent/EN/TXT/?uri=CELEX% 3A32008D0671 [Accessed:

[24] https://ec.europa.eu/transport/ themes/its/c-its\_en [Accessed:

[25] https://www.sae.org/standards/ content/j3016\_201401/ [Accessed:

[Accessed: 2021-03-18]

[14] https://cordis.europa.eu/ programme/id/H2020\_IoT-01-2016

[Accessed: 2021-03-17]

2021-03-18]

2021-03-18]

2021-03-18]

2021-03-18]

2021-03-18]

2021-03-19]

2021-03-20]

2021-03-20]

*DOI: http://dx.doi.org/10.5772/intechopen.97358*

[1] https://www.europarl.europa.eu/ meps/en/96754/WIM\_VAN+DE+ CAMP/history/8 [Accessed: 2021-02-18]

[2] https://eur-lex.europa.eu/legalcontent/EN/TXT/HTML/?uri=CELEX:5 2018DC0283&from=EN [Accessed:

[3] https://www.europarl.europa.eu/ news/en/headlines/economy/

20190110STO23102/self-driving-carsin-the-eu-from-science-fiction-toreality [Accessed: 2021-02-24]

[4] https://ec.europa.eu/eurostat/ statistics-explained/index.php/Causes\_

[5] https://ec.europa.eu/eurostat/ statistics-explained/index.php? title=File:Railway\_accidents\_2019.png

[6] https://ec.europa.eu/eurostat/ statistics-explained/index.php? title=Road\_safety\_statistics\_-\_ characteristics\_at\_national\_and\_ regional\_level [Accessed: 2021-03-11]

[7] https://www.europarl.europa.eu

[8] https://ec.europa.eu/jrc/en/ publication/eur-scientific-andtechnical-research-reports/analysispossible-socio-economic-effectscooperative-connected-and-automatedmobility-ccam [Accessed: 2021-03-11]

[9] https://eur-lex.europa.eu/legalcontent/EN/TXT/HTML/?uri=CELEX:5 2016DC0787&from=EN [Accessed:

[10] https://ec.europa.eu/commission/ presscorner/detail/en/IP\_20\_2458

[Accessed: 2021-03-11]

[Accessed: 2021-03-11]

of\_death\_statistics [Accessed:

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2021-03-11]

*Introductory Chapter: European Union towards Self-Driving Car Pathway. M2M Era DOI: http://dx.doi.org/10.5772/intechopen.97358*

#### **References**

*Self-Driving Vehicles and Enabling Technologies*

and data protection rules [31].

*The 3 trucks platoon formation [21].*

conditions [32, 33].

**5. Conclusion**

**Figure 8.**

by SAE as Cooperative Driving Automation (CDA).

enable self-driving car pathway towards M2M level.

**8**

**Author details**

**Acknowledgements**

Marian Găiceanu

Integrated Energy Conversion Systems and Advanced Control of Complex Processes Research Center, Dunarea de Jos University of Galati, Romania

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

The safety of the vehicle communications becomes a critical safety point. This is a complex task due to the diversity aspects: ethical, legislative framework, technology, governance. The solutions to this task are offered by the cybersecurity

Practically, the J3216 standard improves the level of full automation by facilitating the car road traffic in platoon formation, as in **Figure 8**. This concept is named

Connected eco-driving concept is based on the V2I real time communication

The content of this chapter is structured within 4 Sections. The first Section, there is an Introduction in the European initiative of self-driving technology. The Second Section includes the main motivation of enabling such technologies, the Vision Zero accident fatalities. The third Section, Enabled Actions and Advanced Technologies, includes the main catalysators of implementing self-driving car: the H2020 pilot research projects. The last Section, "*Cooperative Intelligent Transport Systems. Towards M2M*", presents both the promoted EU tools, i.e., cooperative, connected and automated mobility (CCAM), and USA tools, SAEJ3216 standard, to

The project leading to this application has received funding from the Research

to advice the drivers about the traffic congestion or other infrastructure

\*Address all correspondence to: marian.gaiceanu@ugal.ro

provided the original work is properly cited.

Fund for Coal and Steel under grant agreement No 899469.

[1] https://www.europarl.europa.eu/ meps/en/96754/WIM\_VAN+DE+ CAMP/history/8 [Accessed: 2021-02-18]

[2] https://eur-lex.europa.eu/legalcontent/EN/TXT/HTML/?uri=CELEX:5 2018DC0283&from=EN [Accessed: 2021-02-18]

[3] https://www.europarl.europa.eu/ news/en/headlines/economy/ 20190110STO23102/self-driving-carsin-the-eu-from-science-fiction-toreality [Accessed: 2021-02-24]

[4] https://ec.europa.eu/eurostat/ statistics-explained/index.php/Causes\_ of\_death\_statistics [Accessed: 2021-03-11]

[5] https://ec.europa.eu/eurostat/ statistics-explained/index.php? title=File:Railway\_accidents\_2019.png [Accessed: 2021-03-11]

[6] https://ec.europa.eu/eurostat/ statistics-explained/index.php? title=Road\_safety\_statistics\_-\_ characteristics\_at\_national\_and\_ regional\_level [Accessed: 2021-03-11]

[7] https://www.europarl.europa.eu [Accessed: 2021-03-11]

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[9] https://eur-lex.europa.eu/legalcontent/EN/TXT/HTML/?uri=CELEX:5 2016DC0787&from=EN [Accessed: 2021-03-17].

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[13] https://cordis.europa.eu/project/ id/731993 [Accessed: 2021-03-17]

[14] https://cordis.europa.eu/ programme/id/H2020\_IoT-01-2016 [Accessed: 2021-03-17]

[15] https://cordis.europa.eu/project/ id/731993 [Accessed: 2021-03-18]

[16] https://cordis.europa.eu/project/ id/761510/reporting [Accessed: 2021-03-18]

[17] https://5gcar.eu [Accessed: 2021-03-18]

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[20] https://5g-ppp.eu/kpis/ [Accessed: 2021-03-18]

[21] https://platooningensemble.eu/ [Accessed: 2021-03-18]

[22] https://ec.europa.eu/inea/en/ horizon-2020/projects/h2020 transport/automated-road-transport/ ensemble [Accessed: 2021-03-18]

[23] https://eur-lex.europa.eu/legalcontent/EN/TXT/?uri=CELEX% 3A32008D0671 [Accessed: 2021-03-19]

[24] https://ec.europa.eu/transport/ themes/its/c-its\_en [Accessed: 2021-03-20]

[25] https://www.sae.org/standards/ content/j3016\_201401/ [Accessed: 2021-03-20]

[26] https://www.sae.org/news/2019/01/ sae-updates-j3016-automated-drivinggraphic/ [Accessed: 2021-03-20]

[27] https://www.sae.org/standards/ content/j3216\_202005/ [Accessed: 2021-03-20]

[28] https://ec.europa.eu/transport/ themes/its/c-its\_en [Accessed: 2021-03-20]

[29] Collision avoidance systems, https:// ec.europa.eu/transport/road\_safety/ specialist/knowledge/esave/esafety\_ measures\_unknown\_safety\_effects/ collision\_avoidance\_systems\_en [Accessed: 2021-03-20]

[30] Road safety: Commission welcomes agreement on new EU rules to help save lives, https://ec.europa.eu/commission/ presscorner/detail/en/IP\_19\_1793 [Accessed: 2021-03-20]

[31] https://www.eca.europa.eu/Lists/ ECADocuments/BRP\_CYBER SECURITY/BRP\_CYBERSECURITY\_ EN.pdf [Accessed: 2021-03-20]

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**11**

**Chapter 2**

**Abstract**

are realistic.

**1. Introduction**

the offer within a few years.

The Long Journey of the

There has been considerable hype about the expectations around driverless cars but tests and trials have shown that the concept is far more difficult to bring to fruition than expected. Since around 2010, there have been predictions of the imminent arrival of driverless cars. All these predictions have proved to be over optimistic and none of the goals have been achieved. Companies like Waymo, who are most advanced in the field, are beginning to admit that the task they faced is far more difficult than originally envidaged. This chapter will examine the obstacles to the achievement of the driverless car concept and assess whether the models of shared use driverless vehicle posited by the auto manufacturers and tech companies

For more than a decade, a group of auto manufacturers (OEMs, or Original Equipment Manufacturers) and technology companies have been working on the development of autonomous vehicles. There had, in fact, been work on the concept stretching back to the 1930s but it was only towards the end of the first decade of the 21st century that there was widespread interest in the concept. This seems to have been stimulated by the need for the tech companies, which had generated huge surpluses, to find projects in which to invest their money combined with the desperate fear of motor manufacturers that autonomy would be an essential part of

Throughout this period, the claims for this new technology have been ambitious. One of the earliest presentations by a senior motor industry figure was at the Shanghai Expo held in 2010. With a backdrop of a film showing a blind girl being raced through canyons of Shanghai's tower blocks in her driverless pod and a pregnant mother being rushed to hospital in an autonomous ambulance, Kevin Wale, the then boss of General Motors set out his prediction for 2030: 'Our vision for the future is free from petroleum, free form emissions, free from accidents, free from congestion and at the same time fun and fashionable' [1]. The key was for cars to be autonomous. This would ensure, he said, that there would be no traffic jams,

This optimistic view set the tone for much of the subsequent coverage. The presentation of the concept of autonomy has been relentlessly positive emphasising a series of potential advantages. The aspect that is stressed most often is safety.

no accidents and no emissions since all the vehicles would be electric.

Driverless Car

**Keywords:** autonomous vehicles, driverless cars

*Christian Wolmar*

#### **Chapter 2**

*Self-Driving Vehicles and Enabling Technologies*

[26] https://www.sae.org/news/2019/01/ sae-updates-j3016-automated-drivinggraphic/ [Accessed: 2021-03-20]

[27] https://www.sae.org/standards/ content/j3216\_202005/ [Accessed:

[28] https://ec.europa.eu/transport/ themes/its/c-its\_en [Accessed:

[29] Collision avoidance systems, https:// ec.europa.eu/transport/road\_safety/ specialist/knowledge/esave/esafety\_ measures\_unknown\_safety\_effects/ collision\_avoidance\_systems\_en

[30] Road safety: Commission welcomes agreement on new EU rules to help save lives, https://ec.europa.eu/commission/ presscorner/detail/en/IP\_19\_1793

[31] https://www.eca.europa.eu/Lists/

[32] https://ziranw.github.io [Accessed:

[33] Automated vehicles in the EU, 07-01-2016, https://www.europarl. europa.eu/thinktank/en/document. html?reference=EPRS\_BRI(2016)573902

[Accessed: 2021-03-20]

ECADocuments/BRP\_CYBER SECURITY/BRP\_CYBERSECURITY\_ EN.pdf [Accessed: 2021-03-20]

2021-03-20]

2021-03-20]

[Accessed: 2021-03-20]

[Accessed: 2021-03-20]

2021-03-20]

**10**

## The Long Journey of the Driverless Car

*Christian Wolmar*

#### **Abstract**

There has been considerable hype about the expectations around driverless cars but tests and trials have shown that the concept is far more difficult to bring to fruition than expected. Since around 2010, there have been predictions of the imminent arrival of driverless cars. All these predictions have proved to be over optimistic and none of the goals have been achieved. Companies like Waymo, who are most advanced in the field, are beginning to admit that the task they faced is far more difficult than originally envidaged. This chapter will examine the obstacles to the achievement of the driverless car concept and assess whether the models of shared use driverless vehicle posited by the auto manufacturers and tech companies are realistic.

**Keywords:** autonomous vehicles, driverless cars

#### **1. Introduction**

For more than a decade, a group of auto manufacturers (OEMs, or Original Equipment Manufacturers) and technology companies have been working on the development of autonomous vehicles. There had, in fact, been work on the concept stretching back to the 1930s but it was only towards the end of the first decade of the 21st century that there was widespread interest in the concept. This seems to have been stimulated by the need for the tech companies, which had generated huge surpluses, to find projects in which to invest their money combined with the desperate fear of motor manufacturers that autonomy would be an essential part of the offer within a few years.

Throughout this period, the claims for this new technology have been ambitious. One of the earliest presentations by a senior motor industry figure was at the Shanghai Expo held in 2010. With a backdrop of a film showing a blind girl being raced through canyons of Shanghai's tower blocks in her driverless pod and a pregnant mother being rushed to hospital in an autonomous ambulance, Kevin Wale, the then boss of General Motors set out his prediction for 2030: 'Our vision for the future is free from petroleum, free form emissions, free from accidents, free from congestion and at the same time fun and fashionable' [1]. The key was for cars to be autonomous. This would ensure, he said, that there would be no traffic jams, no accidents and no emissions since all the vehicles would be electric.

This optimistic view set the tone for much of the subsequent coverage. The presentation of the concept of autonomy has been relentlessly positive emphasising a series of potential advantages. The aspect that is stressed most often is safety. Protagonists of the new technology point to the fact that about 1.25 million people are killed on roads annually, including around 40,000 in the US. Since more than 90 per cent of these are the result of human error, the claim is that this number could be dramatically reduced. Take out the drivers, and the errors will go with them. Autonomous cars do not get drunk or fall asleep at the wheel, so the argument goes, and therefore they are will undoubtedly be safer. The National Highway Traffic Safety Administration suggested that 'automated vehicles' potential to save lives and reduce injuries is rooted in one critical and tragic fact: 94 per cent of serious crashes are due to human error. Automated vehicles have the potential to remove human error from the crash equation, which will help protect drivers and passengers, as well as bicyclists and pedestrians' [2].

A second key argument is convenience. Regular daily commutes of an hour or more in each direction are commonplace and that time will become available again to the drivers who can use it to answer emails, make calls or even just read a book. There is too, the potential for the technology to enable many more people to use cars, such as blind people or dementia sufferers. This idea was a key part of the presentation by Google's then head of its autonomous car project at to a congressional committee, Chris Urmson who cited the example of 'Justin Harford, a man who is legally blind' who had told him 'what this is really about is who gets to access transportation and commerce and who doesn't' [3]. These comments were met with great enthusiasm by campaigners for people with disabilities such as, for example, Parnell Diggs, the Director of Government Affairs for the National Federation of the Blind, who told the committee 'we anxiously anticipate the day that all blind people will have the opportunity to driver independently, and we believe that autonomous vehicles will make this day possible'.

A third major advantage claimed for the technology is that people will no longer need to own their own cars. The idea is that vehicles will be shared use, ready to be called up at a moment's notice through an app. This, in turn, will enable vast swathes of parking areas to be repurposed since once at their destination people will be able to despatch their vehicle to its next user or to distant car parks.

With reduced car ownership, there will be more road space available as cars will no longer be parked on kerbs. Moreover, because autonomous cars will be driven in a controlled way, without the vagaries of human control, there will be a much more efficient use of highways as the well-known wave effect will be eliminated. Zenzic, the organisation which coordinates the UK's research programme claimed in a press release that connected autonomous vehicles could reduce transport emissions by between 5 to 20 per cent by reducing congestion and was 'the key to becoming climate neutral' [4].

There have been numerous attempts to quantify all the gains from the introduction of autonomous vehicles. A study [5] by KPMG, for example, suggested that British drivers would save £5bn per year in reduced insurance, car parking and running costs. A report by Rand [6] argued that the increase in lane capacity on highways might amount to 500 per cent and that autonomous cars would lead to an improvement in fuel use of between 4 to 10 per cent. Ohio University's Future of Driving report [7] stated that harmful emissions would be reduced by 60 per cent by the introduction of autonomous vehicles. Zenzic claims that the industry will be worth £52 billion in the UK and £907 billion worldwide by 2035 [8].

All this, however, is rather mundane and to make it more exciting the promoters of the technology is that they wrap up these ideas with language that represents a radical and exciting vision for the future such as in the speech by Kevin Wale of GM. There is talk of 'life-changing' experience, of 'freeing up large amounts of time', of clean air and 'emptier roads'.

**13**

*The Long Journey of the Driverless Car DOI: http://dx.doi.org/10.5772/intechopen.93856*

disabilities or without a licence to 'drive'.

**2. The triple revolution**

is given little attention.

electric vehicles.

While the various manufacturers and tech companies have different conceptions

of what this new driverless world may look like, the long term vision converges around a triple revolution: in the future vehicles will be driverless, electric and shared used. This is the Holy Grail for the industry as in this scenario driverless vehicles would dominated the transport landscape, taking over not just the existing privately driven car market but also making deep inroads into public transit and expanding the use of cars by enabling, as mentioned above, many people with

This is based on a variety of assumptions around very profound and radical societal changes. Yet, neither the breadth of these changes nor the huge number of obstacles that need to be overcome before this vision can become a reality are examined by those putting out this vision. Quite apart from the depiction of a transport world completely different from the one in which we live today, the very long period during which there would be a mix of driverless and conventionally-driven vehicles

Indeed, the idea that a totally driverless world is possible stretches credulity. The very example given at the Shanghai Expo of an ambulance carrying a pregnant woman is an unlikely scenario for a driverless vehicle as emergency vehicles are allowed to break the rules precisely because they must have priority. Even in a near driverless world, emergency vehicles, VIP limos, other urgent transport and various

The scenario presented by the concept's enthusiasts is, in fact, three separate revolutions bundled into one. The least innovatory and radical of these assumptions is that vehicles will increasingly be electric. That is highly likely but upscaling the production and sale of electric cars beyond the current minority market has proved difficult because of the high initial cost, the short range (or more pertinently fears about the range) and the slow rate of development of new models. Currently sales represent around 2.6 per cent of the global market [9]. This is growing but only slowly and there are concerns that the biggest constraint will be the production of sufficient batteries to support a rapid expansion in the electric and hybrid share of the market. The availability of charging points, the difficulties many flat dwellers would have in charging their vehicles overnight and the various issues around the sustainability of batteries all point to a relatively slow take-up of

Setting these difficulties aside, the second assumption is an even bigger obstacle, The notion that drivers will happily dispense with their own cars once driverless models become widely available and rely on Uber type services to call up vehicles when they are needed has very little evidence to support it. There are indeed a minority of Millenials living in urban areas who are happy to dispense with car ownership. For people who at the moment live in a city served by good private hire and taxi services including Uber, the option of not owning a car is perfectly feasible. However, once they move to the suburbs, or have children, they tend to purchase their own vehicles. For the past century or so, people have bought their own cars, despite the high cost, for a whole host of reasons: convenience, choice of type of vehicle, accessibility, enjoyment and, for many, keeping up or bettering the Joneses. In fact, driving is still considered by many to be a pleasure. The idea that suddenly this will all be abandoned because vehicles will no longer be driven but will be autonomous has little logic and no research to back it up. Indeed, on the contrary, the providers of shared use vehicles accept that 'car clubs are not for everyone and

other types of vehicle are likely to remain conventionally driven.

#### *The Long Journey of the Driverless Car DOI: http://dx.doi.org/10.5772/intechopen.93856*

*Self-Driving Vehicles and Enabling Technologies*

well as bicyclists and pedestrians' [2].

autonomous vehicles will make this day possible'.

Protagonists of the new technology point to the fact that about 1.25 million people are killed on roads annually, including around 40,000 in the US. Since more than 90 per cent of these are the result of human error, the claim is that this number could be dramatically reduced. Take out the drivers, and the errors will go with them. Autonomous cars do not get drunk or fall asleep at the wheel, so the argument goes, and therefore they are will undoubtedly be safer. The National Highway Traffic Safety Administration suggested that 'automated vehicles' potential to save lives and reduce injuries is rooted in one critical and tragic fact: 94 per cent of serious crashes are due to human error. Automated vehicles have the potential to remove human error from the crash equation, which will help protect drivers and passengers, as

A second key argument is convenience. Regular daily commutes of an hour or more in each direction are commonplace and that time will become available again to the drivers who can use it to answer emails, make calls or even just read a book. There is too, the potential for the technology to enable many more people to use cars, such as blind people or dementia sufferers. This idea was a key part of the presentation by Google's then head of its autonomous car project at to a congressional committee, Chris Urmson who cited the example of 'Justin Harford, a man who is legally blind' who had told him 'what this is really about is who gets to access transportation and commerce and who doesn't' [3]. These comments were met with great enthusiasm by campaigners for people with disabilities such as, for example, Parnell Diggs, the Director of Government Affairs for the National Federation of the Blind, who told the committee 'we anxiously anticipate the day that all blind people will have the opportunity to driver independently, and we believe that

A third major advantage claimed for the technology is that people will no longer need to own their own cars. The idea is that vehicles will be shared use, ready to be called up at a moment's notice through an app. This, in turn, will enable vast swathes of parking areas to be repurposed since once at their destination people will

With reduced car ownership, there will be more road space available as cars will no longer be parked on kerbs. Moreover, because autonomous cars will be driven in a controlled way, without the vagaries of human control, there will be a much more efficient use of highways as the well-known wave effect will be eliminated. Zenzic, the organisation which coordinates the UK's research programme claimed in a press release that connected autonomous vehicles could reduce transport emissions by between 5 to 20 per cent by reducing congestion and was 'the key to becoming

There have been numerous attempts to quantify all the gains from the introduction of autonomous vehicles. A study [5] by KPMG, for example, suggested that British drivers would save £5bn per year in reduced insurance, car parking and running costs. A report by Rand [6] argued that the increase in lane capacity on highways might amount to 500 per cent and that autonomous cars would lead to an improvement in fuel use of between 4 to 10 per cent. Ohio University's Future of Driving report [7] stated that harmful emissions would be reduced by 60 per cent by the introduction of autonomous vehicles. Zenzic claims that the industry will be worth £52 billion in the UK and £907 billion

All this, however, is rather mundane and to make it more exciting the promoters of the technology is that they wrap up these ideas with language that represents a radical and exciting vision for the future such as in the speech by Kevin Wale of GM. There is talk of 'life-changing' experience, of 'freeing up large amounts of

be able to despatch their vehicle to its next user or to distant car parks.

**12**

climate neutral' [4].

worldwide by 2035 [8].

time', of clean air and 'emptier roads'.

While the various manufacturers and tech companies have different conceptions of what this new driverless world may look like, the long term vision converges around a triple revolution: in the future vehicles will be driverless, electric and shared used. This is the Holy Grail for the industry as in this scenario driverless vehicles would dominated the transport landscape, taking over not just the existing privately driven car market but also making deep inroads into public transit and expanding the use of cars by enabling, as mentioned above, many people with disabilities or without a licence to 'drive'.

#### **2. The triple revolution**

This is based on a variety of assumptions around very profound and radical societal changes. Yet, neither the breadth of these changes nor the huge number of obstacles that need to be overcome before this vision can become a reality are examined by those putting out this vision. Quite apart from the depiction of a transport world completely different from the one in which we live today, the very long period during which there would be a mix of driverless and conventionally-driven vehicles is given little attention.

Indeed, the idea that a totally driverless world is possible stretches credulity. The very example given at the Shanghai Expo of an ambulance carrying a pregnant woman is an unlikely scenario for a driverless vehicle as emergency vehicles are allowed to break the rules precisely because they must have priority. Even in a near driverless world, emergency vehicles, VIP limos, other urgent transport and various other types of vehicle are likely to remain conventionally driven.

The scenario presented by the concept's enthusiasts is, in fact, three separate revolutions bundled into one. The least innovatory and radical of these assumptions is that vehicles will increasingly be electric. That is highly likely but upscaling the production and sale of electric cars beyond the current minority market has proved difficult because of the high initial cost, the short range (or more pertinently fears about the range) and the slow rate of development of new models. Currently sales represent around 2.6 per cent of the global market [9]. This is growing but only slowly and there are concerns that the biggest constraint will be the production of sufficient batteries to support a rapid expansion in the electric and hybrid share of the market. The availability of charging points, the difficulties many flat dwellers would have in charging their vehicles overnight and the various issues around the sustainability of batteries all point to a relatively slow take-up of electric vehicles.

Setting these difficulties aside, the second assumption is an even bigger obstacle, The notion that drivers will happily dispense with their own cars once driverless models become widely available and rely on Uber type services to call up vehicles when they are needed has very little evidence to support it. There are indeed a minority of Millenials living in urban areas who are happy to dispense with car ownership. For people who at the moment live in a city served by good private hire and taxi services including Uber, the option of not owning a car is perfectly feasible. However, once they move to the suburbs, or have children, they tend to purchase their own vehicles. For the past century or so, people have bought their own cars, despite the high cost, for a whole host of reasons: convenience, choice of type of vehicle, accessibility, enjoyment and, for many, keeping up or bettering the Joneses. In fact, driving is still considered by many to be a pleasure. The idea that suddenly this will all be abandoned because vehicles will no longer be driven but will be autonomous has little logic and no research to back it up. Indeed, on the contrary, the providers of shared use vehicles accept that 'car clubs are not for everyone and

there are many who still aspire to car ownership, even Millenials. I don't see a time when all vehicles will be shared [10].' People like the convenience of having, say, baby seats, golf clubs or tools in the car and moreover, the guarantee that the car is outside the home for immediate use. Relying on a shared use vehicle accessed through an app when they have to get to work at a particular time or take the kids to school will never be able to replace that flexibility.

There is another practical objection to the model here. At the moment services such as Uber and Lyft are available principally in large urban conurbations. If the world were genuinely to become dominated by share use vehicles, they would have to serve small towns and even villages. There is simply no feasible business model in which such areas would have access to a pool of shared use vehicles at short notice. Even if the shared use model might be widely accepted in central urban areas, it is difficult to envisage it taking off in more sparsely populated suburbs let alone small towns, villages or rural areas. The provision of sufficient cars would simply not be cost effective as no supplier would take the financial risk.

The recent pandemic leads to other difficulties. Who would guarantee that these cars were clean and not full of the previous occupants' litter or, worse, germs? There are a myriad other reasons why this scenario is implausible such as the lack of any business model: the costs of maintaining a service as these vehicles would need supervision and a back-up service; the initial investment required to set up such a business given the cost of the technology; and the reluctance of the public to part with their own vehicles and effectively replace them with an app. This model is, on the face of it, a very strange basis for the massive investment programmes by the tech and auto manufacturers given the lack of evidence that people are prepared to buy into this model. So why has this shared use concept become so important for the autonomous car protagonists?

The reason, in fact, points to their Achilles Heel and demonstrates that the extent to which this triple revolution is an impossible dream that more sensible advocates now see as being 'decades away' [11]. The supporters of autonomous cars have been forced to put forward this shared use scenario because of their fear of the criticism that the advent of driverless cars will lead to an increase in cars on the road and consequently greater congestion. They argue that since cars are in use for only around 5 per cent of their time, having autonomous cars which are shared will lead to a massive reduction in the number of vehicles on the road. There are obvious logical objections to this. Most people want their cars at peak times in the morning and evening, and very few use them at 3 am in the morning. Therefore the parc of vehicles would have to be far higher than the 5 per cent figure which this scenario implies even if all were shared use and driverless. Moreover, no clear business model has been set out for how such a massive business as providing vehicles for, literally, millions of people in a city would work. The practicalities of essentially making available hundreds of thousands of vehicles that would need to be centrally owned by a single entity (competition would add another layer of complexity) has never been set out. This is not an evolutionary process but a revolutionary one. In reality, the prompt for this scenario is the auto manufacturers' concern about understandable concerns that mass autonomy would lead to an increase, not a reduction, in congestion. There is much logic in that argument. If autonomy makes it easier for people to access individual cars rather than public transport, then it is highly likely there will be an increase in demand. Moreover, in a world dominated by autonomous vehicles, there would be considerable mileage undertaken by completely empty cars travelling between users. Uber presently has an average passenger occupancy rate of 0.6 (in addition to the driver) which means their vehicles are been driven for nearly half the time without a passenger. This emphasis on shared use is therefore borne of the necessity to argue that the spread of autonomy will lead

**15**

off road.

**3. Public acceptance**

*The Long Journey of the Driverless Car DOI: http://dx.doi.org/10.5772/intechopen.93856*

vehicle got stuck each time' [13].

to a criticism, not a presentation of a realistic scenario.

conditions with complete safety which is defined at Level 5.

to a reduction in congestion when the opposite has much more logic. It is a defence

The third element of this triple revolution, the widespread use of cars that are entirely capable of driving without human intervention is an even tougher obstacle to overcome. At present, the technology is at what has been called level 3. Cars can perform routine driving tasks such as on highways, even selecting routes and not requiring human input for steering but they still require constant attention from the driver. There have been countless tests and trials, and millions of miles have been driven by vehicles that have many features that allow them to be computercontrolled but despite the investment of an estimated \$100bn [12], the technology is nowhere close to delivering a car that can be driven anywhere in any weather

Waymo's 'robo taxi' service in Phoenix, Arizona, and Silicon Valley (for employees only) started operating in December 2018 but has been beset with problems. In fact, all the cars still have safety drivers, except for a minority which are 'geofenced' and all are monitored - and sometimes controlled – remotely. Passengers have complained of being dropped off in the wrong place, experiencing unexplained stops sometimes so sudden that they have caused whiplash and near collisions with cyclists: 'In about 2.5 per cent of Phoenix rides and 6.5per cent of Silicon Valley rides, Waymo vehicles stood still for a long period of time before either the human driver took over or a Waymo representative monitoring the vehicle from a remote location helped the car figure out how to start moving again. One Waymo rider *The Information* that during three trips in one week this summer, the Waymo

Most of the testing in the US has been carried out by cars monitored by an operator who is supposed to intervene when things are about to go wrong – something that clearly did not happen when the unfortunate woman wheeling a bike which had bags on its handlebars in Arizona was killed because the car failed to recognise her as human. It identified her initially as a plastic bag and then as a cyclist who was not on a collision course and only too late as a human being. This accident, which caused the death of Elaine Herzberg in Tempe Arizona in March 2018 was a key demonstration of the inability of even the most sophisticated computers to recognise 'outlier' situations. The fact that Herzberg was pushing a bicycle which had bags on its handlebars clearly was not a situation that the on board computer had been programmed to recognise. This is proving to be the biggest single obstacle to progress in the development of the autonomy aspect of these vehicles. However many millions of miles have been covered on the road, they will never be sufficient for the vehicles to learn about all eventualities and therefore the ability to reach full driverlessness must be in doubt. Indeed, despite the large amount of testing that has already taken place, most of the cars still cannot operate in heavy rain, snow or

All of this has helped increase scepticism about the concept. Almost half of Americans say they would not get in a self-driving taxi, according to a poll by the advocacy group Partners for Automated Vehicle Education [14]. The poll, carried out at the beginning of 2020, found that 48 per cent of the 1200 adults surveyed would 'never get in a taxi or ride-share vehicle that was being driven autonomously', while a further 21 per cent said they were unsure about doing so. While a fifth of respondents said that autonomous vehicles would never be safe, another fifth stated, incorrectly, that it is possible 'to own a completely driverless vehicle today',

#### *The Long Journey of the Driverless Car DOI: http://dx.doi.org/10.5772/intechopen.93856*

*Self-Driving Vehicles and Enabling Technologies*

school will never be able to replace that flexibility.

cost effective as no supplier would take the financial risk.

the autonomous car protagonists?

there are many who still aspire to car ownership, even Millenials. I don't see a time when all vehicles will be shared [10].' People like the convenience of having, say, baby seats, golf clubs or tools in the car and moreover, the guarantee that the car is outside the home for immediate use. Relying on a shared use vehicle accessed through an app when they have to get to work at a particular time or take the kids to

There is another practical objection to the model here. At the moment services such as Uber and Lyft are available principally in large urban conurbations. If the world were genuinely to become dominated by share use vehicles, they would have to serve small towns and even villages. There is simply no feasible business model in which such areas would have access to a pool of shared use vehicles at short notice. Even if the shared use model might be widely accepted in central urban areas, it is difficult to envisage it taking off in more sparsely populated suburbs let alone small towns, villages or rural areas. The provision of sufficient cars would simply not be

The recent pandemic leads to other difficulties. Who would guarantee that these cars were clean and not full of the previous occupants' litter or, worse, germs? There are a myriad other reasons why this scenario is implausible such as the lack of any business model: the costs of maintaining a service as these vehicles would need supervision and a back-up service; the initial investment required to set up such a business given the cost of the technology; and the reluctance of the public to part with their own vehicles and effectively replace them with an app. This model is, on the face of it, a very strange basis for the massive investment programmes by the tech and auto manufacturers given the lack of evidence that people are prepared to buy into this model. So why has this shared use concept become so important for

The reason, in fact, points to their Achilles Heel and demonstrates that the extent to which this triple revolution is an impossible dream that more sensible advocates now see as being 'decades away' [11]. The supporters of autonomous cars have been forced to put forward this shared use scenario because of their fear of the criticism that the advent of driverless cars will lead to an increase in cars on the road and consequently greater congestion. They argue that since cars are in use for only around 5 per cent of their time, having autonomous cars which are shared will lead to a massive reduction in the number of vehicles on the road. There are obvious logical objections to this. Most people want their cars at peak times in the morning and evening, and very few use them at 3 am in the morning. Therefore the parc of vehicles would have to be far higher than the 5 per cent figure which this scenario implies even if all were shared use and driverless. Moreover, no clear business model has been set out for how such a massive business as providing vehicles for, literally, millions of people in a city would work. The practicalities of essentially making available hundreds of thousands of vehicles that would need to be centrally owned by a single entity (competition would add another layer of complexity) has never been set out. This is not an evolutionary process but a revolutionary one. In reality, the prompt for this scenario is the auto manufacturers' concern about understandable concerns that mass autonomy would lead to an increase, not a reduction, in congestion. There is much logic in that argument. If autonomy makes it easier for people to access individual cars rather than public transport, then it is highly likely there will be an increase in demand. Moreover, in a world dominated by autonomous vehicles, there would be considerable mileage undertaken by completely empty cars travelling between users. Uber presently has an average passenger occupancy rate of 0.6 (in addition to the driver) which means their vehicles are been driven for nearly half the time without a passenger. This emphasis on shared use is therefore borne of the necessity to argue that the spread of autonomy will lead

**14**

to a reduction in congestion when the opposite has much more logic. It is a defence to a criticism, not a presentation of a realistic scenario.

The third element of this triple revolution, the widespread use of cars that are entirely capable of driving without human intervention is an even tougher obstacle to overcome. At present, the technology is at what has been called level 3. Cars can perform routine driving tasks such as on highways, even selecting routes and not requiring human input for steering but they still require constant attention from the driver. There have been countless tests and trials, and millions of miles have been driven by vehicles that have many features that allow them to be computercontrolled but despite the investment of an estimated \$100bn [12], the technology is nowhere close to delivering a car that can be driven anywhere in any weather conditions with complete safety which is defined at Level 5.

Waymo's 'robo taxi' service in Phoenix, Arizona, and Silicon Valley (for employees only) started operating in December 2018 but has been beset with problems. In fact, all the cars still have safety drivers, except for a minority which are 'geofenced' and all are monitored - and sometimes controlled – remotely. Passengers have complained of being dropped off in the wrong place, experiencing unexplained stops sometimes so sudden that they have caused whiplash and near collisions with cyclists: 'In about 2.5 per cent of Phoenix rides and 6.5per cent of Silicon Valley rides, Waymo vehicles stood still for a long period of time before either the human driver took over or a Waymo representative monitoring the vehicle from a remote location helped the car figure out how to start moving again. One Waymo rider *The Information* that during three trips in one week this summer, the Waymo vehicle got stuck each time' [13].

Most of the testing in the US has been carried out by cars monitored by an operator who is supposed to intervene when things are about to go wrong – something that clearly did not happen when the unfortunate woman wheeling a bike which had bags on its handlebars in Arizona was killed because the car failed to recognise her as human. It identified her initially as a plastic bag and then as a cyclist who was not on a collision course and only too late as a human being. This accident, which caused the death of Elaine Herzberg in Tempe Arizona in March 2018 was a key demonstration of the inability of even the most sophisticated computers to recognise 'outlier' situations. The fact that Herzberg was pushing a bicycle which had bags on its handlebars clearly was not a situation that the on board computer had been programmed to recognise. This is proving to be the biggest single obstacle to progress in the development of the autonomy aspect of these vehicles. However many millions of miles have been covered on the road, they will never be sufficient for the vehicles to learn about all eventualities and therefore the ability to reach full driverlessness must be in doubt. Indeed, despite the large amount of testing that has already taken place, most of the cars still cannot operate in heavy rain, snow or off road.

#### **3. Public acceptance**

All of this has helped increase scepticism about the concept. Almost half of Americans say they would not get in a self-driving taxi, according to a poll by the advocacy group Partners for Automated Vehicle Education [14]. The poll, carried out at the beginning of 2020, found that 48 per cent of the 1200 adults surveyed would 'never get in a taxi or ride-share vehicle that was being driven autonomously', while a further 21 per cent said they were unsure about doing so. While a fifth of respondents said that autonomous vehicles would never be safe, another fifth stated, incorrectly, that it is possible 'to own a completely driverless vehicle today',

highlighting the confusion that still remains over how far the technology has already developed. On the other side of the coin, people want to continue driving. A post-pandemic lockdown survey in *Le Monde* [15] found that half of all car owners actually missed driving while they were unable to travel.

*The fact that so many people believe that the driverless car is already a reality is the product of the tremendous hype that has accompanies the investment. entities. In an article for the online academic magazine Transportation Research Interdisciplinary Perspectives [16], Liza Dixon argues that much of the material put out by the companies developing autonomous vehicles is misleading as it fails to distinguish between autonomy and driving aids. She defines autonowashing as making unverified or misleading claims that misrepresent the appropriate level of human supervision required by a partially or semi-autonomous product, service or technology. This is, in fact, a characteristic of much of the PR output of the industry.*

*She cites the use of vague language and the failure to prove claims as being characteristics of autonowashing, and she highlights the media's culpability in relation to its 'utopian' reporting and exaggeration of the level of autonomy. Indeed, there are numerous examples of articles whose headlines suggest they are about 'driverless' vehicles but that go on to reveal that there is a safety driver at the wheel.*

Dixon points out, the phenomenon is somewhat self-defeating for the industry, which depends on building trust among potential users. By exaggerating claims and failing to consider disadvantages, the industry is weakening its own case. She writes: 'Autonowashing leads to overtrust, which leads to misuse. If a driver management system is unable to assist the user in error prevention, accident, injury or death may occur. This results in negative media coverage which can then stir public distrust in vehicle automation, threatening the return on investment'.

The extraordinary level of hype is, in fact, a key part of the current business model which appear to more about attracting investment funds than actually developing a fully autonomous vehicle. Given the clear and obvious obstacles facing the industry, the reasons to justify the vast level of investment are surprisingly unclear. Yet it continues unabated. Waymo managed to raise \$3bn in the market in the Spring of 2020 while survey of the top thirty companies in the field published in *The Information* [17] revealed that \$16 billion was spent on autonomous vehicle R&D in 2019: 'Just three companies spent half of that money – Alphabet's Waymo, GM's Cruise and Uber… Four other companies, including Apple, Baidu, Ford and Toyota, spent most of the rest.' According to a Fortune magazine article of 7 January 2020, while Waymo remains the market leader after eleven years of research, the company 'remains an expensive science project in search of a business'.

The benefits of removing the driver from cars have been heavily promoted by these companies but as we have seen do not stand up to close scrutiny. Since clearly the model of the triple revolution is unlikely ever to be realised, which means that the notion of blind or infirm people being able to regain autonomous mobility is a myth, what of the other purported benefits of a move to driverless vehicles?

The safety benefits are far less marked than suggested by the industry. The Insurance Institution for Highway Safety has calculated [18] that just a third of accidents would be prevented by the use of autonomous vehicles. This is because only accidents that are what the researchers call 'sensing and perception' errors, such as driver distraction or failure to spot a hazard, will be prevented. The technology cannot prevent the majority of accidents, which the IIHS believes are caused by 'prediction errors', such as misjudging the speed of other vehicles, excessive speed

**17**

*The Long Journey of the Driverless Car DOI: http://dx.doi.org/10.5772/intechopen.93856*

hitting them.

ubiquitous:

will have some constraints'.

christianwolmar.co.uk

**Author details**

Christian Wolmar

Independent Researcher, United Kingdom

provided the original work is properly cited.

\*Address all correspondence to: christian.wolmar@gmail.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

when road conditions are treacherous, and mistaken driver efforts to avoid a crash. One example is when a cyclist swerves into the path of an autonomous car. The vehicle may have seen the cyclist but it cannot manoeuvre quickly enough to avoid

These doubts make the motivation of those seeking to promote this technology unclear. There seems to be no short or medium term prospect of making a return on this capital. One driver of the high levels of investment is the assumption that the first to develop full autonomy will make super profits by establishing a monopoly. However even Waymo is now suggesting that the full driverless model is not achievable. An article on CNET [19] in November 2018 quoted the CEO of Waymo, John Krafcik, as expressing doubts over whether autonomous cars would ever become

'It'll be decades before autonomous cars are widespread on the roads – and even then, they won't be able to drive themselves in certain conditions. Autonomy always

While this suggests that there is a need for a model that is very different from the

Christian Wolmar, author of 20 books principally on transport matters including *Driverless Cars: on a road to nowhere?*, London Partnership Publishing, 2020. www.

ones previously proposed, there is no sign at this stage of what it is.

#### *The Long Journey of the Driverless Car DOI: http://dx.doi.org/10.5772/intechopen.93856*

*Self-Driving Vehicles and Enabling Technologies*

*industry.*

actually missed driving while they were unable to travel.

highlighting the confusion that still remains over how far the technology has already developed. On the other side of the coin, people want to continue driving. A post-pandemic lockdown survey in *Le Monde* [15] found that half of all car owners

*The fact that so many people believe that the driverless car is already a reality is the product of the tremendous hype that has accompanies the investment. entities. In an article for the online academic magazine Transportation Research Interdisciplinary Perspectives [16], Liza Dixon argues that much of the material put out by the companies developing autonomous vehicles is misleading as it fails to distinguish between autonomy and driving aids. She defines autonowashing as making unverified or misleading claims that misrepresent the appropriate level of human supervision required by a partially or semi-autonomous product, service or technology. This is, in fact, a characteristic of much of the PR output of the* 

*She cites the use of vague language and the failure to prove claims as being characteristics of autonowashing, and she highlights the media's culpability in relation to its 'utopian' reporting and exaggeration of the level of autonomy. Indeed, there are numerous examples of articles whose headlines suggest they are about 'driverless' vehicles but that go on to reveal that there is a safety driver at the wheel.*

Dixon points out, the phenomenon is somewhat self-defeating for the industry, which depends on building trust among potential users. By exaggerating claims and failing to consider disadvantages, the industry is weakening its own case. She writes: 'Autonowashing leads to overtrust, which leads to misuse. If a driver management system is unable to assist the user in error prevention, accident, injury or death may occur. This results in negative media coverage which can then stir public

The extraordinary level of hype is, in fact, a key part of the current business model which appear to more about attracting investment funds than actually developing a fully autonomous vehicle. Given the clear and obvious obstacles facing the industry, the reasons to justify the vast level of investment are surprisingly unclear. Yet it continues unabated. Waymo managed to raise \$3bn in the market in the Spring of 2020 while survey of the top thirty companies in the field published in *The Information* [17] revealed that \$16 billion was spent on autonomous vehicle R&D in 2019: 'Just three companies spent half of that money – Alphabet's Waymo, GM's Cruise and Uber… Four other companies, including Apple, Baidu, Ford and Toyota, spent most of the rest.' According to a Fortune magazine article of 7 January 2020, while Waymo remains the market leader after eleven years of research, the

The benefits of removing the driver from cars have been heavily promoted by these companies but as we have seen do not stand up to close scrutiny. Since clearly the model of the triple revolution is unlikely ever to be realised, which means that the notion of blind or infirm people being able to regain autonomous mobility is a myth, what of the other purported benefits of a move to driverless vehicles? The safety benefits are far less marked than suggested by the industry. The Insurance Institution for Highway Safety has calculated [18] that just a third of accidents would be prevented by the use of autonomous vehicles. This is because only accidents that are what the researchers call 'sensing and perception' errors, such as driver distraction or failure to spot a hazard, will be prevented. The technology cannot prevent the majority of accidents, which the IIHS believes are caused by 'prediction errors', such as misjudging the speed of other vehicles, excessive speed

distrust in vehicle automation, threatening the return on investment'.

company 'remains an expensive science project in search of a business'.

**16**

when road conditions are treacherous, and mistaken driver efforts to avoid a crash. One example is when a cyclist swerves into the path of an autonomous car. The vehicle may have seen the cyclist but it cannot manoeuvre quickly enough to avoid hitting them.

These doubts make the motivation of those seeking to promote this technology unclear. There seems to be no short or medium term prospect of making a return on this capital. One driver of the high levels of investment is the assumption that the first to develop full autonomy will make super profits by establishing a monopoly. However even Waymo is now suggesting that the full driverless model is not achievable. An article on CNET [19] in November 2018 quoted the CEO of Waymo, John Krafcik, as expressing doubts over whether autonomous cars would ever become ubiquitous:

'It'll be decades before autonomous cars are widespread on the roads – and even then, they won't be able to drive themselves in certain conditions. Autonomy always will have some constraints'.

While this suggests that there is a need for a model that is very different from the ones previously proposed, there is no sign at this stage of what it is.

Christian Wolmar, author of 20 books principally on transport matters including *Driverless Cars: on a road to nowhere?*, London Partnership Publishing, 2020. www. christianwolmar.co.uk

#### **Author details**

Christian Wolmar Independent Researcher, United Kingdom

\*Address all correspondence to: christian.wolmar@gmail.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **References**

[1] B. Ji, GM: glimpse into auto future, China Daily, 1 May 2010.

[2] https://www.nhtsa.gov/ technology-innovation/ automated-vehicles-safety

[3] Statement by Chris Urmson to the Committee on Commerce, Science and Transportation of the United States Senate, March 15 2016.

[4] http://www.pes.eu.com/ renewable-news/connected-vehicleskey-to-achieving-net-zero-2050-saysuk-self-driving-experts/

[5] https://home.kpmg/content/dam/ kpmg/pdf/2015/04/connected-andautonomous-vehicles.pdf

[6] https://www.rand.org/content/dam/ rand/pubs/research\_reports/RR400/ RR443-2/RAND\_RR443-2.pdf

[7] https://onlinemasters.ohio.edu/blog/ the-future-of-driving/

[8] This figure is taken from a 2017 Market Forecast report by the Connected Places Catapult, a government research organisation supported by Zenzic.

[9] https://www.iea.org/reports/ global-ev-outlook-2020

[10] Jonathan Hampson, head of Zipcar, London, conversation with the author.

[11] https://www.businessinsider. com/self-driving-cars-fullyautonomous-vehicles-futureprediction-timeline-2019- 8?amp&r=US&IR=T&r=DE&IR=T&\_\_ twitter\_impression=true

[12] https://www.ibtimes.com/lookinvestment-self-driving-cars-who-hasspent-most-2848289

[13] https://www.theinformation. com/articles/waymo-riders-describeexperiences-on-the-road

[14] https://www.cnet.com/roadshow/ news/pave-autonomous-vehicle-survey/

[15] May 25 2020

[16] https://www.journals.elsevier. com/transportation-researchinterdisciplinary-perspectives/

[17] https://medium.com/unikie/ the-most-interesting-self-driving-carcompanies-9df5e15c3cac

[18] https://www.roadtraffic-technology. com/news/self-driving-cars-one-thirdcrashes-study/

[19] https://www.cnet.com/news/ alphabet-google-waymo-ceo-johnkrafcik-autonomous-cars-wont-everbe-able-to-drive-in-all-conditions/

**19**

Section 2

Design Issues

Section 2 Design Issues

**18**

*Self-Driving Vehicles and Enabling Technologies*

[1] B. Ji, GM: glimpse into auto future,

[13] https://www.theinformation. com/articles/waymo-riders-describe-

[14] https://www.cnet.com/roadshow/ news/pave-autonomous-vehicle-survey/

[16] https://www.journals.elsevier. com/transportation-researchinterdisciplinary-perspectives/

[17] https://medium.com/unikie/ the-most-interesting-self-driving-car-

[19] https://www.cnet.com/news/ alphabet-google-waymo-ceo-johnkrafcik-autonomous-cars-wont-everbe-able-to-drive-in-all-conditions/

[18] https://www.roadtraffic-technology. com/news/self-driving-cars-one-third-

companies-9df5e15c3cac

crashes-study/

experiences-on-the-road

[15] May 25 2020

[3] Statement by Chris Urmson to the Committee on Commerce, Science and Transportation of the United States

renewable-news/connected-vehicleskey-to-achieving-net-zero-2050-says-

[5] https://home.kpmg/content/dam/ kpmg/pdf/2015/04/connected-and-

[6] https://www.rand.org/content/dam/ rand/pubs/research\_reports/RR400/ RR443-2/RAND\_RR443-2.pdf

[7] https://onlinemasters.ohio.edu/blog/

China Daily, 1 May 2010.

**References**

[2] https://www.nhtsa.gov/ technology-innovation/ automated-vehicles-safety

Senate, March 15 2016.

[4] http://www.pes.eu.com/

uk-self-driving-experts/

autonomous-vehicles.pdf

the-future-of-driving/

supported by Zenzic.

global-ev-outlook-2020

twitter\_impression=true

spent-most-2848289

[8] This figure is taken from a 2017 Market Forecast report by the Connected Places Catapult, a government research organisation

[9] https://www.iea.org/reports/

[11] https://www.businessinsider. com/self-driving-cars-fullyautonomous-vehicles-futureprediction-timeline-2019-

[10] Jonathan Hampson, head of Zipcar, London, conversation with the author.

8?amp&r=US&IR=T&r=DE&IR=T&\_\_

[12] https://www.ibtimes.com/lookinvestment-self-driving-cars-who-has-

**21**

**Chapter 3**

**Abstract**

**1. Introduction**

Design Considerations

for Autonomous Cargo

*Denis Kotarski, Petar Piljek and Josip Kasać*

graphically displayed for payloads from 10 kg up to 100 kg.

electric propulsion system, configuration parameters analysis

Transportation Multirotor UAVs

Unmanned aerial vehicles (UAVs) have proven to be an advanced tool for a variety of applications in the civilian and military sectors. Different categories of UAVs are used in various missions and are also the subject of numerous researches. Due to their characteristics and potential in specific conditions, multirotor UAVs imposes itself as a solution for many tasks, including transport. This chapter presents a conceptual solution of autonomous cargo transportation where the primary research objective is the design of a heavy lift multirotor UAV system. The process of designing a multirotor UAV that can carry heavy lift cargo is quite challenging due to many parameters and constraints. Five selected series of electric propulsion systems are analyzed, with different multirotor configurations, and results are

**Keywords:** multirotor UAV, autonomous cargo transportation, heavy lift transport,

In recent decades, technology has enabled the development of components and systems that have numerous capabilities in the field of autonomous vehicles and robots. From the aspect of the control system, developed control components with higher processing speed and integrated MEMS sensors allow a certain degree of autonomy of the vehicle. On the other hand, the development of the propulsion system and batteries has enabled a wide range of applications in various missions on the ground, in water, or in the air. Such as autonomous cars, unmanned ground vehicles (UGVs) can use existing infrastructure which is vulnerable to failure, and congestion that can be caused by other vehicles. These problems can potentially be overcome by using unmanned aerial vehicles (UAVs) as autonomous vehicles or/and robots. There are different categories of UAVs that are used in various missions such as construction management [1, 2], agriculture [3], surveillance [4], search and rescue [5, 6], firefighting [7, 8], transport (delivery) [9] and many others. Aircraft can generally be divided according to the lifting mechanism into fixed-wing [10], rotarywing [11, 12], and hybrid aircraft [13]. Because of its ability to vertically take-off and land (VTOL), rotary-wing (rotorcraft) UAVs do not need a launchpad or runway so the degree of autonomy can be higher and the cost of supporting infrastructure lower. Rotary-wing UAVs can be further divided into aircraft with variable-pitch

#### **Chapter 3**

## Design Considerations for Autonomous Cargo Transportation Multirotor UAVs

*Denis Kotarski, Petar Piljek and Josip Kasać*

#### **Abstract**

Unmanned aerial vehicles (UAVs) have proven to be an advanced tool for a variety of applications in the civilian and military sectors. Different categories of UAVs are used in various missions and are also the subject of numerous researches. Due to their characteristics and potential in specific conditions, multirotor UAVs imposes itself as a solution for many tasks, including transport. This chapter presents a conceptual solution of autonomous cargo transportation where the primary research objective is the design of a heavy lift multirotor UAV system. The process of designing a multirotor UAV that can carry heavy lift cargo is quite challenging due to many parameters and constraints. Five selected series of electric propulsion systems are analyzed, with different multirotor configurations, and results are graphically displayed for payloads from 10 kg up to 100 kg.

**Keywords:** multirotor UAV, autonomous cargo transportation, heavy lift transport, electric propulsion system, configuration parameters analysis

#### **1. Introduction**

In recent decades, technology has enabled the development of components and systems that have numerous capabilities in the field of autonomous vehicles and robots. From the aspect of the control system, developed control components with higher processing speed and integrated MEMS sensors allow a certain degree of autonomy of the vehicle. On the other hand, the development of the propulsion system and batteries has enabled a wide range of applications in various missions on the ground, in water, or in the air. Such as autonomous cars, unmanned ground vehicles (UGVs) can use existing infrastructure which is vulnerable to failure, and congestion that can be caused by other vehicles. These problems can potentially be overcome by using unmanned aerial vehicles (UAVs) as autonomous vehicles or/and robots.

There are different categories of UAVs that are used in various missions such as construction management [1, 2], agriculture [3], surveillance [4], search and rescue [5, 6], firefighting [7, 8], transport (delivery) [9] and many others. Aircraft can generally be divided according to the lifting mechanism into fixed-wing [10], rotarywing [11, 12], and hybrid aircraft [13]. Because of its ability to vertically take-off and land (VTOL), rotary-wing (rotorcraft) UAVs do not need a launchpad or runway so the degree of autonomy can be higher and the cost of supporting infrastructure lower. Rotary-wing UAVs can be further divided into aircraft with variable-pitch

propellers where the typical representative is a helicopter, and multirotor (multicopter) aircraft with fixed-pitch propellers. The advantages of the multirotor UAVs over other categories of aircraft are agility and maneuverability which is important in missions that include interaction with the environment and precise movements. Therefore this type of UAV is increasingly being considered as an alternative to UGVs in delivery and transport. The design of an autonomous heavy lift cargo transportation multirotor UAV is a quite challenging process since this type of aircraft is characterized by high energy consumption. Various conventional aircraft configurations such as quadrotor [14], hexarotor [15], or octorotor [16], allow a wide range of applications. Numerous research has recently been conducted with the aim of the design and development of new configurations with improved performance [17, 18].

There are several groups of researchers and companies engaged in the research and development of multirotor UAVs for the transportation of heavy loads. Brar et al. in their technical report [19] addressed several aspects of UAVs for deliveries such as the current market, available technology, regulation, and the impact on society. In general, multirotor cargo transport can be achieved with two basic transport strategies. The load can be attached to the multirotor body, or suspended through cables [20]. Ong at al presented design methodology for heavy-lift UAVs with coaxial rotors [21]. Several companies deal with the production of aircraft for the transportation of heavy cargo [22, 23]. The motivation to design an autonomous system stems from the fact that such a system can improve some aspects of society. Life on the islands is specific given the needs of the population and the infrastructure and institutions that exist on certain islands. On the larger islands, there are schools, ambulance, post offices. All other needs of the island's inhabitants are met through the connections that exist with the mainland and are mostly met by sea. Transport of passengers, goods, transport vehicles, and others takes place by ferries and ships. The existing type of transport is characterized by limited line frequency and high transportation costs.

In this chapter, a conceptual solution of on-demand autonomous heavy lift cargo transportation is presented which can reduce operational costs and carbon emissions. The overall system consists of a network of multirotor UAVs and docking facilities with the purpose of transportation from the mainland to the islands and vice versa. Based on the distance analysis and the existing infrastructure on the considered central Adriatic islands in Croatia, the topology (network) of the system was proposed whose endpoints are Zadar ports (mainland). The main focus of this research is on the design of heavy lift multirotor UAVs which can carry loads from 10 kg up to 100 kg. The multirotor UAV system divided into four key subsystems allows a methodological approach to aircraft design. The performance of the multirotor UAV is determined by the parameters and components of the propulsion and energy subsystem. The parameter analysis of conventional configurations for five selected setups of electric propulsion units was performed and presented. Based on the analysis, it is possible to select the aircraft parameters and components for a particular cargo and planned flight route. Furthermore, the parametric design of the aircraft is presented and preliminary simulations are performed.

#### **2. Autonomous cargo transportation system concept**

In this research, the aim is to show the benefits of the autonomous cargo transportation system (ACTS). The implementation of on-demand ACTS using multirotor UAVs can potentially reduce transport costs and increase the frequency and speed of transportation. This is of particular importance for the inhabitants of the islands, for whom such a system would enable better communication with the mainland, and thus would improve the standard of living on the islands. The concept of the system

**23**

**Figure 1.**

*Considered archipelago of central Adriatic islands in Croatia.*

*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs*

on-demand basis that connect islands facilities to the overall system.

allows for a multi-purpose character and could be used for missions involving the delivery of postal packages, the transport of goods such as fresh fish and fruit, and such a system could even be used for fire prevention purposes. The system consists of docking facilities on certain islands and a fleet of multirotor UAVs deployed on an

A case study was considered for the central Adriatic islands, which administratively belong to the city of Zadar, which is located on the coast of the Croatian mainland (**Figure 1**). The archipelago consists of ten smaller and three larger inhabited islands, two of which are connected by a bridge. Common to all islands is that there is the infrastructure to accommodate smaller and/or larger ships and ferries. On these islands, among other facilities, there are 21 post offices as shown in **Table 1**, which is important from the aspect of the delivery and distribution of postal packages. The ACTS can consist of several to several dozen multirotor UAVs, depending on the needs and scope of purposes that such a system can perform. A fleet of aircraft is considered, consisting of five series of aircraft that can carry from 10 kg up to 100 kg of cargo. This also enables the modular character of the overall system, and the use of different aircraft series depending on the cargo they need to carry can potentially reduce the energy consumption. The idea is that the smaller islands are connected to the larger islands with the possibility of using particular islands as an intermediate docking, and the aircraft with the largest payload are

Docking facilities have several functions, among others, they need to perform a user-friendly interface that makes it simple to use for the residents of the island and the services bear in mind that this is an on-demand system. Taking into account the current state of available components and technologies, the docking facility could consist

*DOI: http://dx.doi.org/10.5772/intechopen.95060*

provided for connection to the mainland.

#### *Design Considerations for Autonomous Cargo Transportation Multirotor UAVs DOI: http://dx.doi.org/10.5772/intechopen.95060*

allows for a multi-purpose character and could be used for missions involving the delivery of postal packages, the transport of goods such as fresh fish and fruit, and such a system could even be used for fire prevention purposes. The system consists of docking facilities on certain islands and a fleet of multirotor UAVs deployed on an on-demand basis that connect islands facilities to the overall system.

A case study was considered for the central Adriatic islands, which administratively belong to the city of Zadar, which is located on the coast of the Croatian mainland (**Figure 1**). The archipelago consists of ten smaller and three larger inhabited islands, two of which are connected by a bridge. Common to all islands is that there is the infrastructure to accommodate smaller and/or larger ships and ferries. On these islands, among other facilities, there are 21 post offices as shown in **Table 1**, which is important from the aspect of the delivery and distribution of postal packages. The ACTS can consist of several to several dozen multirotor UAVs, depending on the needs and scope of purposes that such a system can perform. A fleet of aircraft is considered, consisting of five series of aircraft that can carry from 10 kg up to 100 kg of cargo. This also enables the modular character of the overall system, and the use of different aircraft series depending on the cargo they need to carry can potentially reduce the energy consumption. The idea is that the smaller islands are connected to the larger islands with the possibility of using particular islands as an intermediate docking, and the aircraft with the largest payload are provided for connection to the mainland.

Docking facilities have several functions, among others, they need to perform a user-friendly interface that makes it simple to use for the residents of the island and the services bear in mind that this is an on-demand system. Taking into account the current state of available components and technologies, the docking facility could consist

**Figure 1.** *Considered archipelago of central Adriatic islands in Croatia.*

*Self-Driving Vehicles and Enabling Technologies*

propellers where the typical representative is a helicopter, and multirotor (multicopter) aircraft with fixed-pitch propellers. The advantages of the multirotor UAVs over other categories of aircraft are agility and maneuverability which is important in missions that include interaction with the environment and precise movements. Therefore this type of UAV is increasingly being considered as an alternative to UGVs in delivery and transport. The design of an autonomous heavy lift cargo transportation multirotor UAV is a quite challenging process since this type of aircraft is characterized by high energy consumption. Various conventional aircraft configurations such as quadrotor [14], hexarotor [15], or octorotor [16], allow a wide range of applications. Numerous research has recently been conducted with the aim of the design and development of new configurations with improved performance [17, 18]. There are several groups of researchers and companies engaged in the research and development of multirotor UAVs for the transportation of heavy loads. Brar et al. in their technical report [19] addressed several aspects of UAVs for deliveries such as the current market, available technology, regulation, and the impact on society. In general, multirotor cargo transport can be achieved with two basic transport strategies. The load can be attached to the multirotor body, or suspended through cables [20]. Ong at al presented design methodology for heavy-lift UAVs with coaxial rotors [21]. Several companies deal with the production of aircraft for the transportation of heavy cargo [22, 23]. The motivation to design an autonomous system stems from the fact that such a system can improve some aspects of society. Life on the islands is specific given the needs of the population and the infrastructure and institutions that exist on certain islands. On the larger islands, there are schools, ambulance, post offices. All other needs of the island's inhabitants are met through the connections that exist with the mainland and are mostly met by sea. Transport of passengers, goods, transport vehicles, and others takes place by ferries and ships. The existing type of transport is

characterized by limited line frequency and high transportation costs.

the aircraft is presented and preliminary simulations are performed.

In this research, the aim is to show the benefits of the autonomous cargo transportation system (ACTS). The implementation of on-demand ACTS using multirotor UAVs can potentially reduce transport costs and increase the frequency and speed of transportation. This is of particular importance for the inhabitants of the islands, for whom such a system would enable better communication with the mainland, and thus would improve the standard of living on the islands. The concept of the system

**2. Autonomous cargo transportation system concept**

In this chapter, a conceptual solution of on-demand autonomous heavy lift cargo transportation is presented which can reduce operational costs and carbon emissions. The overall system consists of a network of multirotor UAVs and docking facilities with the purpose of transportation from the mainland to the islands and vice versa. Based on the distance analysis and the existing infrastructure on the considered central Adriatic islands in Croatia, the topology (network) of the system was proposed whose endpoints are Zadar ports (mainland). The main focus of this research is on the design of heavy lift multirotor UAVs which can carry loads from 10 kg up to 100 kg. The multirotor UAV system divided into four key subsystems allows a methodological approach to aircraft design. The performance of the multirotor UAV is determined by the parameters and components of the propulsion and energy subsystem. The parameter analysis of conventional configurations for five selected setups of electric propulsion units was performed and presented. Based on the analysis, it is possible to select the aircraft parameters and components for a particular cargo and planned flight route. Furthermore, the parametric design of

**22**


#### **Table 1.**

*Post offices located on the central Adriatic islands.*

of a multirotor UAV docking assembly and storage for depositing or retrieving cargo. It can additionally be contained with other features such as a mini solar power plant or a battery charging module for electric cars or UGVs. The multirotor UAV docking assembly is connected to the aircraft via sensors and telemetry and have to be designed to allow take-off and landing of the aircraft. It consists of a module to recharge the multirotor UAV batteries or additionally replace the batteries when the aircraft needs to be used urgently. The storage for depositing or retrieving cargo is associated with the user interface and is connected to the docking assembly to allow the exchange of cargo between the user and the aircraft. **Figure 2** schematically shows the possible topology of the overall ACTS where the most distant islands are connected to the mainland by three connections. It is important to note that the marked distances are for planned routes where flight over settlements and infrastructure is avoided.

**Figure 2.** *Considered topology of the overall ACTS system.*

#### **3. Multirotor UAV system description**

Multirotor UAVs are mechanical systems represented as rigid bodies with six degrees of freedom. Common to all designs is that they consist of N rotors (propulsion units) whose geometric arrangement also determines the configuration of the

**25**

**Figure 3.**

*Conventional multirotor UAV configurations [24].*

*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs*

aircraft. They are mathematically described by a dynamic model of a rigid body with six second-order differential equations, twelve state variables, and N input variables, making them a multivariable system. Conventional configurations are characterized by a planar arrangement of the rotors, where the typical and most common configurations with four (quadrotor), six (hexarotor), and eight (octorotor) rotors are shown in **Figure 3**. The propulsion units mainly consist of an electric motor, suitable motor driver, and fixed-pitch propeller. It follows that the rotor's angular velocities are the only variables that have a direct impact on flight dynamics

since propellers by their rotation create aerodynamic forces and moments.

shows the multirotor UAV system which consists of four key subsystems.

wind gusts, it is necessary to consider robust control algorithms.

From a control point of view, multirotor UAVs are inherently unstable and highly

nonlinear systems. The inherent instability stems from the fact that this type of UAV cannot return to the equilibrium point on its own if it loses the functionality of the control loops. Furthermore, multirotor UAVs are highly nonlinear systems since the propulsion aerodynamic forces and moments are proportional to the square of the rotor angular velocity, and the transformations of the coordinate systems involve trigonometric functions. The basic task of the control subsystem is to navigate the multirotor UAV according to the given mission. The considered control subsystem is based on PX4 Autopilot. Generated control signals by the PX4 Autopilot, are sent to the electric propulsion units in order to achieve the desired movement in 3D space, ie to perform the mission. Orientation sensors are integrated into the PX4 Autopilot, while the position is estimated using compatible peripheral sensors. In considered concept, a global positioning system (GPS) and sensors for precise docking are incorporated in the control system. Given that the cargo mass in transport missions is unpredictable and there are real external disturbances such as

The development and design of multirotor UAVs are significantly limited by both their size and energy consumption. For simpler analysis, design, and construction of this type of UAV, the aircraft system is divided into four key subsystems regardless of the configuration or purpose of the aircraft. The propulsion subsystem consists of N rotors that generate the necessary forces and moments for the movement of the aircraft in 3D space. The energy subsystem consists of one or more lithium-polymer batteries with joined components that need to deliver a large amount of energy essential to achieve the desired performance. The control subsystem takes care of UAV navigation and the functioning of the overall system by managing and monitoring other subsystems. Another task for the control subsystem is to be the interface between the aircraft and the base station (docking facility). The multirotor payload subsystem includes all equipment and cargo required to perform a particular mission whereby, this paper discusses the missions of heavy lift cargo transportation. Generally, it can be said that the performance of the multirotor UAV is determined by the parameters and components of the propulsion and energy subsystem. **Figure 4** schematically

*DOI: http://dx.doi.org/10.5772/intechopen.95060*

#### *Design Considerations for Autonomous Cargo Transportation Multirotor UAVs DOI: http://dx.doi.org/10.5772/intechopen.95060*

aircraft. They are mathematically described by a dynamic model of a rigid body with six second-order differential equations, twelve state variables, and N input variables, making them a multivariable system. Conventional configurations are characterized by a planar arrangement of the rotors, where the typical and most common configurations with four (quadrotor), six (hexarotor), and eight (octorotor) rotors are shown in **Figure 3**. The propulsion units mainly consist of an electric motor, suitable motor driver, and fixed-pitch propeller. It follows that the rotor's angular velocities are the only variables that have a direct impact on flight dynamics since propellers by their rotation create aerodynamic forces and moments.

The development and design of multirotor UAVs are significantly limited by both their size and energy consumption. For simpler analysis, design, and construction of this type of UAV, the aircraft system is divided into four key subsystems regardless of the configuration or purpose of the aircraft. The propulsion subsystem consists of N rotors that generate the necessary forces and moments for the movement of the aircraft in 3D space. The energy subsystem consists of one or more lithium-polymer batteries with joined components that need to deliver a large amount of energy essential to achieve the desired performance. The control subsystem takes care of UAV navigation and the functioning of the overall system by managing and monitoring other subsystems. Another task for the control subsystem is to be the interface between the aircraft and the base station (docking facility). The multirotor payload subsystem includes all equipment and cargo required to perform a particular mission whereby, this paper discusses the missions of heavy lift cargo transportation. Generally, it can be said that the performance of the multirotor UAV is determined by the parameters and components of the propulsion and energy subsystem. **Figure 4** schematically shows the multirotor UAV system which consists of four key subsystems.

From a control point of view, multirotor UAVs are inherently unstable and highly nonlinear systems. The inherent instability stems from the fact that this type of UAV cannot return to the equilibrium point on its own if it loses the functionality of the control loops. Furthermore, multirotor UAVs are highly nonlinear systems since the propulsion aerodynamic forces and moments are proportional to the square of the rotor angular velocity, and the transformations of the coordinate systems involve trigonometric functions. The basic task of the control subsystem is to navigate the multirotor UAV according to the given mission. The considered control subsystem is based on PX4 Autopilot. Generated control signals by the PX4 Autopilot, are sent to the electric propulsion units in order to achieve the desired movement in 3D space, ie to perform the mission. Orientation sensors are integrated into the PX4 Autopilot, while the position is estimated using compatible peripheral sensors. In considered concept, a global positioning system (GPS) and sensors for precise docking are incorporated in the control system. Given that the cargo mass in transport missions is unpredictable and there are real external disturbances such as wind gusts, it is necessary to consider robust control algorithms.

**Figure 3.** *Conventional multirotor UAV configurations [24].*

*Self-Driving Vehicles and Enabling Technologies*

*Post offices located on the central Adriatic islands.*

**Table 1.**

of a multirotor UAV docking assembly and storage for depositing or retrieving cargo. It can additionally be contained with other features such as a mini solar power plant or a battery charging module for electric cars or UGVs. The multirotor UAV docking assembly is connected to the aircraft via sensors and telemetry and have to be designed to allow take-off and landing of the aircraft. It consists of a module to recharge the multirotor UAV batteries or additionally replace the batteries when the aircraft needs to be used urgently. The storage for depositing or retrieving cargo is associated with the user interface and is connected to the docking assembly to allow the exchange of cargo between the user and the aircraft. **Figure 2** schematically shows the possible topology of the overall ACTS where the most distant islands are connected to the mainland by three connections. It is important to note that the marked distances are for planned

Pašman 23,262 Ugljan 23,275 Veli Rat 23,287 Ždrelac 23,263 Sali 23,281 Sestrunj 23,291 Neviđane 23,264 Žman 23,282 Molat 23,292 Kukljica 23,271 Rava 23,283 Ist 23,293 Kali 23,272 Veli Iž 23,284 Premuda 23,294 Preko 23,273 Brbinj 23,285 Silba 23,295 Lukoran 23,274 Božava 23,286 Olib 23,296

Multirotor UAVs are mechanical systems represented as rigid bodies with six degrees of freedom. Common to all designs is that they consist of N rotors (propulsion units) whose geometric arrangement also determines the configuration of the

routes where flight over settlements and infrastructure is avoided.

**3. Multirotor UAV system description**

*Considered topology of the overall ACTS system.*

**24**

**Figure 2.**

#### **Figure 4.**

*Schematic representation of an electric multirotor UAV system.*

#### **3.1 Electric propulsion subsystem**

The propulsion subsystem provides the aircraft system with the necessary power to move in 3D space. The choice of propulsion subsystem configuration and propulsion unit type affects flight performance and it is a key step in designing a multirotor type of UAV. Electric motor based propulsion unit enables precise and fast control of forces and moments which directly affect the position and orientation of the aircraft. The reliability of electrical systems reduces the possibility of aircraft crash due to motor failure. The required performance of the aircraft, which depends on the type and profile of the mission, determines the choice of propulsion configuration and components. The electric propulsion unit consists of a control unit and a mechanical assembly of the motor on whose rotor a fixed-pitch propeller is mounted, which creates forces and moments by its rotation. Propulsion units with brushless DC (BLDC) motors coupled with electronic speed controllers (ESCs) are suitable for a wide range of tasks, including missions with heavy lift transportation (**Figure 5**).

In this case study, seven setups of electric propulsion units were considered which will be paired with the high voltage (HV) setup of the energy subsystem. Based on the component manufacturer's specification, it is possible to characterize the propulsion units which is the first step in designing the aircraft propulsion subsystem for heavy lift multirotor system. **Table 2** shows the considered electric propulsion components for which characterization is presented. Motor velocity constant (back EMF constant) Kv of motors intended for heavy payloads is typically small (Kv < 200), resulting in lower speeds and higher torques. The propeller designations in the table describe its geometry where the first two numbers indicate the diameter of the propeller, and the other two the propeller pitch, both in inch.

**27**

**Figure 7.**

**Table 2.**

**Figure 6.**

*Considered electric propulsion unit setups [25].*

*Thrust force with respect to rotor angular velocity.*

*Electric current with respect to the thrust force.*

*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs*

larger diameter propeller combined with a suitable motor.

Characterization is necessary for the appropriate selection of propulsion components and analysis of the electric propulsion system which further allows system optimization. **Figure 6** shows thrust force as a function of rotor angular velocity for seven considered setups. As expected, setups consisting of motors with a lower Kv achieve lower angular velocities, and propellers with larger diameter achieve higher thrust forces. **Figure 7** shows the electric current as a function of the required thrust force, which is very important from the aspect of estimating the flight time. **Figure 8** shows the overall efficiency of the propulsion unit which is expressed by the ratio of thrust and electric power. In this case, efficiency is represented as a function of electric power. From the graph, it can be concluded that the increase in efficiency can generally be achieved by choosing propulsion units consisting of a

**BLDC motor Kv ESC Propeller** U15 II 100 FLAME 180A HV 4013 (40 × 13.1) U13 II 130 ALPHA 120A HV 3211 (32 × 11) U11 II 120 ALPHA 80A HV 2892 (28 × 9.2) P80 100 ALPHA 80A HV 3211 (32 × 11) P60 170 FLAME 60A HV 2266 (22x6.6) Antigravity 1005 90 FLAME 60A HV 3211 (32 × 11) Antigravity 7005 115 FLAME 60A HV 2472 (24 × 7.2)

*DOI: http://dx.doi.org/10.5772/intechopen.95060*

**Figure 5.** *Multirotor UAV electric propulsion unit.*

#### *Design Considerations for Autonomous Cargo Transportation Multirotor UAVs DOI: http://dx.doi.org/10.5772/intechopen.95060*

Characterization is necessary for the appropriate selection of propulsion components and analysis of the electric propulsion system which further allows system optimization. **Figure 6** shows thrust force as a function of rotor angular velocity for seven considered setups. As expected, setups consisting of motors with a lower Kv achieve lower angular velocities, and propellers with larger diameter achieve higher thrust forces. **Figure 7** shows the electric current as a function of the required thrust force, which is very important from the aspect of estimating the flight time. **Figure 8** shows the overall efficiency of the propulsion unit which is expressed by the ratio of thrust and electric power. In this case, efficiency is represented as a function of electric power. From the graph, it can be concluded that the increase in efficiency can generally be achieved by choosing propulsion units consisting of a larger diameter propeller combined with a suitable motor.


#### **Table 2.**

*Self-Driving Vehicles and Enabling Technologies*

**3.1 Electric propulsion subsystem**

*Schematic representation of an electric multirotor UAV system.*

**Figure 4.**

transportation (**Figure 5**).

pitch, both in inch.

*Multirotor UAV electric propulsion unit.*

The propulsion subsystem provides the aircraft system with the necessary power to move in 3D space. The choice of propulsion subsystem configuration and propulsion unit type affects flight performance and it is a key step in designing a multirotor type of UAV. Electric motor based propulsion unit enables precise and fast control of forces and moments which directly affect the position and orientation of the aircraft. The reliability of electrical systems reduces the possibility of aircraft crash due to motor failure. The required performance of the aircraft, which depends on the type and profile of the mission, determines the choice of propulsion configuration and components. The electric propulsion unit consists of a control unit and a mechanical assembly of the motor on whose rotor a fixed-pitch propeller is mounted, which creates forces and moments by its rotation. Propulsion units with brushless DC (BLDC) motors coupled with electronic speed controllers (ESCs) are suitable for a wide range of tasks, including missions with heavy lift

In this case study, seven setups of electric propulsion units were considered which will be paired with the high voltage (HV) setup of the energy subsystem. Based on the component manufacturer's specification, it is possible to characterize the propulsion units which is the first step in designing the aircraft propulsion subsystem for heavy lift multirotor system. **Table 2** shows the considered electric propulsion components for which characterization is presented. Motor velocity constant (back EMF constant) Kv of motors intended for heavy payloads is typically small (Kv < 200), resulting in lower speeds and higher torques. The propeller designations in the table describe its geometry where the first two numbers indicate the diameter of the propeller, and the other two the propeller

**26**

**Figure 5.**

*Considered electric propulsion unit setups [25].*

#### **Figure 6.**

*Thrust force with respect to rotor angular velocity.*

**Figure 7.** *Electric current with respect to the thrust force.*

**Figure 8.**

*The overall efficiency of the electric propulsion unit with respect to electric power.*

#### **3.2 Electric energy subsystem**

The energy subsystem must provide sufficient energy for multirotor UAV system in order to perform the intended missions. Multirotor UAVs are characterized by high energy consumption as they consist of a minimum of four propulsion units. When choosing an energy subsystem, it is necessary to take into account several parameters, the most important of which is the type of propulsion subsystem. Electric propulsion units based on BLDC motors are combined with an energy subsystem consisting of one or more lithium-polymer (LiPo) batteries. Each LiPo battery contains one or more electrochemical cells to ensure a continuous flow of energy to power the propulsion and other subsystems. A very important feature of a LiPo battery is high energy density. Compared to other types of batteries such as nickel-metal hydride (NiMh), LiPo batteries have a higher discharge rate, which allows more power and consistent energy flow to the propulsion. LiPo batteries are defined by the capacity, discharge rate (C), and the number of cells that determine the operating voltage (S). The nominal voltage of a single battery cell is 3.7 V, and the voltage of a fully charged cell is 4.2 V.

When selecting batteries, the energy requirements of the propulsion subsystem must be taken into account, which in turn depends on the mass and size of the aircraft and the number of propulsion units. It follows that when designing a system, the relationship between mass and battery capacity is one of the

**29**

the analysis.

**4.1 Mass distribution of the aircraft system**

*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs*

key data. For the characterized propulsion units, commercial high voltage (12S) LiPo batteries of capacity 8000 mAh, 16,000 mAh, and 22,000 mAh, as shown in **Figure 9**, were selected for further analysis [26]. Since the mass of the batteries in relation to other system masses dominantly affects the aircraft dynamics, it is desirable to place the energy subsystem centrally, as close as possible to the aircraft center of gravity. Energy subsystems of large aircraft, such as in this research, have more sophisticated energy distribution circuits (**Figure 10**) that provide different voltage levels and also have the function of measuring the battery's

To ensure overall flight performance, it is necessary to determine the required thrust-to-weight ratio (TWR). As a rule, aircraft are designed with approximately twice the thrust force in comparison with aircraft weight, from which it can be concluded that the mass of the aircraft is a key parameter in the design of the system. The division of the multirotor UAV system into four key subsystems, where the subsystems are determined by masses as the basic parameters, represents the first step in the design of the aircraft. The equipment subsystem is directly determined by the type of mission which in this research is heavy lift transportation. The mass of this subsystem directly affects the selection of the propulsion and energy subsystem. These two subsystems are interdependent and when choosing components it is necessary to maintain a balance with the existing constraints defined by the mission. Parameters which significantly influence the dynamics and duration of the flight were analyzed for five selected aircraft series. The design of the propulsion subsystem affects the performance of the aircraft. Given the interdependence of the propulsion and energy subsystems, the parameters of LiPo batteries are included in

Based on the division of the aircraft system into four key subsystems, the mass distributions of conventional multirotor configurations for five selected aircraft series (S, M, L, XL, XXL) are graphically shown. To ensure basic flight performance, the required TWR was determined according to the propulsion manufacturer's recommendations and is approximately 1.8 for all five series. **Figures 11**–**15** show the mass distributions of payload mass (mPL), energy subsystem mass (mES),

**4. Design considerations for heavy lift multirotor UAV**

*DOI: http://dx.doi.org/10.5772/intechopen.95060*

electrical parameters.

*Power hub MAUCH power cube 4.*

**Figure 10.**

**Figure 9.** *LiPo battery Tattu plus 12S, 22,000 mAh, 25C.*

*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs DOI: http://dx.doi.org/10.5772/intechopen.95060*

**Figure 10.** *Power hub MAUCH power cube 4.*

*Self-Driving Vehicles and Enabling Technologies*

**3.2 Electric energy subsystem**

**Figure 8.**

The energy subsystem must provide sufficient energy for multirotor UAV system in order to perform the intended missions. Multirotor UAVs are characterized by high energy consumption as they consist of a minimum of four propulsion units. When choosing an energy subsystem, it is necessary to take into account several parameters, the most important of which is the type of propulsion subsystem. Electric propulsion units based on BLDC motors are combined with an energy subsystem consisting of one or more lithium-polymer (LiPo) batteries. Each LiPo battery contains one or more electrochemical cells to ensure a continuous flow of energy to power the propulsion and other subsystems. A very important feature of a LiPo battery is high energy density. Compared to other types of batteries such as nickel-metal hydride (NiMh), LiPo batteries have a higher discharge rate, which allows more power and consistent energy flow to the propulsion. LiPo batteries are defined by the capacity, discharge rate (C), and the number of cells that determine the operating voltage (S). The nominal voltage

*The overall efficiency of the electric propulsion unit with respect to electric power.*

of a single battery cell is 3.7 V, and the voltage of a fully charged cell is 4.2 V. When selecting batteries, the energy requirements of the propulsion

subsystem must be taken into account, which in turn depends on the mass and size of the aircraft and the number of propulsion units. It follows that when designing a system, the relationship between mass and battery capacity is one of the

**28**

**Figure 9.**

*LiPo battery Tattu plus 12S, 22,000 mAh, 25C.*

key data. For the characterized propulsion units, commercial high voltage (12S) LiPo batteries of capacity 8000 mAh, 16,000 mAh, and 22,000 mAh, as shown in **Figure 9**, were selected for further analysis [26]. Since the mass of the batteries in relation to other system masses dominantly affects the aircraft dynamics, it is desirable to place the energy subsystem centrally, as close as possible to the aircraft center of gravity. Energy subsystems of large aircraft, such as in this research, have more sophisticated energy distribution circuits (**Figure 10**) that provide different voltage levels and also have the function of measuring the battery's electrical parameters.

### **4. Design considerations for heavy lift multirotor UAV**

To ensure overall flight performance, it is necessary to determine the required thrust-to-weight ratio (TWR). As a rule, aircraft are designed with approximately twice the thrust force in comparison with aircraft weight, from which it can be concluded that the mass of the aircraft is a key parameter in the design of the system. The division of the multirotor UAV system into four key subsystems, where the subsystems are determined by masses as the basic parameters, represents the first step in the design of the aircraft. The equipment subsystem is directly determined by the type of mission which in this research is heavy lift transportation. The mass of this subsystem directly affects the selection of the propulsion and energy subsystem. These two subsystems are interdependent and when choosing components it is necessary to maintain a balance with the existing constraints defined by the mission. Parameters which significantly influence the dynamics and duration of the flight were analyzed for five selected aircraft series. The design of the propulsion subsystem affects the performance of the aircraft. Given the interdependence of the propulsion and energy subsystems, the parameters of LiPo batteries are included in the analysis.

#### **4.1 Mass distribution of the aircraft system**

Based on the division of the aircraft system into four key subsystems, the mass distributions of conventional multirotor configurations for five selected aircraft series (S, M, L, XL, XXL) are graphically shown. To ensure basic flight performance, the required TWR was determined according to the propulsion manufacturer's recommendations and is approximately 1.8 for all five series. **Figures 11**–**15** show the mass distributions of payload mass (mPL), energy subsystem mass (mES), propulsion subsystem mass (mPS), and control subsystem (avionics) mass (mAV) for five generic series of aircraft whose propulsion subsystem consists of four, six, and eight rotors. For the selected battery capacities and the number of rotors, the maximum masses of the payload subsystems for the assumed TWR are expressed in kilograms. The first aircraft series – S (**Figure 11**) whose propulsion subsystem is based on propulsion units with P60 BLDC motors, is considered for payloads up to 10 kg. The second series – M (**Figure 12**) based on propulsion units with Antigravity 1005 motors, is considered for payloads from 10 kg up to 15 kg. The third series – L (**Figure 13**) based on propulsion units with P80 motors, is considered for payloads from 15 kg up to 25 kg. The fourth series – XL (**Figure 14**) based on propulsion units with U13 motors, is considered for payloads from 25 kg up to 50 kg. And lastly, the fifth series – XXL (**Figure 15**) based on propulsion units with U15 motors, is considered for payloads from 50 kg up to 100 kg.

The analysis of the multirotor UAV system mass distribution and the graphical representation, shown in **Figures 11**–**15**, was performed using a script written in the Matlab software package.

**Figure 11.** *Mass distribution of the S aircraft series system (TWR = 1.8).*

**31**

**Figure 15.**

**Figure 13.**

**Figure 14.**

*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs*

*DOI: http://dx.doi.org/10.5772/intechopen.95060*

*Mass distribution of the L aircraft series system (TWR = 1.8).*

*Mass distribution of the XL aircraft series system (TWR = 1.8).*

*Mass distribution of the XXL aircraft series system (TWR = 1.8).*

**Figure 12.** *Mass distribution of the M aircraft series system (TWR = 1.8).*

*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs DOI: http://dx.doi.org/10.5772/intechopen.95060*

**Figure 13.** *Mass distribution of the L aircraft series system (TWR = 1.8).*

**Figure 14.** *Mass distribution of the XL aircraft series system (TWR = 1.8).*

**Figure 15.** *Mass distribution of the XXL aircraft series system (TWR = 1.8).*

*Self-Driving Vehicles and Enabling Technologies*

Matlab software package.

propulsion subsystem mass (mPS), and control subsystem (avionics) mass (mAV) for five generic series of aircraft whose propulsion subsystem consists of four, six, and eight rotors. For the selected battery capacities and the number of rotors, the maximum masses of the payload subsystems for the assumed TWR are expressed in kilograms. The first aircraft series – S (**Figure 11**) whose propulsion subsystem is based on propulsion units with P60 BLDC motors, is considered for payloads up to 10 kg. The second series – M (**Figure 12**) based on propulsion units with Antigravity 1005 motors, is considered for payloads from 10 kg up to 15 kg. The third series – L (**Figure 13**) based on propulsion units with P80 motors, is considered for payloads from 15 kg up to 25 kg. The fourth series – XL (**Figure 14**) based on propulsion units with U13 motors, is considered for payloads from 25 kg up to 50 kg. And lastly, the fifth series – XXL (**Figure 15**) based on propulsion units with

The analysis of the multirotor UAV system mass distribution and the graphical representation, shown in **Figures 11**–**15**, was performed using a script written in the

U15 motors, is considered for payloads from 50 kg up to 100 kg.

**30**

**Figure 12.**

**Figure 11.**

*Mass distribution of the S aircraft series system (TWR = 1.8).*

*Mass distribution of the M aircraft series system (TWR = 1.8).*

#### **4.2 Numerical estimation of stationary flight time**

Very important information is the total time that the aircraft can be in the air, which depends on the mission itself, ie on the required flight performance and the cargo that the aircraft carries. Based on the characteristics of the propulsion units, an estimate of the flight time was performed for selected series of aircraft defined by the parameters of the propulsion and energy subsystem. The basic case is considered, a stationary flight of conventional configurations, assuming that the drop in battery voltage and the power consumption by the control subsystem (possibly also the payload subsystem) are ignored. The estimated flight time is calculated based on the available battery capacity and the electric current required to generate adequate thrust force. It is also important to note that the complete battery capacities were used in the calculation, which is not possible in practice since the batteries must not be completely discharged. The required thrust force to reach the steady state of the aircraft depends on the mass of the system.

**Figure 16** shows the estimated stationary flight time for possible nine configurations of the first aircraft series – S. Configurations for each series are determined by the number of rotors (N) which is a parameter of the propulsion subsystem, and by battery capacity ie the number of considered batteries which is a parameter of the energy subsystem. The first series (S), as mentioned in the last subsection, is considered for payloads up to 10 kg. Furthermore, **Figures 16**–**19** show the estimated stationary flight time for other aircraft series (M, L, XL, and XXL) which were considered and analyzed in the last subsection.

**Figure 16.** *Estimated stationary flight time of the S aircraft series.*

**33**

**Figure 20.**

**4.3 Parametric design of a multirotor UAV**

*Estimated stationary flight time of the XXL aircraft series.*

Based on the analysis, it is possible to select the aircraft parameters and components for a particular cargo and planned flight route. In considered design, the propulsion

*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs*

The estimation of the multirotor UAV system stationary flight time and the graphical representation, shown in **Figures 16**–**20**, based on the parameters of the propulsion and energy subsystems, was performed using a script written in the

*DOI: http://dx.doi.org/10.5772/intechopen.95060*

*Estimated stationary flight time of the L aircraft series.*

*Estimated stationary flight time of the XL aircraft series.*

Matlab software package.

**Figure 18.**

**Figure 19.**

**Figure 17.** *Estimated stationary flight time of the M aircraft series.*

*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs DOI: http://dx.doi.org/10.5772/intechopen.95060*

The estimation of the multirotor UAV system stationary flight time and the graphical representation, shown in **Figures 16**–**20**, based on the parameters of the propulsion and energy subsystems, was performed using a script written in the Matlab software package.

**Figure 18.**

*Self-Driving Vehicles and Enabling Technologies*

of the system.

**4.2 Numerical estimation of stationary flight time**

were considered and analyzed in the last subsection.

*Estimated stationary flight time of the S aircraft series.*

*Estimated stationary flight time of the M aircraft series.*

Very important information is the total time that the aircraft can be in the air, which depends on the mission itself, ie on the required flight performance and the cargo that the aircraft carries. Based on the characteristics of the propulsion units, an estimate of the flight time was performed for selected series of aircraft defined by the parameters of the propulsion and energy subsystem. The basic case is considered, a stationary flight of conventional configurations, assuming that the drop in battery voltage and the power consumption by the control subsystem (possibly also the payload subsystem) are ignored. The estimated flight time is calculated based on the available battery capacity and the electric current required to generate adequate thrust force. It is also important to note that the complete battery capacities were used in the calculation, which is not possible in practice since the batteries must not be completely discharged. The required thrust force to reach the steady state of the aircraft depends on the mass

**Figure 16** shows the estimated stationary flight time for possible nine configurations of the first aircraft series – S. Configurations for each series are determined by the number of rotors (N) which is a parameter of the propulsion subsystem, and by battery capacity ie the number of considered batteries which is a parameter of the energy subsystem. The first series (S), as mentioned in the last subsection, is considered for payloads up to 10 kg. Furthermore, **Figures 16**–**19** show the estimated stationary flight time for other aircraft series (M, L, XL, and XXL) which

**32**

**Figure 17.**

**Figure 16.**

*Estimated stationary flight time of the L aircraft series.*

**Figure 19.** *Estimated stationary flight time of the XL aircraft series.*

**Figure 20.** *Estimated stationary flight time of the XXL aircraft series.*

#### **4.3 Parametric design of a multirotor UAV**

Based on the analysis, it is possible to select the aircraft parameters and components for a particular cargo and planned flight route. In considered design, the propulsion

#### *Self-Driving Vehicles and Enabling Technologies*

unit (rotor) is defined by the propeller diameter and the propulsion subsystem by the number of rotors. The size of the aircraft, which is defined by the aircraft diameter, derives from these two parameters. For given propulsion units defined with propeller diameter (d) in inch, and with the number of rotors (N), **Table 3** shows the propulsion subsystem diameter (D) in mm, which actually defines the construction parameters of the aircraft. In order to reduce the cost of prototyping and the potential production of system parts, it is necessary to achieve a certain degree of modularity. The idea is to turn predefined aircraft subsystems into modules that can be easily connected to each other. Of particular importance is the modularity of the propulsion subsystem. One of the ways to achieve this goal is by parameterizing the propulsion construction that connects the propulsion components with other subsystems.


**Table 3.**

*Conventional multirotor configuration sizes (D).*

#### **5. Conclusion**

In this chapter, the concept of on-demand autonomous cargo transportation is presented by employing multirotor UAVs. The topology of a network of docking facilities and a multirotor UAV fleet was proposed for the considered autonomous transport within the central Adriatic islands in Croatia. Currently available technologies allow relatively simple implementation of the proposed concept, however, regulations applicable in a particular area should also be considered in the future. The market of commercially available components for propulsion and energy subsystem was investigated and it was found that it is possible to develop multirotor UAVs that can carry up to 100 kg of cargo. Based on the considered setups of electric propulsion units, the analysis of the Multirotor UAV propulsion and energy subsystems parameters were performed. In the multirotor UAV design process, the mass of five series of aircraft is considered and the flight time with respect to the payload mass is approximated and shown. The proposed concept of an autonomous cargo transportation system has great potential for future development and implementation since it can reduce transport costs, increase the frequency and speed of transport, and reduce carbon emissions.

#### **Acknowledgements**

This research was funded by European Regional Development Fund, Operational programme competitiveness and cohesion 2014-2020, as part of the call for proposals entitled "Investing in science and innovation – first call", grant number KK.01.1.1.04.0092.

**35**

**Author details**

Denis Kotarski1

Zagreb, Croatia

\*, Petar Piljek<sup>2</sup>

provided the original work is properly cited.

1 Karlovac University of Applied Sciences, Karlovac, Croatia

\*Address all correspondence to: denis.kotarski@vuka.hr

and Josip Kasać2

2 Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb,

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs*

ACTS autonomous cargo transportation system

*DOI: http://dx.doi.org/10.5772/intechopen.95060*

UGV unmanned ground vehicle VTOL vertically take-off and land

GPS global positioning system BLDC brushless direct current ESC electronic speed controller

HV high voltage EMF electromotive force LiPo lithium-polymer NiMh nickel-metal hydride TWR thrust-to-weight ratio

#### **Appendices and Nomenclature**


*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs DOI: http://dx.doi.org/10.5772/intechopen.95060*


#### **Author details**

*Self-Driving Vehicles and Enabling Technologies*

connects the propulsion components with other subsystems.

unit (rotor) is defined by the propeller diameter and the propulsion subsystem by the number of rotors. The size of the aircraft, which is defined by the aircraft diameter, derives from these two parameters. For given propulsion units defined with propeller diameter (d) in inch, and with the number of rotors (N), **Table 3** shows the propulsion subsystem diameter (D) in mm, which actually defines the construction parameters of the aircraft. In order to reduce the cost of prototyping and the potential production of system parts, it is necessary to achieve a certain degree of modularity. The idea is to turn predefined aircraft subsystems into modules that can be easily connected to each other. Of particular importance is the modularity of the propulsion subsystem. One of the ways to achieve this goal is by parameterizing the propulsion construction that

In this chapter, the concept of on-demand autonomous cargo transportation is presented by employing multirotor UAVs. The topology of a network of docking facilities and a multirotor UAV fleet was proposed for the considered autonomous transport within the central Adriatic islands in Croatia. Currently available technologies allow relatively simple implementation of the proposed concept, however, regulations applicable in a particular area should also be considered in the future. The market of commercially available components for propulsion and energy subsystem was investigated and it was found that it is possible to develop multirotor UAVs that can carry up to 100 kg of cargo. Based on the considered setups of electric propulsion units, the analysis of the Multirotor UAV propulsion and energy subsystems parameters were performed. In the multirotor UAV design process, the mass of five series of aircraft is considered and the flight time with respect to the payload mass is approximated and shown. The proposed concept of an autonomous cargo transportation system has great potential for future development and implementation since it can reduce transport costs, increase the frequency and speed of transport, and reduce carbon emissions.

N = 4 1100 1200 1400 1600 2000 N = 6 1400 1600 1800 2000 2500 N = 8 1800 2000 2200 2500 3000

**d = 22″ d = 24″ d = 28″ d = 32″ d = 40″**

This research was funded by European Regional Development Fund, Operational programme competitiveness and cohesion 2014-2020, as part of the call for proposals entitled "Investing in science and innovation – first call",

**34**

**5. Conclusion**

*Conventional multirotor configuration sizes (D).*

**Table 3.**

**Acknowledgements**

grant number KK.01.1.1.04.0092.

**Appendices and Nomenclature**

UAV unmanned aerial vehicle

MEMS micro-electromechanical systems

Denis Kotarski1 \*, Petar Piljek<sup>2</sup> and Josip Kasać2

1 Karlovac University of Applied Sciences, Karlovac, Croatia

2 Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia

\*Address all correspondence to: denis.kotarski@vuka.hr

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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[2] Li Y, Liu C. Applications of multirotor drone technologies in construction management. International Journal of Construction Management. 2018;19(5):401-412. DOI: 10.1080/15623599.2018.1452101

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[10] Escobar-Ruiz AG, Lopez-Botello O, Reyes-Osorio L, Zambrano-Robledo P, Amezquita-Brooks L, Garcia-Salazar O. Conceptual Design of an Unmanned Fixed-Wing Aerial Vehicle Based on Alternative Energy. International Journal of Aerospace Engineering. 2019;2019:1-13. DOI: 10.1155/2019/8104927

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[13] Öznalbant Z, Kavsaoğlu MŞ. Flight control and flight experiments of a tilt-propeller VTOL UAV. Transactions of the Institute of Measurement and

**37**

*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs*

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s10846-019-01088-w

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*DOI: http://dx.doi.org/10.5772/intechopen.95060*

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aerial vehicles with four rotors. Interdisciplinary Description of Complex Systems. 2016;14(1):88-100.

[16] Ikeda T, Yasui S, Fujihara M, Ohara K, Ashizawa S, Ichikawa A, Okino A, Oomichi T, Fukuda T. Wall contact by Octo-rotor UAV with one DoF manipulator for bridge inspection. In: IEEE International Conference on Intelligent Robots and Systems (IROS '17); 24-28 September 2017; Vancouver. Canada: IEEE; 2017. p. 5122-5127. DOI:

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TRO.2015.2479877

ICRA.2017.7989608

[Accessed: 2020-10-16]

[17] Driessens S, Pounds PE. The Triangular Quadrotor: A More Efficient Quadrotor Configuration. IEEE Transactions on Robotics. 2015;31(6):1517-1526. DOI: 10.1109/

[18] Ryll M, Muscio G, Pierri F, Cataldi E, Antonelli G, Caccavale F, Franchi A. 6D Physical Interaction with a Fully Actuated Aerial Robot. In: IEEE International Conference on Robotics and Automation (ICRA '17); 29 May-3 June 2017; Singapore. USA: IEEE; 2017. p. 5190-5195. DOI: 10.1109/

[19] Brar S, Rabbat R, Raithatha V, Runcie G, Yu A: Drones for Deliveries. Technical Report. 2015. Available from: http://scet.berkeley.edu/wp-content/ uploads/ConnCarProjectReport-1.pdf

10.1177/0142331218754618

DOI: 10.7906/indecs.14.1.9

*Design Considerations for Autonomous Cargo Transportation Multirotor UAVs DOI: http://dx.doi.org/10.5772/intechopen.95060*

Control. 2018;40(8):2454-2465. DOI: 10.1177/0142331218754618

[14] Benić Z, Piljek P, Kotarski D. Mathematical modelling of unmanned aerial vehicles with four rotors. Interdisciplinary Description of Complex Systems. 2016;14(1):88-100. DOI: 10.7906/indecs.14.1.9

[15] Jannoura R, Brinkmann K, Uteau D, Bruns C, Joergensen RG. Monitoring of crop biomass using true colour aerial photographs taken from a remote controlled hexacopter. Biosystems Engineering. 2015;129:341-351. DOI: 10.1016/j.biosystemseng.2014.11.007

[16] Ikeda T, Yasui S, Fujihara M, Ohara K, Ashizawa S, Ichikawa A, Okino A, Oomichi T, Fukuda T. Wall contact by Octo-rotor UAV with one DoF manipulator for bridge inspection. In: IEEE International Conference on Intelligent Robots and Systems (IROS '17); 24-28 September 2017; Vancouver. Canada: IEEE; 2017. p. 5122-5127. DOI: 10.1109/IROS.2017.8206398

[17] Driessens S, Pounds PE. The Triangular Quadrotor: A More Efficient Quadrotor Configuration. IEEE Transactions on Robotics. 2015;31(6):1517-1526. DOI: 10.1109/ TRO.2015.2479877

[18] Ryll M, Muscio G, Pierri F, Cataldi E, Antonelli G, Caccavale F, Franchi A. 6D Physical Interaction with a Fully Actuated Aerial Robot. In: IEEE International Conference on Robotics and Automation (ICRA '17); 29 May-3 June 2017; Singapore. USA: IEEE; 2017. p. 5190-5195. DOI: 10.1109/ ICRA.2017.7989608

[19] Brar S, Rabbat R, Raithatha V, Runcie G, Yu A: Drones for Deliveries. Technical Report. 2015. Available from: http://scet.berkeley.edu/wp-content/ uploads/ConnCarProjectReport-1.pdf [Accessed: 2020-10-16]

[20] Villa DKD, Brandão AS, Sarcinelli-Filho M. A Survey on Load Transportation Using Multirotor UAVs. Journal of Intelligent & Robotic Systems. 2020;98:267-296. DOI: 10.1007/ s10846-019-01088-w

[21] Ong W, Srigrarom S, Hesse H. Design Methodology for Heavy-Lift Unmanned Aerial Vehicles with Coaxial Rotors. In AIAA SciTech Forum; 7-11 January 2019; San Diego. USA: American Institute of Aeronautics and Astronautics; 2019. p. 7-11. DOI: 10.2514/6.2019-2095

[22] DRONE VOLT. Hercules 20 Heavy lift drone [Internet]. Available from: https://www.dronevolt.com/en/expertsolutions/hercules-20/ [Accessed: 2020-10-20]

[23] Haris Areal. Carrier HX8 Sprayer Drone [Internet]. Available from: https://www.harrisaerial.com/carrierhx8-sprayer/ [Accessed: 2020-10-20]

[24] PX4 Autopilot User Guide. Airframes Reference [Internet]. Available from: https://docs.px4.io/ v1.9.0/en/airframes/airframe\_reference. html [Accessed: 2020-10-26]

[25] Electric Propulsion Components. Avaivable from: https://store-en.tmotor. com/category.php?id=11 [Accessed: 2020-10-17]

[26] Tattu Lipo Battery Pack. Avaivable from: https://www.gensace.de/tattuplus [Accessed: 2020-10-19]

**36**

rob.21495

*Self-Driving Vehicles and Enabling Technologies*

[1] Palacios AT, Cordero JM,

[2] Li Y, Liu C. Applications of multirotor drone technologies in construction management.

10.1080/15623599.2018.1452101

[3] Yinka-Banjo C, Ajayi O. Sky-Farmers: Applications of Unmanned Aerial Vehicles (UAV) in Agriculture. In: Dekoulis G, editors. Autonomous Vehicles. London: IntechOpen; 2020. DOI: 10.5772/intechopen.89488

[4] Kanistras K, Martins G,

[5] Półka M, Ptak S, Kuziora Ł, Kuczyńska A. The Use of Unmanned Aerial Vehicles by Urban Search and Rescue Groups. In: Dekoulis G, editors. Drones-Applications. London: IntechOpen; 2018. p. 83-96. DOI: 10.5772/intechopen.73325

[6] Briod A, Kornatowski P, Zufferey JC, Floreano D. A Collision-resilient Flying Robot. Journal of Field Robotics. 2014;31(4):496-509. DOI: 10.1002/

[7] Yuan C, Liu Z, Zhang Y. Aerial Images-Based Forest Fire Detection for Firefighting Using Optical Remote

Rutherford MJ, Valavanis KP. Survey of Unmanned Aerial Vehicles (UAVs) for Traffic Monitoring. In: Valavanis K, Vachtsevanos G, editors. Handbook of Unmanned Aerial Vehicles. Dordrecht: Springer; 2015. p. 2643-2666. DOI: 10.1007/978-90-481-9707-1\_122

International Journal of Construction Management. 2018;19(5):401-412. DOI:

intechopen.73325

**References**

Bello MR, Palacios ET, González JL. New Applications of 3D SLAM on Risk Management Using Unmanned Aerial Vehicles in the Construction Industry. In: Dekoulis G, editors. Drones-Applications. London: IntechOpen; 2018. p. 97-118. DOI: 10.5772/

Sensing Techniques and Unmanned Aerial Vehicles. Journal of Intelligent & Robotic Systems. 2017;88:635-654. DOI:). 10.1007/s10846-016-0464-7

Al-Toukhy A, Kablaoui D, El-Abd M. Semi-autonomous indoor firefighting UAV. In: 18th International Conference on Advanced Robotics (ICAR '17); 10-12 July 2017; Hong Kong. China: IEEE; 2017. p. 310-315. DOI: 10.1109/

[9] Otero Arenzana A, Escribano Macias JJ, Angeloudis P. Design of Hospital Delivery Networks Using Unmanned Aerial Vehicles. Transportation Research Record. 2020;2674(5):405-418. DOI: 10.1177/0361198120915891

[10] Escobar-Ruiz AG, Lopez-Botello O, Reyes-Osorio L, Zambrano-Robledo P, Amezquita-Brooks L, Garcia-Salazar O. Conceptual Design of an Unmanned

[11] Rotaru C, Todorov M. Helicopter Flight Physics. In: Volkov K, editors. Flight Physics. London: IntechOpen;

[12] Kotarski D, Kasać J. Generalized Control Allocation Scheme for Multirotor Type of UAVs. In: Dekoulis G, editors. Drones-Applications. London: IntechOpen; 2018. p. 43-58. DOI: 10.5772/

[13] Öznalbant Z, Kavsaoğlu MŞ. Flight control and flight experiments of a tilt-propeller VTOL UAV. Transactions of the Institute of Measurement and

2018. p. 19-48. DOI: 10.5772/

Fixed-Wing Aerial Vehicle Based on Alternative Energy. International Journal of Aerospace Engineering. 2019;2019:1-13. DOI:

10.1155/2019/8104927

intechopen.71516

intechopen.73006

[8] Imdoukh A, Shaker A,

ICAR.2017.8023625

**Chapter 4**

Propulsion

*Richard A. Guinee*

parameter estimation accuracy

**1. Introduction**

**39**

**Abstract**

Novel Application of Fast

Dynamical Parameter

Simulated Annealing Method in

Brushless Motor Drive (BLMD)

Identification for Electric Vehicle

Permanent magnet brushless motor drives (BLMD) are extensively used in electric vehicle (EV) propulsion systems because of their high power and torque to weight ratio, virtually maintenance free operation with precision control of torque, speed and position. An accurate dynamical parameter identification strategy is an essential feature in the adaptive control of such BLMD-EV systems where sensorless current feedback is employed for reliable torque control, with multi-modal penalty cost surfaces, in EV high performance tracking and target ranging. Application of the classical Powell Conjugate Direction optimization method is first discussed and its inaccuracy in dynamical parameter identification is illustrated for multimodal cost surfaces. This is used for comparison with the more accurate Fast Simulated Annealing/Diffusion (FSD) method, presented here, in terms of the returned parameter estimates. Details of the FSD development and application to the BLMD parameter estimation problem based on the minimum quantized parameter step sizes from noise considerations are provided. The accuracy of global parameter convergence estimates returned, cost function evaluation and the algorithm run time are presented. Validation of the FSD identification strategy is provided by excellent correlation of BLMD model simulation trace coherence with experimental

test data at the optimal estimates and from cost surface simulation.

drives, dynamical parameter identification, sensorless current feedback, multimodal cost surfaces, Powell Conjugate Direction optimization, Simulated Annealing, Fast Simulated Diffusion, quantized parameters, cost surface noise,

**Keywords:** electric vehicle propulsion systems, Permanent magnet brushless motor

High performance permanent magnet brushless motor drive (BLMD) systems are now widely used in electric vehicle (EV) propulsion [1–3], because of their

#### **Chapter 4**

## Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD) Dynamical Parameter Identification for Electric Vehicle Propulsion

*Richard A. Guinee*

### **Abstract**

Permanent magnet brushless motor drives (BLMD) are extensively used in electric vehicle (EV) propulsion systems because of their high power and torque to weight ratio, virtually maintenance free operation with precision control of torque, speed and position. An accurate dynamical parameter identification strategy is an essential feature in the adaptive control of such BLMD-EV systems where sensorless current feedback is employed for reliable torque control, with multi-modal penalty cost surfaces, in EV high performance tracking and target ranging. Application of the classical Powell Conjugate Direction optimization method is first discussed and its inaccuracy in dynamical parameter identification is illustrated for multimodal cost surfaces. This is used for comparison with the more accurate Fast Simulated Annealing/Diffusion (FSD) method, presented here, in terms of the returned parameter estimates. Details of the FSD development and application to the BLMD parameter estimation problem based on the minimum quantized parameter step sizes from noise considerations are provided. The accuracy of global parameter convergence estimates returned, cost function evaluation and the algorithm run time are presented. Validation of the FSD identification strategy is provided by excellent correlation of BLMD model simulation trace coherence with experimental test data at the optimal estimates and from cost surface simulation.

**Keywords:** electric vehicle propulsion systems, Permanent magnet brushless motor drives, dynamical parameter identification, sensorless current feedback, multimodal cost surfaces, Powell Conjugate Direction optimization, Simulated Annealing, Fast Simulated Diffusion, quantized parameters, cost surface noise, parameter estimation accuracy

#### **1. Introduction**

High performance permanent magnet brushless motor drive (BLMD) systems are now widely used in electric vehicle (EV) propulsion [1–3], because of their

higher power factor and efficiency, and are central to modern industrial automation [4] in such scenarios as aerospace systems control and maneuverability, numerical control (NC) machine tools and robotics. The benefits accruing [1, 3, 5, 6] from the application of such servodrives over other electric motor systems are higher power and better torque to weight ratio, a considerable saving of energy and higher precision control of torque, speed and position which promote better electric vehicle propulsion performance and optimal EV target ranging along with automation and control. This is due largely to the high torque-to-weight ratio and compactness of permanent magnet (PM) drives, lower heat dissipation and the virtually maintenance free operation of brushless motors in inaccessible locations when compared to conventional DC & AC electric motors. The controllers of these machine drives, which incorporate wide bandwidth speed and torque control loops, are adaptively tuned to meet the essential requirements of system robustness, high tracking performance and EV range acquisition without overstressing the hardware components [3, 7, 8]. An essential feature of the adaptive optimal control procedure in such BLMD-EV systems is the accurate dynamical parameter identification strategy used in conjunction with an accurate BLMD model [9–12], where sensorless feedback current control loops are employed for reliable torque control during EV propulsion, with multi-modal penalty cost surfaces.

identification search strategy based on the FSD method over a multiminima cost

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

as an extension of the SA method is presented, with a multiminima objective function based on step response FC target data, for motor dynamical parameter extraction. Details of the FSD development and integration into the BLMD parameter estimation problem based on the minimum quantized step sizes from noise considerations are provided. The results of global parameter convergence estimates returned, which are very accurate, including the number of iterations, cost function evaluation and the algorithm run time are presented. Validation of the FSD identification strategy is provided by excellent correlation of BLMD model simulation trace coherence, at the optimal parameter estimates, with experimental test data

In the second section the application of the FSD optimization search technique

In the third section the development details of a novel modified form of the FSD algorithm are presented for fast accurate parameter identification [22, 23, 25–28]. This will be based on the heuristics of the FC sinc-like surface topography in an effort to reduce the computational cost and search time to acquire global optimality. The beneficial effect of the incorporation of an approximated gradient search, along with the gathered cost statistics, at the end of each anneal step in the cooling schedule during the high temperature random search phase is discussed. Furthermore the condition, pertaining to the occurrence of random search trapping within the capture cross section of the cost surface containing the global extremum, for elimination of the reheat and thermal condensation phases of the FSD method is explained. Details of a set of tests to establish modified FSD (MFSD) performance in terms of convergence accuracy accompanied with a substantial reduction in search time, for three known cases of motor shaft load inertia (*J*) in the parameter identification process, are furnished with remote initialization in the vicinity of a potential local minimum trap. An error analysis of the returned parameter estimates is provided, which are almost identical to actual *J* values, and a comparison is made with alternative global estimates obtained from cost surface simulation to validate the modified FSD search technique. A theoretical analysis of the effect of FC data training record length on the probability of global minimum capture and capture cross sectional 'area' is provided along with a discussion of the impact of data record

surface that is more selective at the global minimum.

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

length on FC cost surface selectivity for SI purposes.

The benefits accruing from the use of an embedded BLMD system in high performance adjustable speed drive applications has resulted in a need for an accurate physical model [12, 29] for the purpose of parameter identification of the drive dynamics. Allied to this need is a general requirement for an accurate and efficient search strategy of parameter space in the design of optimal drive controllers [30–32] where system identification is an implicit feature during online operation. This is necessary for PID auto-tuning of wide bandwidth current loops in torque control mode to speed up embedded BLMD commissioning and facilitate control optimization through regular retuning. The identification process is dependent on an accurate model of the nonlinear electromechanical system [33] which includes the pulse width modulated (PWM) inverter with power transistor turnon delay to avoid

The extraction of the drive dynamical parameters generally relies on the minimization of some quantitative measure of error cost in terms of the goodness-of-fit,

based on the MSE norm [13], between the observed motor drive output

**2. Motivation**

current shoot-through.

**41**

and from cost surface simulation.

This book chapter, which is divided into three separate but interrelated sections, concerns BLMD dynamical parameter identification in which the choice of target data used in the Minimum Squared Error (MSE) objective function formulation has a significant effect on cost surface topology and selectivity in the vicinity of the global minimum [13, 14]. The penalty cost function selection in the identification of the motor drive dynamics impacts directly on the type of parameter search strategy to be adopted where embedded cost surface multiminima are concerned, which is discussed below, in terms of the accuracy of the returned parameter estimates. A short review of classical identification techniques is provided initially with an explanation of global convergence failure due to local minimum trapping over a multiminima cost surface based on BLMD step response feedback current (FC) target data. This difficulty with classical optimization methods highlights the need for an effective search strategy of parameter space with an in-built adaptive jump mechanism which can facilitate escape from possible local minimum capture and guarantee eventual global convergence. Such identification search features are provided by statistical optimization methods based on a Simulated Annealing (SA) kernel [15–21] which has an adjustable pseudo-temperature parameter that controls the jump related magnitude of the inherent random fluctuations. The Fast Simulated Diffusion algorithm [22–24], which is a more efficient version of SA that exploits the use of the classical gradient search technique at low pseudotemperatures, surmounts the above obstacles and can be deployed as an effective global parameter extraction tool for BLMD identification.

In the first section the classical application of the Powell Conjugate Direction (PCD) optimization technique of motor parameter extraction over a two dimensional shaft velocity cost surface, which has a parabolic wedge shaped topography with a 'line minmum'stationary region [13, 14], is discussed. This will be used later for comparison purposes with the more successful Fast Simulated Diffusion (FSD) method, which is presented in the second section, to show that the FSD method is better in terms of the accuracy of returned FSD parameter estimates. It will also be shown that the PCD method does not converge to the global minimum and that the returned parameter estimates are less than satisfactory in the approximation of the optimal parameter vector when contrasted with the FSD method deployed over a multiminima FC cost surface. The convergence inaccuracy of the PCD method lays the groundwork for the introduction of a more accurate and efficient parameter

#### *Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

identification search strategy based on the FSD method over a multiminima cost surface that is more selective at the global minimum.

In the second section the application of the FSD optimization search technique as an extension of the SA method is presented, with a multiminima objective function based on step response FC target data, for motor dynamical parameter extraction. Details of the FSD development and integration into the BLMD parameter estimation problem based on the minimum quantized step sizes from noise considerations are provided. The results of global parameter convergence estimates returned, which are very accurate, including the number of iterations, cost function evaluation and the algorithm run time are presented. Validation of the FSD identification strategy is provided by excellent correlation of BLMD model simulation trace coherence, at the optimal parameter estimates, with experimental test data and from cost surface simulation.

In the third section the development details of a novel modified form of the FSD algorithm are presented for fast accurate parameter identification [22, 23, 25–28]. This will be based on the heuristics of the FC sinc-like surface topography in an effort to reduce the computational cost and search time to acquire global optimality. The beneficial effect of the incorporation of an approximated gradient search, along with the gathered cost statistics, at the end of each anneal step in the cooling schedule during the high temperature random search phase is discussed. Furthermore the condition, pertaining to the occurrence of random search trapping within the capture cross section of the cost surface containing the global extremum, for elimination of the reheat and thermal condensation phases of the FSD method is explained. Details of a set of tests to establish modified FSD (MFSD) performance in terms of convergence accuracy accompanied with a substantial reduction in search time, for three known cases of motor shaft load inertia (*J*) in the parameter identification process, are furnished with remote initialization in the vicinity of a potential local minimum trap. An error analysis of the returned parameter estimates is provided, which are almost identical to actual *J* values, and a comparison is made with alternative global estimates obtained from cost surface simulation to validate the modified FSD search technique. A theoretical analysis of the effect of FC data training record length on the probability of global minimum capture and capture cross sectional 'area' is provided along with a discussion of the impact of data record length on FC cost surface selectivity for SI purposes.

#### **2. Motivation**

higher power factor and efficiency, and are central to modern industrial automation [4] in such scenarios as aerospace systems control and maneuverability, numerical control (NC) machine tools and robotics. The benefits accruing [1, 3, 5, 6] from the application of such servodrives over other electric motor systems are higher power and better torque to weight ratio, a considerable saving of energy and higher precision control of torque, speed and position which promote better electric vehicle propulsion performance and optimal EV target ranging along with automation and control. This is due largely to the high torque-to-weight ratio and compactness of permanent magnet (PM) drives, lower heat dissipation and the virtually maintenance free operation of brushless motors in inaccessible locations when compared to conventional DC & AC electric motors. The controllers of these machine drives, which incorporate wide bandwidth speed and torque control loops, are adaptively tuned to meet the essential requirements of system robustness, high tracking performance and EV range acquisition without overstressing the hardware components [3, 7, 8]. An essential feature of the adaptive optimal control procedure in such BLMD-EV systems is the accurate dynamical parameter identification strategy used in conjunction with an accurate BLMD model [9–12], where sensorless feedback current control loops are employed for reliable torque control during EV propul-

This book chapter, which is divided into three separate but interrelated sections, concerns BLMD dynamical parameter identification in which the choice of target data used in the Minimum Squared Error (MSE) objective function formulation has a significant effect on cost surface topology and selectivity in the vicinity of the global minimum [13, 14]. The penalty cost function selection in the identification of the motor drive dynamics impacts directly on the type of parameter search strategy to be adopted where embedded cost surface multiminima are concerned, which is discussed below, in terms of the accuracy of the returned parameter estimates. A short review of classical identification techniques is provided initially with an explanation of global convergence failure due to local minimum trapping over a multiminima cost surface based on BLMD step response feedback current (FC) target data. This difficulty with classical optimization methods highlights the need for an effective search strategy of parameter space with an in-built adaptive jump mechanism which can facilitate escape from possible local minimum capture and guarantee eventual global convergence. Such identification search features are provided by statistical optimization methods based on a Simulated Annealing (SA) kernel [15–21] which has an adjustable pseudo-temperature parameter that controls the jump related magnitude of the inherent random fluctuations. The Fast Simulated Diffusion algorithm [22–24], which is a more efficient version of SA that exploits the use of the classical gradient search technique at low pseudo-

temperatures, surmounts the above obstacles and can be deployed as an effective

In the first section the classical application of the Powell Conjugate Direction (PCD) optimization technique of motor parameter extraction over a two dimensional shaft velocity cost surface, which has a parabolic wedge shaped topography with a 'line minmum'stationary region [13, 14], is discussed. This will be used later for comparison purposes with the more successful Fast Simulated Diffusion (FSD) method, which is presented in the second section, to show that the FSD method is better in terms of the accuracy of returned FSD parameter estimates. It will also be shown that the PCD method does not converge to the global minimum and that the returned parameter estimates are less than satisfactory in the approximation of the optimal parameter vector when contrasted with the FSD method deployed over a multiminima FC cost surface. The convergence inaccuracy of the PCD method lays the groundwork for the introduction of a more accurate and efficient parameter

global parameter extraction tool for BLMD identification.

**40**

sion, with multi-modal penalty cost surfaces.

*Self-Driving Vehicles and Enabling Technologies*

The benefits accruing from the use of an embedded BLMD system in high performance adjustable speed drive applications has resulted in a need for an accurate physical model [12, 29] for the purpose of parameter identification of the drive dynamics. Allied to this need is a general requirement for an accurate and efficient search strategy of parameter space in the design of optimal drive controllers [30–32] where system identification is an implicit feature during online operation. This is necessary for PID auto-tuning of wide bandwidth current loops in torque control mode to speed up embedded BLMD commissioning and facilitate control optimization through regular retuning. The identification process is dependent on an accurate model of the nonlinear electromechanical system [33] which includes the pulse width modulated (PWM) inverter with power transistor turnon delay to avoid current shoot-through.

The extraction of the drive dynamical parameters generally relies on the minimization of some quantitative measure of error cost in terms of the goodness-of-fit, based on the MSE norm [13], between the observed motor drive output

experimental test data and its model equivalent. The presence of multiminima in the MSE penalty function, however, results in a large spread of parameter estimates about the global minimum with model accuracy and subsequent controller design performance very dependent on the minimization technique adopted and the initial search point chosen. The existence of a noisy cost function, resulting in 'false' local minima proliferation in the stationary region containing the global extremum [13, 28], depends on the numerical accuracy with which the PWM delayed inverter switching instants are resolved in the model simulation [13]. Furthermore the plurality of genuine local minima is governed by the choice of data training record used in the objective function formulation which in the case of step response feedback current (FC) has a sinc-like topography [13]. The use of a step input (i/p) as a test stimulus is motivated by the fact that in normal industrial applications in the online mode input command changes are generally sudden and step-like and are sufficient for persistent excitation of the BLMD system. The accompanying transients in the observed variables can then be used effectively for parameter identification of motor shaft viscous damping factor and inertia changes during normal operation.

**3. Choice of parameter identification methods**

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

captured at local minima in this instance.

**43**

Two methods of parameter identification, which are based on the PCD and FSD optimization techniques and linked with the shape of the error response surface, will be investigated in sections 4 and 7 in the extraction process of known motor shaft inertia from data training records. The first, rooted in classical optimization techniques [35] where derivative information is not required [36, 37], relies on the application of Powell's conjugate direction search to the concave velocity response surface with single parameter variation [13]. This classical parameter extraction technique is superior to and much more efficient [35], due to the orthogonality of its conjugate directions of search, than other direct search methods [38–40] such as the Simplex method [41] and the method of Hooke and Jeeves [42, 43] which are expensive in CPU time and slow to converge. Other more efficient classical optimization techniques [35, 44–46], such as the Polak-Riebere conjugate gradient method or the Newton-like BFGS method [47, 48] or the hybrid Levenberg–Marquardt method [49–51] are not considered in this case because of cost surface noisiness and the need to calculate partial derivatives which is difficult with the presence of 'noise' related PWM computational uncertainty. These alternative methods are computationally expensive in BLMD simulation time, where the evaluation of the gradient vector and Hessian matrix [35] are concerned, and are difficult to apply in any case because of the model complexity of the complete motor drive system with PWM inverter delay operation without resorting to difference equation approximation of the derivatives [35, 52]. Furthermore partial derivative evaluation is suspect in the presence of computational 'noise', inherent in the cost function, for an infinitesimal change in the relevant parameters. This can result in an erratic hilldescent, associated with the conjugate gradient direction search, over the response surface and entrapment of the minimization procedure in a false minimum in the noise grained incline of the bowl shaped velocity cost function [13, 28]. All classical minimization procedures are well known to have difficulty with the FC cost surface topography illustrated in [13, 28] because they are easily trapped in one of the embedded local minima and thus fail to converge to the optimal parameter set. This problem is accentuated by initialization of the search process remote from the global minimum, due to uncertainty, in a region where there are local minima. Classical hill-decent methods that rely on following the cost gradient are easily

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

The second identification method is based on the statistical search technique of simulated diffusion (SD) [24, 53], as an adjunct of simulated thermal annealing (SA) [15–17] used in combinatorial optimization [25], and has to be deployed to acquire the global minimizer of the FC multiminima cost surface. The SD technique in contrast to the PCD method has been successfully applied to the multioptimal problem of MOSFET parameter extraction [19, 24] and simulated annealing in circuit placement tasks [20, 21], with a cost function having a fractal landscape, in

the VLSI domain. Both the PCD and FSD methods of parameter extraction presented compare favorably in terms of the returned shaft load inertia, for short data records with initialization close to the global minimum, which enhances confidence in the model of the BLMD servodrive system as well as in the performance of both identification strategies. However the sensitivity of the FC objective function to inertia parameter changes is an order of magnitude greater than that of its shaft velocity counterpart [13, 28]. This results in better selectivity and more accurate convergence in the case of the SD method whereas Powell's method is more susceptible to capture in a false minimum due to cost surface noise in the vicinity of the global minimum. Furthermore with longer data records the selectivity of the FC cost function increases to a maximum, when the motor has reached full speed,

Experimental data training sets, of the observed variables [13] for various known shaft load inertia, can be used during the parameter identification procedure with the corresponding BLMD model simulation runs to establish a parameter mean squares error cost surface as the objective function to be minimized. The deployment of step response winding current feedback as a target function is found to be particularly beneficial as it exhibits the frequency modulated (FM) characteristic of a constant amplitude swept frequency sinusoid. The FC response also has better overall cost surface selectivity, which improves with observed data record length, by comparison with shaft velocity target information [13]. The corresponding simulated step response, upon parameter convergence, will be shown to have both frequency and phase coherence which attests to the accuracy of the identification methodology. Furthermore the selection of an FC multiminima cost function as a suitable choice for investigation in motor parameter extraction is motivated by the scenario, as a secondary consideration, that winding current flow information will be the only feedback signal available for sensorless motor control [34] applications.

The step response FC cost function exhibits an apparently smooth continuous one dimensional surface when plotted against either inertia or the damping factor as the free parameter to be identified [13] for coarse step size simulation. The local minimisers appear to be symmetrically disposed about the global minimum in accordance with a sinc function profile. The attendant unimodal velocity cost function appears to be parabolic in the inertia and friction parameter variables [13]. When high resolution of the motor shaft inertia extimates is required, in simulation trials, during system identification both cost functions appear to possess a granulated response surface thus rendering uncertainty in the parameter extraction process [13]. However this difficulty in parameter convergence is somewhat tempered by the observation that the noise floor in the error response surface is eclipsed by the residual error magnitude at the global minimum, which ameliorates the parameter search process, and is alleviated by the adoption of parameter quantization as discussed in [13, 28]. The response surface 'noisiness' arises primarily from the delay nonlinearity in the PWM current loops of the BLMD model structure and the accuracy with which the PWM crossover times are determined with the subsequent timing of the delayed inverter firing signals [9, 10]. The presence of 'genuine' local minimisers in the FC response cost surface is manifested through interference by the relative phasing of the swept frequency motor current sinusoids with target data at different inertia values [13, 28].

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

#### **3. Choice of parameter identification methods**

experimental test data and its model equivalent. The presence of multiminima in the MSE penalty function, however, results in a large spread of parameter estimates about the global minimum with model accuracy and subsequent controller design performance very dependent on the minimization technique adopted and the initial search point chosen. The existence of a noisy cost function, resulting in 'false' local minima proliferation in the stationary region containing the global extremum [13, 28], depends on the numerical accuracy with which the PWM delayed inverter switching instants are resolved in the model simulation [13]. Furthermore the plurality of genuine local minima is governed by the choice of data training record used in the objective function formulation which in the case of step response feedback current (FC) has a sinc-like topography [13]. The use of a step input (i/p) as a test stimulus is motivated by the fact that in normal industrial applications in the online mode input command changes are generally sudden and step-like and are sufficient for persistent excitation of the BLMD system. The accompanying transients in the observed variables can then be used effectively for parameter identification of motor shaft viscous damping factor and inertia changes during normal

*Self-Driving Vehicles and Enabling Technologies*

Experimental data training sets, of the observed variables [13] for various known shaft load inertia, can be used during the parameter identification procedure with the corresponding BLMD model simulation runs to establish a parameter mean squares error cost surface as the objective function to be minimized. The deployment of step response winding current feedback as a target function is found to be particularly beneficial as it exhibits the frequency modulated (FM) characteristic of a constant amplitude swept frequency sinusoid. The FC response also has better overall cost surface selectivity, which improves with observed data record length, by comparison with shaft velocity target information [13]. The corresponding simulated step response, upon parameter convergence, will be shown to have both frequency and phase coherence which attests to the accuracy of the identification methodology. Furthermore the selection of an FC multiminima cost function as a suitable choice for investigation in motor parameter extraction is motivated by the scenario, as a secondary consideration, that winding current flow information will be the only feedback signal available for sensorless motor control [34]

The step response FC cost function exhibits an apparently smooth continuous one dimensional surface when plotted against either inertia or the damping factor as the free parameter to be identified [13] for coarse step size simulation. The local minimisers appear to be symmetrically disposed about the global minimum in accordance with a sinc function profile. The attendant unimodal velocity cost function appears to be parabolic in the inertia and friction parameter variables [13]. When high resolution of the motor shaft inertia extimates is required, in simulation trials, during system identification both cost functions appear to possess a granulated response surface thus rendering uncertainty in the parameter extraction process [13]. However this difficulty in parameter convergence is somewhat tempered by the observation that the noise floor in the error response surface is eclipsed by the residual error magnitude at the global minimum, which ameliorates the parameter search process, and is alleviated by the adoption of parameter quantization as discussed in [13, 28]. The response surface 'noisiness' arises primarily from the delay nonlinearity in the PWM current loops of the BLMD model structure and the accuracy with which the PWM crossover times are determined with the subsequent timing of the delayed inverter firing signals [9, 10]. The presence of 'genuine' local minimisers in the FC response cost surface is manifested through interference by the relative phasing of the swept frequency motor current sinusoids with target data

operation.

applications.

at different inertia values [13, 28].

**42**

Two methods of parameter identification, which are based on the PCD and FSD optimization techniques and linked with the shape of the error response surface, will be investigated in sections 4 and 7 in the extraction process of known motor shaft inertia from data training records. The first, rooted in classical optimization techniques [35] where derivative information is not required [36, 37], relies on the application of Powell's conjugate direction search to the concave velocity response surface with single parameter variation [13]. This classical parameter extraction technique is superior to and much more efficient [35], due to the orthogonality of its conjugate directions of search, than other direct search methods [38–40] such as the Simplex method [41] and the method of Hooke and Jeeves [42, 43] which are expensive in CPU time and slow to converge. Other more efficient classical optimization techniques [35, 44–46], such as the Polak-Riebere conjugate gradient method or the Newton-like BFGS method [47, 48] or the hybrid Levenberg–Marquardt method [49–51] are not considered in this case because of cost surface noisiness and the need to calculate partial derivatives which is difficult with the presence of 'noise' related PWM computational uncertainty. These alternative methods are computationally expensive in BLMD simulation time, where the evaluation of the gradient vector and Hessian matrix [35] are concerned, and are difficult to apply in any case because of the model complexity of the complete motor drive system with PWM inverter delay operation without resorting to difference equation approximation of the derivatives [35, 52]. Furthermore partial derivative evaluation is suspect in the presence of computational 'noise', inherent in the cost function, for an infinitesimal change in the relevant parameters. This can result in an erratic hilldescent, associated with the conjugate gradient direction search, over the response surface and entrapment of the minimization procedure in a false minimum in the noise grained incline of the bowl shaped velocity cost function [13, 28]. All classical minimization procedures are well known to have difficulty with the FC cost surface topography illustrated in [13, 28] because they are easily trapped in one of the embedded local minima and thus fail to converge to the optimal parameter set. This problem is accentuated by initialization of the search process remote from the global minimum, due to uncertainty, in a region where there are local minima. Classical hill-decent methods that rely on following the cost gradient are easily captured at local minima in this instance.

The second identification method is based on the statistical search technique of simulated diffusion (SD) [24, 53], as an adjunct of simulated thermal annealing (SA) [15–17] used in combinatorial optimization [25], and has to be deployed to acquire the global minimizer of the FC multiminima cost surface. The SD technique in contrast to the PCD method has been successfully applied to the multioptimal problem of MOSFET parameter extraction [19, 24] and simulated annealing in circuit placement tasks [20, 21], with a cost function having a fractal landscape, in the VLSI domain. Both the PCD and FSD methods of parameter extraction presented compare favorably in terms of the returned shaft load inertia, for short data records with initialization close to the global minimum, which enhances confidence in the model of the BLMD servodrive system as well as in the performance of both identification strategies. However the sensitivity of the FC objective function to inertia parameter changes is an order of magnitude greater than that of its shaft velocity counterpart [13, 28]. This results in better selectivity and more accurate convergence in the case of the SD method whereas Powell's method is more susceptible to capture in a false minimum due to cost surface noise in the vicinity of the global minimum. Furthermore with longer data records the selectivity of the FC cost function increases to a maximum, when the motor has reached full speed,

accompanied with 'genuine' local minima proliferation. The reverse effect is manifested as a flattening of the response surface in the neighborhood of the global minimum, with the resulting minimization procedure susceptible to remote trapping in noisy local minima, for the shaft velocity cost function. In the former procedure relative phase information can be used effectively for estimating parameter variation at motor speed saturation while the benefits of the initial speed response transient are attenuated in the latter case. The FSD search technique is verified, with initialization far from the global minimum, for known motor shaft inertia. The accuracy of the returned FSD estimates is also checked against the cost surface simulation. Convergence details and comparisons of both identification methods in terms of iteration count, objective function evaluations or motor simulation runs and CPU time are presented.

#### **4. Application of Powell's identification method to velocity cost surface**

The choice of Powell's Conjugate Direction Set method [35, 49, 54, 55] of unconstrained optimization as a method of BLMD dynamical parameter identification within the indicated parameter tolerance bounds was motivated by topographical considerations of the shaft velocity objective function *E*ω(*X*) and ingrained cost surface noisiness. The penalty cost function concerned appears to have a 'line minimum stationary region' predominantly in the *B* parameter direction as elucidated in [13]. Consequently convergence difficulties can arise from application of any of the steepest decent conjugate gradient methods of parameter identification, such as the Polack-Ribiere technique [35], with this type of cost function. This problem results from the requirement that

$$\nabla E\_{\boldsymbol{\alpha}}\left(\mathbf{X}^{(k+1)}\right)^{\mathrm{T}}\mathbf{s}^{(k)}<\mathbf{0}\tag{1}$$

the wedge shaped syncline of the cost velocity surface as illustrated in **Figures 2**–**4**. This difficulty is partially borne out in [13] where the fitted response quadratic model parameters were re-evaluated at successive iteration points to improve the global convergence estimate. Furthermore the presence of point-like singularities due to cost surface noisiness, with 'false' local minima proliferation in the neighborhood of the global minimizer [13], results in a discontinuous cost function with consequent difficulties with derivative calculations. Also the derivative computation burden increases with expensive BLMD cost function evaluation where lengthy

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

**Figure 2.**

**Figure 3.**

**45**

*MSL velocity cost surface.*

*NSL velocity cost surface.*

for hill decent and approaches zero as the global minimum is reached for the possible gradient search directions ∇*E*ω(*Xj* (*<sup>k</sup>*+1)) indicated in **Figure 1**.

The component of the gradient ∇*E*ω(*X*(*<sup>k</sup>*+1)), which is tangential to the cost contour in this instance, vanishes as shown along the *k*th iterate search direction **s** (k) at the points *Xj* (*k*+1) for *j* = 1,2, etc. This condition results in a multiplicity of search directions and possible global minimum values *X*(*k*+2) along the 'line minimum' of


**Figure 1.** *Global minima multiplicity.*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

the wedge shaped syncline of the cost velocity surface as illustrated in **Figures 2**–**4**. This difficulty is partially borne out in [13] where the fitted response quadratic model parameters were re-evaluated at successive iteration points to improve the global convergence estimate. Furthermore the presence of point-like singularities due to cost surface noisiness, with 'false' local minima proliferation in the neighborhood of the global minimizer [13], results in a discontinuous cost function with consequent difficulties with derivative calculations. Also the derivative computation burden increases with expensive BLMD cost function evaluation where lengthy

**Figure 2.** *NSL velocity cost surface.*

accompanied with 'genuine' local minima proliferation. The reverse effect is manifested as a flattening of the response surface in the neighborhood of the global

minimum, with the resulting minimization procedure susceptible to remote trapping in noisy local minima, for the shaft velocity cost function. In the former procedure relative phase information can be used effectively for estimating parameter variation at motor speed saturation while the benefits of the initial speed response transient are attenuated in the latter case. The FSD search technique is verified, with initialization far from the global minimum, for known motor shaft inertia. The accuracy of the returned FSD estimates is also checked against the cost surface simulation. Convergence details and comparisons of both identification methods in terms of iteration count, objective function evaluations or motor

**4. Application of Powell's identification method to velocity cost surface**

The choice of Powell's Conjugate Direction Set method [35, 49, 54, 55] of unconstrained optimization as a method of BLMD dynamical parameter identification within the indicated parameter tolerance bounds was motivated by topographical considerations of the shaft velocity objective function *E*ω(*X*) and ingrained cost surface noisiness. The penalty cost function concerned appears to have a 'line minimum stationary region' predominantly in the *B* parameter direction as elucidated in [13]. Consequently convergence difficulties can arise from application of any of the steepest decent conjugate gradient methods of parameter identification, such as the Polack-Ribiere technique [35], with this type of cost function. This

<sup>∇</sup>*E*<sup>ω</sup> *<sup>X</sup>*ð Þ *<sup>k</sup>*þ<sup>1</sup> <sup>T</sup>

for hill decent and approaches zero as the global minimum is reached for the

The component of the gradient ∇*E*ω(*X*(*<sup>k</sup>*+1)), which is tangential to the cost contour in this instance, vanishes as shown along the *k*th iterate search direction **s**

directions and possible global minimum values *X*(*k*+2) along the 'line minimum' of

*s*

(*k*+1) for *j* = 1,2, etc. This condition results in a multiplicity of search

ð Þ*<sup>k</sup>* <0 (1)

(k)

(*<sup>k</sup>*+1)) indicated in **Figure 1**.

simulation runs and CPU time are presented.

*Self-Driving Vehicles and Enabling Technologies*

problem results from the requirement that

possible gradient search directions ∇*E*ω(*Xj*

at the points *Xj*

**Figure 1.**

**44**

*Global minima multiplicity.*

**Figure 3.** *MSL velocity cost surface.*

*N*-dimensional parameter space *X* for global convergence along independent

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

**5. Application of PCD method to BLMD parameter extraction**

**Gs** ^ ð Þ*<sup>j</sup>* <sup>¼</sup> <sup>1</sup> <sup>∀</sup>*<sup>i</sup>* <sup>¼</sup> *<sup>j</sup>*

The PCD method, which begins with a user supplied estimate **X**(1) and a set *S* of directions based on the column vectors of any orthogonal matrix such as the iden-

initially, proceeds according to a cyclic *N* dimensional search of parameter space as per the flowchart in **Figure 5** until some stopping criterion based on sufficient cost reduction is satisfied. The basic structure of the algorithm can be summarized as a line minimum search routine due to Brent [49, 56] for the *k*th iterative search as

conjugate to all previous excursions into the quantized parameter lattice.

*<sup>X</sup>*ð Þ *<sup>k</sup>*þ<sup>1</sup> <sup>¼</sup> *<sup>X</sup>*ð Þ*<sup>k</sup>* <sup>þ</sup> <sup>α</sup>ð Þ*<sup>k</sup> <sup>s</sup>*

with resolved accuracy given by the worst case quantized step size �δ*X*<sup>L</sup> in [13, 28]. In the above line minimum iterative search procedure along a particular

quadratic polynomial extrapolation. The cost function minimum estimate *X*(*k*+1) is then obtained by successive approximation within the bracketed interval via interpolation from the fitted quadratic model *Q*(*X*) to the triplet of points {*X*1, *X*2, *X*3},

This minimum estimation procedure is assisted, if iterative progress towards quadratic termination is stalled in a non convergent limit cycle, by conducting a golden section search [56] of the bounded interval through contraction in terms of

**<sup>X</sup>***<sup>m</sup>* <sup>¼</sup> ð Þ **<sup>X</sup>**<sup>3</sup> � **<sup>X</sup>**<sup>2</sup> *gm*; If **<sup>X</sup>**<sup>2</sup> <sup>&</sup>lt; ð Þ **<sup>X</sup>**<sup>1</sup> <sup>þ</sup> **<sup>X</sup>**<sup>3</sup> *<sup>=</sup>*<sup>2</sup>

ð Þ **X**<sup>2</sup> � **X**<sup>1</sup> *gm*; If **X**<sup>2</sup> > ð Þ **X**<sup>1</sup> þ **X**<sup>3</sup> *=*2

to trap the least *MSE* cost *E*ω(*X*(*<sup>k</sup>*+1)). During a single cycle iteration of the PCD algorithm the single largest cost decrease Δ*E*ω(*X*) along a particular search direction

(*k*) the minimizer of the cost function is crudely bracketed initially by

½*Eω*ð Þ� **X**<sup>2</sup> *Eω*ð Þ **X**<sup>3</sup> � � ð Þ **X**<sup>2</sup> � **X**<sup>3</sup>

ð Þ **X**<sup>2</sup> � **X**<sup>1</sup> ½*Eω*ð Þ� **X**<sup>2</sup> *Eω*ð Þ **X**<sup>3</sup> � � ð Þ **X**<sup>2</sup> � **X**<sup>3</sup> ½ � *Eω*ð Þ� **X**<sup>2</sup> *Eω*ð Þ **X**<sup>1</sup>

+α(*k*) *s* (*k*)

space *X* based on a quadratic model approximation of *E*ω(*X*) in this direction

� � (4)

�

0 ∀*i* 6¼ *j*

, ∀*k* ¼ 1, … , *N*

) with respect to α in discrete

ð Þ*<sup>k</sup>* (5)

2

½ � *Eω*ð Þ� **X**<sup>2</sup> *Eω*ð Þ **X**<sup>1</sup>

*:*

(6)

(7)

(*k*) in discretized parameter space which is

(3)

**s**ð Þ*<sup>i</sup> <sup>T</sup>*

*<sup>S</sup>* <sup>¼</sup> **<sup>s</sup>**ð Þ <sup>k</sup> <sup>j</sup> **<sup>s</sup>**ð Þ <sup>k</sup> <sup>¼</sup> *<sup>e</sup>*ð Þ <sup>k</sup> <sup>¼</sup> 0, 0, … , 0, 1ð Þ <sup>k</sup> , 0, … , 0 h i<sup>T</sup>

mutually conjugate directions [35] such that

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

• Determine the search direction **s**

where the response surface is concave, as

ð Þ **X**<sup>2</sup> � **X**<sup>1</sup>

�

2

and proceed to set

• Evaluate *α*(*k*) so as to minimize *E*ω(*X*(*k*)

tity *I* with

direction *s*

**<sup>X</sup>**ð Þ *<sup>k</sup>*þ<sup>1</sup> <sup>¼</sup> **<sup>X</sup>***<sup>m</sup>*

**47**

<sup>¼</sup> **<sup>X</sup>**<sup>2</sup> � <sup>1</sup>

2 �

the golden mean *gm* (�0.382) as

**Figure 4.** *LSL velocity cost surface.*

simulation times are concerned with a small time step Δt for accurate resolution of PWM edge transitions. The steepest decent gradient search technique can also suffer from oscillatory behavior and poor convergence results due to numerical round-off effects as reported by Fletcher [35].

The PCD method, which relies on cost function evaluations only without derivative information, is cyclically deployed instead as a line search algorithm in parameter space beginning at *X*(1). This algorithm progresses along *N* mutually orthogonal directions conforming to the dimensionally of parameter space until sufficient accuracy of the global minimum estimate has been attained according to some convergence stopping criterion. With this method the iterate moves gradually towards the neighborhood of the global optimum *Xopt* via inexact line searches initially and then rapidly converges to the stationary point itself. The iteration process is terminated upon some user supplied convergence test of the form [49].

$$2\left\{ \left( E\_{\boldsymbol{\alpha}} \left( \mathbf{X}^{(1)} \right) - E\_{\boldsymbol{\alpha}} \left( \mathbf{X}^{(N+1)} \right) \right) / \left\{ E\_{\boldsymbol{\alpha}} \left( \mathbf{X}^{(N+1)} \right) + E\_{\boldsymbol{\alpha}} \left( \mathbf{X}^{(1)} \right) \right\} < \varepsilon \tag{2}$$

being satisfied with a gradual reduction in the cost *E*(*X*) towards an accumulation point **X**^ *opt* which approximates the global minimum *Xopt* within the specified error bound ε. Furthermore the application of a specific threshold step size δ*X<sup>L</sup>* [13, 28] for parameter space quantization ameliorates the difficulty with response surface noisiness [13, 28]. This methodology results in inexpensive line searching during parameter extraction with a reasonable degree of convergence accuracy maintained. In the application of the PCD algorithm a quadratic model is used to approximate the two dimensional MSE objective function, pertaining to the shaft velocity in terms of the motor dynamical parameters [13], so that a prediction of the location of the local minimum can be made. This localized response surface modeling technique guarantees second order convergence [35] and is a very suitable candidate for the velocity cost function given the parabolic nature of its topography with respect to the inertia parameter which is the most likely to vary in high performance drive applications. The applied PCD method is based on the property of quadratic termination of the approximation model, with Hessian **G**^>0, at the global minimizer. This model strategy, which is similar to the normal form in [13, 28], admits to the existence of at most *N* line searches {**s** (1), **s** (2), … , **s** (N)} in

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

*N*-dimensional parameter space *X* for global convergence along independent mutually conjugate directions [35] such that

$$\mathbf{s}^{(i)^T}\hat{\mathbf{G}}\mathbf{s}^{(j)} = \begin{cases} \mathbf{1} & \forall i = j \\ \mathbf{0} & \forall i \neq j \end{cases} \tag{3}$$

#### **5. Application of PCD method to BLMD parameter extraction**

The PCD method, which begins with a user supplied estimate **X**(1) and a set *S* of directions based on the column vectors of any orthogonal matrix such as the identity *I* with

$$\mathbf{S} = \left\{ \mathbf{s}^{(\mathbf{k})} \mid \mathbf{s}^{(\mathbf{k})} = \mathbf{e}^{(\mathbf{k})} = \left[ \mathbf{0}, \mathbf{0}, \dots, \mathbf{0}, \mathbf{1}^{(\mathbf{k})}, \mathbf{0}, \dots, \mathbf{0} \right]^{\mathrm{T}}, \forall k = \mathbf{1}, \dots, N \right\} \tag{4}$$

initially, proceeds according to a cyclic *N* dimensional search of parameter space as per the flowchart in **Figure 5** until some stopping criterion based on sufficient cost reduction is satisfied. The basic structure of the algorithm can be summarized as a line minimum search routine due to Brent [49, 56] for the *k*th iterative search as


$$\mathbf{X}^{(k+1)} = \mathbf{X}^{(k)} + \mathbf{a}^{(k)} \ s^{(k)} \tag{5}$$

with resolved accuracy given by the worst case quantized step size �δ*X*<sup>L</sup> in [13, 28]. In the above line minimum iterative search procedure along a particular direction *s* (*k*) the minimizer of the cost function is crudely bracketed initially by quadratic polynomial extrapolation. The cost function minimum estimate *X*(*k*+1) is then obtained by successive approximation within the bracketed interval via interpolation from the fitted quadratic model *Q*(*X*) to the triplet of points {*X*1, *X*2, *X*3}, where the response surface is concave, as

$$\begin{split} \mathbf{X}^{(k+1)} &= \mathbf{X}\_{m} \\ &= \mathbf{X}\_{2} - \frac{1}{2} \cdot \frac{(\mathbf{X}\_{2} - \mathbf{X}\_{1})^{2} [E\_{w}(\mathbf{X}\_{2}) - E\_{w}(\mathbf{X}\_{3})] - (\mathbf{X}\_{2} - \mathbf{X}\_{3})^{2} [E\_{w}(\mathbf{X}\_{2}) - E\_{w}(\mathbf{X}\_{1})]}{(\mathbf{X}\_{2} - \mathbf{X}\_{1})[E\_{w}(\mathbf{X}\_{2}) - E\_{w}(\mathbf{X}\_{3})] - (\mathbf{X}\_{2} - \mathbf{X}\_{3})[E\_{w}(\mathbf{X}\_{2}) - E\_{w}(\mathbf{X}\_{1})]} . \end{split} \tag{6}$$

This minimum estimation procedure is assisted, if iterative progress towards quadratic termination is stalled in a non convergent limit cycle, by conducting a golden section search [56] of the bounded interval through contraction in terms of the golden mean *gm* (�0.382) as

$$\mathbf{X}\_m = \begin{cases} (\mathbf{X}\_3 - \mathbf{X}\_2)\mathbf{g}\_m; & \text{If } \mathbf{X}\_2 < (\mathbf{X}\_1 + \mathbf{X}\_3)/2\\ (\mathbf{X}\_2 - \mathbf{X}\_1)\mathbf{g}\_m; & \text{If } \mathbf{X}\_2 > (\mathbf{X}\_1 + \mathbf{X}\_3)/2 \end{cases} \tag{7}$$

to trap the least *MSE* cost *E*ω(*X*(*<sup>k</sup>*+1)). During a single cycle iteration of the PCD algorithm the single largest cost decrease Δ*E*ω(*X*) along a particular search direction

simulation times are concerned with a small time step Δt for accurate resolution of PWM edge transitions. The steepest decent gradient search technique can also suffer from oscillatory behavior and poor convergence results due to numerical

The PCD method, which relies on cost function evaluations only without deriv-

*<sup>=</sup> <sup>E</sup>*<sup>ω</sup> *<sup>X</sup>*ð Þ *<sup>N</sup>*þ<sup>1</sup> � �

being satisfied with a gradual reduction in the cost *E*(*X*) towards an accumulation point **X**^ *opt* which approximates the global minimum *Xopt* within the specified error bound ε. Furthermore the application of a specific threshold step size δ*X<sup>L</sup>* [13, 28] for parameter space quantization ameliorates the difficulty with response surface noisiness [13, 28]. This methodology results in inexpensive line searching during parameter extraction with a reasonable degree of convergence accuracy maintained. In the application of the PCD algorithm a quadratic model is used to approximate the two dimensional MSE objective function, pertaining to the shaft velocity in terms of the motor dynamical parameters [13], so that a prediction of the location of the local minimum can be made. This localized response surface modeling technique guarantees second order convergence [35] and is a very suitable candidate for the velocity cost function given the parabolic nature of its topography with respect to the inertia parameter which is the most likely to vary in high performance drive applications. The applied PCD method is based on the property of quadratic termination of the approximation model, with Hessian **G**^>0, at the global minimizer. This model strategy, which is similar to the normal form in

<sup>þ</sup> *<sup>E</sup>*<sup>ω</sup> *<sup>X</sup>*ð Þ<sup>1</sup> n o � �

(1), **s**

(2), … , **s**

(N)} in

<ε (2)

ative information, is cyclically deployed instead as a line search algorithm in parameter space beginning at *X*(1). This algorithm progresses along *N* mutually orthogonal directions conforming to the dimensionally of parameter space until sufficient accuracy of the global minimum estimate has been attained according to some convergence stopping criterion. With this method the iterate moves gradually towards the neighborhood of the global optimum *Xopt* via inexact line searches initially and then rapidly converges to the stationary point itself. The iteration process is terminated upon some user supplied convergence test of the form [49].

round-off effects as reported by Fletcher [35].

*Self-Driving Vehicles and Enabling Technologies*

2 �

**46**

**Figure 4.**

*LSL velocity cost surface.*

*<sup>E</sup>*<sup>ω</sup> *<sup>X</sup>*ð Þ<sup>1</sup> � �

� *<sup>E</sup>*<sup>ω</sup> *<sup>X</sup>*ð Þ *<sup>N</sup>*þ<sup>1</sup> n o � �

[13, 28], admits to the existence of at most *N* line searches {**s**

replacing that in *S* along which the largest cost decrease Δ*E*<sup>ω</sup> was observed, is made

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

*<sup>X</sup>EXT* <sup>¼</sup> *<sup>X</sup>*ð Þ *<sup>k</sup>*þ<sup>1</sup> <sup>þ</sup> *<sup>s</sup>*

to avoid linear dependence windup and resultant loss of conjugacy. This cost is then compared with that at the initial search point *X*(*S*) along with the differential

<sup>Δ</sup>*<sup>E</sup>* <sup>¼</sup> *<sup>E</sup>*ð Þ*<sup>S</sup>* � *<sup>E</sup><sup>ω</sup> <sup>X</sup>*ð Þ *<sup>k</sup>*þ<sup>1</sup> � i � � � <sup>Δ</sup>*E<sup>ω</sup>*

is regarded as the average path traversed over all possible *N* directions in *S*, other

is also checked for possible minimum convergence of the iterative search along

If the test condition Eq. (12) is true then the old set of directions is retained for the next Powell iteration either because cost reduction is already exhausted or no significant reduction is observed in any particular direction or a substantial second

*AV* indicating minimum convergence of the search

*AV* before embarking on the next pass of the Powell algorithm

<sup>2</sup>*<sup>κ</sup>* � <sup>Δ</sup>*E*<sup>2</sup> <sup>≥</sup> <sup>Δ</sup>*E<sup>ω</sup> <sup>E</sup><sup>ω</sup> <sup>X</sup>*ð Þ*<sup>S</sup>* � � � *<sup>E</sup><sup>ω</sup> <sup>X</sup>EXT* n o � �

estimate. Conversely if Eq. (12) is false then the direction set *S* is updated by

which is usually restricted to some maximum user supplied iteration count *Nmax* of

The PCD method was applied to the identification of three known values of BLMD shaft load inertia with experimental shaft velocity target data deployed in the MSE objective function *E*ω(*X*) formulation displayed in **Figures 2**–**4**. An insight into the progress of this optimization method towards global optimality in the extraction of the dynamical *J* and *B* parameters with initialization at the tolerance band edge can be obtained, for example with zero shaft inertial load conditions, from **Figure 2** over the generated velocity cost surface. After one cycle of the Powell method the iterate has reached the 'line minimum' of the cost surface syncline by completing alternate line searches along the *J* and *B* parameter directions. Quadratic convergence of the PCD method thereafter is relatively 'slow' in that a further three iteration steps of the PCD algorithm are required to reach a limit point estimate **X**^ *opt* of the global minimum. This is manifested as a zigzag search pattern over the stationary region of the response surface in the quantized *J* and *B* parameter directions along the 'line minimum', which is essentially in the *B* direction, where the cost function curvature is low with inadequate selectivity for global minimum

. Furthermore the curvature estimate at *X*(*k*+1) in the direction

*<sup>κ</sup>* <sup>¼</sup> *<sup>E</sup><sup>ω</sup> <sup>X</sup>*ð Þ*<sup>S</sup>* � � � <sup>2</sup>*E<sup>ω</sup> <sup>X</sup>*ð Þ *<sup>k</sup>*þ<sup>1</sup> � � <sup>þ</sup> *<sup>E</sup><sup>ω</sup> <sup>X</sup>EXT* n o � � (11)

*s*

h

with Eq. (10) using the flowchart test condition in **Figure 5** as

to determine if any reduction is achievable along *s*

*AV* (8)

(10)

th iteration, which

*:* (12)

*AV* <sup>¼</sup> *<sup>X</sup>*ð Þ *<sup>k</sup>*þ<sup>1</sup> � *<sup>X</sup>*ð Þ*<sup>k</sup>* (9)

*AV* for the *J*

2

by first evaluating the cost at the extension point

along the proposed average direction

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

comparison

than that via *s*

*AV*, given by

*s*

(*dm*)

derivative exists along *s*

(*dm*) with *s*

replacing *s*

typically 200.

reachability.

**49**

#### **Figure 5.**

*Flowchart of Powell's conjugate direction set optimization technique.*

*s* (*dm*) is monitored. This cost reduction metric is then used to determine whether or not the set *S* of conjugate directions needs to updated before commencing the next Powell (*J*+1)th iteration cycle. The decision to include a new search direction, by

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

replacing that in *S* along which the largest cost decrease Δ*E*<sup>ω</sup> was observed, is made by first evaluating the cost at the extension point

$$\mathbf{X}^{EXT} = \mathbf{X}^{(k+1)} + \mathbf{s}^{AV} \tag{8}$$

along the proposed average direction

$$\mathbf{s}^{AV} = \mathbf{X}^{(k+1)} - \mathbf{X}^{(k)} \tag{9}$$

to avoid linear dependence windup and resultant loss of conjugacy. This cost is then compared with that at the initial search point *X*(*S*) along with the differential comparison

$$
\Delta E = \left[ \left( E^{(S)} - E\_{\rm av} \left( X^{(k+1)} \right) \right) \right] - \Delta E\_{\rm av} \tag{10}
$$

to determine if any reduction is achievable along *s AV* for the *J* th iteration, which is regarded as the average path traversed over all possible *N* directions in *S*, other than that via *s* (*dm*) . Furthermore the curvature estimate at *X*(*k*+1) in the direction *s AV*, given by

$$\kappa = \left\{ E\_{a^o} \left( X^{(S)} \right) - 2E\_{a^o} \left( X^{(k+1)} \right) + E\_{a^o} \left( X^{\text{EXT}} \right) \right\} \tag{11}$$

is also checked for possible minimum convergence of the iterative search along with Eq. (10) using the flowchart test condition in **Figure 5** as

$$
\Delta \mathbf{k} \cdot \Delta E^2 \ge \Delta E\_{oo} \left\{ E\_{oo} \left( X^{(S)} \right) - E\_{oo} \left( X^{\text{EXT}} \right) \right\}^2. \tag{12}
$$

If the test condition Eq. (12) is true then the old set of directions is retained for the next Powell iteration either because cost reduction is already exhausted or no significant reduction is observed in any particular direction or a substantial second derivative exists along *s AV* indicating minimum convergence of the search estimate. Conversely if Eq. (12) is false then the direction set *S* is updated by replacing *s* (*dm*) with *s AV* before embarking on the next pass of the Powell algorithm which is usually restricted to some maximum user supplied iteration count *Nmax* of typically 200.

The PCD method was applied to the identification of three known values of BLMD shaft load inertia with experimental shaft velocity target data deployed in the MSE objective function *E*ω(*X*) formulation displayed in **Figures 2**–**4**. An insight into the progress of this optimization method towards global optimality in the extraction of the dynamical *J* and *B* parameters with initialization at the tolerance band edge can be obtained, for example with zero shaft inertial load conditions, from **Figure 2** over the generated velocity cost surface. After one cycle of the Powell method the iterate has reached the 'line minimum' of the cost surface syncline by completing alternate line searches along the *J* and *B* parameter directions. Quadratic convergence of the PCD method thereafter is relatively 'slow' in that a further three iteration steps of the PCD algorithm are required to reach a limit point estimate **X**^ *opt* of the global minimum. This is manifested as a zigzag search pattern over the stationary region of the response surface in the quantized *J* and *B* parameter directions along the 'line minimum', which is essentially in the *B* direction, where the cost function curvature is low with inadequate selectivity for global minimum reachability.

*s*

**48**

**Figure 5.**

(*dm*) is monitored. This cost reduction metric is then used to determine whether or not the set *S* of conjugate directions needs to updated before commencing the next Powell (*J*+1)th iteration cycle. The decision to include a new search direction, by

*Flowchart of Powell's conjugate direction set optimization technique.*

*Self-Driving Vehicles and Enabling Technologies*

#### **6. Parameter convergence results for the PCD method**

The optimal estimates of the BLMD dynamics returned by the PCD method including convergence details for three known cases of shaft load inertia are summarized in **Table 1**. The penalty cost reduction sequence associated with the application of the Powell algorithm is displayed in **Figures 6**–**8** for each of identified shaft inertial loads along with the cumulative number of bracketing intervals and cost function evaluations required at each iterative step. Substantial cost reduction, which can be attributed mostly to the adjustment of the inertial parameter, ceases after one iterative cycle of the PCD method in each case signifying the arrival of the parameter estimate in the stationary region along the 'line minimum' as in **Figure 2**.

This observation can be adduced from **Table 1** where the listed parameter estimates after the first iteration, in each test case, are reasonably close to the eventual global minimizer estimates. Further gains in MSE reduction are expensive in this zone of the cost surface, due to poor selectivity as explained in [13], with the bulk of the PCD effort devoted towards improving global minimum convergence estimate of the returned parameter vectors. The computational runtime of Powell's algorithm increases in accordance with the iterative count and the accumulated number of BLMD simulation related MSE evaluations for each of the inertial test cases displayed in **Figures 9**–**11**. The corresponding averaged BLMD simulation time increases almost in proportion with the inertial loading for a fixed experimental shaft velocity data capture *V*ωr, normalized to about 10 equivalent machine cycles of motor FC transient as in **Tables 2** and **3**, with time decimation to 4095 sample points.


This capture restriction of the shaft velocity target data is due to the experimental constraints of the data acquisition system used, which limited the size of the data record acquired. These returned PCD statistics are also based on a fixed time step of

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

**Figure 6.**

**Figure 7.**

**Figure 8.**

**51**

*LSL iterative cost reduction.*

*MSL iterative cost reduction.*

*NSL iterative cost reduction.*

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

#### **Table 1.**

*Returned BLMD dynamical parameter estimates via PCD algorithm.*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

#### **Figure 6.**

**6. Parameter convergence results for the PCD method**

*Self-Driving Vehicles and Enabling Technologies*

as in **Tables 2** and **3**, with time decimation to 4095 sample points.

**Figure 2 - NSL No Shaft Load** *Jm* **= 3.0**

Parameter Initialization: {*Jinit* = 0.82 *J*, *Binit* = 1.09*Bm*} with *Bm* = 2.14x10�<sup>3</sup> Nm/rad/sec

Optimal Parameter Estimates returned from Powell's Conjugate Direction Method

Returned Parameter Estimates after first Iteration Cycle of PCD Method

Initial Cost *Einit* 10.2481x10�<sup>2</sup> 36.5942x10�<sup>3</sup> 54.4345 x10�<sup>3</sup>

) 3.02659 12.0721 21.292

) 3.168237 12.29243 21.51233

Min. Cost *<sup>E</sup>*^*opt* 3.278108x10�<sup>2</sup> 5.910952x10�<sup>3</sup> 2.456056x10�<sup>2</sup>

Total No. of PCD Iterations 4 4 2 No. of Cost Func.-Eval<sup>s</sup> 99 121 56 Initial Bracketing 24 31 15 Line Searching 74 89 40

Total Time (sec) 3584 5234 2918 Average Itern Time (sec) 896 1308.5 1459 Time/MSE Cost Eval. (sec) 36.202 43.256 52.106

*Returned BLMD dynamical parameter estimates via PCD algorithm.*

.sec) 2.10405x10�<sup>3</sup> 2.14214x10�<sup>3</sup> 2.06596x10�<sup>3</sup>

.sec) 1.913588x10�<sup>3</sup> 1.989772x10�<sup>3</sup> 1.95168x10�<sup>3</sup>

/Itern �<sup>25</sup> �<sup>30</sup> <sup>28</sup>

**Figure 3 - MSL Medium Inertia** *J* **= 12.303687**

**Figure 4 - LSL Large Inertia** *J* **= 20.822**

**Total Shaft Load Inertia**

*J* **(kg.cm<sup>2</sup> )**

*J* ð Þ1 *opt* (kg.cm<sup>2</sup>

**Table 1.**

**50**

*B*ð Þ<sup>1</sup>

*opt* (Nm.rad�<sup>1</sup>

^*Jopt* (kg.cm<sup>2</sup>

*B*^*opt* (Nm.rad�<sup>1</sup>

Av. No. of Func Evals

The optimal estimates of the BLMD dynamics returned by the PCD method including convergence details for three known cases of shaft load inertia are summarized in **Table 1**. The penalty cost reduction sequence associated with the application of the Powell algorithm is displayed in **Figures 6**–**8** for each of identified shaft inertial loads along with the cumulative number of bracketing intervals and cost function evaluations required at each iterative step. Substantial cost reduction, which can be attributed mostly to the adjustment of the inertial parameter, ceases after one iterative cycle of the PCD method in each case signifying the arrival of the parameter estimate in the stationary region along the 'line minimum' as in **Figure 2**. This observation can be adduced from **Table 1** where the listed parameter estimates after the first iteration, in each test case, are reasonably close to the eventual global minimizer estimates. Further gains in MSE reduction are expensive in this zone of the cost surface, due to poor selectivity as explained in [13], with the bulk of the PCD effort devoted towards improving global minimum convergence estimate of the returned parameter vectors. The computational runtime of Powell's algorithm increases in accordance with the iterative count and the accumulated number of BLMD simulation related MSE evaluations for each of the inertial test cases displayed in **Figures 9**–**11**. The corresponding averaged BLMD simulation time increases almost in proportion with the inertial loading for a fixed experimental shaft velocity data capture *V*ωr, normalized to about 10 equivalent machine cycles of motor FC transient

*NSL iterative cost reduction.*

**Figure 7.** *MSL iterative cost reduction.*

#### **Figure 8.**

*LSL iterative cost reduction.*

This capture restriction of the shaft velocity target data is due to the experimental constraints of the data acquisition system used, which limited the size of the data record acquired. These returned PCD statistics are also based on a fixed time step of

1 μs, in relation to BLMD model exercise in the MSE penalty cost formulation, for

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

The shaft velocity data sets can also be deployed in the construction of MSE response surfaces *E*<sup>ω</sup> over the two dimensional [*J*,*B*] quantized parameter manifold [13], with mesh size details given in **Table 2**, as a secondary means of parameter extraction for qualification of the PCD method and verification of the returned PCD optimal estimates in terms of accuracy. These cost surfaces, pertaining to the various motor shaft inertial loads, are illustrated in **Figures 2**–**4** and appear to posses a parabolic ravine-like structure with an embedded elliptical stationary region stretched into a 'line minimum'shape [13]. These cost constructs can be used as the basis for an error analysis as given in **Table 4** by which the accuracy of PCD

The percentage relative error in the returned PCD optimal estimate ^*Jopt* appears

to increase with shaft inertial load but with no apparent trend noticeable in the damping parameter estimate. The percentage error in the identified *B*^*opt* parameter, however, exceeds that for the inertia in all three test cases which highlights the problem in accurately extracting the damping coefficient due to presence of a pronounced 'line minimum' of admissible friction values predominantly in the *B*

The opposite error pattern will be shown to occur in the extraction of the inertia estimate, coupled with lower relative error in the identification of the friction coefficient, upon application of the modified form of the FSD method with details given in **Table 5**. This contrast in error pattern for the returned FSD parameters is due to better discriminating features of the corrugated FC cost surface in terms of its selectivity, with greater curvature in the *B* parameter direction for increased data capture length, and lower threshold parameter step

The observed phase-a current demand, feedback and controller o/p waveforms,

*No Shaft Load* 20 μs 20

> **Figure 2** [2*δJ L* , *δB<sup>L</sup>* ]

3.184 1.875 x 10<sup>3</sup> 3.26 x 10<sup>2</sup>

*δB<sup>L</sup>* = 38.092x10<sup>6</sup> Nm.rad<sup>1</sup>

*Bm* = 2.14x10<sup>3</sup> Nm.rad<sup>1</sup>

*Medium Inertia* 40 μs 40

9.75 11.5 10.5

**Figure 3** [4*δJ L* , *δB<sup>L</sup>* ]

12.38 1.875 x 10<sup>3</sup> 5.819 x 10<sup>3</sup>

.sec 1.78%*Bm*;

*Large Inertia* 49.6 μs 50

**Figure 4** [7*δJ L* , *δB<sup>L</sup>* ]

22.36 1.875 x 10<sup>3</sup> 2.453 x 10<sup>2</sup>

.sec

displayed in **Figures 12**–**20** at critical internal nodes of the BLMD model [10], appear to be to be coherent with similar test data in the early phase of the transient response of an actual drive system to a unit torque demand step i/p. However there is an eventual loss of synchronism, with the evolution of the model step response

accurate realization of the PWM edge transitions and for computation benchmarking purposes in both the PCD and modified FSD methods of

identification.

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

estimates are gauged.

parameter direction.

*δJ*

sizes as shown in **Tables 7**–**9** in [13].

*<sup>L</sup>* = 15.7386x10<sup>3</sup> kg.cm<sup>2</sup> 0.51%*Jm*; *Jm* = 3.086x10<sup>4</sup> kg.m<sup>2</sup> (NSL - Rotor Inertia)

Shaft Velocity Target Data Vω<sup>r</sup> Data Sample Rate *TS* Decimation Factor

No of Equivalent FC Cycles for Computation Benchmarking

Simulation Grid Size in E<sup>ω</sup> [Δ*J*, Δ*B*] as per [13]

Surface Minimum Estimates

.sec)

*Details of velocity cost surface generation with parameter quantization.*

) *Bopt* (Nm.rad<sup>1</sup>

*Jopt* (kg.cm<sup>2</sup>

*Eopt*

**Table 2.**

**53**

#### **Figure 9.**

*NSL cumulative iteration time.*

**Figure 10.** *MSL cumulative iteration time.*

**Figure 11.** *LSL cumulative iteration time.*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

1 μs, in relation to BLMD model exercise in the MSE penalty cost formulation, for accurate realization of the PWM edge transitions and for computation benchmarking purposes in both the PCD and modified FSD methods of identification.

The shaft velocity data sets can also be deployed in the construction of MSE response surfaces *E*<sup>ω</sup> over the two dimensional [*J*,*B*] quantized parameter manifold [13], with mesh size details given in **Table 2**, as a secondary means of parameter extraction for qualification of the PCD method and verification of the returned PCD optimal estimates in terms of accuracy. These cost surfaces, pertaining to the various motor shaft inertial loads, are illustrated in **Figures 2**–**4** and appear to posses a parabolic ravine-like structure with an embedded elliptical stationary region stretched into a 'line minimum'shape [13]. These cost constructs can be used as the basis for an error analysis as given in **Table 4** by which the accuracy of PCD estimates are gauged.

The percentage relative error in the returned PCD optimal estimate ^*Jopt* appears to increase with shaft inertial load but with no apparent trend noticeable in the damping parameter estimate. The percentage error in the identified *B*^*opt* parameter, however, exceeds that for the inertia in all three test cases which highlights the problem in accurately extracting the damping coefficient due to presence of a pronounced 'line minimum' of admissible friction values predominantly in the *B* parameter direction.

The opposite error pattern will be shown to occur in the extraction of the inertia estimate, coupled with lower relative error in the identification of the friction coefficient, upon application of the modified form of the FSD method with details given in **Table 5**. This contrast in error pattern for the returned FSD parameters is due to better discriminating features of the corrugated FC cost surface in terms of its selectivity, with greater curvature in the *B* parameter direction for increased data capture length, and lower threshold parameter step sizes as shown in **Tables 7**–**9** in [13].

The observed phase-a current demand, feedback and controller o/p waveforms, displayed in **Figures 12**–**20** at critical internal nodes of the BLMD model [10], appear to be to be coherent with similar test data in the early phase of the transient response of an actual drive system to a unit torque demand step i/p. However there is an eventual loss of synchronism, with the evolution of the model step response


#### **Table 2.**

*Details of velocity cost surface generation with parameter quantization.*

**Figure 9.**

**Figure 10.**

**Figure 11.**

**52**

*LSL cumulative iteration time.*

*MSL cumulative iteration time.*

*NSL cumulative iteration time.*

*Self-Driving Vehicles and Enabling Technologies*

#### *Self-Driving Vehicles and Enabling Technologies*


*Nominal Shaft Inertial*

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

Current Feedback

Current command

Current Controller o/p

Motor Shaft Velocity

*No Shaft Load* **(NSL - Rotor)** *Jm* **= 3.0**

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

**Figure 12** 47.4%

**Figure 15** 44.2%

**Figure 18** 18.1%

**Figure 21** 93.7

*BLMD simulation trace coherence correlation coefficient ρ.*

*Medium Shaft Load* **(MSL) 12.304**

> **Figure 13** 67.2%

**Figure 16** 67.6%

**Figure 19** 38.8%

**Figure 22** 99.1%

*Large Shaft Load* **(LSL) 20.822**

> **Figure 14** 61.0%

**Figure 17** 53.0%

**Figure 20** 20.4

**Figure 23** 98.6%

*Load Jnom* **(kg***:***cm2)**

*Ifa*

*Ida*

*Vca*

*V*ω*<sup>r</sup>*

**Table 6.**

**Figure 12.** *NSL FC simulation.*

**Figure 13.** *MSL FC simulation.*

**55**

#### **Table 3.**

*Quantized parameter FC response surface simulation details.*


#### **Table 4.**

*Error analysis for returned PCD parameter estimates (% relative error).*


#### **Table 5.**

*Error analysis for returned FSD parameter estimates (% relative error).*

towards steady state conditions, in the waveform comparison due to the impact of the estimated *J/B* dynamic time constant mismatch in relation to the intrinsic value τ*<sup>m</sup>* of the actual motor drive system.

This is borne out by the low correlation measurement coefficients in **Table 6**, which gauges the degree of FM coherence, between the respective experimental and simulated trace responses. Further evidence of this mismatch, though small, can be visualized in the deviation of the shaft velocity characteristics depicted in **Figures 21**–**23**, despite the high correlation coefficient to the contrary, as the motor drive accelerates towards rated shaft speed. A possible explanation for the correla-

tion discrepancy between waveform types may attributed to the application in this instance of shaft velocity target data in BLMD parameter extraction process which results in a good fit between shaft velocity waveforms based on returned estimates due to PCD cost minimization. The returned estimates, however, result in a less than satisfactory trace coherence measure of fit in the current related characteristics *Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*


#### **Table 6.**

*BLMD simulation trace coherence correlation coefficient ρ.*

**Figure 12.** *NSL FC simulation.*

**Figure 13.** *MSL FC simulation.*

towards steady state conditions, in the waveform comparison due to the impact of the estimated *J/B* dynamic time constant mismatch in relation to the intrinsic value

This is borne out by the low correlation measurement coefficients in **Table 6**, which gauges the degree of FM coherence, between the respective experimental and simulated trace responses. Further evidence of this mismatch, though small, can be

**Figures 21**–**23**, despite the high correlation coefficient to the contrary, as the motor drive accelerates towards rated shaft speed. A possible explanation for the correlation discrepancy between waveform types may attributed to the application in this instance of shaft velocity target data in BLMD parameter extraction process which results in a good fit between shaft velocity waveforms based on returned estimates due to PCD cost minimization. The returned estimates, however, result in a less than satisfactory trace coherence measure of fit in the current related characteristics

visualized in the deviation of the shaft velocity characteristics depicted in

τ*<sup>m</sup>* of the actual motor drive system.

**FC Target Data No. of Cycles Data Sample Rate** *Ts* **Decimation Factor**

Simulation Mesh Size

Surface Minimum Jopt (kg*:*cm2) *Bopt* Nm*:*rad‐<sup>1</sup> *:*sec

**Motor Inertia** *Jopt*

**100%**

Damping Factor *Bopt*

Global Cost *Eopt <sup>E</sup>*^*opt<sup>E</sup> E* 

**Motor Inertia** *Jopt*

**100%**

Damping Factor *Bopt*

Global Cost *Eopt <sup>E</sup>*^*opt<sup>E</sup> E* 

^*Jopt<sup>J</sup> J* 

*<sup>B</sup>*^*opt<sup>B</sup> B* 

**Table 5.**

**54**

^*Jopt<sup>J</sup> J* 

*<sup>B</sup>*^*opt<sup>B</sup> B* 

**Table 4.**

**Table 3.**

[ΔJ, ΔB] 2*δJ*

*Self-Driving Vehicles and Enabling Technologies*

*Quantized parameter FC response surface simulation details.*

**No Shaft Load 9.75 20μS 20**

> 3.089 1.921<sup>10</sup>‐<sup>3</sup>

*No Shaft Load* **0.495%**

*Error analysis for returned PCD parameter estimates (% relative error).*

*Error analysis for returned FSD parameter estimates (% relative error).*

**No Shaft Load 0.29%**

*<sup>L</sup>*, *δBL* 6*δJ*

Min Cost *Eopt* 4.922<sup>10</sup>‐<sup>2</sup> 1.877<sup>10</sup>‐<sup>2</sup> 1.236<sup>10</sup>‐<sup>2</sup>

100% 2.058% 6.121% 4.09%

100% 0.555% 1.58% 0.125%

100% 1.98% 4.16% 1.98%

100% 5.99% 17.37% 5.42%

**Medium Inertia 11.5 40μS 40**

> 12.158 1.921<sup>10</sup>‐<sup>3</sup>

*Medium Shaft Inertia* **0.707%**

**Medium Shaft Inertia 0.15%**

*<sup>L</sup>*, *δB<sup>L</sup>* 10*δJ*

**Large Inertia 10.5 49.6μS 50**

*<sup>L</sup>*, *δB<sup>L</sup>*

20.877 1.921<sup>10</sup>‐<sup>3</sup>

*Large Shaft Inertia* **3.79%**

**Large Shaft Inertia 0.19%**

**Figure 14.** *LSL FC simulation.*

**Figure 17.**

**Figure 18.**

**Figure 19.**

**57**

*MSL - current controller o/p.*

*NSL - current controller o/p.*

*LSL current demand Simul<sup>n</sup>*

*.*

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

**Figure 15.** *NSL current demand simulation.*

**Figure 16.** *MSL current demand Simuln .*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

**Figure 17.** *LSL current demand Simul<sup>n</sup> .*

**Figure 14.** *LSL FC simulation.*

*Self-Driving Vehicles and Enabling Technologies*

**Figure 15.**

**Figure 16.**

**56**

*MSL current demand Simuln*

*.*

*NSL current demand simulation.*

**Figure 18.** *NSL - current controller o/p.*

**Figure 19.** *MSL - current controller o/p.*

**Figure 20.** *LSL - current controller o/p.*

**Figure 21.** *ZSL - shaft velocity simulation.*

pertaining to the BLMD current loop operation in toque control mode. Furthermore the use of larger quantized parameter step sizes, in conjunction with shaft velocity target data in the PCD parameter extraction process, results in a greater spread of

Data Record Length *Nd* 4095 8000 12000 24000 32000

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

*Shaft Inertia Jm* = 3.0

*<sup>J</sup>* 3.122x10<sup>7</sup> 2.843x10<sup>7</sup> 2.036x10<sup>7</sup> 1.026x10<sup>7</sup> 7.692x10<sup>3</sup>

*<sup>L</sup>* = 15.739x10<sup>3</sup> kg.cm<sup>2</sup>

*Large Inertia* 20.822

*Medium Inertia* 12.304

*<sup>J</sup>* 10.3 10.8 12.8 18 20.8

*/J* 0.525% 0.128% 0.0756%

**Figure 23.**

*LSL - shaft velocity simulation.*

Surface *E*ω(*Jopt*) Curvature *κ<sup>E</sup>*

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

Best Parameter Resolution Possible with PCD Algorithm for *δJ*

*L*

*Cost surface selectivity measure – Figures 24, 25 and 26.*

Convergence Metric *N<sup>δ</sup>*

*Total Shaft Inertial Load J*

% parameter Resolution *δJ*

(kg*:*cm2)

**Table 7.**

**Figure 24.**

**59**

*Cost surface variation with data record length.*

**Figure 22.** *MSL - shaft velocity simulation.*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

#### **Figure 23.**

**Figure 20.**

**Figure 21.**

**Figure 22.**

**58**

*MSL - shaft velocity simulation.*

*ZSL - shaft velocity simulation.*

*LSL - current controller o/p.*

*Self-Driving Vehicles and Enabling Technologies*

*LSL - shaft velocity simulation.*


#### **Table 7.**

*Cost surface selectivity measure – Figures 24, 25 and 26.*

#### **Figure 24.**

*Cost surface variation with data record length.*

pertaining to the BLMD current loop operation in toque control mode. Furthermore the use of larger quantized parameter step sizes, in conjunction with shaft velocity target data in the PCD parameter extraction process, results in a greater spread of

**Figure 25.** *Cost surface selectivity.*

**Figure 26.** *Global convergence variation.*

returned optimal estimates about the global extremum compared with the threshold values deployed with current feedback data in the FSD algorithm.

The initial impact of the shaft velocity transient step response decays and is ultimately swamped with the onset of steady state conditions as maximum shaft speed is reached with lengthening data records. The quadratic shape of the response surface *E***<sup>ω</sup>** is de-emphasized with reduced curvature, as more velocity target data is accumulated for MSE cost formulation, resulting in a loss of selectivity at the global minimizer.

This flattening of the cost profile about *Xopt* is clearly evident in **Figure 24** for response surface cross sections in the inertia parameter *J,* based on simulated BLMD model target data, with increased data record length. The resultant ill conditioned surface admits a multitude of possible global minimum estimates about *Xopt*. The variation in cost function selectivity can be obtained by fitting a quadratic polynomial approximation [13] to each of the response surface cross sections *E*ω(*J*) in **Figure 24** and estimating the curvature at the fitted parabolic vertex *Jopt* as

$$\kappa\_{\!\!\!\!J}^{E} = d^2 \mathbf{Q}(\!\!\!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/ \!/} \mathbf{1}\_{\text{\!\!\!/} \!/ \!/} = 2b\_2 \tag{13}$$

in **Table 7** with

*Initial details of FSD exploratory search phase.*

**Table 8.**

**61**

This curvature *κ<sup>E</sup>*

*<sup>Q</sup> Jopt* � � <sup>¼</sup> 0 and *dQ J*ð Þ*=dJ*<sup>j</sup>

different data training record sizes *Nd* via Eq. (13) as

linear dependency with target data length and indicates as a consequence poor response surface selectivity and large convergence radius in the stationary region containing the global minimum. An estimate of the global convergence radius *rJ* of the *J* parameter stationary zone can be obtained in terms of the fixed cost noise estimate *σ*^, due to inexact PWM simulation [13], and the curvature variation with

*Ifa* **Cost Surface Target Data [13] Sample Size** *Ni* **= 200 ≈ 10%***NC* **Parameters** *x* **Inertia** *Jm* **kg.cm<sup>2</sup> Damping** *Bm* **Nm/rad/sec**

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

Nominal Values *xm* 3.0 2.14x10�<sup>3</sup> Parameter Bounds �Δ*xm* �20% �10% Quantized Step Size *δxL* 9.1125x10�<sup>3</sup> 2.6712x10�<sup>5</sup> Population Size *Nx* 141 16

Histograms **Figure 30 Figure 31**

Minimum Value *xmin* 2.408 1.953 Maximum Value *xmax* 3.592 2.327 Actual Mean Value *xmean* 3.041 2.153 Theoretical Mean Value *x* 3.0163 1.9934 % Error in Mean Value 0.82% 8% Actual Standard Deviation *σ*^*<sup>x</sup>* 0.343 0.109 Theoretical Standard Deviation *σ<sup>x</sup>* 0.518 0.750 Optimal Parameter Estimate *x*^*iopt* 3.06379 1.953

Initial Global Minimum Estimate *<sup>E</sup>*^*iopt* 5.473x10�<sup>2</sup> Maximum Value *Emax* 6.936x10�<sup>1</sup> Mean Value *E* 3.6671x10�<sup>1</sup> Standard Deviation σ 1.6538x10�<sup>1</sup> Initial Temperature *Ti* (= *kσ* for *k* = 10) 1.6538

*<sup>L</sup> δB<sup>L</sup>*

Results of Initial Exploratory Search of Parameter Space

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

Class Interval Size 10*δJ*

FSD Exploratory Search Results of FC - MSE Cost Surface

*rJ* ¼

order to establish the scale of the bounded region of convergence, with metric

This radial width can be referenced to the threshold step size *δJ*

variation for different data sequence lengths *Nd* given in **Table 7** as

ffiffiffiffiffi 8*σ*^ *κE J*

s

*<sup>J</sup>* variation, shown in **Figure 25**, exhibits a decreasing quasi-

*<sup>J</sup>*¼*Jopt* <sup>¼</sup> <sup>0</sup>*:* (14)

*:* (15)

*<sup>L</sup>* in **Table 2**, in


Mean Value *E* 3.6671x10�<sup>1</sup> Standard Deviation σ 1.6538x10�<sup>1</sup> Initial Temperature *Ti* (= *kσ* for *k* = 10) 1.6538

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

#### **Table 8.**

returned optimal estimates about the global extremum compared with the threshold

The initial impact of the shaft velocity transient step response decays and is ultimately swamped with the onset of steady state conditions as maximum shaft speed is reached with lengthening data records. The quadratic shape of the response surface *E***<sup>ω</sup>** is de-emphasized with reduced curvature, as more velocity target data is accumulated for MSE cost formulation, resulting in a loss of selectivity at the global

This flattening of the cost profile about *Xopt* is clearly evident in **Figure 24** for response surface cross sections in the inertia parameter *J,* based on simulated BLMD model target data, with increased data record length. The resultant ill conditioned surface admits a multitude of possible global minimum estimates about *Xopt*. The variation in cost function selectivity can be obtained by fitting a quadratic polynomial approximation [13] to each of the response surface cross sections *E*ω(*J*) in **Figure 24** and estimating the curvature at the fitted parabolic vertex *Jopt* as

*Q j* ð Þ*=dJ*<sup>2</sup>

 *J*¼*Jopt*

¼ 2*b*<sup>2</sup> (13)

values deployed with current feedback data in the FSD algorithm.

*κE <sup>J</sup>* <sup>¼</sup> *<sup>d</sup>*<sup>2</sup>

minimizer.

**60**

**Figure 26.**

*Global convergence variation.*

**Figure 25.**

*Cost surface selectivity.*

*Self-Driving Vehicles and Enabling Technologies*

*Initial details of FSD exploratory search phase.*

in **Table 7** with

$$Q\left(\tilde{f}\_{opt}\right) = \mathbf{0} \quad \text{and} \quad dQ(f)/d\!\!/ \_{\vert f=\tilde{f}\_{opt}} = \mathbf{0}.\tag{14}$$

This curvature *κ<sup>E</sup> <sup>J</sup>* variation, shown in **Figure 25**, exhibits a decreasing quasilinear dependency with target data length and indicates as a consequence poor response surface selectivity and large convergence radius in the stationary region containing the global minimum. An estimate of the global convergence radius *rJ* of the *J* parameter stationary zone can be obtained in terms of the fixed cost noise estimate *σ*^, due to inexact PWM simulation [13], and the curvature variation with different data training record sizes *Nd* via Eq. (13) as

$$r\_f = \sqrt{\frac{8\hat{\sigma}}{\kappa\_f^E}}.\tag{15}$$

This radial width can be referenced to the threshold step size *δJ <sup>L</sup>* in **Table 2**, in order to establish the scale of the bounded region of convergence, with metric variation for different data sequence lengths *Nd* given in **Table 7** as

*Self-Driving Vehicles and Enabling Technologies*

$$N\_I^\delta = r\_I / \delta \mathcal{J}^L \tag{16}$$

**7. Description of FSD method of parameter identification**

controlled random driving force ffiffiffiffiffiffi

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

with space time coordinates (*x*, *t*) as

continuous "parameter" path *xi* as

thus avoid local minimum capture with

Boltzman probability density [58].

**63**

The simulated annealing technique used here as a global optimization algorithm for motor parameter identification [22, 23] is based on the Fast Simulated Diffusion (FSD) method proposed by Sakurai et al. [24]. This method, motivated by quantum mechanics (QM), is modeled on the diffusion ∇*E x*ð Þ*<sup>i</sup>* of a particle, with position trajectory *xi*, across a barrier potential *E*(*xi*) under the influence of a temperature

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

ensemble dynamics [53] can be described by the Ito stochastic differential equation

*dx* ¼ �∇*E x*ð Þ*dt* <sup>þ</sup> ffiffiffiffiffiffi

The down-hill gradient term -∇*E*(*x*) in Eq. (17), which is effective at low temperature, has the tendency to minimize the particle potential *E x*ð Þ along the

and thus improve the cost of the objective function *E*(*x*). The stochastic pertur-

If a proper cooling procedure [57] is implemented the global minimum potential

*T*

which peaks with a value of one at the global minimizer as *T* approaches zero. The global minimizer of *E*(*x*) can be obtained according to Aluffi-Pentini et al. [53] from inspection of the asymptotic value of a numerically computed sample trajectory *x*(t) as time *t* ! ∞ via numerical integration of Eq. (17) from *x*(0) at *t* = 0 as

The differential random process in Eq. (17) has been mapped into an algorithmic procedure for approximating the global minimizer [24] of multiminima objective functions with a large *N*-Dimensional parameter manifold. Notable applications of discrete SA type methodology include the time scheduling problem of a traveling salesman to *N* cities which is NP-complete [15] and to cell placement in integrated circuit design. The SA method, however, requires very large computing resources [49] for global minimum convergence in such problem solutions whereas the introduction of the gradient search component in Eq. (17) with an aggressive cooling schedule can results in significant gains in the reduction of CPU time. In general the true location in parameter space of the global minimum of a multiminima cost function cannot be guaranteed with certainty in practical applications of the SA algorithm but a good suboptimal approximation can be obtained with reasonable computational effort which is an acceptable estimate **X**^ *opt* of the optimal parameter vector *Xopt*. Similar comments

bation component of motion *dwi* along a particular trajectory *xi*(*t*), which is an essential coherent energy interaction at high temperature *T*, imparts enough momentum to enable the particle to "hill climb" its way out of a potential well and

*dxi* ¼ �∇*E x*ð Þ*<sup>i</sup> dt* <sup>þ</sup> ffiffiffiffiffiffi

*Emin* is reached after infinite time with a Gibb's distribution having a limiting

*p x*ð Þ<sup>∝</sup> exp � *E x*ð Þ

the stochastic temperature *T* is reduced very slowly to zero with time *t*.

*dxi*

<sup>2</sup>*<sup>T</sup>* <sup>p</sup> *dwi* resulting in Brownian motion. The particle

*dt* ¼ �∇*E x*ð Þ*<sup>i</sup>* (18)

<sup>2</sup>*<sup>T</sup>* <sup>p</sup> *dw:* (17)

<sup>2</sup>*<sup>T</sup>* <sup>p</sup> *dwi:* (19)

� � as *<sup>t</sup>* ! <sup>∞</sup> (20)

and displayed in **Figure 26**. This characteristic illustrates clearly the emergence of a pattern of reduced cost selectivity, which is mirrored as a radial extension of the global minimum region, with increased target data capture. The opposite trend prevails in **Figure 27** with the application of current feedback in the MSE penalty cost and is the main motivation for its use as a target function with a tighter bound, besides sensorless motor control issues, in the identification of the BLMD dynamics despite the FSD computational intensity. The use of a fixed threshold step size establishes the degree of accuracy possible in parameter resolution during BLMD system identification as shown in **Tables 7** and **9**. The relative percentage accuracy in the returned estimates improves with motor shaft inertial loading as tabulated with a greater resolution possible with the deployment of current feedback target data in MSE cost reduction. If a coarser step size δ**X\*** is adopted, which may be tolerable at large inertial loads without adversely affecting the percentage resolution in the returned estimates, both the FSD and PCD methods of parameter extraction can proceed much faster with smaller computational burdens. This results from the reduced number of the feasible lattice points to be searched in the quantized parameter domain with small changes in the percentage accuracy. The required parameter accuracy can be user defined in such circumstances at the start of the identification search routine and encoded in the relevant step size δ**X\*** as a measure of the desired coarseness of resolution.

**Figure 27.** *Motor shaft speed variation.*


#### **Table 9.**

*Cost surface selectivity measure.*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

#### **7. Description of FSD method of parameter identification**

The simulated annealing technique used here as a global optimization algorithm for motor parameter identification [22, 23] is based on the Fast Simulated Diffusion (FSD) method proposed by Sakurai et al. [24]. This method, motivated by quantum mechanics (QM), is modeled on the diffusion ∇*E x*ð Þ*<sup>i</sup>* of a particle, with position trajectory *xi*, across a barrier potential *E*(*xi*) under the influence of a temperature controlled random driving force ffiffiffiffiffiffi <sup>2</sup>*<sup>T</sup>* <sup>p</sup> *dwi* resulting in Brownian motion. The particle ensemble dynamics [53] can be described by the Ito stochastic differential equation with space time coordinates (*x*, *t*) as

$$d\mathfrak{x} = -\nabla E(\mathfrak{x})dt + \sqrt{2T}dw.\tag{17}$$

The down-hill gradient term -∇*E*(*x*) in Eq. (17), which is effective at low temperature, has the tendency to minimize the particle potential *E x*ð Þ along the continuous "parameter" path *xi* as

$$\frac{d\mathbf{x}\_i}{dt} = -\nabla E(\mathbf{x}\_i) \tag{18}$$

and thus improve the cost of the objective function *E*(*x*). The stochastic perturbation component of motion *dwi* along a particular trajectory *xi*(*t*), which is an essential coherent energy interaction at high temperature *T*, imparts enough momentum to enable the particle to "hill climb" its way out of a potential well and thus avoid local minimum capture with

$$d\mathfrak{x}\_{i} = -\nabla E(\mathfrak{x}\_{i})dt + \sqrt{2T}dw\_{i}.\tag{19}$$

If a proper cooling procedure [57] is implemented the global minimum potential *Emin* is reached after infinite time with a Gibb's distribution having a limiting Boltzman probability density [58].

$$p(\boldsymbol{x}) \propto \exp\left(-\frac{E(\boldsymbol{x})}{T}\right) \text{ as } t \to \infty \tag{20}$$

which peaks with a value of one at the global minimizer as *T* approaches zero. The global minimizer of *E*(*x*) can be obtained according to Aluffi-Pentini et al. [53] from inspection of the asymptotic value of a numerically computed sample trajectory *x*(t) as time *t* ! ∞ via numerical integration of Eq. (17) from *x*(0) at *t* = 0 as the stochastic temperature *T* is reduced very slowly to zero with time *t*.

The differential random process in Eq. (17) has been mapped into an algorithmic procedure for approximating the global minimizer [24] of multiminima objective functions with a large *N*-Dimensional parameter manifold. Notable applications of discrete SA type methodology include the time scheduling problem of a traveling salesman to *N* cities which is NP-complete [15] and to cell placement in integrated circuit design. The SA method, however, requires very large computing resources [49] for global minimum convergence in such problem solutions whereas the introduction of the gradient search component in Eq. (17) with an aggressive cooling schedule can results in significant gains in the reduction of CPU time. In general the true location in parameter space of the global minimum of a multiminima cost function cannot be guaranteed with certainty in practical applications of the SA algorithm but a good suboptimal approximation can be obtained with reasonable computational effort which is an acceptable estimate **X**^ *opt* of the optimal parameter vector *Xopt*. Similar comments

*Nδ*

of the desired coarseness of resolution.

*Self-Driving Vehicles and Enabling Technologies*

**Figure 27.**

**Table 9.**

**62**

*Motor shaft speed variation.*

Selectivity Measure *SE*

*Total Shaft Inertial Load J* (kg.cm<sup>2</sup>

% parameter Resolution *δJ*

*Cost surface selectivity measure.*

Parameter Resolution Accuracy in FSD Estimation with *δJ*

*L*

*<sup>J</sup>* ¼ *rJ=δJ*

and displayed in **Figure 26**. This characteristic illustrates clearly the emergence of a pattern of reduced cost selectivity, which is mirrored as a radial extension of the global minimum region, with increased target data capture. The opposite trend prevails in **Figure 27** with the application of current feedback in the MSE penalty cost and is the main motivation for its use as a target function with a tighter bound, besides sensorless motor control issues, in the identification of the BLMD dynamics despite the FSD computational intensity. The use of a fixed threshold step size establishes the degree of accuracy possible in parameter resolution during BLMD system identification as shown in **Tables 7** and **9**. The relative percentage accuracy in the returned estimates improves with motor shaft inertial loading as tabulated with a greater resolution possible with the deployment of current feedback target data in MSE cost reduction. If a coarser step size δ**X\*** is adopted, which may be tolerable at large inertial loads without adversely affecting the percentage resolution in the returned estimates, both the FSD and PCD methods of parameter extraction can proceed much faster with smaller computational burdens. This results from the reduced number of the feasible lattice points to be searched in the quantized parameter domain with small changes in the percentage accuracy. The required parameter accuracy can be user defined in such circumstances at the start of the identification search routine and encoded in the relevant step size δ**X\*** as a measure

Data Record Length *Nd* 6280 9000 12000 24000 32000 Fitted Coefficient *b0* 3.708x10<sup>9</sup> 7.053x10<sup>9</sup> 9.495x109 1.93x10<sup>10</sup> 2.398x10<sup>10</sup>

> ) *Shaft Inertia Jm* = 3.0

*<sup>J</sup>* 3.379x10<sup>3</sup> 6.427x10<sup>3</sup> 8.652x10<sup>3</sup> 1.759x10<sup>4</sup> 2.186x10<sup>4</sup>

*/J* 0.304% 0.074% 0.0438%

*<sup>L</sup>* = 9.1125x10�<sup>3</sup> kg.cm2

*Large Inertia* 20.822

*Medium Inertia* 12.304

*<sup>L</sup>* (16)

pertain to the FSD global minimum approximation during BLMD parameter extraction over the FC cost surface which is described herein.

In BLMD model parameter optimization the particle energy *E*(*x*) is replaced by the FC cost function *EIfa*(*X*) and its positional *xi* configuration space by the parameter set *X* bounded by the permissible tolerance band � Δ*Xm*. The FSD algorithm relies on two modifications, instead of integrating Eq. (19) directly, to accelerate convergence and prune wayward or non profitable moves in parameter space. The first is based on the use of an accept/non-accept function rule after Metropolis et al. [59] where the probability of acceptance of the next move

$$\mathbf{X}\_{k+1} = \mathbf{X}\_k + d\mathbf{X} \tag{21}$$

high temperature value *Ti*. This annealing technique permits the generation of a population of parameter vector *X* adjustments at each anneal temperature step to simulate the effect of cooling tardiness for the parameter ensemble to reach a steady

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

arrangement in the neighborhood of the global minimum cost.

The cooling process also includes an equilibrium condition based on some minimum level of acceptance at each temperature step before progressing on to the next step. The temperature *Tk* is reduced very slowly, according to a prescribed anneal curve [60] or exponentially [15], to avoid premature quenching and resultant parameter configuration trapping in a metastable state. The outer temperature loop decrementation sequence and parameter adjustment acceptances at each inner loop equilibrium temperature constitute the simulated annealing schedule. The temperature reduction should be rapid with an early detection of equilibrium for effective cooling without quenching. Condensation followed by termination of the anneal method occurs when the cost function value tends to reduce slowly and remain unchanged for several consecutive temperature steps according to some stopping criterion. At this stage the parameter configuration has frozen to an optimal

The flowchart of the complete FSD algorithm is presented in **Figures 28** and **29** with details of the inner and outer temperature loops. The high temperature melting phase, used in initialization, and the cooling procedure for the FSD algorithm are adopted from Huang et al. [60]. The annealing start temperature *Ti* is statistically determined from the standard deviation σ of the cost function distribution over *Ni* sample points from an initial exploratory search of parameter space. During this hot phase the feasible parameter domain is uniformly sampled with the temperature *Ti*

state configuration.

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

**Figure 28.**

**65**

*Flowchart of fast simulated diffusion algorithm – Heating phase.*

in the parameter identification search is governed by the Boltzman's distribution. If the next move yields a lower cost *E*(*Xk*+1) than the current value *E*(*Xk*) at *X<sup>k</sup>* then the new parameter configuration *Xk*+1 is accepted. Alternatively in an error increasing move a random number

$$R\_n \in [0, 1] \tag{22}$$

is chosen for arbitration in the move selection process and the transition probability

$$P\_{k+1} = \exp\left(\frac{-\{E(\mathbf{X}\_{k+1}) - E(\mathbf{X}\_k)\}}{T}\right) \tag{23}$$

is computed. If the resulting decision is

$$P\_{k+1} > RN \tag{24}$$

then the displacement *Xk*+1 is accepted, as a controlled uphill step as part of the iterative improvement process for a better solution, otherwise it is rejected in which case *Xk*+1 has to be regenerated. The second modification involves the alternate application of the hill-descending gradient search term -∇*E*(*X*) with the temperature dependent stochastic term in Eq. (19) in the generation of the next move. This alternate application ensures limited hill-descent at high temperature than otherwise would be the case if the two terms were added together as in the conventional method where ineffective moves due to the stochastic term would negate gains made in the gradient search. Instead of calculating the direction of steepest descent -∇*E*(*X*), which is expensive for large dimensional parameter space, the alternative directional entity

$$<\nabla E(\mathbf{X}).\hat{r} > \hat{r} \tag{25}$$

is used instead because its expected value approaches -∇*E*(*X*) in the long term where ^**r** is a unit vector along a randomly chosen axis in parameter *X* space. A quadratic fit is then employed if the cost function is concave along the randomly chosen axis and the minimum is estimated via the Newton–Raphson method. If the cost function happens to be convex in the chosen direction a small *dX* is first used and then doubled up a prescribed number of times until *E*ð Þ *X<sup>k</sup>* þ *dX* fails to decrease. This approach gives a crude but inexpensive estimate of the minimum.

#### **8. Application of FSD method to motor parameter estimation**

The FSD iterative process proceeds slowly in accordance with a pseudo temperature control parameter *Tk*, with the same units as the cost surface, from an initial

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

high temperature value *Ti*. This annealing technique permits the generation of a population of parameter vector *X* adjustments at each anneal temperature step to simulate the effect of cooling tardiness for the parameter ensemble to reach a steady state configuration.

The cooling process also includes an equilibrium condition based on some minimum level of acceptance at each temperature step before progressing on to the next step. The temperature *Tk* is reduced very slowly, according to a prescribed anneal curve [60] or exponentially [15], to avoid premature quenching and resultant parameter configuration trapping in a metastable state. The outer temperature loop decrementation sequence and parameter adjustment acceptances at each inner loop equilibrium temperature constitute the simulated annealing schedule. The temperature reduction should be rapid with an early detection of equilibrium for effective cooling without quenching. Condensation followed by termination of the anneal method occurs when the cost function value tends to reduce slowly and remain unchanged for several consecutive temperature steps according to some stopping criterion. At this stage the parameter configuration has frozen to an optimal arrangement in the neighborhood of the global minimum cost.

The flowchart of the complete FSD algorithm is presented in **Figures 28** and **29** with details of the inner and outer temperature loops. The high temperature melting phase, used in initialization, and the cooling procedure for the FSD algorithm are adopted from Huang et al. [60]. The annealing start temperature *Ti* is statistically determined from the standard deviation σ of the cost function distribution over *Ni* sample points from an initial exploratory search of parameter space. During this hot phase the feasible parameter domain is uniformly sampled with the temperature *Ti*

**Figure 28.** *Flowchart of fast simulated diffusion algorithm – Heating phase.*

pertain to the FSD global minimum approximation during BLMD parameter extrac-

In BLMD model parameter optimization the particle energy *E*(*x*) is replaced by the FC cost function *EIfa*(*X*) and its positional *xi* configuration space by the parameter set *X* bounded by the permissible tolerance band � Δ*Xm*. The FSD algorithm relies on two modifications, instead of integrating Eq. (19) directly, to accelerate convergence and prune wayward or non profitable moves in parameter space. The first is based on the use of an accept/non-accept function rule after Metropolis et al.

in the parameter identification search is governed by the Boltzman's distribution. If the next move yields a lower cost *E*(*Xk*+1) than the current value *E*(*Xk*) at *X<sup>k</sup>* then the new parameter configuration *Xk*+1 is accepted. Alternatively in an error

is chosen for arbitration in the move selection process and the transition probability

*T* 

*Pk*þ<sup>1</sup> <sup>¼</sup> exp �f g *<sup>E</sup>*ð Þ� *<sup>X</sup><sup>k</sup>*þ<sup>1</sup> *<sup>E</sup>*ð Þ *<sup>X</sup><sup>k</sup>*

then the displacement *Xk*+1 is accepted, as a controlled uphill step as part of the iterative improvement process for a better solution, otherwise it is rejected in which case *Xk*+1 has to be regenerated. The second modification involves the alternate application of the hill-descending gradient search term -∇*E*(*X*) with the temperature dependent stochastic term in Eq. (19) in the generation of the next move. This alternate application ensures limited hill-descent at high temperature than otherwise would be the case if the two terms were added together as in the conventional method where ineffective moves due to the stochastic term would negate gains made in the gradient search. Instead of calculating the direction of steepest descent -∇*E*(*X*), which is expensive for large dimensional parameter space, the alternative directional entity

is used instead because its expected value approaches -∇*E*(*X*) in the long term where ^**r** is a unit vector along a randomly chosen axis in parameter *X* space. A quadratic fit is then employed if the cost function is concave along the randomly chosen axis and the minimum is estimated via the Newton–Raphson method. If the cost function happens to be convex in the chosen direction a small *dX* is first used and then doubled up a prescribed number of times until *E*ð Þ *X<sup>k</sup>* þ *dX* fails to decrease. This approach gives a crude but inexpensive estimate of the minimum.

The FSD iterative process proceeds slowly in accordance with a pseudo temperature control parameter *Tk*, with the same units as the cost surface, from an initial

**8. Application of FSD method to motor parameter estimation**

**64**

**X***<sup>k</sup>*þ<sup>1</sup> ¼ **X***<sup>k</sup>* þ *d***X** (21)

*Rn* ∈½ � 0, 1 (22)

*Pk*þ<sup>1</sup> >*RN* (24)

< ∇*E*ð Þ *X :*^*r*>^*r* (25)

(23)

tion over the FC cost surface which is described herein.

*Self-Driving Vehicles and Enabling Technologies*

[59] where the probability of acceptance of the next move

increasing move a random number

is computed. If the resulting decision is

**Figure 29.** *Flowchart of fast simulated diffusion algorithm – Cooling phase.*

assumed high enough at 'infinity' *T*<sup>∞</sup> such that all generated states are accepted. An adequate sample size is established from the tolerance bounds �Δ*X<sup>m</sup>* imposed, which define a hypercube of feasible lattice points in parameter space, with interstitial distance based on the quantized step sizes [13]. A sample size of 10% of the total number determined [13, 28] as

$$N\_C = N\_B \cdot N\_{\bar{J}} = \left(\frac{2\Delta B\_m}{\delta B^L}\right)\left(\frac{2\Delta J\_m}{\delta \bar{l}^L}\right) = (1\mathfrak{G}) \cdot (1\mathfrak{sl}1) = 225\mathfrak{G} \tag{26}$$

respectively, gives a good search coverage of parameter space for tolerance bounds given in **Table 8** with *Ni* ¼ 200. This is evident from the histograms of the near uniform parameter search distributions shown in **Figures 30** and **31** with details in **Table 8** for interval sizes of δ*B<sup>L</sup>* and 10δ*LL* . The uniformity of the exploratory search distribution can be checked from theoretical consideration of the population size *Nx* of quantized parameter values, for the given tolerance bounds, as

$$N\_{\mathbf{x}} = (2\Delta\mathbf{x}\_m) / \delta\mathbf{x}^L \tag{27}$$

*px* ¼ 1*=Nx*, (28)

(29)

ð Þþ *xm* � <sup>Δ</sup>*xm* ð Þ *<sup>j</sup>* � <sup>1</sup> *<sup>δ</sup>xL* � �

is given by

*Histogram of* B *search value.*

**Figure 31.**

**Figure 30.**

*Histogram of* J *search value.*

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

from the variance *σ*<sup>2</sup>

**67**

*<sup>x</sup>* <sup>¼</sup> <sup>1</sup> *Nx* X *Nx*

*j*¼1

<sup>¼</sup> *Nx* � <sup>1</sup> 2*Nx*

*<sup>x</sup>* with

*Xi* <sup>¼</sup> <sup>1</sup> *Nx* X *Nx*

*j*¼1

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

� � <sup>2</sup>ð Þþ *xm* � <sup>Δ</sup>*xm* ð Þ *Nx* � <sup>1</sup> *<sup>δ</sup>xL* � �

This theoretical estimate compares favorably with those in **Table 8** obtained from FSD simulation with low relative error percentages, which verifies the randomness quality of the initial search. The standard deviation *σ<sup>x</sup>* of the parameter search estimates can be likewise determined theoretically via Eqs. (28) and (29)

The mean parameter estimate obtained from a random search of discretized parameter space, with sample space size *Nx* and uniform probability of occurrence *Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

**Figure 30.** *Histogram of* J *search value.*

**Figure 31.** *Histogram of* B *search value.*

assumed high enough at 'infinity' *T*<sup>∞</sup> such that all generated states are accepted. An adequate sample size is established from the tolerance bounds �Δ*X<sup>m</sup>* imposed, which define a hypercube of feasible lattice points in parameter space, with interstitial distance based on the quantized step sizes [13]. A sample size of 10% of the

> *δJ L*

respectively, gives a good search coverage of parameter space for tolerance bounds given in **Table 8** with *Ni* ¼ 200. This is evident from the histograms of the near uniform parameter search distributions shown in **Figures 30** and **31** with

exploratory search distribution can be checked from theoretical consideration of the population size *Nx* of quantized parameter values, for the given tolerance

The mean parameter estimate obtained from a random search of discretized parameter space, with sample space size *Nx* and uniform probability of occurrence

¼ ð Þ� 16 ð Þ¼ 141 2256 (26)

. The uniformity of the

*Nx* <sup>¼</sup> ð Þ <sup>2</sup>Δ*xm <sup>=</sup>δxL* (27)

total number determined [13, 28] as

bounds, as

**66**

**Figure 29.**

*NC* <sup>¼</sup> *NB* � *NJ* <sup>¼</sup> <sup>2</sup>Δ*Bm*

*Flowchart of fast simulated diffusion algorithm – Cooling phase.*

*Self-Driving Vehicles and Enabling Technologies*

details in **Table 8** for interval sizes of δ*B<sup>L</sup>* and 10δ*LL*

*δBL* 2Δ*Jm*

$$p\_\mathbf{x} = \mathbf{1}/N\_\mathbf{x},\tag{28}$$

is given by

$$\begin{split} \overline{\mathbf{x}} &= \frac{\mathbf{1}}{N\_{\mathbf{x}}} \sum\_{j=1}^{N\_{\mathbf{x}}} X\_{i} = \frac{\mathbf{1}}{N\_{\mathbf{x}}} \sum\_{j=1}^{N\_{\mathbf{x}}} \left[ (\mathbf{x}\_{m} - \Delta \mathbf{x}\_{m}) + (\boldsymbol{j} - \mathbf{1}) \delta \mathbf{x}^{L} \right] \\ &= \left( \frac{N\_{\mathbf{x}} - \mathbf{1}}{2N\_{\mathbf{x}}} \right) \left\{ 2(\mathbf{x}\_{m} - \Delta \mathbf{x}\_{m}) + (N\_{\mathbf{x}} - \mathbf{1}) \delta \mathbf{x}^{L} \right\} \end{split} \tag{29}$$

This theoretical estimate compares favorably with those in **Table 8** obtained from FSD simulation with low relative error percentages, which verifies the randomness quality of the initial search. The standard deviation *σ<sup>x</sup>* of the parameter search estimates can be likewise determined theoretically via Eqs. (28) and (29) from the variance *σ*<sup>2</sup> *<sup>x</sup>* with

$$\begin{aligned} \sigma\_x^2 &= \overline{\mathbf{x}^2} - \overline{\mathbf{x}}^2 = \frac{1}{N\_x} \sum\_{j=1}^{N\_x} \mathbf{x}\_j^2 - \overline{\mathbf{x}}^2 \\\\ \mathbf{x} &= \left(\mathbf{x}\_m - \Delta \mathbf{x}\_m\right)^2 + (N\_x - 1) \cdot (\mathbf{x}\_m - \Delta \mathbf{x}\_m) \delta \mathbf{x}^L + \frac{\left(\delta \mathbf{x}^L\right)^2}{6} (N\_x - 1)(2N\_x - 1) - \overline{\mathbf{x}}^2 \end{aligned} \tag{30}$$

The standard error *σ*^*<sup>x</sup>* in the simulated parameter search estimates in **Table 8** is of the same order of magnitude as that obtained from Eq. (30) with a sizeable discrepancy in the viscous friction coefficient which is possibly due to the limited *B* parameter sample space used. The initial temperature *Ti* is determined from the resultant sample cost distribution illustrated in **Figure 32**, with details in **Table 8**, as

$$T\_i = k\sigma = \mathbf{1.654.}\tag{31}$$

*Tk*þ<sup>1</sup> ¼ *α<sup>k</sup>* ∗ *Tk* (34)

*min α<sup>k</sup>* ¼ 0*:*5 (36)

<sup>2</sup>*<sup>T</sup>* <sup>p</sup> term of the FSD equation in Eq. (17), in accordance

, 0*:*5≤r≤ 1*:*0*:* (37)

*opt* trap avoidance. At the

� � (35)

is based on the step reduction factor

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

typically lower bounded by

which is an attribute of the ffiffiffiffiffiffi

minimiser.

**69**

with a temperature dependent multiplier proportional to

temperatures and consequent metastable state **<sup>X</sup>**^ *<sup>i</sup>*

*Tk*þ<sup>1</sup> *Ti* � �*<sup>r</sup>*

**9. Results obtained from FSD parameter identification**

*α<sup>k</sup>* ¼ exp �*λ*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

with a typical value for λ of 0.8 and has been reported to work well in practice [24, 60] for a diversity of applications. The following numerical constants used in the FSD parameter extraction process have been obtained from heuristics and are known to give good performance of the algorithm with accurate estimates of global minimum convergence [60]. In practical applications the reduction process is

to prevent too rapid a reduction. Acceptance of large cost function jumps is a feature of the high temperature phase as in simulated annealing obviating the need for the ineffective gradient term in the iteration process and thus only a random search of parameter space is made initially for the first 10 external loops. At each temperature step the number of iterations performed is predefined at 15 times the dimensionality of parameter space (NDIM) to ensure equilibrium of the method. As the control temperature is reduced the volume of random search space is pruned,

This enhances convergence towards the global parameter optimizer *Xopt* and curtails non profitable random moves. Another useful feature of the FSD random search [24] is the application of a long tailed Lorentzian parameter distribution, which permits the occurrence of large cost jumps from local minima at low

termination stage of the FSD algorithm, when there is little observed change in the cost function over successive temperature steps, a controlled reheat phase is introduced with gradual temperature increase to reduce the risk of premature quenching and local minima trapping. The final phase of temperature decrease to the freeze condition results in convergence to the best approximation of the global

The extraction of the dynamical parameters for a typical brushless motor drive system with zero shaft load (NSL) inertia using the FSD method [26] is qualitatively illustrated in **Figures 33** and **34** with returned estimates summarized in **Table 10**. The application of a uniform random exploratory search of parameter space initially is rewarded by the provision of a good estimate of the optimal parameter set for initialization of the FSD algorithm. The returned estimate **X**^ *iopt* in **Table 10**, which has a cost *E*^*iopt* equal to 15% of the exploratory sample mean *E*, in this case is very close to the best possible estimate **X***opt* of the optimal vector with the minimal

*Tk σ*

The anneal temperature scaling factor *k* is chosen [60] with a typical value of 10 on the basis of acceptance of parameter configuration costs, assumed normally distributed, worse than the present value by 3*σ* with a successful Boltzmann jump probability of

$$P = \exp\left(-\Delta E/T\_i\right) = \exp\left(-\mathbf{3}\sigma/T\_i\right) \approx \mathbf{0.75} \tag{32}$$

such that

$$k = -\Im/\ln P = \mathbf{10} \tag{33}$$

In this statistical gathering phase the best estimate **X**^ *iopt* of the optimal parameter vector with cost *E*^*iopt* is retained for initialization of the ensuing FSD algorithm if required. The cooling schedule is the most critical feature of the FSD method to guarantee global convergence and avoid trapping at local minima due to premature quenching. The update temperature algorithm consists of a sequence of temperature decrements and a condition to secure thermal equilibrium at each stage so that the average cost decreases in a uniform manner overall. The sequential temperature decrease

**Figure 32.** *Histogram of exploratory search costs.*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

$$T\_{k+1} = \alpha\_k \* T\_k \tag{34}$$

is based on the step reduction factor

*σ*2

probability of

such that

decrease

**Figure 32.**

**68**

*Histogram of exploratory search costs.*

*<sup>x</sup>* <sup>¼</sup> *<sup>x</sup>*<sup>2</sup> � *<sup>x</sup>*<sup>2</sup> <sup>¼</sup> <sup>1</sup>

*Nx* X *Nx*

*Self-Driving Vehicles and Enabling Technologies*

*j*¼1 *x*2 *<sup>j</sup>* � *<sup>x</sup>*<sup>2</sup>

<sup>¼</sup> ð Þ *xm* � <sup>Δ</sup>*xm* <sup>2</sup> <sup>þ</sup> ð Þ� *Nx* � <sup>1</sup> ð Þ *xm* � <sup>Δ</sup>*xm <sup>δ</sup>xL* <sup>þ</sup>

*δxL* � �<sup>2</sup>

*Ti* ¼ *kσ* ¼ 1*:*654*:* (31)

*k* ¼ �3*=* ln *P* ¼ 10 (33)

*P* ¼ exp ð Þ¼ �Δ*E=Ti* exp ð Þ �3*σ=Ti* ≈0*:*75 (32)

The standard error *σ*^*<sup>x</sup>* in the simulated parameter search estimates in **Table 8** is

The anneal temperature scaling factor *k* is chosen [60] with a typical value of 10

In this statistical gathering phase the best estimate **X**^ *iopt* of the optimal parameter vector with cost *E*^*iopt* is retained for initialization of the ensuing FSD algorithm if required. The cooling schedule is the most critical feature of the FSD method to guarantee global convergence and avoid trapping at local minima due to premature quenching. The update temperature algorithm consists of a sequence of temperature decrements and a condition to secure thermal equilibrium at each stage so that the average cost decreases in a uniform manner overall. The sequential temperature

on the basis of acceptance of parameter configuration costs, assumed normally distributed, worse than the present value by 3*σ* with a successful Boltzmann jump

of the same order of magnitude as that obtained from Eq. (30) with a sizeable discrepancy in the viscous friction coefficient which is possibly due to the limited *B* parameter sample space used. The initial temperature *Ti* is determined from the resultant sample cost distribution illustrated in **Figure 32**, with details in **Table 8**, as

<sup>6</sup> ð Þ *Nx* � <sup>1</sup> ð Þ� <sup>2</sup>*Nx* � <sup>1</sup> *<sup>x</sup>*<sup>2</sup>

(30)

$$a\_k = \exp\left(-\lambda \frac{T\_k}{\sigma}\right) \tag{35}$$

with a typical value for λ of 0.8 and has been reported to work well in practice [24, 60] for a diversity of applications. The following numerical constants used in the FSD parameter extraction process have been obtained from heuristics and are known to give good performance of the algorithm with accurate estimates of global minimum convergence [60]. In practical applications the reduction process is typically lower bounded by

$$\min \, a\_k = 0.5 \,\tag{36}$$

to prevent too rapid a reduction. Acceptance of large cost function jumps is a feature of the high temperature phase as in simulated annealing obviating the need for the ineffective gradient term in the iteration process and thus only a random search of parameter space is made initially for the first 10 external loops. At each temperature step the number of iterations performed is predefined at 15 times the dimensionality of parameter space (NDIM) to ensure equilibrium of the method. As the control temperature is reduced the volume of random search space is pruned, which is an attribute of the ffiffiffiffiffiffi <sup>2</sup>*<sup>T</sup>* <sup>p</sup> term of the FSD equation in Eq. (17), in accordance with a temperature dependent multiplier proportional to

$$\left(\frac{T\_{k+1}}{T\_i}\right)^r, \mathbf{0.5} \le \mathbf{r} \le \mathbf{1.0}.\tag{37}$$

This enhances convergence towards the global parameter optimizer *Xopt* and curtails non profitable random moves. Another useful feature of the FSD random search [24] is the application of a long tailed Lorentzian parameter distribution, which permits the occurrence of large cost jumps from local minima at low temperatures and consequent metastable state **<sup>X</sup>**^ *<sup>i</sup> opt* trap avoidance. At the termination stage of the FSD algorithm, when there is little observed change in the cost function over successive temperature steps, a controlled reheat phase is introduced with gradual temperature increase to reduce the risk of premature quenching and local minima trapping. The final phase of temperature decrease to the freeze condition results in convergence to the best approximation of the global minimiser.

#### **9. Results obtained from FSD parameter identification**

The extraction of the dynamical parameters for a typical brushless motor drive system with zero shaft load (NSL) inertia using the FSD method [26] is qualitatively illustrated in **Figures 33** and **34** with returned estimates summarized in **Table 10**. The application of a uniform random exploratory search of parameter space initially is rewarded by the provision of a good estimate of the optimal parameter set for initialization of the FSD algorithm. The returned estimate **X**^ *iopt* in **Table 10**, which has a cost *E*^*iopt* equal to 15% of the exploratory sample mean *E*, in this case is very close to the best possible estimate **X***opt* of the optimal vector with the minimal

**Figure 33.** *FSD cooling sequence record.*

**Figure 34.** *Iterative cost reduction sequence.*

quadratic penalty *Eopt* for the parameter tolerance range chosen. The best estimate **X***opt* for the optimal parameter set can be obtained by visual inspection from the experimental *Ifa* cost surface in **Figure 35** employing worst case quantized parameter step sizes in **Table 8**. This estimate **X***opt*, which will be referred to from here on as the 'optimal' vector for convenience and brevity of expression, is used as a reference against which the accuracy of the returned FSD parameter estimates can be judged. The proximity of **X**^ *iopt* to **X***opt*, as determined from the error analysis in **Table 11**, is indicated by the degree of quantized resolution of parameter space with error differential

$$d\hat{\mathbf{X}}\_{iopt} = \left[\mathbf{2}\delta^{L}, \delta \mathbf{B}^{L}\right]^{\mathrm{T}}.\tag{38}$$

The effectiveness of the FSD method in achieving parameter 'optimality' over the FC undulating cost surface is demonstrated by deliberately initializing the search far from the global minimum in the neighborhood of a local minimum at Xi

Total Simulation Time for FSD Algorithm: ! 20546 secs for a 486-DX-66 MHz CPU

Optimal Estimates obtained via Experimental Cost Surface in **Figure 35** Quantized Parameter FC Response Surface Simulation Mesh Size 2*δJ*

Initial Exploratory Search and Returned FSD Estimates - **Table 8**

^*Jiopt* = 3.0638 kg�cm2 =99.5%*Jopt*

Observations

Returned FSD Optimal Parameter Estimates

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

After First Temperature Step *T*1: !

• After Fifth Temperature Step *T*5: ! • First Reheat Cycle Completed: !

• Total Number of Temperature Steps: !

*Summary of returned FSD parameter estimates.*

FSD Global Convergence Estimate: *<sup>X</sup>*^*opt* <sup>¼</sup> *<sup>J</sup>*

Computational Details of FSD Algorithm in **Figures 28** and **29** No. of External Temperature Loops with Random Search only *mj* = 10

*Jopt* =3.0797x10�<sup>4</sup> kg�m<sup>2</sup> *Bopt*=1.9207x10�<sup>3</sup> Nm/rad/sec *Eopt*=5.0051x10�<sup>2</sup>

=102%*Bopt*

*FSD Initialization: X<sup>i</sup> Ji* = 82%*Jm Bi* = 109%*Bm*

*B*^*iopt* = 1.953x10�<sup>3</sup> Nm/rad/sec

ð Þ2 *opt*, *B*ð Þ<sup>2</sup> *opt* n o

No. of Parameter Adjustments per Temp. Step to reach Equilibrium *uj* = 15�NDIM = 30

Execution Time per BLMD Simul. Trial: ! 20546/(405+387) ≈ 26 sec

No. of MSE Evals.! Random: 405 Gradient: 387 Av. No. of BLMD Simulns per Temp. Step: ! (405+387)/18 = 44

*Sample Statistics Ni* = 200 σ = 1.654x10�<sup>1</sup> mean *E* =0.37

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

*<sup>L</sup>*, *δBL* � �

*E*^*iopt* = 5.473x10�<sup>2</sup> =109%*Eopt*

*J*

*J*

Main Lobe Capture as in **Figure 36**

(1)*opt* = 3.0341 kg�cm<sup>2</sup> = 98.5%*Jopt B*(1)*opt* = 2.199 mNm/rad/sec =114.5%*Bopt*

(2)*opt* = 3.07058 kg�cm2 = 99.7%*Jopt B*(2)*opt* = 1.9586 mNm/rad/sec =102%*Bopt E*(2)*opt* = 5.295x10�<sup>2</sup> < *E*(1)*opt* < σ 18 {First 10 used for Random Search}

*E*(1)*opt* = 7.346x10�<sup>2</sup> < σ

Cost Reduction Ceases 4 Temperature Steps {NF = 4}

A scatter diagram of iterative search costs levied by the FSD process is portrayed in **Figure 36** and contrasted with a cross section of the FC cost surface shown in **Figure 37** for variable *J* and fixed *B* ¼ *Bopt*. Application of a Boltzmann probability step transition in surmounting significant cost barriers, with cost elevations of 2σ above E which conceal the global minimum, is evident in the iterative search improvement process for a global optimum. Thus a means of escape from local minimum capture, which causes problems for traditional identification methods with non-optimal convergence, is provided for parameter extraction in an effort to

In the early stages of the cooling schedule the temperature reduction is matched by a rapid reduction in iterative cost which eventually saturates as the parameter estimates approach the optimal LMS values. After the first temperature step the

as given in **Table 10**.

**Table 10.**

**71**

secure the least mean squares (LMS) estimates.

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*


#### **Table 10.**

quadratic penalty *Eopt* for the parameter tolerance range chosen. The best estimate **X***opt* for the optimal parameter set can be obtained by visual inspection from the experimental *Ifa* cost surface in **Figure 35** employing worst case quantized parameter step sizes in **Table 8**. This estimate **X***opt*, which will be referred to from here on as the 'optimal' vector for convenience and brevity of expression, is used as a reference against which the accuracy of the returned FSD parameter estimates can be judged. The proximity of **X**^ *iopt* to **X***opt*, as determined from the error analysis in **Table 11**, is indicated by the degree of quantized resolution of parameter space with

*<sup>d</sup>X*^ *iopt* <sup>¼</sup> <sup>2</sup>*δ<sup>J</sup>*

*<sup>L</sup>*, *δBL* <sup>T</sup>

*:* (38)

error differential

**70**

**Figure 34.**

*Iterative cost reduction sequence.*

**Figure 33.**

*FSD cooling sequence record.*

*Self-Driving Vehicles and Enabling Technologies*

*Summary of returned FSD parameter estimates.*

The effectiveness of the FSD method in achieving parameter 'optimality' over the FC undulating cost surface is demonstrated by deliberately initializing the search far from the global minimum in the neighborhood of a local minimum at Xi as given in **Table 10**.

A scatter diagram of iterative search costs levied by the FSD process is portrayed in **Figure 36** and contrasted with a cross section of the FC cost surface shown in **Figure 37** for variable *J* and fixed *B* ¼ *Bopt*. Application of a Boltzmann probability step transition in surmounting significant cost barriers, with cost elevations of 2σ above E which conceal the global minimum, is evident in the iterative search improvement process for a global optimum. Thus a means of escape from local minimum capture, which causes problems for traditional identification methods with non-optimal convergence, is provided for parameter extraction in an effort to secure the least mean squares (LMS) estimates.

In the early stages of the cooling schedule the temperature reduction is matched by a rapid reduction in iterative cost which eventually saturates as the parameter estimates approach the optimal LMS values. After the first temperature step the

#### **Figure 35.** *MSE cost surface without shaft load.*


During this phase of cost immobility a reheat cycle is introduced [24], as part of the FSD cooling schedule shown in **Figure 29** to overcome local minimum trapping, which is irrelevant in this case as the current estimate is circumjacent the optimal value. After the fifth iteration further cost reduction ceases with the global

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

**<sup>X</sup>**^ *opt* <sup>¼</sup> **<sup>X</sup>**ð Þ<sup>2</sup>

A second reheat phase followed by freeze conditions does not improve the parameter estimate. The total execution time on a 486-DX-66 MHz processor for the FSD method in this parameter identification procedure amounted to 20546 seconds with a computation burden of 792 cost function evaluations over 18 temperature steps. This translates on average into 44 BLMD model simulation runs per

*opt:* (39)

convergence estimate given by

*Acquisition of Global Minimum from experimental Ifa cost surface.*

**Figure 37.**

**73**

**Figure 36.**

*FSD parameter search with local minimum escape.*

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

#### **Table 11.**

*Error Analysis for Returned FSD Parameter Estimates.*

estimation cost, which is less than the exploratory *σ*, is captured within the main lobe of the response surface containing the global minimum. Subsequent progress in cost improvement is minimal which is mainly due to the fact that the parameter estimate at *X*(1) *opt* is relatively close to the global minimizer and that random searching is employed for the first ten temperature steps without the assistance of a gradient search. In addition to this the selectivity of the cost surface to *B* parameter variation is poor along the valley floor, which is flat near the global minimum as illustrated in **Figure 35** as per [13, 28], making it difficult for global minimum convergence.

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

#### **Figure 36.**

*FSD parameter search with local minimum escape.*

#### **Figure 37.** *Acquisition of Global Minimum from experimental Ifa cost surface.*

During this phase of cost immobility a reheat cycle is introduced [24], as part of the FSD cooling schedule shown in **Figure 29** to overcome local minimum trapping, which is irrelevant in this case as the current estimate is circumjacent the optimal value. After the fifth iteration further cost reduction ceases with the global convergence estimate given by

$$
\hat{\mathbf{X}}\_{opt} = \mathbf{X}\_{opt}^{(2)}.\tag{39}
$$

A second reheat phase followed by freeze conditions does not improve the parameter estimate. The total execution time on a 486-DX-66 MHz processor for the FSD method in this parameter identification procedure amounted to 20546 seconds with a computation burden of 792 cost function evaluations over 18 temperature steps. This translates on average into 44 BLMD model simulation runs per

estimation cost, which is less than the exploratory *σ*, is captured within the main lobe of the response surface containing the global minimum. Subsequent progress in cost improvement is minimal which is mainly due to the fact that the parameter

searching is employed for the first ten temperature steps without the assistance of a gradient search. In addition to this the selectivity of the cost surface to *B* parameter variation is poor along the valley floor, which is flat near the global minimum as illustrated in **Figure 35** as per [13, 28], making it difficult for global minimum

*opt* is relatively close to the global minimizer and that random

**Damping Factor** *Bopt* **<sup>B</sup>**^**opt<sup>B</sup>**�**opt B**�**opt** 

> 14.49% 1.976%

Current command *Ida* 95.815%

**100%**

**Global Cost** *Eopt* **<sup>E</sup>**^**opt<sup>E</sup>**�**opt E**�**opt** 

> 46.77% 5.808%

Cur. Controller o/p *Vca* 94.9%

**100%**

estimate at *X*(1)

**Table 11.**

**Figure 35.**

*FSD Method* Post Temp Step *T*<sup>1</sup> Post Temp Step *T*<sup>5</sup>

*NSL - Correlation Coefficient ρ*

*MSE cost surface without shaft load.*

*BLMD Parameter* **Motor Inertia** *Jopt*

*Self-Driving Vehicles and Enabling Technologies*

Shaft Velocity Correlation Coefficient Vω<sup>r</sup> *=* 97.9%*.*

*Error Analysis for Returned FSD Parameter Estimates.*

^**JoptJopt Jopt** 

> 1.479% 0.296%

Current Feedback *Ifa* 94.62%

Coherence of BLMD Simulation Waveforms with Experimental Test Data

**100%**

*Exploratory Search* 0.515% 1.682% 9.348%

convergence.

**72**

temperature step with a processor runtime of 26 seconds per simulation trial. This puts into perspective the computational intensity and the cost in terms of CPU time of this optimization technique. A breakdown of the overall search effort deployed in the FSD process projects into 405 random search calculations with a punitive computational overhead of 387 evaluations necessary for anticipated downhill movement factored in only for the last 9 temperature steps. This overhead is manifested, after the random search epoch during which the parameter estimates have reached a minimum potential, in the lengthy reheat and condensation phases shown in **Figure 33**. The inadequacy of the gradient search procedure in this instance, with approximate global convergence already achieved, is compounded by the tendency of the FSD method to dither about in a region of parameter space where the response surface has poor selectivity in the *B* parameter with little iterative progress in cost reduction expected. The comparison of BLMD step response simulation with experimental drive test data, at internal observation nodes based on returned FSD optimal estimates, provides an excellent fit in terms of frequency and phase coherence as per **Figures 38**–**40** pertaining to BLMD current control.

These simulated step responses are almost identical to those based on returned estimates for the modified form of the FSD method (MFSD), with zero inertial load conditions (NSL), discussed in Section 11 below. These simulation traces are

**Figure 40.**

**Figure 41.**

**Figure 42.**

**75**

*FC simulation via MFSD estimates.*

*ZSL – MFSD Shaft Velocity Simulation.*

*ZSL-current controller Simuln*

*.*

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

**Figure 38.** *ZSL FC Simuln via MFSD estimates.*

**Figure 39.** *ZSL- current demand Simul<sup>n</sup>*

*.*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

#### **Figure 40.**

temperature step with a processor runtime of 26 seconds per simulation trial. This puts into perspective the computational intensity and the cost in terms of CPU time of this optimization technique. A breakdown of the overall search effort deployed in the FSD process projects into 405 random search calculations with a punitive computational overhead of 387 evaluations necessary for anticipated downhill movement factored in only for the last 9 temperature steps. This overhead is manifested, after the random search epoch during which the parameter estimates have reached a minimum potential, in the lengthy reheat and condensation phases shown in **Figure 33**. The inadequacy of the gradient search procedure in this instance, with approximate global convergence already achieved, is compounded by the tendency of the FSD method to dither about in a region of parameter space where the response surface has poor selectivity in the *B* parameter with little iterative progress in cost reduction expected. The comparison of BLMD step response simulation with experimental drive test data, at internal observation nodes based on returned FSD optimal estimates, provides an excellent fit in terms of frequency and phase coherence as per

These simulated step responses are almost identical to those based on returned estimates for the modified form of the FSD method (MFSD), with zero inertial load conditions (NSL), discussed in Section 11 below. These simulation traces are

**Figures 38**–**40** pertaining to BLMD current control.

*Self-Driving Vehicles and Enabling Technologies*

**Figure 38.**

**Figure 39.**

**74**

*ZSL- current demand Simul<sup>n</sup>*

*.*

*ZSL FC Simuln via MFSD estimates.*

*ZSL-current controller Simuln .*

**Figure 41.** *ZSL – MFSD Shaft Velocity Simulation.*

**Figure 42.** *FC simulation via MFSD estimates.*

displayed together along with other waveforms for MFSD comparison purposes in **Figures 38**–**41** and **Figures 42**–**49** at different shaft inertial load bearing conditions. The goodness-of-fit measure is determined by the degree of correlation, expressed

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

**Figure 46.**

**Figure 47.**

**Figure 48.**

**77**

*LSL - current controller simulation.*

*MFSD – MSL Shaft Velocity Simulation.*

*LSL - current demand simulation.*

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

#### **Figure 43.**

*MSL - current demand simulation.*

**Figure 44.** *Current controller o/p simulation.*

**Figure 45.** *FC–LSL Simulation via MFSD Estimates.*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

displayed together along with other waveforms for MFSD comparison purposes in **Figures 38**–**41** and **Figures 42**–**49** at different shaft inertial load bearing conditions. The goodness-of-fit measure is determined by the degree of correlation, expressed

**Figure 46.** *LSL - current demand simulation.*

**Figure 43.**

**Figure 44.**

**Figure 45.**

**76**

*FC–LSL Simulation via MFSD Estimates.*

*Current controller o/p simulation.*

*MSL - current demand simulation.*

*Self-Driving Vehicles and Enabling Technologies*

#### **Figure 47.**

*LSL - current controller simulation.*

**Figure 48.** *MFSD – MSL Shaft Velocity Simulation.*

**Total Nominal Inertial**

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

*Quantized Parameter Space*:

*Initial Optimal Estimates*

^*Jiopt* kg*:*cm2 ð Þ *B*^*iopt* Nm*:*rad‐<sup>1</sup> *:*sec

**Table 12.**

**Figure 50.**

**Figure 51.**

**79**

*Histogram of MSL-*J *search values.*

*Histogram of MSL exploratory costs.*

**No Shaft Load NSL - (0.0) 3.0**

> 3.064 <sup>1</sup>*:*<sup>953</sup> � <sup>10</sup>‐<sup>3</sup>

*Statistical estimates for initial exploratory search of parameter space.*

Tolerance: �Δ*Xnom* = [�20% *Jnom*, �10% *Bnom*] Sample Size: *Ni* ¼ 200

Sample Percentage 9.542% 2.315% 1.19% Max Cost Emax 0.694 0.655 0.653 Mean Cost *E* 0.367 0.444 0.457 Min Cost *<sup>E</sup>*^*iopt* <sup>5</sup>*:*<sup>473</sup> � <sup>10</sup>‐<sup>2</sup> <sup>2</sup>*:*<sup>054</sup> � <sup>10</sup>‐<sup>2</sup> <sup>1</sup>*:*<sup>497</sup> � <sup>10</sup>‐<sup>2</sup> Standard Deviation <sup>σ</sup> <sup>1</sup>*:*<sup>654</sup> � <sup>10</sup>�<sup>1</sup> <sup>1</sup>*:*<sup>651</sup> � <sup>10</sup>�<sup>1</sup> <sup>1</sup>*:*<sup>694</sup> � <sup>10</sup>�<sup>1</sup>

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

**Medium Shaft Load MSL - (9.304) 12.304**

> 12.121 <sup>1</sup>*:*<sup>953</sup> � <sup>10</sup>‐<sup>3</sup>

**Large Shaft Load LSL - (17.822) 20.822**

> 20.767 <sup>2</sup>*:*<sup>033</sup> � <sup>10</sup>‐<sup>3</sup>

**Shaft Load** *Jnom* **(kg***:***cm2)**

**Figure 49.** *MFSD – LSL - Shaft Velocity Simulation.*

as the correlation coefficient in **Table 11**, which exists between the simulated and experimental test data. This value is almost 95% for all three internal node observations which confirms the success of the FSD method as an accurate method of parameter extraction besides providing BLMD model validation. Further confidence in the FSD method is assured by the degree of correlation in **Table 11** of BLMD shaft velocity simulation with test data as shown in **Figure 41**.

#### **10. Improved FSD method for motor parameter identification**

A drawback with the general form of the FSD method described in Section 8 is the usage of a fixed number of external loops at high temperature for random searching only of parameter space without application of the gradient technique. The lack of adaptation of the method in its present form to the iteration statistics garnered during the initial high temperature phase gives rise to lengthy run time of the FSD algorithm. This results in an excessive number of cost calculations, which can be very expensive in central processing unit (CPU) time resources, accompanied by at least one reheat phase before termination of the FSD method without cognisance of the gains made at each temperature step and the shape of the cost surface based on motor feedback current.

It is evident from **Figure 34** that significant reductions in the objection function are obtained during the first couple of high temperature steps only, with very little improvement thereafter. A more lucrative strategy [27] can be based on adaptation of the FSD method during the high temperature random search phase in the absence of good initialization of the parameter vector and on the initial exploratory search statistics where the maximum value *Emax*, mean *E* and standard deviation *σ* of the resultant cost distribution are known.

The initial exploratory search statistics, for three known cases of motor shaft inertia to be 'identified', are listed in **Table 12**. The histograms associated with the initial exploration of inertial parameter space, along with those for the related costs, are shown in **Figures 50**–**53**. These histograms possess the same uniform randomness attributes as that for the zero shaft load inertia case discussed in Section 8 with cost distribution depicted in **Figure 32**.

It is evident that all the tabulated exploration costs fall within �3*σ* of the sample mean *E* with worst case estimates *Emax* less than *E* þ 2*σ*, for different shaft load inertia as illustrated in **Figure 37**, which according to Chebyshev's theorem of

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*


#### **Table 12.**

as the correlation coefficient in **Table 11**, which exists between the simulated and experimental test data. This value is almost 95% for all three internal node observations which confirms the success of the FSD method as an accurate method of parameter extraction besides providing BLMD model validation. Further confidence in the FSD method is assured by the degree of correlation in **Table 11** of

A drawback with the general form of the FSD method described in Section 8 is

It is evident from **Figure 34** that significant reductions in the objection function are obtained during the first couple of high temperature steps only, with very little improvement thereafter. A more lucrative strategy [27] can be based on adaptation of the FSD method during the high temperature random search phase in the absence of good initialization of the parameter vector and on the initial exploratory search statistics where the maximum value *Emax*, mean *E* and standard deviation *σ*

The initial exploratory search statistics, for three known cases of motor shaft inertia to be 'identified', are listed in **Table 12**. The histograms associated with the initial exploration of inertial parameter space, along with those for the related costs, are shown in **Figures 50**–**53**. These histograms possess the same uniform randomness attributes as that for the zero shaft load inertia case discussed in Section 8 with

It is evident that all the tabulated exploration costs fall within �3*σ* of the sample

mean *E* with worst case estimates *Emax* less than *E* þ 2*σ*, for different shaft load inertia as illustrated in **Figure 37**, which according to Chebyshev's theorem of

the usage of a fixed number of external loops at high temperature for random searching only of parameter space without application of the gradient technique. The lack of adaptation of the method in its present form to the iteration statistics garnered during the initial high temperature phase gives rise to lengthy run time of the FSD algorithm. This results in an excessive number of cost calculations, which can be very expensive in central processing unit (CPU) time resources, accompanied by at least one reheat phase before termination of the FSD method without cognisance of the gains made at each temperature step and the shape of the cost

BLMD shaft velocity simulation with test data as shown in **Figure 41**.

**10. Improved FSD method for motor parameter identification**

surface based on motor feedback current.

**Figure 49.**

*MFSD – LSL - Shaft Velocity Simulation.*

*Self-Driving Vehicles and Enabling Technologies*

of the resultant cost distribution are known.

cost distribution depicted in **Figure 32**.

**78**

*Statistical estimates for initial exploratory search of parameter space.*

#### **Figure 50.**

*Histogram of MSL-*J *search values.*

**Figure 51.** *Histogram of MSL exploratory costs.*

where the objective function value is large and in the vicinity of a local minimum. The best optimal parameter estimates are obtained separately by inspection from quantized parameter FC cost surface simulations, utilizing the same experimental FC target data, for comparison purposes with the MFSD method as shown in **Figures 35, 54** and **55** for different inertial loads. The modified version of the FSD algorithm uses a discretized parameter space with step sizes as listed in [13] and

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

a. proceed with normal random probing of parameter space for the first high temperature step as in **Figures 28** and **29** with the best parameter estimate retained. At the end of this iterative sequence a 'greedy'search is performed, from the current best estimate obtained thus far, along each of the parameter directions in turn using the gradient method with a quantized parameter step size to take advantage of any possible further cost improvement that may accrue. The resultant optimal parameter estimates are trimmed to the nearest

incorporates the following improvements:

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

step size.

**Figure 54.**

**Figure 55.**

**81**

*MSE surface with large shaft load.*

*MSE surface with medium shaft load.*

**Figure 52.** *Histogram of LSL-J Search Values*

**Figure 53.** *Histogram of LSL exploratory costs.*

measurements [13, 28, 61] should account for at least 89% of all costs. Furthermore exploratory parameter estimates **X**^ *iopt* with costs less than the rms deviation *σ* about the mean are very close to being optimal and are in the ambit of global minimum convergence given the shape of the FC response surface. Such estimation costs, which are less than *E* � *σ*, are confined to the main lobe of the objective function which has for an apex the global minimizer **X***opt*. For the purpose of validation and demonstration of the effectiveness of the MFSD method as a parameter extraction tool in identifying various motor shaft inertial loads the exploratory least squares parameter estimates in **Table 12** are ignored in the initialization process.

Instead the method is deliberately initiated far from the global estimates in all three cases at

$$X\_{init} = \left[ 82\text{\%}J\_{nom}, 109\text{\%}6B\_m \right]^T,\tag{40}$$

based on parameter tolerance bounds given in **Table 12** with initial temperature given by

$$T\_i = T\_{init} = \mathbf{10}\sigma,\tag{41}$$

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

where the objective function value is large and in the vicinity of a local minimum. The best optimal parameter estimates are obtained separately by inspection from quantized parameter FC cost surface simulations, utilizing the same experimental FC target data, for comparison purposes with the MFSD method as shown in **Figures 35, 54** and **55** for different inertial loads. The modified version of the FSD algorithm uses a discretized parameter space with step sizes as listed in [13] and incorporates the following improvements:

a. proceed with normal random probing of parameter space for the first high temperature step as in **Figures 28** and **29** with the best parameter estimate retained. At the end of this iterative sequence a 'greedy'search is performed, from the current best estimate obtained thus far, along each of the parameter directions in turn using the gradient method with a quantized parameter step size to take advantage of any possible further cost improvement that may accrue. The resultant optimal parameter estimates are trimmed to the nearest step size.

**Figure 54.** *MSE surface with medium shaft load.*

**Figure 55.** *MSE surface with large shaft load.*

measurements [13, 28, 61] should account for at least 89% of all costs. Furthermore exploratory parameter estimates **X**^ *iopt* with costs less than the rms deviation *σ* about the mean are very close to being optimal and are in the ambit of global minimum convergence given the shape of the FC response surface. Such estimation costs, which are less than *E* � *σ*, are confined to the main lobe of the objective function which has for an apex the global minimizer **X***opt*. For the purpose of validation and demonstration of the effectiveness of the MFSD method as a parameter extraction tool in identifying various motor shaft inertial loads the exploratory least squares

Instead the method is deliberately initiated far from the global estimates in all

based on parameter tolerance bounds given in **Table 12** with initial temperature

*Xinit* <sup>¼</sup> 82%*<sup>J</sup>* ½ � *nom*, 109%*Bm* T, (40)

*Ti* ¼ *Tinit* ¼ 10σ, (41)

parameter estimates in **Table 12** are ignored in the initialization process.

three cases at

**Figure 52.**

**Figure 53.**

*Histogram of LSL exploratory costs.*

*Histogram of LSL-J Search Values*

*Self-Driving Vehicles and Enabling Technologies*

given by

**80**


**11. Parameter convergence results for the modified FSD method**

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

approach.

**Figure 56.**

**Figure 57.**

**83**

*MSL cooling temperature history.*

*NSL cooling temperature history.*

the objective function formulation.

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

The optimized parameter estimates of the motor dynamics, returned by the modified FSD method [25], with convergence details for three cases of shaft load inertia to be identified are summarized in **Table 13**. The number of iterative temperature steps and functional evaluations required, for the motor parameter identification process to reach minimum potential, in each of the three cases of shaft load inertia are almost identical for the modified FSD method with considerable savings effected in computational effort over the conventional FSD

The anneal temperature profiles realized during the MFSD extraction process of the three shaft inertial loads are depicted in **Figures 56**–**58**. Global optimality, to within the limits of the quantized parameter step sizes listed in [13], is achieved in all three cases in at most two temperature steps as shown in **Figures 59**–**61**. The CPU runtime however increases with the mechanical time constant *τ<sup>m</sup>* given in [9], for a similar number of motor simulation trials as indicated in **Figure 62**, in symphony with the time duration of the observed FC target data used as an argument in

#### **Table 13.**

*Modified FSD method of motor shaft inertial load parameter extraction.*


Once the motor friction coefficient *B* has been resolved further pruning of CPU run time can availed of if only the inertial parameter is to be identified, for which the FC response surface is more sensitive near the global minimum, by abrupt termination of the FSD method after two non profitable temperature steps.

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

#### **11. Parameter convergence results for the modified FSD method**

The optimized parameter estimates of the motor dynamics, returned by the modified FSD method [25], with convergence details for three cases of shaft load inertia to be identified are summarized in **Table 13**. The number of iterative temperature steps and functional evaluations required, for the motor parameter identification process to reach minimum potential, in each of the three cases of shaft load inertia are almost identical for the modified FSD method with considerable savings effected in computational effort over the conventional FSD approach.

The anneal temperature profiles realized during the MFSD extraction process of the three shaft inertial loads are depicted in **Figures 56**–**58**. Global optimality, to within the limits of the quantized parameter step sizes listed in [13], is achieved in all three cases in at most two temperature steps as shown in **Figures 59**–**61**. The CPU runtime however increases with the mechanical time constant *τ<sup>m</sup>* given in [9], for a similar number of motor simulation trials as indicated in **Figure 62**, in symphony with the time duration of the observed FC target data used as an argument in the objective function formulation.

#### **Figure 56.**

b. If the current Least Mean Squares (LMS) error is less than *σ* then the

**Figure 35 - NSL No Shaft Load** *Jm* **= 3.0**

Initial Cost *Ei* 0.414 0.590 *0.616*

3.07965 1.95863<sup>10</sup>‐<sup>3</sup>

Min Cost *<sup>E</sup>*^*opt* 5.21677 <sup>10</sup><sup>2</sup> 2.20282 <sup>10</sup><sup>2</sup> 1.30295 <sup>10</sup><sup>2</sup>

No. of Temp Steps to reach *E*^*opt* 222

110 45 65

Total Time (sec) 2834 5562 6499 Average Iteration Time *tITER* 1417 2781 3250 Simul<sup>n</sup> Time/Func. Eval. *tSIM* 25.76 s 51.03 s 63.10 s

Parameter Initialization: [*Ji* = 0.82*Jnom*, *Bi* = 1.09*Bm*] with *Bm* = 2.14<sup>10</sup>‐<sup>3</sup>

*Modified FSD method of motor shaft inertial load parameter extraction.*

**Figure 54 - MSL Medium Inertia 12.304**

12.13966 2.00082<sup>10</sup>‐<sup>3</sup>

> 109 45 64

**Figure 55 - LSL Large Inertia 20.822**

20.8375 1.95863<sup>10</sup>‐<sup>3</sup>

> 103 45 58

achieved.

**Total Nominal Shaft Load Inertia**

Returned FSD Optimal Parameter Estimates

*Self-Driving Vehicles and Enabling Technologies*

*Jnom* **(kg***:***cm2)**

^Jopt (kg*:*cm2) B^opt Nm*:*rad‐<sup>1</sup> *:*sec

No. of Func\_Evals Random Search Gradient Search

**Table 13.**

estimates.

**82**

alternate application of hill descent with random search is pursued during subsequent temperature steps in the iterative improvement process towards optimality. This approach is adopted because the best estimate available with cost σ most likely resides within the capture zone of the main cost lobe as depicted in **Figure 37** for example. If the converse is true then random searching is continued as in step (a) until sufficient cost reduction has been

c. A gradient search at the termination of each temperature step is maintained for further gain in cost reduction. This has the effect of forcing and hastening the convergence of the parameter estimates towards optimality. If however there is no cost improvement for several temperature steps, typically 3 and pending step (b), the gradient search is ceased and the FSD process enters the termination stage after the fourth step which corresponds with the onset of the freeze condition in the normal FSD method. The termination process can be speeded up by halting the algorithm at this point without the necessity of the freeze condition as subsequent parameter convergence information bears out in **Table 13**. This three step stalled cost reduction phase allows for improved convergence in the *B* parameter estimate along the valley of the response surface, where it is very flat in this parameter direction, without undue expenditure of computational effort. Secondly the anneal temperature rises during this interregnum, in line with the reheat phase of the FSD method, nullifying the possibility of false minima trapping of parameter

Once the motor friction coefficient *B* has been resolved further pruning of CPU run time can availed of if only the inertial parameter is to be identified, for which the FC response surface is more sensitive near the global minimum, by abrupt termination of the FSD method after two non profitable temperature steps.

*NSL cooling temperature history.*

**Figure 57.** *MSL cooling temperature history.*

**Figure 58.** *MSL cooling temp. Sequence.*

**Figure 59.** *Iterative NSL cost reduction.*

length of each data training record is fixed at 4095 sample points (*Nd*) with a normalized time duration of approximately 10 machine cycles for reference purposes and response surface comparison with details given in **Table 3**.

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

parameter set.

**85**

**Figure 61.**

**Figure 62.**

*MFSD computation time.*

*Iterative LSL cost reduction.*

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

Response surface simulation, although computationally expensive, provides an alternative route of accurately obtaining the optimal parameter vector by means of inspection of the surface minimum cost. It can thus be used as a yardstick by which the overall convergence performance of the MFSD method can be contrasted over a range of motor shaft load inertia. The cost simulations are based on an initial crude parameter mesh size given in **Table 3** with a 1 μs time step Δ*t* in all cases as shown in **Figures 35, 54** and **55** with further refinement down to quantized step sizes necessary in the vicinity of the global minimum for resolution of the optimal

The optimal shaft inertia values extracted by this approach are used in the error analysis given in **Table 5** as a reference by which the accuracy of the FSD optimal estimates are gauged. The parameter estimates extracted by the FSD optimization technique are very accurate in the shaft inertia only with fractional

#### **Figure 60.** *Iterative MSL cost reduction.*

While in general increasing the number of FC cycles improves the accuracy of the extracted global parameter estimates, measurement constraints limited the size of the FC transient data record to 10 cycles used in the MSE cost formulation. The

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

**Figure 61.** *Iterative LSL cost reduction.*

**Figure 62.** *MFSD computation time.*

length of each data training record is fixed at 4095 sample points (*Nd*) with a normalized time duration of approximately 10 machine cycles for reference purposes and response surface comparison with details given in **Table 3**.

Response surface simulation, although computationally expensive, provides an alternative route of accurately obtaining the optimal parameter vector by means of inspection of the surface minimum cost. It can thus be used as a yardstick by which the overall convergence performance of the MFSD method can be contrasted over a range of motor shaft load inertia. The cost simulations are based on an initial crude parameter mesh size given in **Table 3** with a 1 μs time step Δ*t* in all cases as shown in **Figures 35, 54** and **55** with further refinement down to quantized step sizes necessary in the vicinity of the global minimum for resolution of the optimal parameter set.

The optimal shaft inertia values extracted by this approach are used in the error analysis given in **Table 5** as a reference by which the accuracy of the FSD optimal estimates are gauged. The parameter estimates extracted by the FSD optimization technique are very accurate in the shaft inertia only with fractional

While in general increasing the number of FC cycles improves the accuracy of the extracted global parameter estimates, measurement constraints limited the size of the FC transient data record to 10 cycles used in the MSE cost formulation. The

**Figure 58.**

**Figure 59.**

**Figure 60.**

**84**

*Iterative MSL cost reduction.*

*Iterative NSL cost reduction.*

*MSL cooling temp. Sequence.*

*Self-Driving Vehicles and Enabling Technologies*

percentage relative errors achieved in global convergence performance as indicated in **Table 5**.

The errors appear to decrease with increasing inertial load coupled with a general trend in the global cost reduction. The error performance in *B* parameter estimation is 'poor' by comparison and is responsible for the increase in relative global cost in column 2 of the error summary. The wider error margins can be inferred from the deployment of the larger quantized relative step size listed in [13] and attributed to poor selectivity of the cost surface, in the friction coefficient, in the region of the global minimum as discussed in [13]. The quality of the MFSD probe of parameter space in obtaining the global estimates and evading local minimum capture is demonstrated in **Figures 63**–**65** by the asterisked search costs over cross sections of the simulated FC response surfaces for contrast.

The accuracy of the returned MFSD estimates can also be checked by employing these optimal parameter vectors in BLMD dynamical simulation and resultant comparison with experimental motor drive step response data. The model simulation traces are compared with observed test data, on the basis of accuracy of fit at critical internal nodes of the drive system, for the dual purpose of validation of the MFSD identification method and enhancement of BLMD model confidence which are essential intrinsic component features of system identification [35].

The goodness of fit of the simulation traces, at various BLMD model observation nodes in [13] in terms of frequency and phase coherence, with sampled test data is obvious from **Figures 38**–**40** and from **Figures 42**–**47** for BLMD feedback current, current demand and compensator outputs at different inertial loads. This measure of trace coherence, indicative of MFSD parameter extraction accuracy, can be gauged by the excellent correlation coefficient for the fixed amplitude swept frequency waveforms listed in **Table 14** (**Figures 38**–**41, 42–49**). The accuracy of the MFSD method is further substantiated in **Figures 41, 48** and **49** by the correlation

*No Shaft Load* **(NSL)** *Jm* **= 3.0**

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

**Figure 38** 94.6%

**Figure 39** 95.8%

**Figure 40** 94.9%

**Figure 41** 97.9%

*BLMD simulation trace coherence correlation coefficient ρ in [13].*

*Medium Inertia* **(MSL) 12.304**

> **Figure 42** 98.6%

> **Figure 43** 97.8%

**Figure 44** 99%

**Figure 48** 99%

*Large Inertial Load* **(LSL) 20.822**

> **Figure 45** 99.4%

**Figure 46** 99.7%

**Figure 47** 98.7

**Figure 49** 93.8%

of the model shaft velocity step response with BLMD output test data.

**Figure 65.**

*Ifa*

*Ida*

*Vca*

*V*ω*<sup>r</sup>*

**Table 14.**

**87**

*FSD identification of inertial LSL.*

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

*Nominal Shaft Inertial Load*

*Jnom* **(kg***:***cm2)**

Current Feedback

Current command

Current Controller o/p

Motor Shaft Velocity

**12. FC response surface selectivity with MFSD application**

The above application of the modified version of the FSD method in inertial mass *J* identification evolved from the nature of the FC objective function deployed. The fixed sample number *Ni* (200) of random searches during the exploratory phase, or the first temperature step employing 15\*NDIM random searches with user supplied initialization only and an absent exploratory phase, tended to give less coverage of quantized parameter space for the cases with increased shaft inertia presented in **Table 12**. It therefore seems more difficult to find a good starting vector, as it takes longer to probe a sufficient volume of parameter space, from which to anchor all subsequent searches. The modified method would, it appears,

**Figure 63.** *FSD identification of rotor dynamics.*

**Figure 64.** *FSD identification of inertial MSL.*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

#### **Figure 65.**

percentage relative errors achieved in global convergence performance as indicated

The errors appear to decrease with increasing inertial load coupled with a gen-

The accuracy of the returned MFSD estimates can also be checked by employing

these optimal parameter vectors in BLMD dynamical simulation and resultant comparison with experimental motor drive step response data. The model simulation traces are compared with observed test data, on the basis of accuracy of fit at critical internal nodes of the drive system, for the dual purpose of validation of the MFSD identification method and enhancement of BLMD model confidence which

are essential intrinsic component features of system identification [35].

eral trend in the global cost reduction. The error performance in *B* parameter estimation is 'poor' by comparison and is responsible for the increase in relative global cost in column 2 of the error summary. The wider error margins can be inferred from the deployment of the larger quantized relative step size listed in [13] and attributed to poor selectivity of the cost surface, in the friction coefficient, in the region of the global minimum as discussed in [13]. The quality of the MFSD probe of parameter space in obtaining the global estimates and evading local minimum capture is demonstrated in **Figures 63**–**65** by the asterisked search costs over

cross sections of the simulated FC response surfaces for contrast.

in **Table 5**.

*Self-Driving Vehicles and Enabling Technologies*

**Figure 63.**

**Figure 64.**

**86**

*FSD identification of inertial MSL.*

*FSD identification of rotor dynamics.*

*FSD identification of inertial LSL.*


#### **Table 14.**

*BLMD simulation trace coherence correlation coefficient ρ in [13].*

The goodness of fit of the simulation traces, at various BLMD model observation nodes in [13] in terms of frequency and phase coherence, with sampled test data is obvious from **Figures 38**–**40** and from **Figures 42**–**47** for BLMD feedback current, current demand and compensator outputs at different inertial loads. This measure of trace coherence, indicative of MFSD parameter extraction accuracy, can be gauged by the excellent correlation coefficient for the fixed amplitude swept frequency waveforms listed in **Table 14** (**Figures 38**–**41, 42–49**). The accuracy of the MFSD method is further substantiated in **Figures 41, 48** and **49** by the correlation of the model shaft velocity step response with BLMD output test data.

#### **12. FC response surface selectivity with MFSD application**

The above application of the modified version of the FSD method in inertial mass *J* identification evolved from the nature of the FC objective function deployed. The fixed sample number *Ni* (200) of random searches during the exploratory phase, or the first temperature step employing 15\*NDIM random searches with user supplied initialization only and an absent exploratory phase, tended to give less coverage of quantized parameter space for the cases with increased shaft inertia presented in **Table 12**. It therefore seems more difficult to find a good starting vector, as it takes longer to probe a sufficient volume of parameter space, from which to anchor all subsequent searches. The modified method would, it appears,

then terminate prematurely if trapped in a false minimum potential well after four anneal steps without adequate sampling of the parameter domain thus generating uncertainty as to the quality of returned estimates. However this is not the case when the topography of the cost surface in the observed FC variable is examined for different shaft inertial loads.

The number of feedback current cycles is fixed, at about ten in **Table 3**, as this influences the FC response surface "nuclear capture cross section" [62] shown in **Figure 66**. This can be defined as the waist of the main lobe containing the global minimum 'energy' *Eopt*, with value less than the exploratory search **σ**, and the penalty costs of all excursions into the parameter space kernel forming a nucleus about *Xopt* with values less than the next excited level *E*<sup>1</sup> or local minimum above the ground state *Eopt*. The probability of capture *Pc* of a random search can be formulated as the ratio of the capture cross section to the tolerance band of parameter variation in [13] about the nominal value *xm* as

$$P\_C = \frac{\Delta \mathbf{x}\_{\text{cap} \cdot \mathbf{x} \text{-} \text{set}}}{\mathbf{x}\_{\text{max}} - \mathbf{x}\_{\text{min}}} = \frac{t d \mathbf{x}^L}{2md \mathbf{x}^L} = \frac{t}{2m} \tag{42}$$

implementation of the modified FSD method. The tabulated cross section percentages stabilize at about 30% for medium to large mass loading which shows that the probability of reaching the target zone is independent of the number of searches conducted owing to the shape of the optimal cost surface sections employed. This removes any uncertainty as to the effectiveness of the FSD method of entering the global region and possible lockup in an excited state in the event of a short anneal

**No Shaft Load Figure 35 38.97%**

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

127 out of 200 63.5%

> 15 ex 30 50%

81 out of 110 73.64%

**Medium Inertia Figure 54 30.15%**

> 85 out of 200 42.5%

> > 16 ex 30 53.33%

75 out of 109 68.81%

**Large Inertia Figure 55 29.69%**

71 out of 200 35.5%

> 12 ex 30 40%

78 out of 103 75.73%

Also the various FSD entrapment estimates at different phases of the search algorithm provide a rough independent confirmatory measure of the probability of capture where a uniform random search of parameter space is conducted. The percentage of all search excursions into the optimal parameter nucleus, in both the optional exploration phase and the mandatory random initial anneal step, exceed the cross section estimates in all cases and thus enhances user confidence in the modified method. The rationale behind this approach is based on the FC cost surface topography, which has a ravine like capture region shown in [13], with both *J* and *B* parameters considered. This target zone, which has essentially parallel contour lines in the direction of the 'line minimum' in [13], can be condensed into a single dimension in the percentage ratio carve up of parameter space for target

Further confidence in the capture cross section estimate for different shaft inertial loads can be gained by employing fixed length data records in the observed current feedback *Ifa*. This is based on ten FC machine cycles as the target reference for FC cost surface simulation in the *J* parameter at *Bopt* for estimation purposes as summarized in **Table 16** with data sampling rates *fs* and displayed in **Figure 67**. The probability of capture can be more accurately defined by the weighted contribution of all tabulated cross section estimates at different inertial loads as

> *Ji* ∗C\_X\_S P *i Ji*

*Ifa* [*fs*] 50 kHz 37 kHz 31 kHz 27 kHz 24 kHz 21 kHz 17 kHz 15 kHz

*C\_X\_S* 36.3% 33.9% 32.3% 31.7% 31.2% 30.5% 30.2% 30.3%

3.0 6.0 9.0 12.0 15.0 20.0 30.0 40.0

¼ 0*:*31*:* (43)

sequence where a large quantized parameter space is concerned.

*Estimation of % capture cross section from simulated FC cost surfaces.*

**Capture Cross Section**

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

FSD Target Acquisition Exploration Phase Trapped States %

Random Search Only: %Trapping

Random + Mixture: %Capture

First Anneal Step

First 2 Temp Steps

**at** *Bopt*

**Table 15.**

Inertia kg*:*cm2

**Table 16.**

**89**

acquisition calculations in the *J* parameter as shown **Figure 66**.

*PC* ¼

*% capture cross section (C\_X\_S) estimates from Ifa target data.*

P *i*

where it is assumed that the least important *B* parameter value has been resolved. Thus for a uniform random search the impingement of target parameter space, given by *NPc*, increases directly with the number of trials *N*. Once the barrier potential *E***1**(*X*) to the kernel of capture is breached at any stage during the MFSD iterative improvement process, the related parameter vector is then installed as the best estimate by which all subsequent searches are adjudicated on for any further cost decrease. At the end of an anneal step a gradient search is performed which forces the best estimate to date, if trapped in the main lobe region, to converge towards the global minimum.

The capture cross section percentages, expressed in terms of allowed parameter tolerance and quantization step size, for the three cases of motor shaft inertia are presented in **Table 15** along with details of search cost capture during

**Figure 66.** *FC cost surface 'nuclear' capture zone.*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*


**Table 15.**

then terminate prematurely if trapped in a false minimum potential well after four anneal steps without adequate sampling of the parameter domain thus generating uncertainty as to the quality of returned estimates. However this is not the case when the topography of the cost surface in the observed FC variable is examined for

The number of feedback current cycles is fixed, at about ten in **Table 3**, as this influences the FC response surface "nuclear capture cross section" [62] shown in **Figure 66**. This can be defined as the waist of the main lobe containing the global minimum 'energy' *Eopt*, with value less than the exploratory search **σ**, and the penalty costs of all excursions into the parameter space kernel forming a nucleus about *Xopt* with values less than the next excited level *E*<sup>1</sup> or local minimum above the ground state *Eopt*. The probability of capture *Pc* of a random search can be formulated as the ratio of the capture cross section to the tolerance band of

> <sup>¼</sup> *tdxL* <sup>2</sup>*mdxL* <sup>¼</sup> *<sup>t</sup>*

2*m*

(42)

parameter variation in [13] about the nominal value *xm* as

*PC* <sup>¼</sup> *<sup>Δ</sup>x*cap‐x‐sect *x*max � *x*min

presented in **Table 15** along with details of search cost capture during

where it is assumed that the least important *B* parameter value has been resolved. Thus for a uniform random search the impingement of target parameter space, given by *NPc*, increases directly with the number of trials *N*. Once the barrier potential *E***1**(*X*) to the kernel of capture is breached at any stage during the MFSD iterative improvement process, the related parameter vector is then installed as the best estimate by which all subsequent searches are adjudicated on for any further cost decrease. At the end of an anneal step a gradient search is performed which forces the best estimate to date, if trapped in the main lobe region, to converge

The capture cross section percentages, expressed in terms of allowed parameter tolerance and quantization step size, for the three cases of motor shaft inertia are

different shaft inertial loads.

*Self-Driving Vehicles and Enabling Technologies*

towards the global minimum.

**Figure 66.**

**88**

*FC cost surface 'nuclear' capture zone.*

*Estimation of % capture cross section from simulated FC cost surfaces.*

implementation of the modified FSD method. The tabulated cross section percentages stabilize at about 30% for medium to large mass loading which shows that the probability of reaching the target zone is independent of the number of searches conducted owing to the shape of the optimal cost surface sections employed. This removes any uncertainty as to the effectiveness of the FSD method of entering the global region and possible lockup in an excited state in the event of a short anneal sequence where a large quantized parameter space is concerned.

Also the various FSD entrapment estimates at different phases of the search algorithm provide a rough independent confirmatory measure of the probability of capture where a uniform random search of parameter space is conducted. The percentage of all search excursions into the optimal parameter nucleus, in both the optional exploration phase and the mandatory random initial anneal step, exceed the cross section estimates in all cases and thus enhances user confidence in the modified method. The rationale behind this approach is based on the FC cost surface topography, which has a ravine like capture region shown in [13], with both *J* and *B* parameters considered. This target zone, which has essentially parallel contour lines in the direction of the 'line minimum' in [13], can be condensed into a single dimension in the percentage ratio carve up of parameter space for target acquisition calculations in the *J* parameter as shown **Figure 66**.

Further confidence in the capture cross section estimate for different shaft inertial loads can be gained by employing fixed length data records in the observed current feedback *Ifa*. This is based on ten FC machine cycles as the target reference for FC cost surface simulation in the *J* parameter at *Bopt* for estimation purposes as summarized in **Table 16** with data sampling rates *fs* and displayed in **Figure 67**.

The probability of capture can be more accurately defined by the weighted contribution of all tabulated cross section estimates at different inertial loads as

$$P\_C = \frac{\sum J\_i \* \mathcal{C}\_{-} X\_{-} \mathcal{S}}{\sum J\_i} = \mathbf{0}.31. \tag{43}$$


**Table 16.**

*% capture cross section (C\_X\_S) estimates from Ifa target data.*

**Figure 67.** *C\_X\_S variation with inertia.*

The adoption of a fixed threshold step size *δJ <sup>L</sup>* during MFSD parameter extraction results in improved parameter resolution, given by the reduction in the variability estimate as

$$V\_{\infty}^{L} = \frac{\delta \mathbf{x}^{L}}{\mathbf{x}},\tag{44}$$

manifestation is due to the contributory interference effect of the two frequency modulated sinusoids, during the machine speed step response, in the penalty function construct as explained in [13]. The selectivity is obtained by fitting a quadratic polynomial, expressed in terms of the parameter *J*, to the main lobe of the cost surface cross section centred on the vertex **X***opt* as shown in **Figure 69** with

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

*E J*ð Þ� *Eopt* <sup>¼</sup> *<sup>b</sup>*<sup>0</sup> *<sup>J</sup>* � *Jopt* <sup>2</sup>

and least squares coefficient b0 determined [9, 10]. The selectivity measure is based on the first order variation *δE*(*J*) of the penalty cost function about the global

<sup>¼</sup> *<sup>δ</sup><sup>E</sup>*

This measure indicates a quasi linear dependency with increased data record length *Nd* as detailed in **Table 9** and shown in **Figure 70**. Further increase in data

*<sup>δ</sup><sup>J</sup>* <sup>¼</sup> *<sup>b</sup>*0*δ<sup>J</sup>*

minimum estimate *Xopt* in terms of the worst case parameter step size δ*J*

*SE J Xopt*

**Figure 68.**

**Figure 69.**

**91**

*Local minimum proliferation.*

*C\_X\_S versus data length.*

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

(45)

*<sup>L</sup>* as

*<sup>L</sup>:* (46)

with increased shaft inertial loads as shown in **Table 9**.

This percentage reduction results in better accuracy of the returned *J* parameter values for increased shaft inertial loads with smaller relative errors as indicated by error analysis in **Table 5**. The selectivity of the FC objective function in parameter identification can be improved somewhat by increasing the length of the *Ifa* sampled data record used as the target reference in the least squares cost formulation. The convergence domain is reduced with the data record length in an inverse time relationship thus improving the accuracy of the returned parameter estimates. This is articulated by the accompanying reduction in capture cross section thus restricting the search for optimality to a smaller kernel within the parameter nucleus surrounding *Xopt*. The raison d'être is the eclipsing of the finite length motor speed exponential ramp up transient by the ever lengthening presence of steady state speed saturation. The capture cross section variation for different simulated data file lengths, with a fixed sampling rate of 50 kHz and � 20% parameter tolerance, is illustrated in **Table 17** for nominal rotor inertia *Jm* anchored at *Bopt*.

The accompanying graph in **Figure 68** shows that the capture cross section of the optimal parameter kernel decreases with increasing data block size and ultimately stabilizes to a constant value for modest lengths which is indicative of the fact that the motor has reached maximum shaft speed. The increased selectivity is accompanied by a plurality of excited states, shown in **Figure 69**, which eventually level off in number as the shaft speed reaches its maximum value. This


**Table 17.**

*Response surface selectivity improvement with target data length.*

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

**Figure 68.** *C\_X\_S versus data length.*

The adoption of a fixed threshold step size *δJ*

*Self-Driving Vehicles and Enabling Technologies*

variability estimate as

*C\_X\_S variation with inertia.*

**Figure 67.**

**Table 17.**

**90**

extraction results in improved parameter resolution, given by the reduction in the

This percentage reduction results in better accuracy of the returned *J* parameter values for increased shaft inertial loads with smaller relative errors as indicated by error analysis in **Table 5**. The selectivity of the FC objective function in parameter identification can be improved somewhat by increasing the length of the *Ifa* sampled data record used as the target reference in the least squares cost formulation. The convergence domain is reduced with the data record length in an inverse time relationship thus improving the accuracy of the returned parameter estimates. This is articulated by the accompanying reduction in capture cross section thus restricting the search for optimality to a smaller kernel within the parameter nucleus surrounding *Xopt*. The raison d'être is the eclipsing of the finite length motor speed exponential ramp up transient by the ever lengthening presence of steady state speed saturation. The capture cross section variation for different simulated data file lengths, with a fixed sampling rate of 50 kHz and � 20% parameter tolerance, is illustrated in

The accompanying graph in **Figure 68** shows that the capture cross section of the optimal parameter kernel decreases with increasing data block size and ultimately stabilizes to a constant value for modest lengths which is indicative of the fact that the motor has reached maximum shaft speed. The increased selectivity is accompanied by a plurality of excited states, shown in **Figure 69**, which eventually

No. Samples 4120 6280 9000 12000 24000 Shaft Speed RPM 1953 2441 2686 2808 2930 C\_X\_S 36.3% 19.69% 12.56% 9.24% 5.1%

*<sup>T</sup>* <sup>¼</sup> <sup>3</sup>*:*<sup>0</sup> � <sup>10</sup>�4, 1*:*<sup>921</sup> � <sup>10</sup>�<sup>3</sup> *<sup>T</sup>*

level off in number as the shaft speed reaches its maximum value. This

Parameter Vector Fulcrum: *X* ¼ *Jm*, *Bopt*

*Response surface selectivity improvement with target data length.*

*VL <sup>x</sup>* <sup>¼</sup> *<sup>δ</sup>x<sup>L</sup>*

with increased shaft inertial loads as shown in **Table 9**.

**Table 17** for nominal rotor inertia *Jm* anchored at *Bopt*.

*<sup>L</sup>* during MFSD parameter

*<sup>x</sup>* , (44)

**Figure 69.** *Local minimum proliferation.*

manifestation is due to the contributory interference effect of the two frequency modulated sinusoids, during the machine speed step response, in the penalty function construct as explained in [13]. The selectivity is obtained by fitting a quadratic polynomial, expressed in terms of the parameter *J*, to the main lobe of the cost surface cross section centred on the vertex **X***opt* as shown in **Figure 69** with

$$E(f) - \overline{E}\_{\rm opt} = b\_0 \left( f - \overline{f}\_{\rm opt} \right)^2 \tag{45}$$

and least squares coefficient b0 determined [9, 10]. The selectivity measure is based on the first order variation *δE*(*J*) of the penalty cost function about the global minimum estimate *Xopt* in terms of the worst case parameter step size δ*J <sup>L</sup>* as

$$\left.S\_f^E\right|\_{\overline{X}\_{\rm qt}} = \frac{\delta E}{\delta \mathcal{J}} = b\_0 \delta \mathcal{J}^L. \tag{46}$$

This measure indicates a quasi linear dependency with increased data record length *Nd* as detailed in **Table 9** and shown in **Figure 70**. Further increase in data

accurate as those returned by the FSD method. This discrepancy is apparent for BLMD waveform simulation over long spans, using returned PCD parameter estimates for three known cases of inertial load to be identified, with poor correlation estimates spanning 20–70% as per **Table 6** for FM related current traces. The reasons, relating to cost surface selectivity and returned parameter accuracy, underpinning the choice of target data in the MSE objective function have been discussed. The obscuration of shaft velocity transient response detail by the onset of steady state conditions, as a consequence of lengthy data records, results in impairment of the PCD method in terms of reduced cost surface selectivity and loss of returned parameter accuracy with increased convergence metric in **Table 7**. The reverse trend emerges during FSD optimization, with better selectivity and improved parameter accuracy with smaller capture cross section, for current feedback usage with this being the preferred target data choice in MSE cost formulation. The effectiveness of the modified version of the FSD algorithm has been demonstrated in the extraction of the BLMD dynamics with enhanced speed in global convergence which is less than 15% of the runtime for the original FSD algorithm based on zero inertial shaft load conditions. The accuracy of the method is verified with initialization far from the global minimum at the edge of the parameter tolerance band and supported by the returned results with relative errors less than 0.3% as per **Table 5** for three known cases of motor shaft inertia. The correlation accuracy of BLMD waveform simulation with measured data is greater than 94% in **Table 14** for all cases of returned inertial parameter estimates by the FSD method. The computation intensity of the method can be reduced by adopting coarser quantization step sizes, instead of the specified noise threshold value, within an acceptable bounded parameter relative error. This improved FSD method can be potentially used, as an effective optimizer in the dynamical parameter extraction

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

phase, to facilitate autotuning during embedded system commissioning.

1.Eolas (Science Fundation Ireland) – The Irish Science and Technology Agency

2.Moog Ireland Ltd. for brushless motor drive equipment for research purposes.

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

**Acknowledgements**

**Author details**

Richard A. Guinee

**93**

The author wishes to acknowledge

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

Munster Technological University (MTU), Cork, Ireland

\*Address all correspondence to: richard.guinee@cit.ie

provided the original work is properly cited.

– for research funding.

**Figure 70.** *FC cost surface selectivity.*

record length causes the capture cross section to tend asymptotically to zero, with the nearest local minimum to the global entity approaching the same minimum energy as the ground state *Eopt*, due to the gradual onset of steady state conditions. The increased data length results in a proliferation and clustering of genuine local minima, other than noise induced cost surface granularity, about the global extremum as the initial transient step response is swamped by the onset of steady state motor speed.

It is noteworthy that a judicious application of the Fast Fourier Transform (FFT) to the FC target data, after the initial transient has partially expired, provides an estimate of the motor speed variation with residual data record length as shown in **Figure 27**. The BLMD shaft speed can be approximated by the FFT of the FC step response over a short time span at the end of each FC data sequence where machine speed is quasi constant and shaft velocity fluctuations have almost disappeared. The exponential buildup of the motor shaft speed with data record length/time in **Figure 27** is indicative of the characteristic response to the torque demand step input [9, 10].

#### **13. Conclusions**

The FSD optimization technique has been shown, although computationally intensive, to be a very accurate and effective parameter identification method over a noisy cost surface with embedded local minima. This novel method avoids the convergence difficulties associated with the application of classical optimization techniques during parameter extraction by providing an anneal temperature related Boltzmann probability of escape from local minimum capture. The accuracy of the FSD returned parameter estimates is independently confirmed with values found to be in substantial agreement with those extracted through cost surface simulation, with worst case relative error in the damping parameter *B* of 2%, for known BLMD dynamics. Further confidence enhancement in the FSD identification strategy is provided by the degree of correlation (94%) of BLMD model simulations, based on returned FSD parameter estimates, with observed test data. The application of the Powell Conjugate Direction method, as an alternative competitive identification strategy to the FSD method, with a simple unimodal velocity cost function has been discussed. The identified BLMD dynamics, though reasonable by comparison with known nominal values in that relative errors are less than 6% in **Table 4**, are not as

#### *Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

accurate as those returned by the FSD method. This discrepancy is apparent for BLMD waveform simulation over long spans, using returned PCD parameter estimates for three known cases of inertial load to be identified, with poor correlation estimates spanning 20–70% as per **Table 6** for FM related current traces. The reasons, relating to cost surface selectivity and returned parameter accuracy, underpinning the choice of target data in the MSE objective function have been discussed. The obscuration of shaft velocity transient response detail by the onset of steady state conditions, as a consequence of lengthy data records, results in impairment of the PCD method in terms of reduced cost surface selectivity and loss of returned parameter accuracy with increased convergence metric in **Table 7**. The reverse trend emerges during FSD optimization, with better selectivity and improved parameter accuracy with smaller capture cross section, for current feedback usage with this being the preferred target data choice in MSE cost formulation.

The effectiveness of the modified version of the FSD algorithm has been demonstrated in the extraction of the BLMD dynamics with enhanced speed in global convergence which is less than 15% of the runtime for the original FSD algorithm based on zero inertial shaft load conditions. The accuracy of the method is verified with initialization far from the global minimum at the edge of the parameter tolerance band and supported by the returned results with relative errors less than 0.3% as per **Table 5** for three known cases of motor shaft inertia. The correlation accuracy of BLMD waveform simulation with measured data is greater than 94% in **Table 14** for all cases of returned inertial parameter estimates by the FSD method. The computation intensity of the method can be reduced by adopting coarser quantization step sizes, instead of the specified noise threshold value, within an acceptable bounded parameter relative error. This improved FSD method can be potentially used, as an effective optimizer in the dynamical parameter extraction phase, to facilitate autotuning during embedded system commissioning.

#### **Acknowledgements**

record length causes the capture cross section to tend asymptotically to zero, with the nearest local minimum to the global entity approaching the same minimum energy as the ground state *Eopt*, due to the gradual onset of steady state conditions. The increased data length results in a proliferation and clustering of genuine local minima, other than noise induced cost surface granularity, about the global extremum as the initial transient step response is swamped by the onset of steady state

It is noteworthy that a judicious application of the Fast Fourier Transform (FFT) to the FC target data, after the initial transient has partially expired, provides an estimate of the motor speed variation with residual data record length as shown in **Figure 27**. The BLMD shaft speed can be approximated by the FFT of the FC step response over a short time span at the end of each FC data sequence where machine speed is quasi constant and shaft velocity fluctuations have almost disappeared. The exponential buildup of the motor shaft speed with data record length/time in **Figure 27** is indicative of the characteristic response to the torque demand step

The FSD optimization technique has been shown, although computationally intensive, to be a very accurate and effective parameter identification method over a noisy cost surface with embedded local minima. This novel method avoids the convergence difficulties associated with the application of classical optimization techniques during parameter extraction by providing an anneal temperature related Boltzmann probability of escape from local minimum capture. The accuracy of the FSD returned parameter estimates is independently confirmed with values found to be in substantial agreement with those extracted through cost surface simulation, with worst case relative error in the damping parameter *B* of 2%, for known BLMD dynamics. Further confidence enhancement in the FSD identification strategy is provided by the degree of correlation (94%) of BLMD model simulations, based on returned FSD parameter estimates, with observed test data. The application of the Powell Conjugate Direction method, as an alternative competitive identification strategy to the FSD method, with a simple unimodal velocity cost function has been discussed. The identified BLMD dynamics, though reasonable by comparison with known nominal values in that relative errors are less than 6% in **Table 4**, are not as

motor speed.

**Figure 70.**

*FC cost surface selectivity.*

*Self-Driving Vehicles and Enabling Technologies*

input [9, 10].

**92**

**13. Conclusions**

The author wishes to acknowledge


#### **Author details**

Richard A. Guinee Munster Technological University (MTU), Cork, Ireland

\*Address all correspondence to: richard.guinee@cit.ie

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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*DOI: http://dx.doi.org/10.5772/intechopen.97370*

[22] Guinee R A, Lyden C. A Novel Application of the Fast Simulated Diffusion Algorithm in Brushless Motor Parameter Identification. In: The 3rd IEEE European Workshop on

[23] Guinee R A, Lyden C. A Novel Application of the Fast Simulated Diffusion Algorithm for Dynamical Parameter Identification of Brushless Motor Drive Systems. In: The 2000 IEEE International Symposium on Circuits and Systems (ISCAS 2000); May 2000; Geneva. Switzerland.

[24] Sakurai T, Lin B, and Newton A R.

[25] Guinee R A, Lyden C. Parameter Identification of a Motor Drive using a Modified Fast Simulated Diffusion Algorithm. In: Proc. of the IASTED Intern. Conf. on Modelling and Simulation; May 1998; Pittsburgh. Pa.

[26] Guinee R A, Lyden C. A Novel Application of the Fast Simulated Diffusion Optimization Technique for Brushless Motor Parameter Extraction. In: International Conference on Control (UKACC); Sep 2000; Cambridge Univ..

[27] Guinee R A, Lyden C. Parameter Identification of a Brushless Motor Drive System using a Modified Version

of the Fast Simulated Diffusion Algorithm. In: Proc. of American Control Conference (IEEE ACC-1999);

June 1999; San Diego. USA.

[28] Guinee R A. Mathematical Modelling, Simulation and Parameter Identification of a Permanent Magnet

USA. IEEE; p. 224-228.

Fast Simulated Diffusion:An Optimization Algorithm for Multiminimum Problems and Its Application to MOSFET Model Parameter Extraction. IEEE Trans. on Computer-Aided Design. Feb. 1992;

Vol. 11.

Prague Czech Republic.

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

Computer-Intensive Methods in Control and Data Processing; Sep. 1998; UTIA.

[15] Kirkpatrick S, Gelatt Jr. C D, Vecchi

[16] Johnson D S, Aragon C R, McGeogh L A, Schevon C. Optimization by simulated annealing: an experimental evaluation; Part 1, graph partitioning. Operations Res.; Nov-Dec 1989; Vol. 37;

[17] Ellams P, Mansell A D. Simulated annealing in the analysis of resonant DC link inverters. In: IEE Proc.-Electr. Power Appl.; May 1994; Vol. 141; No. 3,

[18] Sorkin G B. Simulated Annealing on Fractals: Theoretical Analysis and Relevance for Combinatorial Optimization. In: Proc. 6th ann. MIT Conf. Advanced Res. VLSI.; Apr 1990;

[19] Hu Y H, Pan S W. SaPOSM: An Optimization Method Applied to Parameter Extraction of MOSFET Models. IEEE Trans on Computer-Aided Des. of Integ. Cir. And Sys.. Oct. 1993;

[20] Vai M –K, Ng M F D. A technologyindependent device modelling program using simulated annealing optimization. In: Proc. C.I.C.C.'89; May 1989; p 381-384.

[21] Chandy J A, Kim S, Ramkumar B, Parkes S, Banerjee P, An Evaluation of Parallel Simulated Annealing Strategies with Application to Standard Cell Placement. IEEE Trans on Computer-Aided Des. of Integ. Cir. And Sys.. Apr.

[10] Guinee R A. Extended Simulation of an Embedded Brushless Motor Drive (BLMD) System for Adjustable Speed Control Inclusive of a Novel Impedance Angle Compensation Technique for Improved Torque Control in Electric Vehicle Propulsion Systems [Internet]. In: Electric Vehicles–Modelling & Simulation. IntechOpen Open Access Publisher; Aug 2011. p. 417-466. Ch19. DOI: 10.5772/29821. Available from: https://www.intechopen.com/books/e lectric-vehicles-modelling-and-simula tions/extended-simulation-of-an-e mbedded-brushless-motor-drive-blmdsystem-for-adjustable-speed-control-in

[11] Guinee R A, Lyden C. Accurate Modelling and Simulation of a High Performance Permanent Magnet Adjustable Speed Drive System for Embedded Systems. In: 8th European Conference on Power Electronics and Applications (EPE '99); Sep. 1999; Lausanne. Switzerland.

[12] Guinee R A, Lyden C. Accurate Modelling And Simulation Of A DC Brushless Motor Drive System For High Performance Industrial Applications. In: IEEE International Symposium on Circuits and Systems (ISCAS '99); May/ June 1999; Orlando. Florida.

[13] Guinee R A. Mathematical Analysis for Response Surface Parameter Identification of Motor Dynamics in Electric Vehicle Propulsion Control [Internet]. In: New Generation of Electric Vehicles. IntechOpen Open Access Publisher; Dec 2012; p. Ch11. DOI: 10.5772/54483. Available from: https://www.intechopen.com/books/ new-generation-of-electric-vehicles/ mathematical-analysis-for-response*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

surface-parameter-identificationof-motor-dynamics-in-electric-ve

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[11] Guinee R A, Lyden C. Accurate Modelling and Simulation of a High Performance Permanent Magnet Adjustable Speed Drive System for Embedded Systems. In: 8th European Conference on Power Electronics and Applications (EPE '99); Sep. 1999;

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[13] Guinee R A. Mathematical Analysis for Response Surface Parameter Identification of Motor Dynamics in Electric Vehicle Propulsion Control [Internet]. In: New Generation of Electric Vehicles. IntechOpen Open Access Publisher; Dec 2012; p. Ch11. DOI: 10.5772/54483. Available from: https://www.intechopen.com/books/ new-generation-of-electric-vehicles/ mathematical-analysis-for-response-

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[17] Ellams P, Mansell A D. Simulated annealing in the analysis of resonant DC link inverters. In: IEE Proc.-Electr. Power Appl.; May 1994; Vol. 141; No. 3,

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[19] Hu Y H, Pan S W. SaPOSM: An Optimization Method Applied to Parameter Extraction of MOSFET Models. IEEE Trans on Computer-Aided Des. of Integ. Cir. And Sys.. Oct. 1993; Vol. 12; No. 10.

[20] Vai M –K, Ng M F D. A technologyindependent device modelling program using simulated annealing optimization. In: Proc. C.I.C.C.'89; May 1989; p 381-384.

[21] Chandy J A, Kim S, Ramkumar B, Parkes S, Banerjee P, An Evaluation of Parallel Simulated Annealing Strategies with Application to Standard Cell Placement. IEEE Trans on Computer-Aided Des. of Integ. Cir. And Sys.. Apr. 1997; Vol. 16; No. 4.

[22] Guinee R A, Lyden C. A Novel Application of the Fast Simulated Diffusion Algorithm in Brushless Motor Parameter Identification. In: The 3rd IEEE European Workshop on Computer-Intensive Methods in Control and Data Processing; Sep. 1998; UTIA. Prague Czech Republic.

[23] Guinee R A, Lyden C. A Novel Application of the Fast Simulated Diffusion Algorithm for Dynamical Parameter Identification of Brushless Motor Drive Systems. In: The 2000 IEEE International Symposium on Circuits and Systems (ISCAS 2000); May 2000; Geneva. Switzerland.

[24] Sakurai T, Lin B, and Newton A R. Fast Simulated Diffusion:An Optimization Algorithm for Multiminimum Problems and Its Application to MOSFET Model Parameter Extraction. IEEE Trans. on Computer-Aided Design. Feb. 1992; Vol. 11.

[25] Guinee R A, Lyden C. Parameter Identification of a Motor Drive using a Modified Fast Simulated Diffusion Algorithm. In: Proc. of the IASTED Intern. Conf. on Modelling and Simulation; May 1998; Pittsburgh. Pa. USA. IEEE; p. 224-228.

[26] Guinee R A, Lyden C. A Novel Application of the Fast Simulated Diffusion Optimization Technique for Brushless Motor Parameter Extraction. In: International Conference on Control (UKACC); Sep 2000; Cambridge Univ..

[27] Guinee R A, Lyden C. Parameter Identification of a Brushless Motor Drive System using a Modified Version of the Fast Simulated Diffusion Algorithm. In: Proc. of American Control Conference (IEEE ACC-1999); June 1999; San Diego. USA.

[28] Guinee R A. Mathematical Modelling, Simulation and Parameter Identification of a Permanent Magnet Brushless Motor Drive System. Ph.D Thesis, National Microelectronics Research Centre (NMRC) – Tyndall Institute: University College Cork - National University of Ireland; 2003.

[29] Leu M C, Liu S, Zhang H. Modelling, Analysis and Simulation of Brushless DC Drive System. In: Winter Annual Meeting of ASME; 89-WA/DSC-1; 1989; San Fran. USA.

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[34] Holtz J. Sensorless Position Control of Induction Motors - an Emerging Technology *-* invited paper. In: Proc. of the 24th Annual Conf. of the IEEE Indus. Electronics Society (IECON '98); Sep. 1998; Aachen, Germany.

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[37] Powell M J D. A method for minimizing a sum of squares of non-linear functions without calculating derivatives. Computer J. 1965:11: 302-304.

[38] Swann W H. Direct Search Methods. Numerical Methods for Unconstrained Optimization. London: Academic Press; 1972.

[50] Levenberg K. A method for the solution of certain nonlinear problems

*DOI: http://dx.doi.org/10.5772/intechopen.97370*

[61] Mosteller F, Rourke R E K, Thomas

G B. Probability with Statistical Applications. Addison-Wesley Publ.

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Macmillan & Co. Ltd; 1956.

Co.; 1961

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)…*

[51] Doganis K, Scharfetter D L. General Optimization and Extraction of IC Device Model Parameters. IEEE Trans. on Elect. Dev.. 1983; Vol. 30:

[52] Stewart G W. A modification of Davidson's minimization method to accept difference approximations of derivatives. J. Assoc. Comput. Mach..

[53] Aluffi-Pentini F, Parisi V, Zirilli F. Global optimization and stochastic differential equations. J. Optimization Theory and Applications. Sep. 1985; vol.

[54] Fletcher R. Optimization. London:

[55] Hestenes M R. Conjugate Direction

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[56] Brent R P. Algorithms for Minimization Without Derivatives.

[57] S. Geman and C-R. Hwang, "Diffusions for global optimization", SIAM J. Contr. Optimization, Vol. 24, No. 5, Sep. 1986, pp. 1031-1043.

[58] Eisberg R, Resnick R. Quantum Physics. NY: J. Wiley & Sons; 1974.

[59] Metropolis M, Rosenbluth A, Rosenbluth M, Teller A, Teller E. Equation of State Calculations by Fast Computing Machines. J. Chem. Phys..

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47: no. 1

PHI; 1973.

[39] Goldfeld S M, Quandt R E, Trotter H F. Maximization by Quadratic Hill-Climbing. Econometrica. July 1966: Vol. 34; No.3.

[40] Box M J. A comparison of several current optimization methods, and the use of transformations in constrained problems. Computer J. 1966;9:67-77.

[41] Spendley W, Hext G R, Himsworth F R. Sequential Applications of Simplex Designs and Evolutionary Operation. Technometrics. 1962; Vol. 4: No. 4.

[42] Walsh G R. Methods of Optimization. John Wiley & Sons; 1979.

[43] Bunday B D. Basic Optimization Methods. London: E. Arnold Publishers; 1984.

[44] Fiacco A V, McCormick G P. Computational Algorithm for the sequential unconstrained minimization technique for nonlinear programming. Management Science. July 1964; Vol. 10: No. 4.

[45] Spang H A. A review of minimization techniques for nonlinear functions. SIAM Review. Oct. 1962: Vol. 4, No. 4.

[46] Gill P E, Murray W. Algorithms for the solution of the nonlinear least squares problem. SIAM J. Numer. Anal.. Oct 1978;Vol. 15: No. 5

[47] Adby P R, Dempster M A H. Introduction to Optimization Methods. London: Chapman and Hall; 1974

[48] Shanno D F. Conjugate gradient methods with inexact searches. Mathematics of Operations Research. Aug 1978; Vol. 3: No. 3.

[49] Press W H, Flannery B F, Teukolsky S A, Vetterling W T. NUMERICAL RECIPES in C. CUP; 1990.

*Novel Application of Fast Simulated Annealing Method in Brushless Motor Drive (BLMD)… DOI: http://dx.doi.org/10.5772/intechopen.97370*

[50] Levenberg K. A method for the solution of certain nonlinear problems in least squares. Quart. Appl. Math..1944; No. 2: p. 164-168.

Brushless Motor Drive System. Ph.D Thesis, National Microelectronics Research Centre (NMRC) – Tyndall Institute: University College Cork - National University of Ireland; 2003.

*Self-Driving Vehicles and Enabling Technologies*

Unconstrained Optimization. London:

[39] Goldfeld S M, Quandt R E, Trotter H F. Maximization by Quadratic Hill-Climbing. Econometrica. July 1966: Vol.

[40] Box M J. A comparison of several current optimization methods, and the use of transformations in constrained problems. Computer J. 1966;9:67-77.

[41] Spendley W, Hext G R, Himsworth F R. Sequential Applications of Simplex Designs and Evolutionary Operation. Technometrics. 1962; Vol. 4: No. 4.

Optimization. John Wiley & Sons; 1979.

[45] Spang H A. A review of minimization techniques for nonlinear functions. SIAM

[46] Gill P E, Murray W. Algorithms for the solution of the nonlinear least squares problem. SIAM J. Numer. Anal..

Review. Oct. 1962: Vol. 4, No. 4.

[47] Adby P R, Dempster M A H. Introduction to Optimization Methods. London: Chapman and Hall; 1974

[48] Shanno D F. Conjugate gradient methods with inexact searches. Mathematics of Operations Research.

[49] Press W H, Flannery B F, Teukolsky S A, Vetterling W T. NUMERICAL

Oct 1978;Vol. 15: No. 5

Aug 1978; Vol. 3: No. 3.

RECIPES in C. CUP; 1990.

[43] Bunday B D. Basic Optimization Methods. London: E. Arnold Publishers;

[44] Fiacco A V, McCormick G P. Computational Algorithm for the sequential unconstrained minimization technique for nonlinear programming. Management Science. July 1964; Vol. 10:

[42] Walsh G R. Methods of

Academic Press; 1972.

34; No.3.

1984.

No. 4.

Modelling, Analysis and Simulation of Brushless DC Drive System. In: Winter Annual Meeting of ASME; 89-WA/DSC-

Identification. In: IEEE Control Systems IEEE; Jan 1991. P. 25-29. 0272-1708/91/

[31] Ljung L. A Discussion Of Model Accuracy In System Identification. International Journal Of Adaptive Control and Signal Processing. J. Wiley

[32] Ljung L. System identification: Theory For The User. PHI; 1987.

[33] Moog Brushless Technology: Brushless Servodrives User Manual. Moog GmbH; 1988. D-7030 Böblingen. Germany. D310.01.03 En/De/It 01.88.

Electronics Society (IECON '98); Sep. 1998; Aachen, Germany.

[35] Fletcher R. Practical Methods of Optimization. 2nd ed. J.Wiley & Sons;

[36] Fletcher R. Function minimization without evaluating derivatives - a review. Computer J. 1965:8:33-41.

minimizing a sum of squares of non-linear functions without calculating derivatives.

[37] Powell M J D. A method for

Computer J. 1965:11: 302-304.

[38] Swann W H. Direct Search Methods. Numerical Methods for

1993.

**96**

[34] Holtz J. Sensorless Position Control of Induction Motors - an Emerging Technology *-* invited paper. In: Proc. of the 24th Annual Conf. of the IEEE Indus.

[29] Leu M C, Liu S, Zhang H.

[30] Ljung L. Issues in System

1; 1989; San Fran. USA.

0100-0025,

& Sons; 1992. Vol.6.

[51] Doganis K, Scharfetter D L. General Optimization and Extraction of IC Device Model Parameters. IEEE Trans. on Elect. Dev.. 1983; Vol. 30: No. 9.

[52] Stewart G W. A modification of Davidson's minimization method to accept difference approximations of derivatives. J. Assoc. Comput. Mach.. 1967; 14: p.72-83.

[53] Aluffi-Pentini F, Parisi V, Zirilli F. Global optimization and stochastic differential equations. J. Optimization Theory and Applications. Sep. 1985; vol. 47: no. 1

[54] Fletcher R. Optimization. London: Academic Press; 1969.

[55] Hestenes M R. Conjugate Direction Methods in Optimization. New York:Springer-Verlag; 1980.

[56] Brent R P. Algorithms for Minimization Without Derivatives. PHI; 1973.

[57] S. Geman and C-R. Hwang, "Diffusions for global optimization", SIAM J. Contr. Optimization, Vol. 24, No. 5, Sep. 1986, pp. 1031-1043.

[58] Eisberg R, Resnick R. Quantum Physics. NY: J. Wiley & Sons; 1974.

[59] Metropolis M, Rosenbluth A, Rosenbluth M, Teller A, Teller E. Equation of State Calculations by Fast Computing Machines. J. Chem. Phys.. June 1953; vol. 21.

[60] Huang M D, Romeo F, Sangiovanni-Vincentelli A. An efficient general cooling schedule for simulated annealing. In: Proc. ICCAD'86; Nov. 1986.

[61] Mosteller F, Rourke R E K, Thomas G B. Probability with Statistical Applications. Addison-Wesley Publ. Co.; 1961

[62] Glasstone S, Edlund M C. The Elements of Nuclear Reactor Theory. Macmillan & Co. Ltd; 1956.

Section 3

Enabling Technologies

**99**

Section 3
