**A Hybrid of Fuzzy and Fuzzy Self-Tuning PID Controller for Servo Electro-Hydraulic System**

Kwanchai Sinthipsomboon, Issaree Hunsacharoonroj, Josept Khedari, Watcharin Po-ngaen and Pornjit Pratumsuwan

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/48614

## **1. Introduction**

298 Fuzzy Controllers – Recent Advances in Theory and Applications

Organization, Geneva 2001, 228 págs.

15-17, 2006, 2006.

October 16, 2009)

October 16, 2009).

Online Journal

[1] International classification of functioning, disability and health: ICF. World health

[2] G. Krishnamurthy and M. Ghovanloo, *"Tongue Drive: A Tongue Operated Magnetic sensor Based Wireless Assistive Technology for people with severe Disabilities"*, IEEE Circuits and

[14] P. Ponce, et al. *Neuro-Fuzzy Controller Using LabVIEW*. Paper presented at the Intelligent Systems and Control Conference by IASTED, in Cambridge, MA, Nov. 19 - 21, 2007.

[3] United States Department of Veterans Affairs, " New Head Control for Quadriplegic

 http://www.rehab.research.va.gov/jour/75/12/1/lozach.pdf , (accesed October 21, 2009) [4] Quickie-Wheelchair.com, "Quickie P222 SE – Wheelchair – Quickie-Wheelchair.com", http://www.quickie-wheelchairs.com/products/Quickie-P222-SE-2974.html, (accesed

[6] National Instruments Corporation, "NI LabVIEW – The Software That Powers Virtual Instrumentation – National Instruments", http://www.ni.com/labview/ , (accesed

[8] National Instruments Corporation, "NI USB-6210 – National Instruments", http://sine.ni.com/nips/cds/print/p/lang/en/nid/203189 , (accesed October 16, 2009). [9] National Instruments Corporation, "NI Crio-9014 – National Instruments", http://sine.ni.com/nips/cds/print/p/lang/en/nid/203500 , (accesed October 16, 2009). [10] National Instruments Corporation, "NI 9505 – National Instruments", http://sine.ni.com/nips/cds/print/p/lang/en/nid/202711 , (accesed October 16, 2009). [11] Parallax Inc. "BASIC Stamp Discovery Kit – Serial (With USB Adapter and Cable)", http://www.parallax.com/StoreSearchResults/tabid/768/txtSearch/bs2/List/0/SortField/4/

Patients, 1970," Rehabilitation Research & Development Service,

ProductID/320/Default.aspx , (accesed October 21, 2009). [12] XNA libraries, http://msdn.microsoft.com/en-us/aa937791.aspx

Systems, 2006. ISCAS 2006.Proceedings. 2006 IEEE International Symposium [13] P. Ponce, et al. *A Novel Neuro-Fuzzy Controller Based on Both Trigonometric Series and Fuzzy Clusters.*IEEE International Conference an Industrial Technology. India. ICIT, Dec

Journal

The application of hydraulic actuation to heavy duty equipment reflects the ability of the hydraulic circuit to transmit larger forces and to be easily controlled. It has many distinct advantages such as the response accuracy, self-lubricating and heat transfer properties of the fluid, relative large torques, large torque-to-inertia ratios, high loop gains, relatively high stiffness and small position error. Although the high cost of hydraulic components and power unit, loss of power due to leakage, inflexibility, nonlinear response, and errorprone low power operation tends to limit the use of hydraulic drives, they nevertheless constitute a large subset of all industrial drives and are extensively used in the transportation and manufacturing industries (Merrit, 1976; Rong-Fong Fung *et al*, 1997; Aliyari *et al*, 2007).

The Servo Electro-hydraulic System (SEHS), among others, is perhaps the most important system because it takes the advantages of both the large output power of traditional hydraulic systems and the rapid response of electric systems. However, there are also many challenges in the design of SEHS. For example, they are the highly nonlinear phenomena such as fluid compressibility, the flow/pressure relationship and dead-band due to the internal leakage and hysteresis, and the many uncertainties of hydraulic systems due to linearization. Therefore, it seems to be quite difficult to perform a high precision servo control by using linear control method Rong-Fong Fung *et al*, 1997; Aliyari *et al*, 2007; Pratumsuwan *et al*, 2010).

Classical PID controller is the most popular control tool in many industrial applications because they can improve both the transient response and steady state error of the system at the same time. Moreover, it has simple architecture and conceivable physical intuition

© 2012 Sinthipsomboon et al., licensee InTech. This is an open access chapter 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. © 2012 The Author(s). Licensee InTech. 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.

of its parameter. Traditionally, the parameters of a classical PID controller, i.e. *KP*, *KI*, and *KD*, are usually fixed during operation. Consequently, such a controller is inefficient for control a system while the system is disturbed by unknown facts, or the surrounding environment of the system is changed (Panichkun & Ngaechroenkul, 2000; Pratumsuwan *et al*, 2010).

A Hybrid of Fuzzy and Fuzzy Self-Tuning PID Controller for Servo Electro-Hydraulic System 301

*Q Kx KP L qv cL* (1)

(2)

(3)

(4)

(5)

is the nonlinear stiffness of the spring.

(6)

is the angular velocity of the motor shaft, *Cl* is

is the fluid mass density, and

*<sup>e</sup>* is the

the motor. The entire system equations are described as follows. The servo valve flow

where *QL* is the load flow, *Xv* is the displacement of the spool in the servo valve, *Kc* is the flow-pressure coefficient, *PL* is the load pressure, and *Kq* is the flow gain which varies at

*PP X K Cw*

*q d*

where *Cd* is the discharge coefficient, *w* is the area gradient,

The continuity equation to the motor is formulated as

where *Dm* is the volumetric displacement, *<sup>m</sup>*

effective bulk modulus of the system.

Substituting (1) into (3) leads to

equation as follows:

( )sgn( ) *SL v*

4 *t*

*e*

4 *t*

*e*

*L mm l L L*

*q v mm l L L*

*<sup>V</sup> KX D KP P* 

<sup>3</sup> ( ) *PD J B G G T L m tm mm m nm d* 

where *Jt* is the total inertial of motor and load, *Bm* is the viscous damping coefficient of the

From (1) to (5), the hydraulic servomechanism system equation can be described by a state

*X a X bU N X t d t*

( ,) () *i i*

*<sup>V</sup> Q D CP P* 

the total leakage coefficient of the motor, *Vt* is the total compressed volume, and

where *Kl=Kc+Cl* is the total leakage coefficient of the hydraulic system.

*X X X X*

 

 

> 1 1

*i*

*ZrX* 

3

The torque balance equation for the motor is described as follows:

load, *Td* is the disturbance of the system, and 3 *Gn m*

equation (1) is described as:

*PS* is the supply pressure.

different operating points. *Kq* is given by

Fuzzy control is robust to the system with variation of system dynamics and the system of model free or the system which precise information is not required. It has been successfully used in the complex ill-defined process with better performance than that of a PID controller. Another important advance of fuzzy controller is a short rise time and a small overshoot (Aliyari *et al*, 2007; Panichkun & Ngaechroenkul, 2000). However, PID controller is better able to control and minimize the steady state error of the system. To enhance the controller performance, hybridization of these two controller structures comes to one mind immediately to exploit the beneficial sides of both categories, know as a hybrid of fuzzy and PID controller (Panichkun & Ngaechroenkul, 2000; Pratumsuwan *et al*, 2010).

Nevertheless, a hybrid of fuzzy and PID does not perform well when applied to the SEHS, because when the SEHS parameters changes will require new adjustment of the PID gains. A hybrid of fuzzy and fuzzy self-tuning PID controller is proposed in this paper. The proposed control scheme is separated into two parts, fuzzy controller and fuzzy self-tuning PID controller. Fuzzy controller is used to control systems when the output value of system far away from the target value. Fuzzy self-tuning PID controller is applied when the output value is near the desired value. In terms of adjusting the PID gains tuning using fuzzy as to obtain an optimum value.

## **2. Servo electro-hydraulic system**

The physical model of a nonlinear servo electro-hydraulic system is shown in Figure 1.

**Figure 1.** The physical model of a servo electro-hydraulic system.

The inertial-damping with a nonlinear torsional spring system is driven by a hydraulic motor and the rotation motion of the motor is controlled by a servo valve. Higher control input voltage can produce larger valve flow from the servo valve and fast rotation motion of the motor. The entire system equations are described as follows. The servo valve flow equation (1) is described as:

$$\mathbf{Q}\_{\perp} = \mathbf{K}\_{q}\mathbf{x}\_{v} - \mathbf{K}\_{c}\mathbf{P}\_{\perp} \tag{1}$$

where *QL* is the load flow, *Xv* is the displacement of the spool in the servo valve, *Kc* is the flow-pressure coefficient, *PL* is the load pressure, and *Kq* is the flow gain which varies at different operating points. *Kq* is given by

$$\mathbf{K}\_q = \mathbf{C}\_d w \sqrt{\frac{(P\_s - P\_\perp)\text{sgn}(\mathbf{X}\_v)}{\rho}} \tag{2}$$

where *Cd* is the discharge coefficient, *w* is the area gradient, is the fluid mass density, and *PS* is the supply pressure.

The continuity equation to the motor is formulated as

$$\mathcal{Q}\_{\perp} = \mathcal{D}\_{m}\dot{\theta}\_{m} + \mathcal{C}\_{l}P\_{\perp} + \frac{V\_{\circ}}{4\mathcal{J}\_{\circ}}\dot{P}\_{\perp} \tag{3}$$

where *Dm* is the volumetric displacement, *<sup>m</sup>* is the angular velocity of the motor shaft, *Cl* is the total leakage coefficient of the motor, *Vt* is the total compressed volume, and *<sup>e</sup>* is the effective bulk modulus of the system.

Substituting (1) into (3) leads to

300 Fuzzy Controllers – Recent Advances in Theory and Applications

*et al*, 2010).

*al*, 2010).

obtain an optimum value.

**2. Servo electro-hydraulic system** 

**Figure 1.** The physical model of a servo electro-hydraulic system.

of its parameter. Traditionally, the parameters of a classical PID controller, i.e. *KP*, *KI*, and *KD*, are usually fixed during operation. Consequently, such a controller is inefficient for control a system while the system is disturbed by unknown facts, or the surrounding environment of the system is changed (Panichkun & Ngaechroenkul, 2000; Pratumsuwan

Fuzzy control is robust to the system with variation of system dynamics and the system of model free or the system which precise information is not required. It has been successfully used in the complex ill-defined process with better performance than that of a PID controller. Another important advance of fuzzy controller is a short rise time and a small overshoot (Aliyari *et al*, 2007; Panichkun & Ngaechroenkul, 2000). However, PID controller is better able to control and minimize the steady state error of the system. To enhance the controller performance, hybridization of these two controller structures comes to one mind immediately to exploit the beneficial sides of both categories, know as a hybrid of fuzzy and PID controller (Panichkun & Ngaechroenkul, 2000; Pratumsuwan *et* 

Nevertheless, a hybrid of fuzzy and PID does not perform well when applied to the SEHS, because when the SEHS parameters changes will require new adjustment of the PID gains. A hybrid of fuzzy and fuzzy self-tuning PID controller is proposed in this paper. The proposed control scheme is separated into two parts, fuzzy controller and fuzzy self-tuning PID controller. Fuzzy controller is used to control systems when the output value of system far away from the target value. Fuzzy self-tuning PID controller is applied when the output value is near the desired value. In terms of adjusting the PID gains tuning using fuzzy as to

The physical model of a nonlinear servo electro-hydraulic system is shown in Figure 1.

m

Load

G

 Servo valve Hydraulic Motor

Jt

Jt 

Td

The inertial-damping with a nonlinear torsional spring system is driven by a hydraulic motor and the rotation motion of the motor is controlled by a servo valve. Higher control input voltage can produce larger valve flow from the servo valve and fast rotation motion of

$$K\_q X\_v = D\_m \dot{\theta}\_m + K\_l P\_\perp + \frac{V\_\iota}{4\beta\_\iota} \dot{P}\_\perp \tag{4}$$

where *Kl=Kc+Cl* is the total leakage coefficient of the hydraulic system.

The torque balance equation for the motor is described as follows:

$$P\_{\perp}D\_{\boldsymbol{m}} = f\_{\boldsymbol{\iota}}\ddot{\boldsymbol{\theta}}\_{\boldsymbol{m}} + B\_{\boldsymbol{m}}\dot{\boldsymbol{\theta}}\_{\boldsymbol{m}} + G(\boldsymbol{\theta}\_{\boldsymbol{m}} + G\_{\boldsymbol{m}}\boldsymbol{\theta}\_{\boldsymbol{m}}^{3}) + T\_{\boldsymbol{\iota}}\tag{5}$$

where *Jt* is the total inertial of motor and load, *Bm* is the viscous damping coefficient of the load, *Td* is the disturbance of the system, and 3 *Gn m* is the nonlinear stiffness of the spring.

From (1) to (5), the hydraulic servomechanism system equation can be described by a state equation as follows:

$$\begin{aligned} \dot{X}\_1 &= X\_2\\ \dot{X}\_2 &= X\_3\\ \dot{X}\_3 &= -\sum\_{i=1}^3 a\_i X\_i + b\mathcal{U} - N(X, t) - d(t) \\ \dot{Z} &= r - X\_1 \end{aligned} \tag{6}$$

where

$$\begin{aligned} X(t) &= \left[X\_1(t)X\_2(t)X\_3(t)\right]^\top = \left[\theta\_n(t)\dot{\theta}\_n(t)\ddot{\theta}\_n(t)\right]^\top\\ a\_1(t) &= \frac{4\mathcal{J}\_c}{V\_.}\frac{K\_v}{I\_.}G\\ a\_2(t) &= \frac{4\mathcal{J}\_c}{V\_.}\frac{D\_v^2}{I\_.} + \frac{4\mathcal{J}\_c}{V\_.}\frac{K\_w}{I\_.}B\_w + \frac{G}{I\_.}\\ a\_3(t) &= \frac{4\mathcal{J}\_c}{V\_.}K\_\alpha + \frac{B\_w}{I\_.}\\ b(X) &= \frac{4\mathcal{J}\_c}{V\_.}\frac{D\_w}{I\_.}K\_\circ K\_V\\ N(x,t) &= \frac{4\mathcal{J}\_cK\_wG\_\pi}{V\_.I\_.}GX\_i^3 + \frac{3G\_v}{I\_.}GX\_i^2X\_2\\ d(t) &= \frac{4\mathcal{J}\_c}{V\_.}\frac{K\_v}{I\_.}T\_i + \frac{1}{I\_.}T\_i\end{aligned}$$

A Hybrid of Fuzzy and Fuzzy Self-Tuning PID Controller for Servo Electro-Hydraulic System 303

nominal flow rate 60l/min (at pN = 6.9 bar/control edge), nominal current 1600 mA, repeatability < 1%, hysteresis <5%

resolutions 16 bits (output range 10V), 833 kS/s (6 s full-

Servo Valve

Motor & Sensor

?

**0 . 00 Ba r**

Max. Speed 1000 rpm, Max. torque 25Nm

V, dither frequency 200 Hz, max power 45W.

Elements Descriptions

Max. pressure drop 100bar Max. oil flow 20l/min Proportional valve directly actuated spool valve, grade of filtration 10 m,

Amplifier card set point values 5 VDC, solenoid outputs (PWM signal) 24

DAQ Card NI 6221 PCI analog input resolutions 16 bits (input range 10V), output

Windows XP, and LabVIEW 8.6

A closed loop system, whither the reference signal is set manually or automatically, can perform control of motor speed. Figure 3 represents typical of an "Automatic Closed Loop" control system. As shown in the figure, the velocity of a hydraulic motor is controlled by a servo valve. The servo valve solenoid is receiving driving electrical current from an amplifier card, which is generating the driving current based on a control signal supplied by a controller. The controller responsibility is to continuously compare the reference signal and the actual motor speed feedback by the velocity sensor, after consequently generate the

**Figure 3.** Block diagram of using a hybrid fuzzy and fuzzy self-tuning PID controls the SEHS.

Power Supply Power Unit

Amplifier

Hydraulic Motor Geometric displacement 19.9 cm3

Encoder 8 c/t, I(optical shaft encoder)

Hybrid of Fuzzy and Fuzzy selftuning PID Controller

DAC Resolution 15 bit DAC, output 0-10V

scale settling)

Pump (supply pressure) 100 bar

Operating systems &

**Table 1.** Specifications of the SEHS.

**4. Controller designs** 

adequate control signal.

Program

in which *N(X,t)* represents the nonlinear terms of the system.

## **3. System descriptions**

We are considering a PC-based speed control of the SEHS that will use either a hybrid fuzzy PID or a hybrid of fuzzy and fuzzy self-tuning PID controller. The motor speed of this system is controlled. In order to construct fair test case for comparing both controllers, the experiments are constructed based on the same hardware elements. The specifications of this system are depicted in Table 1 and Figure 2 respectively.

**Figure 2.** Experimental Setup.


**Table 1.** Specifications of the SEHS.

## **4. Controller designs**

302 Fuzzy Controllers – Recent Advances in Theory and Applications

1

<sup>4</sup> ( )

*<sup>K</sup> at G V J*

<sup>4</sup> ( )

<sup>4</sup> ( )

in which *N(X,t)* represents the nonlinear terms of the system.

this system are depicted in Table 1 and Figure 2 respectively.

**3. System descriptions** 

**Figure 2.** Experimental Setup.

2

3

123

() () () () () () ()

*Xt X tX tX t t t t*

*m*

*e lt n n t t t*

*d d tt t*

We are considering a PC-based speed control of the SEHS that will use either a hybrid fuzzy PID or a hybrid of fuzzy and fuzzy self-tuning PID controller. The motor speed of this system is controlled. In order to construct fair test case for comparing both controllers, the experiments are constructed based on the same hardware elements. The specifications of

*KG G Nxt GX GX X VJ J*

*T T mmm*

3 2 1 1 2

2

*e m lt t t e m*

*e m e lt*

 

*D K <sup>G</sup> a t <sup>B</sup> VJ VJ J*

*q V*

4 3 ( ,)

<sup>4</sup> <sup>1</sup> ( )

*e lt*

*<sup>K</sup> dt T T VJ J*

*t t tt t*

*e lt t t*

4 4 ( )

*<sup>B</sup> at K V J*

*<sup>D</sup> bX KK V J*

*t t*

where

A closed loop system, whither the reference signal is set manually or automatically, can perform control of motor speed. Figure 3 represents typical of an "Automatic Closed Loop" control system. As shown in the figure, the velocity of a hydraulic motor is controlled by a servo valve. The servo valve solenoid is receiving driving electrical current from an amplifier card, which is generating the driving current based on a control signal supplied by a controller. The controller responsibility is to continuously compare the reference signal and the actual motor speed feedback by the velocity sensor, after consequently generate the adequate control signal.

**Figure 3.** Block diagram of using a hybrid fuzzy and fuzzy self-tuning PID controls the SEHS.

There are various types of control system used in classical control, modern control and intelligent control systems, each having been studied and implemented in many industrial applications. Every control system method has its advantages and disadvantages. Therefore, the trend is to implement hybrid systems consisting of more than one type of control technique.

## **4.1. PID controller**

The PID control method has been widely used in industry during last several decades because of its simplicity. The implementation of PID control, as shown in (7), requires finding suitable values for the gain parameters *KP*, *KI*, and *KD*. To tune these parameters, the model is linearized around different equilibrium points,

$$u(k) = K\_{\
u} e(k) + K\_{\
u} \sum\_{i=0}^{k} e(i) + K\_{\rm D} \left[ e(k) - e(k-1) \right] \tag{7}$$

A Hybrid of Fuzzy and Fuzzy Self-Tuning PID Controller for Servo Electro-Hydraulic System 305

*e)* is presented as

Figure 5 & 6 show a schematic diagram of a fuzzy control system. Input variables go through the fuzzification interface and are converted to linguistic variables. Then, a database and rule base holding the decision-making logic are used to infer the fuzzy output. Finally, a defuzzification method converts the fuzzy output into a signal to be sent out.

First, the two input variables must be defined in terms of linguistics. The error *(e)* in velocity is expressed by a number in the interval from -10 to 10. There are five linguistic terms of the error in velocity: negative big (NB), negative (N), zero (Z), positive (P), and positive big (PB).

{NB, N, Z, P, PB} over the interval from -10 to 10V. Finally, the fuzzy set of the output signal

FC SEHS

e u yp

The knowledge base for a fuzzy controller consists of a rule base and membership functions. It is reasonable to present these linguistic terms by triangular-shape membership functions, as shown in Figure 6. A fuzzy control knowledge base must be developed that uses the linguistic description of the input variable. In this paper, an expert's experience and knowledge method is used to build a rule base (Zhang *et a*l, 2004). The rule base consists of a set of linguistic IF-THEN rules containing two antecedences and one consequence, as

The decision-making output can be obtained using a max-min fuzzy inference where the

NB NB NB N N Z N NB N N Z P Z N N Z P P P N Z P P PB PB Z P P PB PB

NB N Z P PB

, , <sup>i</sup> <sup>j</sup> k : IF e A e B THEN u C , *Rijk and* (8)

 *5*. The total number of IF-THEN rules is 25 and is

Similarly, the fuzzy set of the error change of the velocity or acceleration *(*

e

is presented as {NB, N, Z, P, PB} over the interval from -5 to 5V.

ym 

 *5*, and *1* 

 e e

 *k* 

crisp output is calculated by the center of gravity (COG) method.

represented in matrix form, called a fuzzy rule matrix, as shown in Table 2.

**Figure 6.** Block digram of a FC.

expressed in the following form:

where *1* 

 *i 5*, *1 j* 

**Table 2.** Fuzzy Rules of a FC.

where *e(k)* is the error signal.

**Figure 4.** Block diagram of a PID controller.

However, the PID method is not suitable for controlling a system with a large amount of lag, parameter variations, and uncertainty in the model. Thus, PID control cannot accurately control velocity in a SEHS (Rong-Fong Fung *et al*, 1997; Aliyari *et al*, 2007).

#### **4.2. Fuzzy controller**

Fuzzy Control (FC) has the advantage that it does not require an accurate mathematical model of the process. It uses a set of artificial rules in a decision-making table and calculates an output based on the table (Aliyari *et al*, 2007; Panichkun & Ngaechroenkul, 2000).

**Figure 5.** Structure of FC.

Figure 5 & 6 show a schematic diagram of a fuzzy control system. Input variables go through the fuzzification interface and are converted to linguistic variables. Then, a database and rule base holding the decision-making logic are used to infer the fuzzy output. Finally, a defuzzification method converts the fuzzy output into a signal to be sent out.

First, the two input variables must be defined in terms of linguistics. The error *(e)* in velocity is expressed by a number in the interval from -10 to 10. There are five linguistic terms of the error in velocity: negative big (NB), negative (N), zero (Z), positive (P), and positive big (PB). Similarly, the fuzzy set of the error change of the velocity or acceleration *(e)* is presented as {NB, N, Z, P, PB} over the interval from -10 to 10V. Finally, the fuzzy set of the output signal is presented as {NB, N, Z, P, PB} over the interval from -5 to 5V.

**Figure 6.** Block digram of a FC.

304 Fuzzy Controllers – Recent Advances in Theory and Applications

model is linearized around different equilibrium points,

technique.

**4.1. PID controller** 

where *e(k)* is the error signal.

**Figure 4.** Block diagram of a PID controller.

ym

**4.2. Fuzzy controller** 

**Figure 5.** Structure of FC.

There are various types of control system used in classical control, modern control and intelligent control systems, each having been studied and implemented in many industrial applications. Every control system method has its advantages and disadvantages. Therefore, the trend is to implement hybrid systems consisting of more than one type of control

The PID control method has been widely used in industry during last several decades because of its simplicity. The implementation of PID control, as shown in (7), requires finding suitable values for the gain parameters *KP*, *KI*, and *KD*. To tune these parameters, the

> 0 ( ) ( ) ( ) ( ) ( 1) *<sup>P</sup> k*

PID SEHS

KP, KI, KD

e u yp

*I D i uk Kek K ei K ek ek* 

However, the PID method is not suitable for controlling a system with a large amount of lag, parameter variations, and uncertainty in the model. Thus, PID control cannot accurately

Fuzzy Control (FC) has the advantage that it does not require an accurate mathematical model of the process. It uses a set of artificial rules in a decision-making table and calculates

Knowledge

Rule base Database

In Out Fuzzification Inference Engine Defuzzification

an output based on the table (Aliyari *et al*, 2007; Panichkun & Ngaechroenkul, 2000).

control velocity in a SEHS (Rong-Fong Fung *et al*, 1997; Aliyari *et al*, 2007).

(7)

The knowledge base for a fuzzy controller consists of a rule base and membership functions. It is reasonable to present these linguistic terms by triangular-shape membership functions, as shown in Figure 6. A fuzzy control knowledge base must be developed that uses the linguistic description of the input variable. In this paper, an expert's experience and knowledge method is used to build a rule base (Zhang *et a*l, 2004). The rule base consists of a set of linguistic IF-THEN rules containing two antecedences and one consequence, as expressed in the following form:

$$R\_{i,j,k} \quad \text{: IF } \mathbf{e} = \mathbf{A}\_i \text{ and } \Delta \mathbf{e} = \mathbf{B}\_j \text{ THEN } \mathbf{u} = \mathbf{C}\_{k'} \tag{8}$$

where *1 i 5*, *1 j 5*, and *1 k 5*. The total number of IF-THEN rules is 25 and is represented in matrix form, called a fuzzy rule matrix, as shown in Table 2.

The decision-making output can be obtained using a max-min fuzzy inference where the crisp output is calculated by the center of gravity (COG) method.


**Table 2.** Fuzzy Rules of a FC.

A Hybrid of Fuzzy and Fuzzy Self-Tuning PID Controller for Servo Electro-Hydraulic System 307

is the derivation of error. The PID parameters are tuned

SEHS

yp

u

of error to PID

, and

*<sup>D</sup>* respectively. Mamdani

Fuzzy self-tuning PID controller means that the tree parameters *KP*, *KI*, and *KD* of PID controller are tuned by using fuzzy tuner (Zhang *et al*, 2004; Song & Liu, 2010; Zulfatman & Rahmat, 2006; Feng *et al*, 2009). The coefficients of the conventional PID controller are not often property tuned for the nonlinear plant with unpredictable parameter variations. Hence, it is necessary to automatically tune the PID parameters. The structure of the fuzzy self-tuning PID controller is shown in Figure 10. Where *e* is the error between desired

FC

Fuzzy Controller

PID

PID Controller

e

**Figure 10.** Block diagram of a fuzzy self-tuning PID controller.

there outputs for each PID controller parameter *K*

can be calibrated over the interval [0,1] as follows:

by using fuzzy tuner, which provide a nonlinear mapping from *e* and *e*

Regarding to the fuzzy structure, there are two inputs to fuzzy inference: *e* and *e*

PID

e Fuzzy tuner

Set-point Output

KP KI KD

model is applied as structure of fuzzy inference with some modification to obtain the optimum value for *KP*, *KI*, and *KD*. Suppose the variable ranges of the parameters of PID controller are [*KPmin, KPmax*], [*KImin, KImax*], and [*KDmin, KDmax*] respectively. The range of each parameters was determined based on the experimental on PID controls the SEHS. The range of each parameters are, *KP*[8,15], *KI*[0.003,0.01], and *KD*[0.0001,0.000001]. Therefore, they

*P*, *KI*, and *K*

Controller SEHS

**Figure 9.** Block diagram of a hybrid fuzzy PID controller.

e

ym

?ee <sup>0</sup>

Selector

**4.4. Fuzzy self-tuning PID controller** 

velocity set point and the output, *e*

parameters.

**Figure 7.** Fuzzy sets of a FC.

**Figure 8.** Input-output mapping of a FC.

## **4.3. Hybrid of fuzzy and PID controller**

While conventional PID controllers are sensitive to variations in the system parameters, fuzzy controllers do not need precise information about the system variables in order to be effective. However, PID controllers are better able to control and minimize the steady state error of the system. Hence, a hybrid system, as shown in figure 9, was developed to utilize the advantages of both PID controller and fuzzy controller (Parnichkul & Ngaecharoenkul, 2000; Erenoglu *et al*., 2006; Pratumsuwan *et al*., 2009;).

Figure 9 shows a switch between the fuzzy controller and the PID controller, where the position of the switch depends on the error between the actual value and set point value. If the error in velocity reaches a value higher than that of the threshold *e0*, the hybrid system applies the fuzzy controller, which has a fast rise time and a small amount of overshoot, to the system in order to correct the velocity with respect to the set point. When the velocity is below the threshold *e0* or close to the set point, the hybrid system shifts control to the PID, which has better accuracy near the set velocity (Parnichkul & Ngaecharoenkul, 2000; Erenoglu *et al*., 2006; Pratumsuwan *et al*., 2009;).

**Figure 9.** Block diagram of a hybrid fuzzy PID controller.

#### **4.4. Fuzzy self-tuning PID controller**

306 Fuzzy Controllers – Recent Advances in Theory and Applications

0

1

1

0

1

0

10

0

Out

put


10

0


NB N Z P PB -10 -4 -2 0 2 4 10


NB N Z PB P

NB N Z PB P

e

e

Output (u)

10

**Figure 7.** Fuzzy sets of a FC.

**Figure 8.** Input-output mapping of a FC.

**4.3. Hybrid of fuzzy and PID controller** 

2000; Erenoglu *et al*., 2006; Pratumsuwan *et al*., 2009;).

Erenoglu *et al*., 2006; Pratumsuwan *et al*., 2009;).

While conventional PID controllers are sensitive to variations in the system parameters, fuzzy controllers do not need precise information about the system variables in order to be effective. However, PID controllers are better able to control and minimize the steady state error of the system. Hence, a hybrid system, as shown in figure 9, was developed to utilize the advantages of both PID controller and fuzzy controller (Parnichkul & Ngaecharoenkul,


<sup>e</sup> <sup>e</sup>

0

Figure 9 shows a switch between the fuzzy controller and the PID controller, where the position of the switch depends on the error between the actual value and set point value. If the error in velocity reaches a value higher than that of the threshold *e0*, the hybrid system applies the fuzzy controller, which has a fast rise time and a small amount of overshoot, to the system in order to correct the velocity with respect to the set point. When the velocity is below the threshold *e0* or close to the set point, the hybrid system shifts control to the PID, which has better accuracy near the set velocity (Parnichkul & Ngaecharoenkul, 2000; Fuzzy self-tuning PID controller means that the tree parameters *KP*, *KI*, and *KD* of PID controller are tuned by using fuzzy tuner (Zhang *et al*, 2004; Song & Liu, 2010; Zulfatman & Rahmat, 2006; Feng *et al*, 2009). The coefficients of the conventional PID controller are not often property tuned for the nonlinear plant with unpredictable parameter variations. Hence, it is necessary to automatically tune the PID parameters. The structure of the fuzzy self-tuning PID controller is shown in Figure 10. Where *e* is the error between desired velocity set point and the output, *e* is the derivation of error. The PID parameters are tuned by using fuzzy tuner, which provide a nonlinear mapping from *e* and *e* of error to PID parameters.

**Figure 10.** Block diagram of a fuzzy self-tuning PID controller.

Regarding to the fuzzy structure, there are two inputs to fuzzy inference: *e* and *e* , and there outputs for each PID controller parameter *KP*, *KI*, and *K<sup>D</sup>* respectively. Mamdani model is applied as structure of fuzzy inference with some modification to obtain the optimum value for *KP*, *KI*, and *KD*. Suppose the variable ranges of the parameters of PID controller are [*KPmin, KPmax*], [*KImin, KImax*], and [*KDmin, KDmax*] respectively. The range of each parameters was determined based on the experimental on PID controls the SEHS. The range of each parameters are, *KP*[8,15], *KI*[0.003,0.01], and *KD*[0.0001,0.000001]. Therefore, they can be calibrated over the interval [0,1] as follows:

$$\begin{aligned} K\_{\rho}' &= \frac{K\_{\rho} - K\_{p\_{\min}}}{K\_{p\_{\max}} - K\_{p\_{\min}}} = \frac{K\_{\rho} - 8}{15 - 8}, K\_{\rho} = 7K\_{\rho}' + 8\\ K\_{\iota}' &= \frac{K\_{\iota} - K\_{\min}}{K\_{\max} - K\_{\min}} = \frac{K\_{\iota} - 0.003}{0.01 - 0.003}, K\_{\iota} = 0.007K\_{\iota}' + 0.003\\ K\_{\Box}' &= \frac{K\_{\Box} - K\_{\Box\min}}{K\_{\Box\max} - K\_{\Box\min}} = \frac{K\_{\Box} - 0.0000001}{0.000001 - 0.000001}, K\_{\Box} = 0.0000009 K\_{\Box}' + 0.0000001 \end{aligned}$$

A Hybrid of Fuzzy and Fuzzy Self-Tuning PID Controller for Servo Electro-Hydraulic System 309

Output KP

Output KI

Output KD

e

e

**Figure 11.** Fuzzy sets of a fuzzy self-tuning PID controller.

.0003

1E-6

1

0

1

0

1

0

1

0

1

0

all of these described in section 4.1, 4.2, 4.3, and 4.4.

Set-point

**Figure 12.** Block diagram of a fuzzy self-tuning PID controller.

Fuzzy Controller SEHS

Select

Output

PID Controller

KP KI KD

?ee <sup>0</sup>

Fuzzy tuner

**4.5. Hybrid of fuzzy and fuzzy self-tuning PID controller** 

A hybrid of fuzzy and fuzzy self-tuning PID controller, as shown in Figure 12, was developed to combine the advantages of both fuzzy and PID controller together. In addition, the adjustment gain of PID with a fuzzy tuner is included to purposed controller also, which

NB N Z P PB


NB N PB Z P


N PB Z P NB

11 10 9 8 12 13 14 15

NB N Z P PB

NB N Z P PB

.002 .004 .006 .008 .01

2E-6 4E-6 6E-6 8E-6 1E-5

The membership functions of these inputs fuzzy sets are shown in Figure 8. The linguistic variable levels are assigned as: negative big (NB), negative (N), zero (Z), positive (P), and positive big (PB). Similarly, the fuzzy set of the error change of the velocity or acceleration *(e)* is presented as {NB, N, Z, P, PB}. These levels are chosen from the characteristics and specification of the SEHS. The ranges of these inputs are from -10 to 10. Finally, whereas the membership functions of outputs *KP*, *KI*, and *K<sup>D</sup>* are shown in Fig. 8. The linguistic levels of these outputs are assigned as: negative big (NB), negative (N), zero (Z), positive (P), and positive big (PB) similarly where the ranges from 0 to 1.


**Table 3.** Fuzzy Rules of KP Gain.


**Table 4.** Fuzzy Rules of KI Gain.


**Table 5.** Fuzzy Rules of KD Gain.

**Figure 11.** Fuzzy sets of a fuzzy self-tuning PID controller.

*P P*

*K K*

*K K*

*ax in*

*D D*

*K K*

membership functions of outputs *K*

**Table 3.** Fuzzy Rules of KP Gain.

**Table 4.** Fuzzy Rules of KI Gain.

**Table 5.** Fuzzy Rules of KD Gain.

*(*

min max min Im Im Im

*PP P P P P*

*KK K <sup>K</sup> K K*

<sup>8</sup> ,78 15 8

0.00001 0.000001

*D D D*

*KK K <sup>K</sup> K K*

*I I I*

*P*, *KI*, and *K*

*K K <sup>K</sup> <sup>K</sup> K K*

0.003 , 0.007 0.003 0.01 0.003

The membership functions of these inputs fuzzy sets are shown in Figure 8. The linguistic variable levels are assigned as: negative big (NB), negative (N), zero (Z), positive (P), and positive big (PB). Similarly, the fuzzy set of the error change of the velocity or acceleration

*e)* is presented as {NB, N, Z, P, PB}. These levels are chosen from the characteristics and specification of the SEHS. The ranges of these inputs are from -10 to 10. Finally, whereas the

these outputs are assigned as: negative big (NB), negative (N), zero (Z), positive (P), and

 NB N Z P PB NB NB NB NB N Z N NB N N N Z Z NB N Z P PB P Z P P P PB PB Z P PB PB PB

 NB N Z P PB NB PB PB PB N NB N PB P P Z NB Z P P Z N NB P Z P N N NB PB Z N NB NB NB

 NB N Z P PB NB NB NB NB P PB N NB N N Z PB Z N N Z P PB P Z N P P PB PB Z P PB PB PB

0.000001 , 0.0000009 0.000001

*<sup>D</sup>* are shown in Fig. 8. The linguistic levels of

min max min

positive big (PB) similarly where the ranges from 0 to 1.

*D D D*

*I in I*

#### **4.5. Hybrid of fuzzy and fuzzy self-tuning PID controller**

A hybrid of fuzzy and fuzzy self-tuning PID controller, as shown in Figure 12, was developed to combine the advantages of both fuzzy and PID controller together. In addition, the adjustment gain of PID with a fuzzy tuner is included to purposed controller also, which all of these described in section 4.1, 4.2, 4.3, and 4.4.

**Figure 12.** Block diagram of a fuzzy self-tuning PID controller.

## **5. The experimental results**

The effectiveness of the proposed hybrid of fuzzy and fuzzy-tune PID controller is evaluated experimentally with the SEHS and is compared with that of the hybrid fuzzy PID controller which uses the nominal values of the gains obtained by experiment. The control algorithms described in section 4.1, 4.2, 4.3, and 4.4 were hybridized and applied to the SEHS using by LabVIEW program as the development platform and shown in Figure 13.

A Hybrid of Fuzzy and Fuzzy Self-Tuning PID Controller for Servo Electro-Hydraulic System 311

fuzzy and PID controller. This is because the proposed controller does not require to adjustment the new parameters of PID controller although the parameters of the SEHS will

**Figure 14.** Comparison of the results of the five controls when the pressure was set at 50 bar

Error

. . 100 *<sup>O</sup> v*

0 -100 99.552 0.022 0 0.325 0.2 0.525

Rise time (Tr)(s)

Time delay (Td)(s) Settling Time (Ts)(s)

*<sup>M</sup> P O <sup>F</sup>* % Overshoot

PID 0 -100 99.932 0.003 0 0.675 0.25 2.15 Fuzzy 0 -100 99.919 0.004 0 0.325 0.25 0.5

Fuzzy PID 0 -100 99.952 0.002 0 0.325 0.25 2.6

tuning PID 0 -100 99.860 0.006 0 0.25 0.2 0.525

**Table 6.** Comparison of the results of the five controls when the pressure was set at 50 bar.

Results

Velocity (rpm) Output

change.

Controller Velocity

Hybrid

Hybrid Fuzzy and Fuzzy selftuning PID

Fuzzy Self-

(rpm)

**Figure 13.** The control algorithms are developed by LabVIEW program.

The proposed of a hybrid of fuzzy and fuzzy self-tuning PID controller is evaluated experimentally with the motor speed control of SEHS and is compared with that of the conventional of a hybrid of fuzzy and PID controller. For the first experiment to observe the response of the SEHS control output of the both controller, which shown in Figure. 14 and Table 6, respectively. Then, change the parameters of the SEHS, because existing experimental set is difficult to change the load so that this change in pressure of the SEHS instead. The change in pressure will make many values, but the parameters of the both controller still use the original setting from the previous first. Figure 14, Table 6, and Figure 15, Table 7 show examples of the responses of the output of the both controller, which resulted from changing the original value of system pressure are 50 bar and 10 bar pressure. However, all these experiments the value of *e0* which is used as a reference in the selection of a controller is set at 0.92 that is the optimum value from experiment.

When the experiment has changed the parameters of the SEHS will find that the hybrid of fuzzy and fuzzy self-tuning PID would lead to a satisfactory response over the hybrid of fuzzy and PID controller. This is because the proposed controller does not require to adjustment the new parameters of PID controller although the parameters of the SEHS will change.

310 Fuzzy Controllers – Recent Advances in Theory and Applications

**Figure 13.** The control algorithms are developed by LabVIEW program.

experiment.

The proposed of a hybrid of fuzzy and fuzzy self-tuning PID controller is evaluated experimentally with the motor speed control of SEHS and is compared with that of the conventional of a hybrid of fuzzy and PID controller. For the first experiment to observe the response of the SEHS control output of the both controller, which shown in Figure. 14 and Table 6, respectively. Then, change the parameters of the SEHS, because existing experimental set is difficult to change the load so that this change in pressure of the SEHS instead. The change in pressure will make many values, but the parameters of the both controller still use the original setting from the previous first. Figure 14, Table 6, and Figure 15, Table 7 show examples of the responses of the output of the both controller, which resulted from changing the original value of system pressure are 50 bar and 10 bar pressure. However, all these experiments the value of *e0* which is used as a reference in the selection of a controller is set at 0.92 that is the optimum value from

When the experiment has changed the parameters of the SEHS will find that the hybrid of fuzzy and fuzzy self-tuning PID would lead to a satisfactory response over the hybrid of

The effectiveness of the proposed hybrid of fuzzy and fuzzy-tune PID controller is evaluated experimentally with the SEHS and is compared with that of the hybrid fuzzy PID controller which uses the nominal values of the gains obtained by experiment. The control algorithms described in section 4.1, 4.2, 4.3, and 4.4 were hybridized and applied to the SEHS using by LabVIEW program as the development platform and shown in Figure 13.

**5. The experimental results** 

**Figure 14.** Comparison of the results of the five controls when the pressure was set at 50 bar


**Table 6.** Comparison of the results of the five controls when the pressure was set at 50 bar.

A Hybrid of Fuzzy and Fuzzy Self-Tuning PID Controller for Servo Electro-Hydraulic System 313

optimum value. We demonstrate the performance of control scheme via experiments performed on the motor speed control of the SEHS. The results from the experiments show that the proposed a hybrid of fuzzy and fuzzy self-tuning PID controller has superior performance compared to a hybrid of fuzzy and PID controller. This is because the proposed controller does not require to readjustment the parameters of PID controller

The authors would like to thank USE FLO-LINE Co., Ltd. and mechatronics educational

Rong-Fong Fung, Yun-Chen Wang, Rong-Tai Yang, and Hsing-Hsin Huang., "A variable structure control with proportional and integral compensatios for electrohydraulic

M. Aliyari, Shoorehdeli, M. Teshnehlab, and Aliyari Shoorehdeli., "Velocity control of an

Parnichkun, M. and C. Ngaecharoenkul., "Hybrid of fuzzy and PID in kinematics of a pneumatic system," Proceeding of the 26th Annual Conference of the IEEE Industrial

Pornjit Pratumsuwan, Siripun Thongchai, and Surapan Tansriwong., "A Hybrid of Fuzzy and Proportional-Integral-Derivative Controller for Electro-Hydraulic Position Servo

Jianming Zhang, Ning Wang, and Shuqing Wang., "Developed method of tuning PID controllers with fuzzy rules for integrating processes," Proceeding of the 2004 American

Shoujun Song and Weiguo Liu.,"Fuzzy parameters self-tuning PID control of switched reluctance motor based on Simulink/NCD," CIMCA-IAWTIC'06, IEEE, 2006. Zulfatman and M.F. Rahmat.., "Application of self-tuning fuzzy PID controller on industrial hydraulic actuator using system identification approach," International journal on

research group for their equipments and technical support of this research project.

position servo control system," Mechatronics vol.7, no. 1, 1997, pp. 67-81.

Merrit, H.E., "Hydraulic Control System"*.* John Wiley, New York, 1976.

electro hydraulic servosystem," IEEE, 2007, pp. 1536-1539.

System" Energy Research Journal, vol. 1,issue 2, 2010, pp. 62–67.

amart sensing and intelligent system, vol. 2, no. 2, 2009, pp. 246-261.

control Conference, Massachusetts, 2004, pp. 1109-1114.

Electronics Society, Japan, 2000, pp: 1485-1490.

although the parameters of the SEHS will change any.

*Rajamangala University of Technology, Rattanakosin, Thailand* 

*King Mongkut's University of Technology North Bangkok, Thailand* 

Watcharin Po-ngaen and Pornjit Pratumsuwan

Kwanchai Sinthipsomboon, Issaree Hunsacharoonroj and Josept Khedari,

**Author details** 

**Acknowledgement** 

**7. References** 

**Figure 15.** Comparison of the results of the five controls when the pressure was set at 10 bar


**Table 7.** Comparison of the results of the five controls when the pressure was set at 10 bar.

## **6. Conclusions**

The objective of this study, we proposed the hybrid of fuzzy and fuzzy self-tuning PID controller for motor speed control of a SEHS. The proposed control scheme is separated into two parts, fuzzy controller and fuzzy self-tuning PID controller. Fuzzy controller is used to control systems when the output value of system far away from the target value. Fuzzy selftuning PID controller is applied when the output value is near the desired value. In the terms of adjusting the PID parameters are tuned by using fuzzy tuner as to obtain the optimum value. We demonstrate the performance of control scheme via experiments performed on the motor speed control of the SEHS. The results from the experiments show that the proposed a hybrid of fuzzy and fuzzy self-tuning PID controller has superior performance compared to a hybrid of fuzzy and PID controller. This is because the proposed controller does not require to readjustment the parameters of PID controller although the parameters of the SEHS will change any.

## **Author details**

312 Fuzzy Controllers – Recent Advances in Theory and Applications

Controller Velocity

Hybrid

Hybrid Fuzzy and Fuzzy selftuning PID

Fuzzy Self-

**6. Conclusions** 

(rpm)

**Figure 15.** Comparison of the results of the five controls when the pressure was set at 10 bar

Error

. . 100 *<sup>O</sup> v*

0 -100 99.847 0.007 0 1 0.4 1.8

Rise time (Tr)(s)

Time delay (Td)(s) Settling Time (Ts)(s)

*<sup>M</sup> P O <sup>F</sup>* % Overshoot

PID 0 -100 99.697 0.015 2.5 0.875 0.55 2.45 Fuzzy 0 -100 99.874 0.006 0 1 0.7 1.7

Fuzzy PID 0 -100 99.889 0.001 3 1 0.7 3.05

tuning PID 0 -100 99.513 0.024 0 0.825 0.55 2.6

The objective of this study, we proposed the hybrid of fuzzy and fuzzy self-tuning PID controller for motor speed control of a SEHS. The proposed control scheme is separated into two parts, fuzzy controller and fuzzy self-tuning PID controller. Fuzzy controller is used to control systems when the output value of system far away from the target value. Fuzzy selftuning PID controller is applied when the output value is near the desired value. In the terms of adjusting the PID parameters are tuned by using fuzzy tuner as to obtain the

**Table 7.** Comparison of the results of the five controls when the pressure was set at 10 bar.

Results

Velocity (rpm) Output

Kwanchai Sinthipsomboon, Issaree Hunsacharoonroj and Josept Khedari, *Rajamangala University of Technology, Rattanakosin, Thailand* 

Watcharin Po-ngaen and Pornjit Pratumsuwan *King Mongkut's University of Technology North Bangkok, Thailand* 

## **Acknowledgement**

The authors would like to thank USE FLO-LINE Co., Ltd. and mechatronics educational research group for their equipments and technical support of this research project.

## **7. References**

Merrit, H.E., "Hydraulic Control System"*.* John Wiley, New York, 1976.

	- Bin Feng, Guofang Gong, and Huayong Yang.,"Self-tuning parameter fuzzy PID temperature control in a large hydraulic system," International Conference on Advanced Intelligent Mechatronics, IEEE/ASME,2009, pp.1418-142

**Chapter 14** 

© 2012 Al Mashhadany, licensee InTech. This is an open access chapter 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.

© 2012 The Author(s). Licensee InTech. 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,

**Design and Simulation of Anfis Controller** 

Fuzzy logic (FL) and artificial neural networks (ANNs), despite their successful use in many challenging control situations, still have drawbacks that limit them to only some applications. Their combined advantages have thus become the subject of much research into ways of overcoming their disadvantages. Neuro-fuzziness is one resulting rapidly emerging field. ANFIS network, proposed by Jang, is one popular neuro-fuzzy system

For specific-problem training of an ANFIS network, [1] proposes use of hybrid learning rule, which combines gradient descent technique and least-square estimator (LSE). Being a method of supervised learning, it needs a teaching signal, which can be difficult to provide when the ANFIS network is to be a feedback controller, as the desired control actions that the teaching signal represents are unknown. Literatures have proposed several ANFIS learning methods in which ANFIS is applied as a MIMO controller. Djukanović *et al.*, for example, uses a special ANFIS learning technique called temporal back propagation (TBP); control of a nonlinear MIMO system is by considering both the controller and the plant as a single unit each time step. The method, however, is complex and distinctly computation-

Another training approach for ANFIS-controller of nonlinear MIMO systems is inverse learning; the ANFIS network is trained to learn the inverse dynamics of the plant it controls. Its success, however, is crucial on three elements: accurate modeling of the original system (a problem when the system is complex), availability of the system's inverse dynamics (they do not always exist), and appropriate distribution of the training data (could be impossible, given the constraints of the system's dynamics). [10-13] has another training approach

and reproduction in any medium, provided the original work is properly cited.

**for Virtual-Reality-Built Manipulator** 

Yousif I. Al Mashhadany

http://dx.doi.org/10.5772/48383

**1. Introduction** 

[1-4].

heavy [5-9].

besides the ones already mentioned.

Additional information is available at the end of the chapter
