Speed control system of induction motor with fuzzy-sliding mode controller for traction applications

Transcription

1 Speed control system of induction motor with fuzzy-sliding mode controller for traction applications D-H Kim', H-J Ryoo', Y-J Kim2, G-H Rim2, D. 0. Kisck3 & C-Y Won4 1 Dept. of Railroad Electricig, Catholic SangJi College, Korea. 2 Industry Application Research Laboratory, KEN, Korea. 3 Faculty of Electrical Emgineering, University POLITEHNICA of Bucharest, Romania. 4 School of E & C Engineering, Sungkyunkwan UniversiQ, Korea. Abstract The application of sliding mode control for improving the dynamic response of an induction motor based speed control system is presented. It provides attractive features such as fast response, good transient performance, insensitivity to variations in plant parameters and external disturbance. However, one difficult problem for which the popular is due to chattering. This paper presents a new fuzzy-sliding mode controller for a senserless vector controlled induction motor servo system to practically eliminate the chattering problem for traction applications. DSP based implementation of speed control system is employed. Experimental results are presented using propulsion system simulator. The performance of the drive is shown to be practically free from chattering problem. 1 Introduction In the area of high performance induction motor drives, the drive inertia and load characteristics change widely. It is desirable to have a drive system that can provide fast dynamic response, steady-state operation without error between reference speed and measured speed, nice transient behavior, insensitivity to parameter variations, disturbance rejection and robustness with respect to modeled dynamics. Recently, application of variable structure system (VSS) control using sliding mode [2] has received wide attention in order to cope with these

2 306 Computers in Railways VIII features. The sliding mode control law is inherently discontinuous in nature. If the controller is directly applied to control the developed torque with the inner loop of a vector controlled drive, the system results in torque pulsation, current ripple, corresponding speed ripple and acoustic noise. Therefore, a lot of papers [6-91 proposed the algorithm to reduce the command torque ripple. However, this does not solve the problem completely. Fuzzy logic or fuzzy set theory has received attention of a number of researches in the area of power electronics and motion control. The fuzzy logic control is somewhat easy to implement because it does not need the mathematical model of a system. Hence, the interest for practical application [3-41 of fuzzy logic is growing rapidly. However, it is difficult to guarantee the stability of the system because fuzzy logic controller is designed on the basis of human experience. In this paper, a new fuzzy-sliding mode (FSM) control has been applied to a speed control that uses senserless vector controlled induction motor not only to overcome the chattering problem of sliding mode control but also to guarantee the stability of fizzy logic control system. The control is accomplished with dual TMS32OC44 floating-point digital signal processor. The validity of the proposed method is verified by experiment on the propulsion system simulator, used for the development of Korean High-speed Railway Train. 2 Vector control of induction motor The fundamental equations of the induction motor with respect to a synchronously rotating reference frame are the following: It,= 7[ Vs- is]= 7[ K,. i*,] From this model, the rotor field oriented equations in the rotating reference frame, with d-axis along the rotor field space vector, may be written as the following set. All the quantities are in [P.u.] system, excepting the time t, which is measured in seconds. The rotor field oriented control is performed, using the indirect-rotor field control method, as is presented in Figure 1.

3 Computers in Railways VIII 307 Speed Volt age Figure 1: The indirect-rotor field control of the induction motor with fuzzy-sliding mode speed controller The drive system is composed by a speed estimator based on the measured stator quantities, fuzzy-sliding mode speed controller, two PI controllers (one for the rotor flux control and the other one for the electromagnetic torque control), a function generator to set the rotor flux in the weakening region and voltage controlled PWM inverter. 3 Sliding mode control with integral compensation The sliding mode control technique has been mostly applied in position drive systems. The required feedback quantities for the position drives are speed and position, which can be easily obtained. However, in the speed drive systems, acceleration and speed signals are required. The acceleration is a high bandwidth signal, and in general, it is difficult to acquire. In practice, this signal is obtained by estimation techniques. The quality of sliding mode control is strongly influenced by the accuracy of these feedback signals. The use of a estimated acceleration signal for sliding mode control speed drive systems introduces complex control dynamics that require additional attention in the design and implementation of these systems. In order to reduce the steady-state error and easily make the second-order system for speed control,

4 308 Computers in Railways VIII an integral compensation is employed in the feedforward path [12], as shown in Figure 2. VECTOR t, CONTROLLER I t I Figure 2: Sliding mode control with integral compensation With the inner-loop vector controller incorporated (Figure 2), the electromechanical governing equation of the machine can be written as where t*, is the command torque input of the inner-loop vector controller, and its control structure is represented by y. An insertion of integral operation in the feedforward path is essential since the control signal ' U ' is a bidirectional PWM signal that should not be fed into the command torque input of the vector controller directly. For the design of sliding mode control, it is convenient to use a phase variable state representation (3) of the speed drive system (Figure 2). For simplicity of design, all feedback quantities including acceleration are assumed to be a constant gain, and it is conveniently taken as one in the following design. The phase variable state representation of Figure 2 can then be simplified as B where xl=wm-u~, x2=xl, b=- 1 a=-. The control signal J ' Jr ' U' is generated such that the speed error follows certain prescribed dynamics irrespective of plant parameter ( a, b) variations. The sliding mode is introduced along the sliding line in the phase plane and is described as follows: The prescribed dynamics in (5) is a frst-order response with ' p ', which is the time constant of the speed response. For the control system, the

5 equivalent control signal is Computers in Railways VIII 309 Various control laws [13] can be used to force the system to sliding along the sliding line (5). The control law that provides faster responses is given by The values of the controller gains ( 41, &) can be obtained based on the existence condition of sliding mode control given by lima; I o ec The implication of (8) is that the system trajectories should always be directed towards the sliding line (5). With the defmition of 4l and 42 given in (7), the existence condition can be satisfied if min $-a max '" a,bi b I a,b ' Q2 If condition (9) is satisfied, the system trajectories from any point in the phase plane will be directed towards the sliding line. It may be noticed from (9) that the maximum allowable sliding slope ' p ' is limited by the available system gains (az, &). 4 Fuzzy-sliding mode speed controller Figure 3 shows the block diagram of the ideal vector controlled servo system with fuzzy-sliding mode controller. The actual speed o, is compared to the reference speed to produce an error signal x1 that is used with the motor acceleration determining the motor control action. Control signal ' U' is expressed as equivalent control ' ua' and switched control ' Llu '. (9) On the condition that du = 0 and tl = 0, the control drive the state onto a sliding surface and convergence to origin in the phase plane. Proposed fuzzy-sliding mode controller is divided into calculating ' U,, ' from (6) and

6 3 10 Computers in Railways VIII generating ' du' with fuzzy logic to adjust for the tradeoff between robustness and chatter elimination. CONTROLLER q G E q CONTROLLER t +q.is + B Figure 3: Speed control of induction motor with fuzzy-sliding mode controller. 4.1 Fuzzification In case of general fizzy controller for speed drive systems, the input variables are motor speed error and change of it. But the input variables of fuzzy-sliding mode controller are phase state error E and change of error CE, where E is the difference between reference sliding line and actual representative point of the system on the phase plane. At a sampling instant K, the variables E( K) and CE( k) are expressed as follows Shl NS 7.0 I'S I'hl 1'U -1.u 4 5 u.u u.5 1.u -l.u -0.5 u.0 u (a) input variable E (b) input variable CE -l.u u.u u (c) output variable du Figure 4: Membership function of linguistic variables

7 Computers in Railways VIII The values of membership function are assigned to the linguistic variables, using seven basic fuzzy subset : PB(Positive Big), PM(Positive Midium), PS(Positive Small), ZO(Zero), NS(Negative Small), NM(Negative Midium) and NB(Negative Big). Figure 4 shows the fuzzy linguistic variables for the control. Especially, in order to prevent torque current ripple in steady-state, we select wide range of ZO. 4.2 Inference method Table 1 shows the rule table of fuzzy-sliding mode controller. Where all the entries of the matrix are fuzzy sets of E, CE and du for the speed control of the induction motor. In case of fuzzy-sliding mode control, the control rule must be designed that the actual trajectory always turns towards and does not cross reference sliding line on phase plane to satisfy the existence condition (8). Table 1. Rule base of fuzzy-sliding mode control ZO PS PM PB PB PM PS ZO NS NM NB PS PM NS NB NS NM NB NB NM NM NM NM NB NB NB NB NB NB NB NB NB The stablility is analyzed using Lyapunov theorem, and the results become the design tool for the proposed control rule. Let V be semipositive defmite function as The derivative of V becomes: The function (12) is a Lyapunov function along a line perpendicularly, the fuzzy controller makes the closed loop system stable, if the existence condition is satisfied. A example control rule in Table 1 is : IF E is NB AND CE is NS THEN du is PB This can be implied that IF phase state error is Negative Big AND be Positive Big. The MAX-MIN composition is chosen as the fuzzy inference method and we can get:

8 3 12 Computers in Railways VIII where, R is fuzzy relation function. 4.3 Defuzzification The output of the fuzzy controller is a fuzzy set of control. As the plant usually requires a nonfuzzy value of a control, a defuzzification stage is needed. Defuzzification can be performed normally by two algorithms: center of gravity (COG) and the mean of maximum (MOM). For a sampled data representation, the center of gravity du is computed point-wise by where, n is the number of quantization levels of the output, Buj is the amount of control output at the quantization level j and Co(duj) represents its membership value. 5 Experimental results In this paper, the experiments are performed to verify the performance of the proposed algorithm. The experimental tests were made on the propulsion system simulator, used for the development of Korean High-speed Railway Train (KHSRT). From the baseline model of KHSRT, a downscaled model of propulsion system was developed [ll]. This simulator can be divided into two parts. One is the electrical part consisting of traction and electrical braking units and the other is a mechanical part simulating train characteristics and the mechanical brakes. Electrical parts of the system consist of a main transformer, two traction units and four traction motors, two rheostat braking systems and an eddy current brake system. The PWM inverter generates the three-phase voltages for two induction motors at a switching frequency of 540Hz. The maximum speed of KHSRT is 350km/h, which corresponds to the motor speed of 4200rpm. The specification of the induction motor used in simulation and experiments is presented in Table 2. For showing the performances of the proposed fuzzy-sliding mode control, were made experiments using three kind of speed controllers: PI controller (Figure 5.a), conventional sliding mode controller (Figure 5.b) and fuzzysliding mode controller (Figure 5.c). It can be seen that the proposed fuzzy-sliding mode control has the best response avoiding the overshoot and the chattering in steady-state operation. Another main advantage of the fuzzy-sliding mode controller over the PI controller is that the overshoot can be cut in the same manner also at low speed. It is known that a PI controller leads to different overshoot, which depends on the reference speed.

9 Computers in Railways VIII 3 13 One can be seen that, in the case of fuzzy-sliding mode controller, the perturbation is practically rejected and comparing the sliding mode controller, the chattering is also avoided. Quantity Phase voltage, rms. Phase current, rms. Stator frequency Rotor speed Pole-pairs Stator resistance Rotor resistance Stator leakage reactance Rotor leakage reactance Magnetising reactance Apparent torque Symbol Value Usn 220 v Is, 15 A fn 60 Hz n 1730 rpm P 2 r,s [P.u.] rr [P.u.] xss [P.u.] xsr [P.u.] xm [P.u.] Tn Nm Slopped l CHl.5OOmV CWSOOmVoc 101 Dc 101 ~ms/dlvl WMsOFIs Y a <- (a) PI speed controller (b) sliding mode speed controller (c) fuzzy-sliding mode speed controller Figure 5: Experimental results( 1 :reference speed, 2:real speed, 3:real torque current, 4:reference torque current, 278[rpm/div], 37.5[A/div], 2O[s/div])

10 3 14 Computers in Railways VIII 6 Conclusion In this paper, a new fuzzy-sliding mode controller has been presented. It was applied to improve the speed response, to reduce the overshot of a PI controller and also to avoid chattering in steady-state of a conventional sliding mode controller which causes unacceptable vibration stress of the load. With the proposed fuzzy-sliding mode controller, the main goals of a well-tuned system such as, the disturbance rejection, and also the minimizing of the overshoot have been obtained. The performance improvement of this fuzzy-sliding mode controller over the PI controller or standard sliding mode controller is clearly shown in the experimental results. A hlly digital realization of drive system with induction motor using the indirect rotor flux orientation was studied and experimented on the propulsion system simulator, used for the development of KHSRT. References [l] W. Leonhard, Control of electrical drives, Springer Verlag, [2] V.I. Utkin, Sliding modes and their applications in variable structure systems, MR, Moscow, [3] W. Pedrez, Fuzzy control and fuzzy systems, John Willy & Sons Inc., 1989 [4] L. A Zadeh, Fuzzy set, Information and Control, Vol.8, pp , [5] K.T. Hung, A slip gain error model-based correction scheme of neardeadbeat response for indirect field orientation, Master Thesis, Univ. of Wisconsin-Madison, [6] A. Kawamura, K. Miura, T. Ishizava, Trajectory control of two axis robot by sliding mode control with observer, IEEE Proc. of IECON89, 1989, pp [7] M.H. Park, K.S. Kim, Chattering reduction in the position control of induction motor using sliding mode, IEEE Trans. Power Electronics, Vol.6, July 1991, pp [8] C.Y. Won, D.H. Kim, B.K. Bose, An induction motor servo system with improved sliding mode control, IEEE Proc. of IECON92, 1992, pp [9] G. Cordeschi, F. Parasiliti, A variable structure approach for speed control of field-oriented induction motor, EPE'91, Firenze, Italy, 1991, pp, [lo J. Moerschell, Digital sliding mode torque control for induction servo drives, Motion Control for Intelligent Automation, Perugia'92, Italy, 1992, pp [ 11 Hong-Je Ryoo, Jong-Soo Kim, Myung-Ho Woo, Won-Ho Kim, Geun-Hie Rim, Propulsion system simulator of a high-speed railway train, MET99, Warsaw, Poland, 1999, pp [12] Edward Y. Y. Ho, Paresh C. Sen, "Control Dynamics of Speed Drive Sytems Using Sliding Mode Controllers with Integral Compensation," IEEE Trans. on Ind Appl., Vo1.27, No.5, pp , [13] F. Harashima, H. Hashimoto, and S. Kondo, Mosfet converter-fed position servo system with sliding mode control, IEEE Trans. Ind. Electron., Vol.IE-32, No.3, 1985.