A Performance Study of PI controller and Fuzzy logic controller in V/f Control of Three Phase Induction Motor Using Space Vector Modulation Safdar Fasal T K & Unnikrishnan L Department of Electrical and Electronics Engineering, Rajagiri School of engineering and technology, Cochin, India E-mail : safdarfasal@gmail.com & unnikrishnanl@rajagiritech.ac.in Abstract - This paper presents a comparative study of the proportional integral controller and the fuzzy logic controller in V/f control of three phase squirrel cage induction motor drive using space vector modulation technique. Here the speed control is possible by varying supply frequency using a voltage source inverter while keeping voltage to frequency ratio as a constant. Proportional integral controller input is speed error while in fuzzy logic controller inputs are speed error and speed error variation. The controller output used to control the reference of space vector modulation. Hence, the fundamental frequency and fundamental voltage of voltage source inverter output can be varied to control the rotor speed. The performance of proportional integral controller and fuzzy logic controller under load torque variation is evaluated using simulation results in MATLAB/Simulink. Keywords Three phase Induction motor, Proportional integral controller, Fuzzy logic controller, Space vector modulation, Voltage source inverter. I. INTRODUCTION Now-a-days Three Phase Induction Motors are widely used in industries because of its rugged construction, easy speed control, low cost of repairs and adaptation to speed and load torque deviations. Usually Induction motor (IM) drives are used in fan, pump and conveyor applications for energy saving by speed control. Scalar control and Vector control are the two important methods of speed control of three phase induction motor [1]. V/f control is a scalar control which has wide application. Several studies are going on in the field of vector control due to better dynamic response. However, Scalar control has wide applications in industries because of its simple structure characterized by low steady-state error. Therefore, constant voltage-frequency ratio (V/f) scalar controlis considered in this paper for comparison [2]. Proportional integral (PI) controllers are normally used in V/f control of induction motors. In this case a mathematical model of the real plant is required for the controller design with conventional methods. Identifying the accurate parameters for a complex nonlinear and time-varying nature of real plant is difficult. Also fine tuning of parameters is time consuming. PI controllers are sensitive to parameter variations inherent in real plant operations. Conversely, the V/f control using fuzzy logic controller(flc) overcomes disadvantages of Conventional PI controllers [4]-[6]. FLCs have the ability to adapt with nonlinearity. Also the control performance is not much affected by plant parameter variations. FLCs are based on certain well defined linguistic rules; hence necessity of precise mathematical model of a real plant can be avoided. This paper is organized as follows. In section II, modeling of three phase IM in stationary reference frame in per-unit system is explained. Section III describes the basics of Space vector pulse width modulation (SVPWM)[3] technique. In section IV Induction motor with PI controller is presented. In section V, Fuzzy logic controller design is described. In section VI, Induction motor with fuzzy logic controller is presented. In section VII, comparative analysis of PI 45
controller and FL controller under various conditions is discussed based on simulation results using MATLAB/Simulink [7]. Finally, section VIII gives conclusion of this work. II. INDUCTION MOTOR PER-UNIT MODEL In this section per-unit modeling of three phase squirrel cage induction motor in stator reference frame is discussed. The modeling equations for per unit currents are as follows: rotor flux linkages in q-axis and d-axis respectively. Torque and speed equations are given as follows: (9) (10) Where, T en is per-unit electromagnetic torque produced by IM. T ln is load torque in per unit. w rn is rotor speed in per-unit and J n is Inertia constant in per-unit. (1) (2) (4) Where, I qsn and I dsn are per unit stator currents in q-axis and d-axis respectively. V qsn and V dsn are per unit stator voltages in q-axis and d-axis respectively. I qrn and I drn are per unit rotor current in q-axis and d-axis respectively. W b is base frequency. R sn and R rn are per unit stator and rotor resistance respectively. X sn and X rn are per unit stator and rotor reactance respectively. X mn is per unit mutual reactance. The modeling equations for per unit flux linkages are as follows: (7) (8) (6) (5 Figure 1. Simulink model of Induction motor Figure. 1 shows Simulink model of three phase IM using (1) to (10). Here V asn, V bsn and V csn are the input voltages to the IM. Using this model, simulations are done in section VII to analyze the performance of PI controller and FLC. III. SPACE VECTOR MODULATION Space vector modulation is a one of the advanced pulse width modulation (PWM) technique used for inverter switching. Usually there are eight possible switching states in an inverter. In these six are active vectors viz. V 1,V 2, V 3, V 4, V 5, V 6 and two are null vectors viz. V 0, V 7 as shown in Fig. 2. We utilize only six active vectors in sinusoidal pulse width modulation but SVPWM uses six active vectors and null vectors to generate the required space voltage vector. Where, F qsn and F dsn are per unit stator flux linkages in q-axis and d-axis respectively. F qrn and F drn are per-unit 46
from the FLC based on certain linguistic rules defined in FLC to achieve the reference speed. Figure 2. Basic active vectors and null vectors The required space vector V ref can be generated using two neighboring active vectors V 1 and V 2 for a time period of t 1 and t 2 respectively along with null vectors for a time period of (T s -(t 1 +t 2 )), where T s is the switching period. IV. INDUCTION MOTOR WITH PI CONTROLLER Figure. 3 shows basic block diagram of three phase IM with PI controller. IM motor is supplied from a variable voltage variable frequency (VVVF) Voltage source inverter (VSI). The switching signal for VSI is obtained by Space vector pulse width modulation (SVPWM). Speed is measured using speed sensor and is compared with reference speed. Speed error is input to the PI controller which gives the frequency variation to achieve the reference speed as output. This frequency variation is added to the actual frequency obtained from the actual speed to get the reference frequency. Figure 4. Input variables of fuzzy system (e)and (Δe) Input variables, speed error (e) and speed error variation (Δe), have samemembership functions which vary between the interval [-1, 1]. Figure 5. Output variable of fuzzy system (Δe) TABLE I. FUZZY RULES Δe e NL NM NS ZZ PS PM PL NL NL NL NL NM NS NVS ZZ NM NL NL NM NS NVS ZZ PVS NS NL NM NS NVS ZZ PVS PS ZZ NM NS NVS ZZ PVS PS PM Figure 3. Basic block diagram of IM drive with PI controller Reference frequency is multiplied with constant voltage to frequency ratio (V/f) to obtain the amplitude of reference signal for SVPWM. V. FUZZY LOGIC CONTROLLER DESIGN In the case of three phase IM drive, speed error (e) and speed error variation (Δe) are input variables to the FLC. Frequency variation (Δf) is the output obtained PS NS NVS ZZ PVS PS PM PL PM NVS ZZ PVS PS PM PL PL PL ZZ PVS PS PM PL PL PL Frequency variation has nine membership functions vary between the interval [-1,1]. The membership functions are described as follows: NL is Negative and large ; NM is Negative and Medium ; NS is 47
Negative and Small ; NVS is Negative and Very small ; ZZ is Zero ; PVS is Positive and Very small ; PS is Positive and small ; PM is Positive and Medium ; PL is Positive and Large. The linguistic rules used in FL controller are shown by TABLE I. The linguistic rules of fuzzy system can be explained using examples: If (speed error is NL) and (change in speed error is NL), Then (frequency variation is NL) If (speed error is ZZ) and (change in speed error is NS), Then (frequency variation is NVS) If (speed error is PM) and (change in speed error is PL), Then (frequency variation is PL) and so on. VI. INDUCTION MOTOR WITH FLC Fig. 6 shows the basic block diagram of an IM drive with FLC A. Performance of PI controller under load torque variations Fig.7 shows performance of PI controller under load torque variations. Here, reference speed is 1pu. Step load of 0.5pu is given to IM at 5sec. (a) Figure 6. Basic block diagram of IM drive with FL controller As explained in section IV, inputs to the FLC are speed error and speed error variation. By giving these inputs to the fuzzy logic controller, the output can be obtained as frequency variation according to the linguistic rules of the FLC. The working of SVPWM generator, VSI and IM are similar to that of a drive which uses PI controller as explained in section IV. VII. SIMULATION RESULTS Performance study of PI controller and FLC are carried out using simulation result in MATLAB/Simulink. Per- unit IM model in section II is used for simulation of a 1hp, 380V, 50Hz, 6 pole three phase squirrel cage induction motor. All simulation values are in per unit. (b) Figure 6. Performance of PI controller (a)rotor speed (pu) (b) Torque (pu) In fig. 7, Rotor speed is increased gradually and settled to reference value at 5sec. Due to application of load torque of 0.5 pu at 5sec, speed is suddenly reduced to a lower value compared to reference speed. Also, torque is increased gradually and settled to 0.5 pu at 8sec with irregularity. B. Performance of FLC under load torque variations Fig. 8 shows the performance of FLC under load torque variation. Here, reference speed is 1pu. Step load of 0.5pu is given at 5sec. 48
(a) (b) Figure 7. Performance of FL controller (a) Rotor speed (pu) (b) Torque ( pu).in fig. 8, Rotor speed is increased gradually and settled to reference value at 5sec. Application of load torque of 0.5 pu at 5sec cause a very small dip in rotor speed but within seconds rotor speed follow reference speed.also, torque is increased suddenly and settled to 0.5 pu within mille-seconds. C. Comparison between PI controller and FLC performance The comparison between PI controller and FLC can be explained using simulation results shown in figure. 7 and figure. 8, important observations are: Initial torque variations in IM drive using PI controller is much higher compared to the IM drive using FLC. Torque ripple is high in the case of PI controller but torque ripple is very small in the case of FLC. In the case of PI controller, under load torque variations, there have some irregularity in torque produced which is absent in FLC Under load torque variations, speed is settled to a lower value of reference speed in the case of PI controller. But the rotor speed follows reference speed in the case of a FLC. Under load torque variations, the desired torque can be obtained gradually in the case of PI controller. While using FLC desired torque can be obtained in a fraction of a second. So, overall performance of FLC is much better than PI controller. VIII. CONCLUSION In this paper FLCfor V/f control of induction motor is designed. The designing has been done with the help of MATLAB/Simulink. This controller takes inputs, viz. speed error (e) and speed error variation (Δe) and gives an output as frequency variation. The output changes according to the rules of fuzzy system. From simulation results it is proved that performance of FLC is much better compared to the PI controller. Under load torque variations, FLC response is rapid and rotor speed is able to follow the reference speed. In addition, desired load torque can also be achieved. The performance of controller can be further increased by using a combination of PI controller and FLC. This ensures precise control of speed under load torque and speed variations. IX. REFERENCES [1] Bimal K. Bose, Modern Power Electronics and Ac Drives, Prentice Hall, 2001. 49
[2] R. Krishnan, Electric Motor Drives Modeling, Analysis, and Control.Upper Saddle River, NJ: Prentice-Hall, 2001. [3] Barry W Williams, Principles and Elementsof Power Electronics, University ofstrathclyde Glasgow,2006. [4] Marcelo Suetake, Ivan N. da Silva, Member, IEEE, and Alessandro Goedtel Embedded DSP- Based Compact Fuzzy System and Its Application for Induction-Motor Vf Speed Control - IEEE trans on industrial electronics, vol. 58, no. 3, March 2011. [5] D. Neema R. N. Patel, A. S. Thoke, Speed Control of Induction Motor using Fuzzy Rule Base, International Journal of Computer Applications (0975 8887),Volume 33 No.5, November 2011. [6] N B Muthuselven, Subharansu Sekhar Dash, P Somasundaram A High Performance IM Drive System Using Fuzzy Logic Controller - IEEE 2006. [7] MATLAB/SIMULINK version 2009a, The MathWorks Inc., USA 50