Real Time Implementation of Fuzzy Gain Scheduling of ... - Springer Link

Neural Processing Letters (2006) 24:203–215 DOI 10.1007/s11063-006-9018-5

© Springer 2006

Real Time Implementation of Fuzzy Gain Scheduling of PI Controller for Induction Motor Machine Control A. HAZZAB1, , I. K. BOUSSERHANE1 , M. ZERBO2 and P. SICARD2 1

University center of Bechar, B.P 417, Bechar, 08000, Algeria. e-mail: a [email protected] ´ Groupe de recherche en e´ lectronique industrielle, Ecole d’Ing´enierie, D´epartement de G´enie e´ lectrique et G´enie informatique, Universit´e du Qu´ebec a` , Trois-Rivi`eres, Canada. e-mails: bou [email protected], [email protected], [email protected]. 2

Abstract. In this work the control of an induction motor using fuzzy gain scheduling of PI controller (adaptive FLC-PI) is presented. Fuzzy rules are utilized on-line to determine the controller parameters based on tracking error and its first time derivative. Simulation and experimental results of the proposed scheme show good performances compared to the PI controller with fixed parameters. Key words. fuzzy control, gain scheduling, induction motor, PI controller, real-time implementation

1.

Introduction

Due to important progress in power electronics and micro-computing, the control of the ac electric machines has known considerable developments that lead to the possibility of high performance real time implantation applications. The induction machine (IM), known for its robustness, cost, reliability, and effectiveness is the subject of several researches [1]. However, it has traditionally been used in industrial applications that do not require high-performances, because of its highly non-linear behavior and coupled structure. On the other hand, separately excited dc machines were largely used for variable speed applications since they produce torque and flux that are naturally decoupled and that can be controlled independently. Since Blashke and Hasse have developed the technique known as vector control [1–3], the use of the induction machine has become more and more frequent. This control strategy can provide the same performance as achieved from a separately excited dc machine, and it is proven to be well adapted to all types of electrical drives associated with induction machines [4]. The most widely used controllers in industrial applications are PID-type controllers because of their simple structure and good performances in a wide range of 

Author for correspondence.

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operating conditions [5]. In fixed gain controllers, these parameters are selected by methods such as the Ziegler and Nichols, pole placement, etc. These PID controllers are simple but cannot always effectively control systems with changing parameters or strong nonlinearities; and they may need frequent on-line retuning [6]. In adaptive PID controllers, the parameters are adapted on-line based on the process parameter estimation. In recent years, fuzzy logic control (FLC) techniques have also been applied to the control of motor drives [3]. The mathematical tool for the FLC is the fuzzy set theory introduced by Zadeh [6–8]. In FLC, the linguistic description of human expertise in controlling a process is represented as fuzzy rules or relations [8, 9]. This knowledge base is used by an inference mechanism, in conjunction with some knowledge of the states of the process (say, of measured response variables) in order to determine control actions. The controllers based on FLC can be considered as non-linear PID controllers where their parameters are determined on-line based on an error signal and its derivative [5, 6]. The main advantages of FLC are: (a) there is no need for an exact system mathematical model, (b) they can handle nonlinearities of arbitrary complexity, and (c) they are based on linguistic rules with an if-then general structure, which is the basis of human logic. However, standard FLC can not react to changes in operating conditions. The FLCs need more information to compensate nonlinearities when the operation conditions change. When the number of the fuzzy logic inputs is increased, the dimension of the rule base increases too. Thus, maintenance of the rule base is more time-consuming. Another disadvantage of the FLCs is the lack of systematic, effective and useful design methods and adequate analysis, which can use a priori knowledge of the plant dynamics. Moreover, the application of FLC has faced some disadvantages during hardware and software implementation due to its high-computational burden [7]. The earlier reported works for fuzzy-logic applications in motor drives [8, 10, 11] are mainly theoretical and based on either simulation or experimental results at low-speed operating conditions. To overcome the disadvantages of PID controllers and of FLC, a hybrid controller is proposed: PID controller parameters are tuned on-line by an adaptive mechanism based on fuzzy logic (adaptive FLC-PI) for induction machine speed control. The proposed scheme utilizes fuzzy rules to determine the PI controller parameters, and the PI controller generates the control action signal (Section 3). The performances of the proposed vector control scheme of IM incorporating the adaptive FLC-PI are compared with those obtained with a well tuned conventional PI controller, both theoretically and experimentally, in Sections 4 and 5. The drive has been successfully implemented for real time applications using digital-signal processor (DSP) controller-board DS1102 (dSpace). It is found that the proposed adaptive FLC-PI is insensitive to temperature changes, inertia variations, and load torque disturbances.

FUZZY GAIN SCHEDULING OF PI CONTROLLER FOR INDUCTION MOTOR

2.

205

Indirect Field-Oriented Control of the IM

The dynamic model of three-phase, Y -connected induction motor can be expressed in the d-q synchronously rotating frame as [1, 3, 4]:   disd 1−σ Lm Rs isd + ωe isq + + φrd =− dt σ · Ls σ τr σ L s Lr τr L m ωr 1 + φrq + Vsd , σ L s L r Lr σ Ls   disq Rs 1−σ L m ωr isq − = −ωe isd − + φrd dt σ Ls σ τr σ L s Lr 1 Lm φrq + Vqs , + σ L s L r τr σ Ls dφrd Lm 1 (1) isd − φrd + (ωe − ωr ) φrq , = τr τr dt dφrq Lm 1 isq − (ωe − ωr ) φrd − φrq , = τr dt τr  fc dωr 3 P 2 Lm  P isq φrd − isd φrq − ωr − Tl , = dt 2 J Lr J J where σ is the coefficient of dispersion and is given by σ = 1 − L2m /(Ls Lr ).

(2)

Ls , Lr , Lm : the stator, rotor, and mutual inductances. Rs , Rr : the stator and rotor resistances. ωe , ωr : the electrical and rotor angular frequency. ωsl : the slip frequency (ωe − ωr ). τr : the rotor time constant (Lr/Rr ). P : the number of pole pairs. The main objective of the vector control of induction motors is to independently control the torque and the flux; this is done by using a d–q reference frame rotating synchronously with the rotor flux space vector [2, 3]. In ideal field-oriented control, the rotor flux linkage axis is forced to align with the d-axis, and it follows that [3, 4]: φrq =

dφrq = 0, dt

φrd = φr .

(3)

(4)

Considering (3) and (4), the torque equation becomes analogous to that of the dc machine and can be described as: Te =

3 p · Lm · φr · isq 2 Lr

(5)

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and the slip frequency can be given as follows [1, 5]: ωsl =

L m · Rr · isq . Lr · φrd

Consequently, the dynamic equations (1) yield:   disd 1−σ Lm 1 Rs isd + ωe isq + + φrd + Vsd , =− σ Ls σ τr σ Ls Lr τr σ Ls dt   disq Rs 1−σ L m ωr 1 isq − + φrd + Vqs , = −ωe isd − dt σ Ls σ τr σ Ls Lr σ Ls dφrd Lm 1 isd − φrd , = τr dt τr dωr 3 P 2 Lm fc P ∗ = isq φrd − ω r − Tl . dt 2 J Lr J J

(6)

(7)

The decoupling control method with compensation is to choose inverter output voltages such that [12]:    1 ∗ ∗ ∗ Vsd isd − isd − ωe σ Ls isq = Kp + Ki , (8) s    1 Lm ∗ ∗ ∗ Vsq isq = Kp + Ki − isq + ωe σ Ls isd + ωe φrd . (9) s Lr According to the above analysis, the indirect field-oriented control (IFOC) [3, 10, 12] of induction motor with current-regulated PWM drive system can reasonably be presented by the block diagram shown in the Figure 1.

3.

Speed Control of the IM by an Adaptive FLC-PI Controller

To overcome the disadvantages of PID controllers and FLC, we propose a hybrid controller, in which the PI controller parameters are adjusted by an adaptive

Figure 1. Block diagram of IFOC for an induction motor.

FUZZY GAIN SCHEDULING OF PI CONTROLLER FOR INDUCTION MOTOR

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Figure 2. PI control system with fuzzy gain adapter.

mechanism based on fuzzy inference (adaptive FLC-PI). We now describe how the two types of controllers are combined. 3.1.

gain scheduling using fuzzy logic

Gain scheduling is a technique where PI controller parameters (kp and ki gains) are tuned during control of the system in a predefined way [5–7]. It enlarges the operation area of the linear controller (PI) to perform well also with a nonlinear system [5]. The structure of the control system is illustrated in Figure 2. The fuzzy adapter adjusts the PI parameters to operating conditions, in this case based on the error and its first difference, which characterizes its first time derivative, during process control. 3.2.

description of the fuzzy gain scheduler

The parameters of the PI controller used in the direct chain, kp and ki , are normalized into the range between zero and one by using the following linear transformations [5]:    kp = kp − kp min kp max − kp min ,

(10)

 ki = (ki − ki min ) (ki max − ki min ).

(11)

The inputs of the fuzzy adapter are the error e and the first time difference of the error e, normalized using a predefined maximum error and a maximum first time difference. The outputs are the normalized value of the proportional action (kp ) and of the integral action (ki ). The parameters kp and ki are determined by a set of fuzzy rules of the form: If e is Ai , and e is Bi , then kp is Ci , and ki is Di .

(12)

where Ai , Bi , Ci and Di are fuzzy sets on corresponding supporting sets. The membership functions for the inputs e and e are defined in the range [−1, 1] (Figure 3), and for the outputs are defined in the range [0, 1] (Figure 4). The fuzzy subsets of the input variables are defined as follows: Negative Big (NB),

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Figure 3. Membership functions e and e.

Figure 4. Membership functions Kp and Ki .

Negative Medium (NM), Negative Small (NS), Zero (ZE), Positive Small (PS), Positive Medium (PM), Positive Big (PB). The fuzzy subsets of the output variables are defined as: Big (B), Small (S). The fuzzy rules in (12) may be extracted from operator’s expertise or based on the step response of the process [5]. The tuning rules for kp and ki are given in Tables I and II respectively. Table 1. Fuzzy rules base for computing kp . e e

NB

NM

NS

ZE

PS

PM

PB

NB NM NS ZE PS PM PB

B S S S S S B

B B S S S B B

B B B S B B B

B B B B B B B

B B B S B B B

B B S S S B B

B S S S S S B

FUZZY GAIN SCHEDULING OF PI CONTROLLER FOR INDUCTION MOTOR

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Table 2. Fuzzy rules base for computing ki . e e

NB

NM

NS

ZE

PS

PM

PB

NB NM NS ZE PS PM PB

B B B B B B B

B S B B B S B

B S S B S S B

B S S S S S B

B S S B S S B

B S B B B S B

B B B B B B B

By using the membership functions shown in Figure 4, we satisfy the following condition m

μi = 1.

(13)

i=1

The defuzzification rule is chosen as: kp =

m

 μi kp,i ,

(14)

 μi ki,i ,

(15)

i=1

ki =

m i=1

 is  is the value of kp corresponding to the grade μi for the ith rule. ki,i where kp,i similarly defined. Once the values of kp and ki are obtained, the new parameters of the PI controller are calculated by the following equations:

  kp = kp max − kp min · kp + kp min ,

(16)

ki = (ki max − ki min ) · ki + ki min .

(17)

Figure 5 shows the block diagram of the indirect field oriented control by an adaptive FLC-PI controller.

4.

Simulation Results

To demonstrate the effectiveness of the proposed control scheme, we apply the proposed scheme to the control of a three phase induction motor with the following characteristics: Y connected, four poles, 175 W, 1670 min−1 120/208 V, 60 Hz. The other machine parameters are given in appendix. The configuration of the overall control system is shown in Figure 5. It consists of an induction motor, a ramp comparison current-controlled pulse width

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Figure 5. Block diagram of IM control by a PI controller adapted by an FLC (adaptive FLC-PI).

modulated (PWM) inverter, a slip angular speed estimator, an inner indirect field oriented controller, and an outer speed feedback control loop with fuzzy gain adaptation of the PI controller gains. Figure 6 shows the response to disturbance of the continuous time implementation of the adaptive FLC-PI controller when the machine is stepped up to 100 rad/s under no load and load torque disturbance equal to 0.3 N· m is suddenly applied at 10 sec and eliminated at 20 sec, followed by a set point inversion (−100 rad/sec) at 30 sec. The adaptive FLC-PI controller rejects the load disturbance rapidly with a negligible steady state error. Figure 7 shows the resulting parameters of the PI controller with fuzzy gain tuning during the control operation. The adaptive FLC-PI controller rejects the load disturbance more rapidly than a well tuned fixed gain PI controller as shown on Figure 8.

5.

Experimental Results

Experimental results are provided to further demonstrate the effectiveness of the proposed control system. The block diagram of the co-processor computer control system for the indirect field oriented control of induction motor is shown in Figure 9. The adaptive FLC-PI speed controller, indirect field-oriented control, and the current regulation are all executed in a Pentium III microcomputer via Matlab/Simulink software with Real-Time Workshop to deliver the PWM signals to the drive circuit. Motor current feedback signals are obtained using Hall-effect current sensors, and the speed is measured with a tachometer. To reduce the calculation burden of the CPU and to increase the accuracy of the three-phase current command, an AD2S100 AC vector processor (dSpace) implements the coordinate transformations in the field-oriented mechanism. Sampling time is 2 × 10−3 sec. The machine is stepped up to 100 rad/s under no load and load torque disturbance approximately equal to 0.3 N· m (Variable load resistor Rch = 5) is

FUZZY GAIN SCHEDULING OF PI CONTROLLER FOR INDUCTION MOTOR

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4

300 200

2 i qs [A]

w [rad/sec]

100 0 -100

0

-2

-200 -300

-4 0

10

20 30 Time [Sec]

40

0

10

20

30

40

Time [Sec]

Current iqs [A]

Rotor speed [rad/s] 1.5

60

1

20 v a s [V ]

ids [A]

40

0.5

0

-20 -40

0

0

-60

10

20 30 40 Time [Sec] Current ids [A]

0

10

20

30

40

Time [Sec] Voltage Vas [V]

Figure 6. Simulated results of adaptive FLC-PI controller for IM. 0.745

1.1

0.74

1.05

0.735

1 0.95

Ki

Kp

0.73 0.725

0.9 0.85

0.72

0.8

0.715

0.75

0.71 0

5

10 15 20 25 30 35 40 45 50

Time [sec]

0.7

0

5

10 15 20 25 30 35 40 45 50

Time [sec]

Figure 7. Parameter variation of the adapted PI using an FLC (adaptive FLC-PI) during simulation test.

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A. HAZZAB ET AL. 300

PI 200

PI-FLC

w [rad/sec]

100 0 -100 -200 -300

0

10

20 30 Time [sec]

40

50

Figure 8. Simulated results of the comparison between the PI and PI-FLC of IM control.

Figure 9. Block diagram of the co-processor computer control system for the IFOC of IM.

suddenly applied at 10 sec and eliminated at 20 sec, followed by a set point inversion (−100 rad/sec) at 30 sec (Figure 10). From the experimental results, the adaptive FLC-PI controller rejects the load disturbance rapidly with a negligible steady state error. Figure 11 shows the resulting parameters of the PI controller with fuzzy gain tuning during the control operation.

150

3

100

2

50

1

i qs [A]

w [rad/sec]

FUZZY GAIN SCHEDULING OF PI CONTROLLER FOR INDUCTION MOTOR

0 -50

0 -1 -2

-100 -150

213

0

10

20 30 Time [Sec]

-3

40

0

10

20 30 Time [Sec]

40

Current iqs [A]

Rotor speed [rad/s] 5

200

100

v a s [V ]

ids [A]

0

-5

0

-100

-10

0

10

20 30 Time [Sec]

-200 0

40

10

Current ids [A]

20 30 Time [Sec]

40

Voltage Vas [V]

Kp

Figure 10. Experimental results of adaptive FLC-PI controller for IM. 0.7394 0.7392 0.739 0.7388 0.7386 0.7384 0.7382 0.738 0.7378 0.7376

0

5

10

15

20

25

30

35

40

45

50

30

35

40

45

50

Time [sec]

Ki

1.1 1.05 1 0.95 0.9 0.85 0.8 0.75 0.7

0

5

10

15

20

25

Time [sec]

Figure 11. Parameter variation of the adapted PI using an FLC (adaptive PI-FLC) during experimental test.

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A. HAZZAB ET AL. 150 PI-FLC PI

w [rad/sec]

100 50 0 -50 -100 -150

0

10

20

30

40

50

Time [Sec] Figure 12. Experimental results of the comparison between the PI and FLC-PI of IM.

Furthermore, compared with the experimental results of the PI with fixed parameters control system shown in Figure 12, the responses are much improved using the proposed adaptive FLC-PI controller.

6.

Conclusion

In this work, we proposed a hybrid fuzzy controller and traditional PI controller in order to overcome the disadvantages of PI controllers and FLC; this combination gave us an adaptive FLC-PI controller. This study has successfully demonstrated the design and implementation of the adaptive FLC-PI for the speed control of an induction motor. The proposed scheme has presented satisfactory performances (no overshoot, minimal rise time, best disturbance rejection) for parameter variations and time-varying external force disturbances. The effectiveness of the PI controller and the proposed adaptive FLC-PI has been verified through simulation and experimental results. Appendix. Induction motor parameters Pn [kW] Vn [V] η Cos ϕn ωn [min−1 ]

0.175 120 0.78 0.8 1670

Rs [] Rr [] Lr [H] Ls [H] Lm [H]

12.0296 7.1 0.565 0.565 0.546

fn [Hz] Jn [kg/m2 ] fc [N·m·s/rad] P

60 0.0022 0.0011 2

References 1. Hazzab, A., Bousserhane, I. K. and Kamli, M.: Design of fuzzy sliding mode controller by genetic algorithms for induction machine speed control. International Journal of Emerging Electric Power Systems, Berkeley Electronic Press (Bepress), USA 1(2) (2004). http://www.bepress.com/ijeeps/vol1/iss2/art1008

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2. Hazzab, A., Bousserhane, I. K., Kamli, M. and Rahli, M.: New Adaptive fuzzy PI-Sliding mode controller for induction motor speed control. Third International Conference on Systems, Signals & Devices, SSD’05, (Sousse, Tunisia, 2003). 3. Caron, J. P. and Hautier, J. P.: Modeling and Control of Induction Machine, Technip Edn, France (1995) (text in french). 4. Lorenz, R. D. and Lawson, D. B.: A simplified approach to continuous on-line tuning of field-oriented induction machine drives. IEEE Transactions on Industry Applications, 26(3) (1990), 420–424. 5. Baghli, L.: Contribution to induction machine control: using fuzzy logic. Neural Networks and Genetic Algorithms, Doctoral Thesis, Henri Poincare University, January 1999 (text in french). 6. Ouhrouche, M. A. and Volet, C.: Simulation of a direct field-Oriented controller for an induction motor using Matlab/Simulink software package. Proc. of IASTED Int. Conf. Modeling and Simulation (MS’2000), USA, 2000. 7. Zhao, Z.-Y., Tomizuka, M. and Isaka, S.: Fuzzy gain scheduling of PID controllers. IEEE Transactions on Systems, Man. and Cybernetics, 23(5) (1993), 1392–1398. 8. Viljamaa, P. and Koivo, H. N.: Fuzzy logic in PID gain scheduling. Third European Congress on Fuzzy and Intelligent Technologies EUFIT’95, 28–31 August, ELITE-foundation, vol. 2, pp. 927–931, Aachen, Germany, 1999. 9. Viljamaa, P.: Fuzzy gain scheduling and tuning of multivariable fuzzy control-methods of computing in control systems. Technologic doctoral thesis, Temper University of technology, Finland (2000). 10. Ying, H.: Fuzzy control theory: A non linear case. Automatica Journal, 26(3) (1990), 513–520. 11. Zhen, Li and Xu, L.: On-Line fuzzy tuning of indirect field-oriented induction machine drives. IEEE Transactions on Power Electronics, 13(1) (1998), 134–141. 12. Mendel, J. M.: Fuzzy logic systems of engineering: A Tutorial. Proc. of IEEE 83(3) (1995), 345–377.