Application of adaptive fuzzy control to ac machines

Applied Soft Computing 7 (2007) 899–907 www.elsevier.com/locate/asoc

Application of adaptive fuzzy control to ac machines Hazem N. Nounou *, Habib-ur Rehman 1 College of Engineering, UAE University, P.O. Box 17555, Al-Ain, United Arab Emirates Received 27 October 2004; received in revised form 24 September 2005; accepted 25 February 2006 Available online 5 June 2006

Abstract The decoupled control of torque and flux has made field oriented control an attractive choice for high performance induction motor drives. However, changes in the speed tracking trajectory and external disturbances make it difficult to achieve an acceptable closed-loop tracking performance, especially when traditional linear controllers are used. This paper addresses this issue by applying direct and indirect adaptive fuzzy controllers for performance enhancement of variable speed control of induction machines. Theoretical background of these schemes is outlined, and then a simulation test bench has been established for performance evaluation under a variety of operating conditions. Such conditions include changes in the speed reference trajectory and presence of external disturbances, such as load changes. A comparison has been made among direct adaptive, indirect adaptive, and direct fuzzy controllers to show the potential of applying adaptive fuzzy control techniques to induction machines. # 2006 Elsevier B.V. All rights reserved. Keywords: Fuzzy control; Adaptive fuzzy control; Induction machine

1. Introduction The invention of field oriented control [1] showed that the ac machine drive performance can be comparable to the dc machine drive. The effectiveness of ac induction machine with respect to size, weight, rotor inertia, efficiency, maximum speed, reliability, and cost have made the ac induction machine drives a superior choice over the dc machine drives. Field oriented control can be classified as indirect field oriented (IFO) and direct field oriented (DFO) control [1]. Both of these approaches provide torque control of the induction machine by decoupling the torque and flux. A block diagram for indirect field oriented drive system, whose performance enhancement is the focus of this work, is shown in Fig. 1. The diagram includes two feedback loops to implement the field oriented drive system. The inner loop is a current regulation loop whereas the outer one is a speed regulation loop to accomplish the variable speed control. Traditionally, because of its simplicity, a PI controller is used for both current and speed regulation. However, the performance of PI controller for speed regulation

* Corresponding author. E-mail addresses: [email protected] (H.N. Nounou), [email protected] (H. Rehman). 1 Present address: Department of Electrical Engineering, American University of Sharjah, UAE. 1568-4946/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2006.02.009

degrades under external disturbances and machine parameter variations [2,3]. Parameter adaptation of the ac machine [4–8] is one way to overcome part of the problem outlined above because the external disturbances still remain an issue. Another approach to address the issue is by the use of intelligent controllers like fuzzy logic [9–15], and that is the direction adopted in this work. Intelligent control techniques like fuzzy logic have been explored by several researchers for its potential to improve the speed regulation of the drive system. Fuzzy logic has gained great attention in the area of electromechanical devices due to its ability to incorporate human intuition in the design process. Direct fuzzy and fuzzy model reference learning controllers (FMRLC) have been investigated in refs. [9–15]. The authors in refs. [9–12] explored the potential of direct fuzzy controllers for field oriented drive systems. In refs. [9,10], the authors concluded that fuzzy controllers are capable of improving the tracking performance under external disturbances, or when the IFO drive system experiences imperfect decoupling due to variations in the rotor time constant. Also, the authors in ref. [11] show the effectiveness of fuzzy controllers applied to direct torque-controlled induction motor drives experiencing parameter variations. Moreover, in ref. [12], the authors designed a fuzzy controller for speed regulation, and in ref. [13], the authors used fuzzy systems for rotor time constant identification. Also, it has been

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Nomenclature B dq ia ib ids ids iqr iqs iqs J Lm Lr P r s Tl Tr Vabc Vdc Vds Vqs Vsa Vsb

coefficient of friction synchronous frame of reference phase a current phase b current stator current along d-axis command stator current along d-axis rotor current along q-axis stator current along q-axis command stator current along q-axis moment of inertia of machine magnetizing inductance rotor inductance number of pole pairs rotor stator mechanical load on the rotor shaft rotor time constant three-phase machine voltage dc voltage stator voltage along d-axis stator voltage along q-axis stator voltage along a-axis stator voltage along b-axis

Greek symbols ab stationary frame of reference rotor flux along d-axis ldr ldr command rotor flux along d-axis lqr rotor flux along q-axis ve synchronous speed vr actual rotor speed vr rotor command speed vs command slip speed ue synchronous angle

found in ref. [14] that FMRLC provides a good closed-loop response for an IFO drive system that experiences external disturbances. In ref. [15], an experimental-based comparative performance analysis between direct fuzzy and PI controllers has been presented. In this paper, an attempt have been made to improve the performance of speed regulator by applying direct and indirect adaptive fuzzy controllers presented in ref. [16] for an IFO drive system. It is worth mentioning that the DFO drive system does include the speed regulator as well. Therefore, the work presented in this paper is equally applicable to speed regulation of a DFO drive system. The paper is organized as follows. In Section 2, an IFO drive system is presented. Section 3 highlights some theoretical background on direct and indirect adaptive fuzzy control techniques. Then, in Section 4, a simulation-based comparative study that shows the potential of these techniques is given. The performance of the adaptive controllers is shown when an external load disturbance is

applied. Finally, in Section 5, some concluding remarks are outlined. 2. An IFO induction machine drive system Fig. 1 shows the overall test/simulation system which includes three main components: the control system, the inverter, and finally the device under control which is an induction machine. The control system includes the adaptive fuzzy controller which generates the torque command current to track the command speed. The rest of the control system shows the indirect field orientation [1] for the induction machine. This includes the slip calculator, the angle transformation from the stationary to synchronous, T(u), the synchronous to stationary frame of reference, T1(u), and the three-phase command voltage signal, Vabc, which is sent to the PWM inverter. The inverter then produces the desired voltage which is finally applied to the device under control to track the command speed. This drive system is simulated in this paper using the proposed adaptive fuzzy controller and the results are presented in Section 4. In IFO drive systems, the flux along q-axis, lqr, should be 0 and thus the entire flux will be aligned along the d-axis, and the current ids will control the flux [1]. Under this condition, if the flux is kept constant then the current iqs will control the torque providing a faster dynamic response. This asymptotic decoupling of the torque and flux is guaranteed if and only if the flux along the q-axis is 0, which actually imposes the following slip condition: sve ¼

1 iqs ð1 þ pT˙ r Þ: Tr ids

(1)

This slip is implemented in the slip calculation block of Fig. 1. It guarantees that the controls of flux and torque are decoupled. The speed regulation in this drive system is shown by the outer loop. The speed controller generates a torque command current, iqs , based on the error between the command speed, (vr ), and the actual speed, vr, measured from the encoder shaft. The inner loop is a fast action synchronous current regulation loop which is able to impress the stator currents generated by the controller. The model dynamics for the rotor flux and rotor speed can be represented as: Lm 1 l˙ dr ¼ ids  ldr ; Tr Tr   B P 3PLm vr þ v˙ r ¼ ldr iqs  Tl : J J 2Lr

(2)

Defining the state vector X = [x1, x2]T = [ldr,vr]T and the control command u = iqs, it can be easily verified that the plant dynamics (2) can be expressed by the following single-input single-output continuous-time system: x˙ ¼ AðxÞ þ BðxÞu;

y ¼ CðxÞ;

(3)

where x 2 R2 is the state vector (i.e., the order of the plant, n = 2), u 2 R the input, y ¼ vr ¼ x2 2 R the output of the plant

H.N. Nounou, H. Rehman / Applied Soft Computing 7 (2007) 899–907

901

Fig. 1. Indirect field oriented drive system.

and the functions A(X), BðXÞ 2 R2 , and CðXÞ 2 R are smooth functions. Here, the functions A(x), B(x), and C(x) are defined as: 2

3

1 Lm x þ i 6 Tr 1 Tr ds 7 AðxÞ ¼ 4 5; B P x2  Tl J J " BðxÞ ¼

# 0 3P Lm ; x1 2JLr 2

(4)

(5)

and CðxÞ ¼ x2 :

(6)

It is clear that the system is of relative degree r = 1. Note that r < n (i.e., the relative degree of the system is less than its order), hence it is important to check the zero dynamics of the system [17]. It can be easily verified that the zero dynamics of the system are characterized by: x˙ 1 ¼

1 Lm x1 þ ids : Tr Tr

(7)

It is clear that the zero dynamics of the system are exponentially attractive, and hence the states are ensured to be bounded. It can be shown [16] that the system Eq. (3) can be described by: y˙ ¼ f ðxÞ þ gðxÞu;

(8)

where f(x) and g(x) represent the unknown nonlinear plant dynamics. Here, it is assumed that there exists g0 > 0 such that g(x)  g0, and that x1 and x2 are measurable.

3. Adaptive fuzzy control In the next section, descriptions of direct and indirect adaptive fuzzy control schemes following the ones in ref. [16] are presented. Both of these techniques use adaptive fuzzy approximators to approximate the controller, and both guarantee that the output error decreases at least asymptotically to zero. 3.1. Direct adaptive control The direct adaptive controller considered here seeks to drive the speed of the induction machine y = vr to track a known desired output trajectory ym. Such controller uses an approximator that attempts to approximate the ideal controller dynamics, u*, that is assumed to exist, by adjusting the controller parameters. In additions to the plant assumptions mentioned above, the following plant assumptions are used. Assumption 1. Given y˙ ¼ f ðxÞ þ gðxÞu, we require that there exists positive constants g0 and g1 such that 0 < g0  g(x)  g1 < 1 and some function G(x)  0 such that j˙gðxÞj ¼ j @g ˙ j  GðxÞ for all x 2 Sx. @x x Assumption 2. The desired output trajectory and its derivative (i.e., ym and y˙ m ) are measurable and bounded. Using feedback linearization [18], we know that there exists some ideal controller u ¼

1 ð f ðxÞ þ mðtÞÞ; gðxÞ

(9)

where mðtÞ ¼ y˙ m þ des þ e¯ s , with e¯ s ¼ e˙ s  e˙ o , and d > 0. The tracking error, es, is defined as es = eo, and eo = ym  y, thus e¯ s

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in this case is defined as e¯ s ¼ e˙ s  e˙ o since es = eo. It is also assumed that g(x) is bounded away from zero so that u* in Eq. (9) is well defined. The goal of the adaptive controller is to learn how to control the plant to drive the measure of the tracking error, es, to some neighborhood of zero. We may express u* as:

where

u ¼ uT u z u ðx; mÞ þ du ðxÞ:

 y is bounded;  uˆ d and usd are bounded;  the magnitude of the output error jeoj decreases at least asymptotically to zero.

(10)

The ideal parameter vector, uu , is defined as: uu ¼ arg min ½

sup

uu 2 Vu x 2 Sx ;m 2 Sm

juTu zu ðx; mÞ  u j;

(11)

ksd ðtÞ ¼

GðxÞjes j þ Du ðxÞ 2g20

(20)

will ensure that

The proof can be found in ref. [16].

where uu is assumed to be defined within the compact parameter set Vu, and Sx and Sm  Rn are defined as the spaces through which the state trajectory and the free parameter m(t) may travel under closed-loop control. Also, zu is defined as the partial of the approximator with respect to the parameter vector, and du(x) is the approximation error which arises when u* is represented by an approximator of finite size. It is assumed that jdu(x)j  Du(x), where Du(x) is a known upper bound on the error. Since universal approximators are used for approximation, jdu(x)j may be made arbitrarily small by a proper choice of the approximator structure. To do this, we will require x and m to be available. The ideal control (9) can be approximated by:

In the indirect approach, the plant dynamics f(x) and g(x) are approximated, then the feedback controller uses these estimates of the plant dynamics to adjust the controller parameters so that the plant output, y, tracks the desired output trajectory, ym. The plant dynamics f(x) and g(x) can be expressed as:

uˆ d ¼ uTu zu ;

where

(12)

3.2. Indirect adaptive control

f ðxÞ ¼ uT f z f ðxÞ þ d f ðxÞ;

(21)

gðxÞ ¼ uT g zg ðxÞ þ dg ðxÞ;

(22)

where uu is updated on-line using the following gradient update law:

uf ¼ arg min ½ sup juTf z f ðxÞ  f ðxÞj;

(23)

u˙ u ðtÞ ¼ r1 u z u es ;

ug ¼ arg min ½ sup juTg zg ðxÞ  gðxÞj;

(24)

(13)

where ru is a positive definite adaptation gain. Consider the direct adaptive controller: ud ¼ uˆ d þ usd ;

(14)

where usd is a sliding mode control term that will be defined later. Using the control (14), the second derivative of the output error becomes: e˙ o ¼ y˙ m  y˙ ¼ y˙ m  f ðxÞ  gðxÞðˆud þ usd Þ:

(15)

Using the definition of u* in Eq. (9), we may rearrange Eq. (15) so that e˙ o ¼ y˙ m  f ðxÞ  gðxÞu  gðxÞðˆud  u Þ  gðxÞusd

(16)

e˙ o ¼ des  e¯ s  gðxÞðˆud  u Þ  gðxÞusd :

(17)

We may alternatively express Eq. (17) as: e˙ s þ des ¼ gðxÞðˆud  u Þ  gðxÞusd :

(18)

Next, stability results for the direct adaptive control law are presented.

u f 2 V f x 2 Sx

u f 2 Vg x 2 Sx

The parameter vectors, uf and ug, are assumed to be defined within the compact parameter sets, Vf and Vg, respectively. In addition, we define the subspace Sx  Rn as the space through which the state trajectory may travel under closed-loop control. Also, df (x) and dg(x) are approximation errors which arise when f(x) and g(x) are represented by approximators of finite size. We assume that Df (x)  jdf (x)j, and Dg(x)  jdg(x)j, where Df (x) and Dg(X) are known bounds on the approximation errors. Since universal approximators (e.g., fuzzy systems, neural networks, and others [19]) are used to approximate f(x) and g(x), both jdf (X)j and jdg(X)j may be made arbitrarily small by a proper choice of the approximator if f(x) and g(x) are smooth. It is important to keep in mind that Df (x) and Dg(x) represent the magnitude of error between the actual nonlinear functions describing the system dynamics and the approximators when the ‘‘best’’ parameters are used. We assume that the actual plant dynamics, f(x) and g(x), can be approximated by: ˆ ¼ uT z f ; fðxÞ f

(25)

Theorem 1. Considering the induction machine plant (3) with all of the above assumptions satisfied, then the direct adaptive control law (14) with uˆ d defined in Eq. (12) and usd is defined such that

gˆ ðxÞ ¼ uTg zg ;

(26)

usd ¼ ksd ðtÞ sgnðes Þ

u˙ f ðtÞ ¼ r1 f z f es ;

(19)

where the vectors uf (t) and ug(t) are updated on-line using the following gradient update laws: (27)

H.N. Nounou, H. Rehman / Applied Soft Computing 7 (2007) 899–907

and

4. Simulation results

ˆ i; u˙ g ðtÞ ¼ r1 g z g es u

(28)

where rf and rg are positive definite adaptation gains and uˆ i represents the certainty equivalence control term [20] that is defined as: uˆ i ¼

903

ˆ þ mðtÞ  fðxÞ : gˆ ðxÞ

(29)

Here, mðtÞ ¼ y˙ m þ des þ e¯ s , with es and e¯ s defined as in the direct case, and gˆ ðxÞ is assumed to be bounded away from zero so that Eq. (29) is well defined. Consider the indirect adaptive control law: ui ¼ uˆ i þ usi :

(30)

Using the control law (30), the derivative of the output error becomes e˙ o ¼ y˙ m  y˙ so e˙ o ¼ y˙ m  f ðxÞ 

gðxÞ ˆ þ mðtÞ  gðxÞusi : ½ fðxÞ gˆ ðxÞ

(31)

We may rearrange terms so that

The simulation program which implements the closed-loop system presented in Fig. 1 has been developed using MATLAB software. This program includes the machine model, the inverter model, and the controller. The overall system in this program is realized under the indirect field orientation [1]. The simulation results of direct adaptive, indirect adaptive fuzzy controllers are presented. Also, the results for direct fuzzy controller are included for comparison purposes. 4.1. Direct adaptive approach The direct adaptive fuzzy controller used here has two inputs: the output error and the derivative of the output error. Three Gaussian membership functions are used for each input universe of discourse. The centers of the error and derivative of error membership functions are distributed uniformally over the ranges [3, 3] and [106, 106], respectively. These choices have been made in an attempt to keep the error and the derivative of the error of the closed-loop system within these ranges. The adaptive fuzzy controller has nine rules (R = 9) of the form

ˆ  f ðxÞÞ þ ðˆgðxÞ  gðxÞÞˆui  des  e¯ s  gðxÞusi : e˙ o ¼ ð fðxÞ (32)

j k If e˜ o is A˜ e and e˜˙ o is A˜ de ; then ci ¼ ui;1 eo þ ui;2 e˙ o ;

We may express Eq. (32) as

j where ci is the value of the consequent part of the ith rule, A˜ e is the jth linguistic value on the error universe of discourse, and k A˜ de is the kth linguistic value on the derivative of error universe of discourse. The parameters in the consequent part of the rules are updated using the adaptive law (13). Hence, uˆ d can be defined as:

ˆ  f ðxÞÞ þ ðˆgðxÞ  gðxÞÞˆui  gðxÞusi : e˙ s þ des ¼ ð fðxÞ

(33)

Next, stability results for the indirect adaptive control law are presented. Theorem 2. Considering the induction machine plant (3) with all of the above assumptions satisfied, then the direct adaptive control law (30) with uˆ i defined in Eq. (29) and usi is defined such that usi ¼

ksi ðtÞ sgnðes Þ g0

(34)

where ksi ðtÞ ¼ D f ðxÞ þ Dg ðxÞjˆui j

(35)

will ensure that  y is bounded;  uˆ i and usi are bounded;  the magnitude of the output error jeoj decreases at least asymptotically to zero. The proof can be found in ref. [16]. Theorems 1 and 2 show that the direct and indirect adaptive controllers not only can be applied to the induction machine model (3), but also the controllers can guarantee boundedness of the rotor speed and torque current, and ensure that the speed tracking error asymptotically decreases to zero.

(36)

8 i ¼ 1; 2 . . . ; R:

uˆ d ¼ uTu zu ;

(37)

where zu ¼ ½eo z1 ; eo z2 ; . . . ; eo zR ; e˙ o z1 ; e˙ o z2 ; . . . ; e˙ o zR , uu = [u1,1, u2,1, . . ., uR,1, u1,2, u2,2, . . ., uR,2]T, and zi is the certainty of the ith rule. The parameter vector uu is updated using the adaptive law (13), where r ¼ I 2 RR R (identity matrix). After some fine tuning, the following parameters are selected: g0 = 1, g1 = 2, Du = 0.1, d = 1, and G(x) = 20. To satisfy Assumption 2, the reference input is filtered by the following first-order system: HðsÞ ¼

a : sþb

(38)

where a = 5000 and b = 5000. The controller has been tested subject to several load disturbances, Tl. When no load disturbance is used, the response in Fig. 2 is obtained. The upper plot of this figure shows the speed response relative to the command speed. The middle plot shows the speed error, and the lower plot shows the torque current Iqs. In this case, it has been found that the mean square error (MSE) is 5.0749, where MSE is defined as: Z 1 t¼T 2 e ðtÞ dt (39) MSE ¼ T t¼0

904

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Fig. 2. Direct adaptive fuzzy control when Tl = 0 N m.

where T = 2.25 second is the total time of simulation. Similarly, the closed-loop responses for Tl = 15 N m is shown in Fig. 3. 4.2. Indirect adaptive approach The indirect adaptive fuzzy controller approximates functions f(x) and g(x). Each of these approximators has two inputs: the plant output and the derivative of the plant output. Three Gaussian membership functions are used for each input universe of discourse. The centers of the output and derivative of output membership functions are distributed uniformally over the ranges [500, 500] and [106, 106], respectively.

These choices have been made based on our prior knowledge that the output and the derivative of the output lie within these ranges. Each of the adaptive approximators is a fuzzy system that has nine rules (R = 9) of the form j

k

If y˜ is A˜ y and y˜˙ is A˜ dy ; then ci ¼ ui;1y þ ui;2˙y ;

(40)

8 i ¼ 1; 2; . . . ; R: j where ci is the value of the consequent part of the ith rule, A˜ y is the k jth linguistic value on the output universe of discourse, and A˜ dy is the kth linguistic value on the derivative of output universe of

Fig. 3. Direct adaptive fuzzy control when Tl = 15 N m.

H.N. Nounou, H. Rehman / Applied Soft Computing 7 (2007) 899–907

905

Fig. 4. Indirect adaptive fuzzy control when Tl = 0 N m.

discourse. Hence, fˆ and gˆ can be defined as in Eqs. (25) and (26) where z f ¼ zg ¼ ½yz1 ; yz2 ; . . . ; yzR ; y˙ z1 ; y˙ z2 ; . . . ; y˙ zR , u f ¼ f f f f f f T ½u1;1 ; u2;1 ; . . . ; uR;1 ; u1;2 ; u2;2 ; . . . ; uR;2  , ug ¼ ½ug1;1 ; ug2;1 ; . . . ; g g g g T uR;1 ; u1;2 ; u2;2 ; . . . ; uR;2  , and zi is the certainty of the ith rule. The parameter vectors uf and ug are updated using the adaptive laws (27) and (28), respectively, where rf = 100 I (where I 2 RR R is the identity matrix) and rg = 150 I. After some fine tuning, the following parameters are selected: g0 = 1, g1 = 2, Df = 1, Dg = 0.3, and d = 1. To satisfy Assumption 2, the reference input is filtered by the same first-order system used in the direct case. As in the direct case, the controller has been tested subject to load disturbances. Under no load condition, the

response is shown in Fig. 4. In this case, it has been found that the MSE is 8.798. Similarly, the closed-loop response for full load condition, Tl = 15 N m, is shown in Fig. 5. Just for the sake of comparison, the performance has been tested when nonadaptive direct fuzzy controller is used. The direct fuzzy controller used here has two inputs: the error and the derivative of the error, and eleven triangular membership functions are used for each input universe of discourse. Minimum is used for the premise and implication, and center of gravity defuzzification is used. When such a controller is implemented, it has been found that under no load, the MSE is 11.050. The closed-loop response for this case is shown in Fig. 6. When the load is increased to

Fig. 5. Indirect adaptive fuzzy control when Tl = 15 N m.

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H.N. Nounou, H. Rehman / Applied Soft Computing 7 (2007) 899–907

Fig. 6. Direct fuzzy control when Tl = 0 N m.

Fig. 7. Direct fuzzy control when Tl = 15 N m.

Tl = 15 N m, the closed-loop response is shown in Fig. 7. In this case, the MSE is 42.950, which is much greater than the corresponding ones when direct and indirect adaptive controllers are used. A summary of the MSE for all of the above cases is shown in Table 1. The simulation results from Figs. 2–7 and Table 1 show that all of the fuzzy controllers have a very satisfactory performance for variable speed control of the induction machine. The MSE for both direct and indirect adaptive fuzzy controllers are less than the MSE of the direct fuzzy controller, showing that the proposed adaptive controllers perform better than the direct fuzzy controller. Such performance results are consistent for all load conditions. The pervious work

[9] has already shown that direct fuzzy controller outperformed the PI controller. This means that the adaptive controllers presented in this paper can outperform both PI as well as direct fuzzy controllers. Table 1 MSE summary Controller type

0Nm

5Nm

10 N m

15 N m

Direct adaptive fuzzy Indirect adaptive fuzzy Direct fuzzy

5.0749 8.798 11.050

6.9499 9.949 19.898

9.2125 12.363 30.259

12.0334 14.545 42.950

H.N. Nounou, H. Rehman / Applied Soft Computing 7 (2007) 899–907

5. Conclusion In this paper, the direct and indirect adaptive fuzzy controllers presented in ref. [16] are applied to the IFO induction machine drive system. As a test bench for comparison, the mean squared value of the tracking error over the total simulation time is used. Compared with the direct fuzzy controller, simulation results show that both direct and indirect adaptive fuzzy controllers result in smaller MSE values, and hence a better closed-loop tracking performance under external disturbances, such as load changes. Based on these simulation results, it has been noticed that the performance of the direct adaptive fuzzy controller is better than the performance of the indirect adaptive fuzzy controller. It is worth mentioning that the direct and indirect adaptive controllers can achieve a good performance with only three membership functions, while non-adaptive fuzzy controller is not able to achieve a similar performance even with eleven membership functions. This fact actually shows the effectiveness of the adaptation in the overall performance of the induction machine control. Also the proposed adaptive controllers perform well, even in the presence of large load disturbance. Because of the better performance proven through the simulation results, the work presented in this paper has the potential to replace the traditional PI controller being used for variable speed control of induction machines by a vast industry. The future directions of this work are to explore the potential of adaptive fuzzy controllers for the permanent magnet machine and setup a prototype in the lab to perform the experimental validation. Acknowledgement The authors would like to acknowledge the support of the Scientific Research Affairs of the UAE University under grant number 08-04-7-11/03. References [1] F. Blaschke, The principle of field orientation as applied to the new transvector closed loop vector control system for rotating machines, Siemens Rev. (December 1972) 2037–2042.

907

[2] K. Nordin, D. Novotny, D. Zinger, The influence of motor parameter deviations in feedforward field orientation drive systems, IEEE Trans. Ind. Appl. 21 (July/August 1985) 1009–1015. [3] R. Krishnan, F. Doran, Study of parameter sensitivity in high performance inverter fed induction motor drive systems, IEEE Trans. Ind. Appl. 23 (July/August 1987) 623–635. [4] H. Schierling, Self-commissioning—a novel feature of modern induction motor drives, in: Proceedings of the IEE Conference on Power Electronics and Variable Speed Drives, July 1988, pp. 287–290. [5] H. Schierling, Fast and reliable commissioning of ac variable speed drives by self commissioning, in: IEEE/IAS Annual Meeting Conference Record—Part I, 1988, 489–492. [6] L.J. Graces, Parameter adaptation for speed controlled static ac drives with a squirrel-cage induction motor, IEEE Trans. Ind. Appl. 16 (2) (1980) 173–178. [7] R.D. Lorenz, D.B. Lawson, A simplified approach to continuous on-line tuning of field oriented induction machine drives, in: Proceedings of the IEEE/IAS Annual Meeting Conference, 1988, pp. 444–449. [8] R. Krishnan, A.S. Bharadwaj, A review of parameter sensitivity and adaptation in indirect vector controlled induction motor drive systems, in: Proceedings of the IEEE PESC, 1990, pp. 560–566. [9] B. Heber, L. Xu, Y. Tang, Fuzzy logic enhanced indirect field oriented control of induction machine, IEEE Trans. Power Electron. 15 (September 1997) 772–778. [10] M.N. Uddin, T.S. Radwan, M.A. Rahman, Performance of fuzzy-logicbased indirect vector control of induction machine, IEEE Trans. Ind. Appl. 38 (September/October 2002) 1219–1225. [11] Y.S. Lai, J.C. Lin, New hybrid fuzzy controller for direct torque control induction motor drive, IEEE Trans. Power Electron. 18 (September 2003) 1211–1219. [12] L. Zhen, L. Xu, On-line fuzzy tuning of indirect field oriented induction machine, IEEE Trans. Power Electron. 13 (January 1998) 134–141. [13] E. Bim, Fuzzy optimization for rotor constant identification of an indirect foc induction motor drive, IEEE Trans. Ind. Electron. 48 (December 2001) 1293–1295. [14] L. Zhen, L. Xu, Fuzzy learning enhanced speed control of an indirect-field oriented induction machine drive, IEEE Trans. Control Syst. Technol. 8 (March 2000) 270–278. [15] E.L.Z. Ibrahim, A comparative analysis of fuzzy logic and pi speed control in high performance ac drives using experimental approach, IEEE Trans. Ind. Appl. 38 (September/October 2002) 1210–1218. [16] J.T. Spooner, K.M. Passino, Stable adaptive control using fuzzy systems and neural networks, IEEE Trans. Fuzzy Syst. 4 (August 1996) 339–359. [17] H.K. Khalil, Nonlinear Systems, Macmillan Publishing Company, New York, 1992. [18] S. Sastry, M. Bodson, Adaptive Control: Stability, Convergence, and Robustness, Prentice Hall, Engle-wood Cliffs, NJ, 1989. [19] L.-X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Prentice Hall, Englewood Cliffs, NJ, 1994. [20] S.S. Sastry, A. Isidori, Adaptive control of linearizable systems, IEEE Trans. Automat. Contr. 34 (November 1989) 1123–1131.