A Sliding Mode Controller for a Three Phase Induction Motor

A Sliding Mode Controller for a Three Phase Induction Motor Eman El-Gendy Demonstrator at Computers and systems engineering, Mansoura University, Egypt Sabry F. Saraya Assistant professor at Computers and systems engineering, Mansoura University, Egypt Abdelhameed F. Ibrahim Lecturer at Computers and systems engineering, Mansoura University, Egypt Fayez. F. G. Areed Professor at Computers and system engineering, Mansoura University, Egypt ABSTRACT In this paper, a sliding mode controller (SMC) is designed to control the speed of an induction motor fed by three phase voltage source inverter based on space vector pulse width modulation (SVPWM) technique. The sliding mode controller is a nonlinear, high speed switching, feedback control strategy that provides an effective and robust approach for controlling nonlinear plants. The space vector pulse width modulation technique is advanced, computation-intensive pulse width modulation (PWM) technique and it is possibly the best among all the PWM techniques for variable frequency drive applications. The proposed scheme enables us to adjust the speed of the motor by controlling the frequency and amplitude of the stator voltage; the ratio of the stator voltage to the frequency should be kept constant. It is introduced to maintain a constant speed to when the load varies. Simulation results show the validation of the proposed scheme. Keywords Sliding mode controller, induction motor, space vector pulse width modulation. 1. INTRODUCTION Induction motors are used in many applications such as HVAC (heating, ventilation and air-conditioning), industrial drives (motion control, robotics), automotive control (electric vehicles), etc. [1, 2]. The squirrel-cage induction motor has been widely used in many control systems and industrial automatic systems. It has many advantages, such as simple structure, firmness and low maintenance cost. However, induction motors are difficult to control for several reasons: their dynamics are intrinsically nonlinear and multivariable [1]. Various high-performance control strategies have been developed for the induction motor [3-9]. A well-known method is field-oriented control (FOC) [3]. With fieldoriented techniques, the decoupling of the induction motor's flux and torque can be controlled separately as an excited DC motor. But FOC requires accurate and complex calculation of the decoupling, so it is difficult to operate and easily influenced by load disturbance and parameter uncertainties. The conventional direct torque control (DTC) strategy is useful for overcoming the disadvantages of FOC [4, 5]. DTC doesn't require complex decoupling calculation and is easy to implement due to its simple structure. However, DTC has some drawbacks during induction motor operation, such as large ripples in torque and flux at low speeds. In order to reduce ripples in torque and flux, a discrete space vector modulation (DSVM) has been proposed [6] by means of a new switching table. Since its sampling period is subdivided, this new switching table is more complex, with the result that its DSVM takes more time to calculate and requires a greater sampling time than that of the DTC does. As an alternative, space vector modulation (SVM) is incorporated with DTC for induction motor drives, as described in [7-10], to provide higher control resolution and help improve the drive's behavior. However, this simple controller design based on SVM and DTC techniques is sensitive to parameter variations and load disturbance. The space vector pulse width modulation (SVPWM) method is an advanced, computation-intensive PWM method and it is possibly the best among all the PWM techniques for variable frequency drive applications [11]. Space vector modulation is based on the representation of three phase voltages as space vectors. It exhibits the features of good dc-bus voltage utilization and a low Total Harmonic Distortion (THD) when compared to other PWM methods [12, 13]. Classical control systems like PI (proportional-integral) control have been used for the speed control of induction machines. The main drawbacks of classical PI controllers are their large overshoot and excessive settling time. To face these problems, sliding mode control has recently been applied to the control of electrical drive systems. A sliding mode controller (SMC) is a nonlinear, high speed switching, feedback control strategy that provides an effective and robust approach for controlling nonlinear plants [14-16]. However, the SMC easily produces a chattering phenomenon due to its discontinuous switching control. In this paper, a sliding mode controller is designed to control the speed of an induction motor fed by three phase voltage source inverter based on space vector pulse width modulation technique. Simulation results show the validation of the proposed scheme. The paper is organized as follows: Section 2, presents the space vector pulse width modulation and the sliding mode The sliding mode controller based design is shown in Section 3. In section 4, simulation results are given to validate the proposed approach. Section 5 gives a comparative study. This paper is concluded in Section 6. 33

2. BACKGROUND 2.1 Space Vector Pulse Width Modulation For the AC voltage, drive application sinusoidal voltage sources are usually not used [17]. They are replaced by six power IGBTs that act as on/off switches to the rectified DC bus voltage. Owing to the inductive nature of the phases, a pseudo-sinusoidal current is created by modulating the dutycycle of the power switches. The basic power circuit topology of a three-phase voltage source inverter supplying a star connected three-phase load is given in Figure 1. A three phase bridge inverter, from Figure 1, has eight permissible switching states as shown in Figure 2. trajectory from the sliding surface and its rate of convergence are used to decide the control input. The sign of the control input must change at the intersection of tracking error trajectory with the sliding surface. In this way, the error trajectory is forced to move always towards the sliding surface. Once it reaches the sliding surface, the system is constrained to slide along this surface to the equilibrium point. The condition of sliding mode is : where: is a positive constant. (3) This equation is stricter than the general sliding condition: and is equivalent to. The q-axis stator voltage command is responsible for changing torque. It is defined as: (4) Fig. 1: Three phase voltage source inverter. Fig. 2: Eight switching states of VSI. 2.2 Sliding Mode Controller The control problem is to get the motor speed to track a specific time varying command in the presence of model imprecision, load torque disturbances and measurement noise. In sliding mode control, the system is controlled in such a way that the tracking error and its rate of change always move towards a sliding surface. The sliding surface is defined in the state space by the scalar equation [18]: where: the sliding variable is: where: is a positive constant that depends on the bandwidth of the system. The problem of tracking is equivalent to remaining on the sliding surface for all the time, and the sliding variable is kept at zero. For a second order system the switching surface is a line. Control input is applied to drive the system state onto the switching line, and once on it, the system is constrained to remain on the line. The distance of the error (1) (2) where: is a positive constant, which is the gain of the sliding mode A suitable value of ensures sliding to occur. This controller gives unacceptable performance due to high control activity, resulting in chattering of control variable and system states. To reduce chattering, a boundary layer of width is introduced on both sides of the switching line. This amounts to reduction of the control gain inside the boundary layer and results in a smooth control signal. Then the control law is modified to: (5) where: 3. PROPOSED SLIDING MODE CONTROLLER SCHEME The flow chart of the sliding mode control process is represented in Figure 3. It illustrates that the sliding mode control is performed by reading the value of actual speed and comparing it to the reference speed to generate an error signal. This error signal and the derivative of error are used to determine the switching surface and the state of the system must remain on the sliding surface. The controller then generates the 6 PWM signals for inverter and compares the error value e to a set value. If the error is less than this value, the error value is printed and the control process stops, otherwise the process is repeated to an acceptable error value. The block diagram of the induction motor using speed controller is shown in Figure 4. In this Figure, the value of the actual speed generated by the induction motor is compared to the desired value to generate an error signal. This error signal and its derivative are fed to the sliding mode controller which generates a crisp value. This value is added the motor speed which in turn forms the input to the Voltage Source Inverter and V/f The VSI (Voltage Source Inverter) receives voltage signal from the V/f (6) 34

controller and (frequency signal). The Voltage Source Inverter uses these inputs to generate a three phase voltage whose frequency and amplitude can be varied by the sliding mode The three phase voltage is fed to the induction motor which then runs with a speed which tends to follow the desired speed (reference speed, ). In Figure 5, the block diagram of the sliding mode controller using MATLAB Simulink is represented. The value of the actual speed is subtracted from the value of the reference speed to generate the error signal. Then the error signal is differentiated to generate. The values and are added and the result is passed through the saturation function to generate. This value is added to value of the actual speed to generate the frequency and the voltage required by the voltage source inverter VSI. Start Value of speed, Error & derivative of error Apply sliding mode controller Generate the required voltage and frequency 4. SIMULATION RESULTS AND ANALYSIS The speed set point is 1000 rpm at time t = 0 s,. The speed follows precisely the acceleration ramp. At t = 0.5 s, the full load torque is applied to the motor shaft while the motor speed is still ramping to its final value. This forces the electromagnetic torque to increase to a high value and then to stabilize at 11 N.m once the speed ramping is completed and the motor has reached 1000 rpm. At t = 1 s, the speed set point is changed to 1500 rpm and the electromagnetic torque reaches again a high value so that the speed ramps precisely at 1800 rpm/s up to 1500 rpm under ull load. At t = 1.5 s, the mechanical load passed from 11 N.m to -11 N.m, which causes the electromagnetic torque to stabilize at approximately at -11 N.m shortly after. 4.1 Using PI Controller For speed, the rise time is 1.11 sec and the settling time is 1.514 sec. The maximum overshoot is 25 rpm which is less than 2%. The peak time is 1.514 sec, and the delay time is 0.4 sec as shown in Figure 6. For torque shown in Figure 7, the ratio of ripples varies as follows: From 0 sec to 0.5 sec: the ratio is 12%. From 0.5 sec to 1 sec: the ratio is 18%. From 1 sec to 1.25 sec: the ratio is 3%. From 1.25 sec to 1.5 sec: the ratio is 3%. From 1.5 sec to 2.5 sec: the ratio is 24%. So, when using PI controller, the speed and torque have some ripples. 4.2 Using PID Controller For speed, the rise time remains 1.11 sec and the settling time is 1.53 sec. The maximum overshoot is decreased to 20 rpm which is less than 2%. The peak time is 1.88 sec, and the delay time is 0.4 sec as shown in Figure 8. For torque shown in Figure 9, the ratio of ripples varies as follows: From 0 sec to 0.5 sec: the ratio is 4%. From 0.5 sec to 1 sec: the ratio is 3.8%. From 1 sec to 1.25 sec: the ratio is 4%. From 1.25 sec to 1.5 sec: the ratio is 40%. From 1.5 sec to 2.5 sec: the ratio is 9%. Thus, when using PID controller, the speed and torque ripples are decreased. Print e(t), END Fig. 3: Flow chart of the sliding mode control process. 4.3 Using sliding mode Controller For speed, the rise time remains 1.11 sec and the settling time is 1.1 sec which is less than PI or PID. The maximum overshoot is 5 rpm which is very small and less than 2%. The peak time is 2 sec, and the delay time is 0.4 sec as shown in Figure 10. For torque shown in Figure 11, the ratio of ripples varies as follows: From 0 sec to 0.5 sec: the ratio is 3.8%. From 0.5 sec to 1 sec: the ratio is 3.4%. From 1 sec to 1.25 sec: the ratio is 3%. From 1.25 sec to 1.5 sec: the ratio is 3.5%. From 1.5 sec to 2.5 sec: the ratio is 9.27%. 35

Thus, when using sliding mode controller, the speed and torque have some ripples with magnitude less than either using PI or PID controllers. These results are summarized in Table 1 and Table 2. 5. COMPARATIVE ANALYSIS In this section, we compare our results with A R. Arulmozhiyaly and K. Baskaran [17] using different speeds and load torques. Figure 12 shows the speed using the proposed sliding mode controller and Figure 13 shows the 800 rpm and no load. Figure 14 shows the speed using the proposed sliding mode controller and Figure 15 shows the 800 rpm and load of 5 N.m. Figure 16 shows the speed using the proposed sliding mode controller and Figure 17 shows the 1200 rpm and no load. Figure 18 shows the speed using the proposed sliding mode controller and Figure 19 shows the 1200 rpm and load of 5 N.m. From the results shown in the last figures, it is clear that the sliding mode controller gives better response and lower overshoot than PI and fuzzy PI controllers. Table 3 shows the settling time using the proposed sliding mode controller and fuzzy PI controllers. The results are approximately the same. Table 1: Comparison of speed between PI, PID, and SMC. Speed PI PID Sliding mode Rise time (sec) 1.11 1.11 1.11 Settling time (sec) 1.514 1.53 1.1 Maximum overshoot 25 20 5 Peak time (sec) 1.514 1.88 2 Delay time (sec) 0.4 0.4 0.422 Table 2: Comparison of torque between PI, PID, and SMC. Torque PI PID Sliding Mode Ratio of ripples 0-0.5 12 % 4.0 % 3.8 % 0.5 1 18 % 3.5 % 3.4 % 1 1.25 3.0 % 4.0 % 3.0 % 1.25 1.5 3.0 % 40 % 3.5 % 1.5 2.5 24 % 9.0 % 9.27 % Table 3: Comparison of settling time in sec between fuzzy PI and SMC. Load Condition Fuzzy PI Sliding mode 1000 rpm with no load 0.7 0.71 1000 rpm with load 0.79 0.71 1200 rpm with no load 0.79 0.858 1200 rpm with load 0.85 0.85 6. CONCLUSION This paper proposed a sliding mode controller design to control the speed of an induction motor fed by three phase voltage source inverter based on space vector pulse width modulation technique. The proposed scheme enabled us to adjust the speed of the motor by controlling the frequency and amplitude of the stator voltage; the ratio of the stator voltage to the frequency should be kept constant. It is introduced to maintain a constant speed to when the load varies. Simulation results showed the validation of the proposed scheme. As a conclusion, the sliding mode controller gives lower overshoot than PI and fuzzy PI controllers. As a future work, more analysis is needed to face the sliding mode controller torque ripples which are not completely eliminated. 7. REFERENCES [1] Bimal K. Bose, Modern Power Electronics and AC Drives, Pearson education, Prentice Hall; 1 edition, 2001 [2] Werner Leonhard, Control of Electrical Drives, Springer Verlag, 3nd edition 2001. [3] S. K. Sul and T. A. Lipo, "Field oriented control of an induction machine in a high frequency link power system", IEEE Transactions on Power Electronics, vol.5, no.4, pp.436-445, 1990. [4] I. Takahashi and T. Noguchi, "A new quick-response and high-efficiency control strategy of an induction motor", IEEE Transactions on Industry Applications, vol.a-22, no.5, pp.820-827, 1986. [5] J.-K. Kang and S. K. Sul, "New direct torque control of induction motor for minimum torque ripple and constant switching frequency", IEEE Transactions on Industry Applications, vol.35, no.5, pp.1076-1082, 1999. [6] D. Casadei, G. Serra and A. Tani, "Implementation of a direct torque control algorithm for induction motors based on discrete space vector modulation", IEEE Transactions on Power Electronics, vol.15, no.4, pp.769-777, 2000. [7] N. R. N. Idris and A. H. M. Yatim, "Direct torque control of induction machines with constant switching frequency and reduced torque ripple", IEEE Transactions on Industrial Electronics, vol.51, no.4, pp.758-767, 2004. [8] C. Lascu, I. Boldea and F. Blaabjerg, "A modified direct torque control for induction motor sensorless drive", IEEE Transactions on Industry Applications, vol.36, no.1, pp.122-130, 2000. [9] Y.-S. Lai and J.-H. Chen, "A new approach to direct torque control of induction motor drives for constant inverter switching frequency and torque ripple reduction", IEEE Transactions on Energy Conversion, vol.16, no.3, pp.220-227, 2001. [10] D. Sun, J. G. Zhu and Y. K. He, "A space vector modulation direct torque control for permanent magnet synchronous motor drive systems", Proc. of the Fifth International Conference on Power Electronics and Drive Systems, vol.1, pp.692-697, 2003. [11] Wei-Feng Zhang and Yue-Hui Yu, Comparison of Three SVPWM Strategies, Journal of electronic science and technology of china, No.3, pp. 283-287, Sep. 2007. [12] Iqbal.A, Analysis of space vector pulse width modulation for a five phase voltage source inverter, IE (I) journal-el, Vol. 89, Issue 3, pp.8-15, Sep. 2008. 36

Speed in rpm International Journal of Computer Applications (0975 8887) [13] Mondal, S.K.; Bose, B.K.; Oleschuk, V.; Pinto, J.O.P, Space vector pulse width modulation of three-level inverter extending operation into overmodulation region, IEEE Transactions on Power Electronics, Vol. 18, Issue 2, pp. 604 611, Mar. 2003. [14] J.-J. E. Slotine and W. Li, "Applied nonlinear control", Englewood Cliffs, Prentice-Hall, New Jersey,1991. [15] X. Liu and W. Wang, "High order sliding mode and its application on the tracking control of piezoelectric systems", International Journal of Innovative Computing, Information and Control, vol.4, no.3, pp.697-704, 2008. [16] X.-Z. Zhong, H.-L. Xing and K. Fujimoto, "Sliding mode variable structure control for uncertain stochastic systems", International Journal of Innovative Computing, Information and Control, vol.3, no.2, pp.397-406, 2007. [17] R. Arulmozhiyaly and K. Baskaran, "Implementation of a Fuzzy PI Controller for Speed Control of Induction Motors Using FPGA", Journal of Power Electronics, Vol. 10, No. 1, January 2010. [18] Kanungo Barada Mohanty, "Sensorless Sliding Mode Control of Induction Motor Drives", Electrical Engineering Department, National Institute of Technology, Rourkela-769008, India, May 18, 2009. Fig. 6: Reference vs. actual speed using PI Fig. 8: Reference vs. actual speed using PID 37

Speed in rpm Torque in N.m Torque in N.m Torque in N.m Speed in rpm Speed in rpm Speed in rpm International Journal of Computer Applications (0975 8887) Fig. 10: Reference vs. actual speed using SMC. Fig. 13: Reference vs. actual speed using fuzzy PI 2) Speed is 1000 rpm with load of 5 N.m: Fig. 7: Electromagnetic torque using PI Fig. 14: Reference vs. actual speed using SMC. Fig. 9: Electromagnetic torque using PID Fig. 11: Electromagnetic torque using SMC. 1) Speed is 1000 rpm with no load: Fig. 15: Reference vs. actual speed using fuzzy PI 3) Speed is 1200 rpm with no load: Fig. 12: Reference vs. actual speed using SMC. Fig. 16: Reference vs. actual speed using SMC. 38

Speed in rpm International Journal of Computer Applications (0975 8887) 4) Speed is 1200 rpm with load of 5 N.m: Fig. 17: Reference vs. actual speed using fuzzy PI Fig. 18: Reference vs. actual speed using SMC. Fig. 19: Reference vs. actual speed using fuzzy PI 39