**6. References**


PID Controller Design for Specified Performance 29

Osuský, J.; Veselý, V. & Kozáková, A. (2010). Robust Decentralized Controller Design with

Rotach, V. (1984). Avtomatizacija nastrojki system upravlenija. *Energoatomizdat,* Moskva,

Rotach, V. (1994). Calculation of the Robust Settings of Automatic Controllers, *Thermal* 

Suyama, K. (1992). A Simple Design Method for Sampled-data PID Control Systems with

Visoli, A. (2006). *Practical PID Control, Advances in Industrial Control,* Springer-Verlag London

Vítečková, M. (1998). *Seřízení regulátorů metodou požadovaného modelu (PID Controllers Tuning* 

Vítečková, M. (1999). Seřízení číslicových i analogových regulátorů pro regulované soustavy

Vítečková, M.; Víteček, A. & Smutný, L. (2000). Controller Tuning for Controlled Plants with

Wang, L. & Cluett, W.R. (1997). Tuning PID Controllers for Integrating Processes, *IEE Proceedings - Control Theory and Applications,* Vol. 144, No. 5, pp. 385-392, 1997 Wang, Y.-G. & Shao, H.-H. (1999). PID Autotuner Based on Gain- and Phase-margin Specification, *Industrial Engineering Chemistry Research,* 38, pp. 3007-3012 Wittenmark, B. (2001). A Sample-induced Delays in Synchronous Multirate Systems,

Wojsznis, W.K.; Blevins, T.L. & Thiele, D. (1999). Neural Network Assisted Control Loop

Xue, D.; Chen, Y. & Atherton, D.P. (2007). Linear Feedback Control. Analysis and Design

Yu, Ch.-Ch. (2006). *Autotuning of PID Controllers. A Relay Feedback Approach* (2nd Edition),

Ziegler, J.G. & Nichols, N.B. (1942). Optimum Settings for Automatic Controllers, *ASME* 

Tuner, *Proceedings of the IEEE International Conference on Control Applications*, Vol. 1,

*European Control Conference*, Porto, Portugal, pp. 3276–3281, 2001

with MATLAB, SIAM Press, ISBN 978-0-898716-38-2

Springer-Verlag London Limited, ISBN 1-84628-036-2

*Transactions,* Vol. 64 (1942), pp. 759-768

*by Desired Model Method),* Textbook, VŠB – Technical University of Ostrava, ISBN

s dopravním zpožděním (Tuning Discrete and Continuous Controllers for Processes with Time Delay). *Automatizace,* Vol. 42, No. 2, (1999), pp. 106-111, Czech

Time Delay, *Preprints of Proceedings of PID'00: IFAC Workshop on Digital Control,* pp.

*Electronics, Control, Instrumentation and Automation,* pp. 1117-1122, 1992 Veselý, V. (2003). Easy Tuning of PID Controller. *Journal of Electrical Engineering,* Vol. 54, No. 5-6, (2003), pp. 136-139, ISSN 1335-3632, Bratislava, Slovak Republic Visioli, A. (2001). Tuning of PID Controllers with Fuzzy Logic, *IEE Proceedings-Control* 

Pettit, J.W. & Carr, D.M. (1987). Self-tuning Controller, *US Patent* No. 4669040

*Theory and Applications*, Vol. 148, No. 1, pp. 180-184, 2001

*Engineering (Russia),* Vol. 41, No. 10, pp. 764-769, Moskva, Russia

1881-803X, Kumamoto, Japan

Limited, ISBN 1-84628-585-2

Republic (in Czech)

pp. 427-431, USA, 1999

80-7078-628-0, Czech Republic (in Czech)

83-288, Terrassa, Spain, April 2000

Russia (in Russian)

Performance Specification, *ICIC Express Letters,* Vol. 4, No. 1, (2010), pp. 71-76, ISSN

Adequate Step Responses, *Proceedings of the International Conference on Industrial* 


Bucz, Š.; Marič, L.; Harsányi, L. & Veselý, V. (2010). Design-oriented Identification Based on

Bucz, Š.; Marič, L.; Harsányi, L. & Veselý, V. (2011). Easy Tuning of Robust PID Controllers

Vol. 5, No. 3 (March 2011), pp. 563-572, ISSN 1881-803X, Kumamoto, Japan Bucz, Š. (2011). *Engineering Methods of Robust PID Controller Tuning for Specified Performance.*

Coon, G.A. (1956). How to Find Controller Settings from Process Characteristics, In: *Control* 

Chandrashekar, R.; Sree, R.P. & Chidambaram, M. (2002). Design of PI/PID Controllers for

Chau, P.C. (2002). Process Control - a First Course with MATLAB (1st edition), *Cambridge* 

Chen, D. & Seborg, D.E. (2002). PI/PID Controller Design Based on Direct Synthesis and Disturbance Rejection, *Industrial Engineering Chemistry Research,* 41, pp. 4807-4822 Chien, K.L.; Hrones, J.A. & Reswick, J.B. (1952). On the Automatic Control of Generalised Passive Systems. *Transactions of the ASME,* Vol. 74, February, pp. 175-185 Ford, R.L. (1953). The Determination of the Optimum Process-controller Settings and their

Grabbe, E.M.; Ramo, S. & Wooldrige, D.E. (1959-61). *Handbook of Automation Computation and* 

Haalman, A. (1965). Adjusting Controllers for a Deadtime Process, *Control Engineering,* July Hang, C.C. & Åström, K.J. (1988). Practical Aspects of PID Auto-tuners Based on Relay

Harsányi, L.; Murgaš, J.; Rosinová, D. & Kozáková, A. (1998). *Teória automatického riadenia* 

Hudzovič, P. (1982). *Teória automatického riadenia I. Lineárne spojité systémy (Control theory:* 

Kozáková, A.; Veselý, V. & Osuský, J. (2010). Decentralized Digital PID Design for

Morari, M., Zafiriou, E. (1989). *Robust Processs Control.* Prentice-Hall Inc., Englewood Cliffs,

O´Dwyer, A. (2006). *Handbook of PI and PID Controllers Tuning Rule* (2nd Edition), Imperial

*Engineering,* Vol. 3, No. 5, (May 1956), pp. 66-76

*University Press,* ISBN 978-0521002554, New York

Vol. 101, No. 80, pp. 141-155 and pp. 173-177, 1953

pp. 153-158, Copenhagen, Denmark, 1998

ISBN 0137821530, 07632 New Jersey, USA

College Press, ISBN 1860946224, London

*Section A,* Vol. 44, No. 2, pp. 82-88

*Control,* Vol. 1,2,3, New York

Slovak Republic (in Slovak)

Slovak Republic (in Slovak)

26-2

2010

Slovak)

Sine Wave Signal and its Advantages for Tuning of the Robust PID Controllers. *International Conference Cybernetics and Informatics,* Vyšná Boca, Slovak Republic,

Based on the Design-oriented Sine Wave Type Identification. *ICIC Express Letters,*

Doctoral Thesis, Slovak University of Technology in Bratislava, Slovak Republic (in

Unstable Systems with Time Delay by Synthesis Method, *Indian Chemical Engineer* 

Confirmation by Means of an Electronic Simulator, *Proceedings of the IEE, Part 2,* 

feedback, *Proceedings of the IFAC Adaptive Control of Chemical Processes Conference,* 

*(Control Theory),* Slovak University of Technology in Bratislava, ISBN 80-227-1098-9,

*Linear Continuous-time Systems),* Slovak University of Technology in Bratislava,

Performance. *In: 12th IFAC Symposium on Large Scale Systems: Theory and Applications,* Lille, France, 12.-14.7.2010, Ecole Centrale de Lille, ISBN 978-2-915-913-


**2** 

Ilan Rusnak

*Israel* 

**Family of the PID Controllers** 

The PID controllers (P, PD, PI, PID) are very widely used, very well and successfully applied controllers to many applications, for many years, almost from the beginning of controls applications (D'Azzo & Houpis, 1988)(Franklin et al., 1994). (The facts of their successful application, good performance, easiness of tuning are speaking for themselves and are sufficient rational for their use, although their structure is justified by heuristics: "These ... controls - called proportional-integral-derivative (PID) control - constitute the heuristic approach to controller design that has found wide acceptance in the process

 In this chapter we state a problem whose solution leads to the PID controller architecture and structure, thus avoiding heuristics, giving a systematic approach for explanation of the excellent performance of the PID controllers and gives insight why there are cases the PID controllers do not work well. Namely, by the use of Linear Quadratic Tracking (LQT) theory (Kwakernaak & Sivan, 1972)(Anderson & Moore, 1989) control-tracking problems are

Further, problem of controlling-tracking high order polynomial inputs and rejecting high order polynomial disturbances is formulated. By applying the LQT theory extended family of PID controllers – the family of generalized PID controllers denoted PImDn-1 is derived. This provides tool for application of optimal controllers for those systems that the conventional PID controllers are not satisfactory, for generalization and derivation of further results. The notation of generalized PID controllers, PImDn-1, is consistent with the notation

The present work is strongly motivated by problems-question tackled by the author during a continuous work on high performance servo and motion control applications. Some of the theoretical results that have had motivated and led to the present work have been documented in (Rusnak, 1998, 1999, 2000a, 2000b). Some of the presented architectures appear and are recommended for use in (Leonhard, 1996, pp. 80, 347) without rigorous

By Architecture we mean, loosely, the connections between the outputs/sensors and the inputs/actuators; Structure deals with the specific realization of the controllers' blocks; and Configuration is a specific combination of architecture and structure. These issues fall within the control and feedback organization theory that have been reviewed and presented in a concise form in (Rusnak, 2002, 2005) and in a widened form in (Rusnak, 2006, 2008). It is beyond the scope of this chapter. It is used here as a basis at a system theoretic level to

formulated and those cases when their solution gives the PID controllers are shown.

**1. Introduction** 

industries." (Franklin et al., 1994, pp. 168)).

of controllers for fractional order systems (Podlubny, 1999).

rationale and were partial trigger for the presented approach.

*RAFAEL, Advanced Defense Systems, Haifa* 

Zhuang, M. & Atherton, D.P. (1993). Automatic Tuning of Optimum PID Controllers, *IEE Proceedings, Part D: Control Theory and Applications,* Vol. 140, No. 3, pp. 216-224, ISSN 0143-7054, 1993
