Comparative Analysis of Fuzzy Logic with Reduced Rule Base and PI Controller for A Direct Torque Controlled Induction Motor Drive

Comparative Analysis of Fuzzy Logic with Reduced Rule Base and PI Controller for A Direct Torque Controlled Induction Motor Drive

1Hakan ACIKGOZ, 2O.Fatih KECECOGLU, 2Ahmet GAN

1Dept. of Electrical Science, Kilis Vocational High School, Kilis 7 Aralik University, Turkey

2Dept. Of Electric-Electronics Engineering, K.Maras Sutcu mam University, Turkey

Abstract

Induction motors are most commonly used in the industry. Therefore, many control methods have been developed to obtain accurate speed trajectory and adequate torque values for induction motors. In this study, Simulation studies are realized for speed control of direct torque controlled (DTC) induction motor via MATLAB/Simulink. Firstly, a fuzzy logic controller (FLC) with reduced rule base is developed using MATLAB/Simulink Fuzzy Logic Toolbox. Then, the conventional PI controller and FLC have been applied, to speed control unit of induction motor. Simulation studies are implemented for both of the controllers under same conditions. The results obtained from conventional PI controller and FLC are analyzed and compared. According to obtained simulation results, it is observed that FLC provides better speed and torque response than PI controller.

1. Introduction

   DC motors have high performance in terms of dynamic behaviour and their control is simple. Because its flux and torque can be controlled independently. However, DC motors have certain disadvantages due to the existence of the commutators and brushes. Nowadays, induction motors are extensively used in industrial application. Induction motors have complex mathematical models with high degree of nonlinear differential equations including speed and time dependent parameters. However, they are simple, rugged, inexpensive and available at all power ratings. Therefore, the speed control of induction motor is more important to achieve maximum torque and efficiency [1-5]. By the rapid development of microprocessor, power semiconductor technologies and various intelligent control algorithm, controlling methods of induction motors have been improved. In the recent years, researchs about induction motors which are common in industrial systems due to some important advantages are focused on vector based high

   performans control methods such as field orientation control (FOC) and Direct torque control (DTC) [1-7].

   FOC principles were firstly presented by Blaschke

   [4] and Hasse [5]. FOC of induction motors are based on control principle of DC motors. DC motors have high performance in terms of dynamic behaviour and their control is simple. Armature and excited winding currents of self-excited DC motors can be independently controlled because they are vertical to each other. There isnt such case in induction motors. Made studies on induction motors showed that these motors could be controlled such as DC motors if three- phase variables are converted to dq-axis and dq-axis currents are controlled. Vector control methods which are done transform of axis have been developed. Flux and torque of induction motors can be independently controlled. Thus induction motors can adequately be used for variable speed drive applications [1-4].

   DTC were firstly presented by Depenbrock [6] and Takahashi [7]. DTC method has simple structure and the main advantages of DTC are absence of complex coordinate transformations and current regulator systems. In the DTC method, the flux and torque of the motor are controlled directly using the flux and torque errors which are processed in two different hysteresis controllers (torque and flux). Optimum switching table depending on flux and torque hysteresis controller outputs is used to control of inverter switches in order to provide rapid flux and torque response. However, because of the hysteresis controllers, the DTC has disadvantage like high torque ripple. In the recent years, FLC has found many applications. Fuzzy logic is a technique, improved by Zadeh [8] and it provides human-like behavior for control system. t is widely used because FLC make possible to control nonlinear, uncertain systems even in the case where no mathematical model is available for the controlled system [8-14]. This paper presents comparison of fuzzy logic with reduced rule base and PI controller on speed control of DTC induction motor. The performance of the proposed controller has been researched and compared with PI controller.

2. Direct Torque Control

   DTC design is very simple and practicable. It

   consists of three parts such as DTC controller, torque

   angle between the stator and rotor flux vectors. The equation of induction motor stator is given by [6]:

   and flux calculator and VSI. In principle, the DTC

   V d s i R

   (2)

   method selects one of the inverters six voltage vectors and two zero vectors in order to keep the stator flux and torque within a hysteresis band around the demand flux and torque magnitudes [6-7]. The torque produced by the induction motor can be expressed as shown below:

   s dt s s

   If the stator resistance is ignored, it can be approximated as equation 3 over a short time period [6- 7]:

   e

   e

   		s
   2 2 L	r

   		s
   2 2 L	r

   T 3 P Lm sin

   r

   (1)

   s

   Vs t

   (3)

   Where, is angle between the rotor flux and the stator flux vectors. r is the rotor flux magnitude and

   s is the stator flux magnitude. P is the pairs of poles, Lm is mutual inductance and Lr is rotor inductance. This equation (1) shows the torque is dependent on the stator flux magnitude, rotor flux magnitude and the phase.

   This means that the applied voltage vector determines the change in the stator flux vector. If a voltage vector is applied to system, the stator flux changes to increase the phase angle between the stator flux and rotor flux vectors. Thus, the torque produced will increase [6-7,15].

   0.8

   0.8

   -C- SPEED

   In1 Out1

   In1 Out1

   Fuzzy-PI Controller

   f_ref

   T_er s3 m

   fs

   sa va

   sb vb

   sc vc

   SPWM

   K*u phase

   K*u vs

   3/2

   0

   0

   Switching Table

   Switching Table

   TL

   is wm Te fis fir

   1/z

   1/z

   1/z

   Figure 1. DTC induction motor system in MATLAB/Simulink environment

   Fig. 1 shows closed loop direct torque controlled induction motor system. The closed loop DTC induction motor system is implemented in MATLAB/Simulink environment. DTC induction motor model consists of four parts such as speed control, switching table, inverter and induction motor. d-q model is used for the induction motor design. DTC blog has flux and torque within a hysteresis models. Two-level and three-level flux and torque within hysteresis band comparators are given in Fig. 2 and 3, respectively. Flux control is performed by two-level hysteresis band and three-level hysteresis band provides torque control. Outputs of the hysteresis bands are renewed in each sampling period and changing of the flux and torque are determined by these outputs.

   Voltage vectors are shown in Fig. 4. Flux control output ds, torque control output dTe and voltage vector of the stator flux are determined a Switching Look-up Table as shown in Table 1. In DTC method, stator flux and torque are estimated to compare with references of the flux and torque values by aid of stato current, voltage and stator resistance. The obtained flux and torque errors are applied to the hysteresis layers. In these hysteresis layers, flux and torque bandwidth are defined. Afterwards, the amount of deflection is determined and the most appropriate voltage vectors are selected to apply to the inverter using Switching Look-up Table.

   If a torque increment is required then dTe equals to

   +1, if a torque reduction is required then dTe equals to – 1 and if no change in the torque is required then dTe equals to 0. If a stator flux increment is required then ds is equals to +1, if a stator flux reduction is required then ds equals to 0. In this way, the flux and torque control is implemented.

   1

   1

   +1

3. Fuzzy Logic Controller

   In this paper, the FLC is proposed to control the speed of the motor to be constant. The proposed FLC and conventional PI controller are designed and applied to the DTC model. FLC is an appropriate method for designing nonlinear controllers via the use of heuristic information [15-17]. A FLC system allows changing the control laws in order to deal with parameter variations and disturbances. Fig. 5 shows the block diagram of fuzzy logic controller using simulation

   *

   +-

   ds

   study. Where e and e are the input, u is output fuzzy variables.

   s

   Figure 2. Two-level flux hysteresis comparator

   e(k) z -1

   Ke

   e

   -+ Kce

   e

   Fuzzy-PI Controller

   Ku z-1

   ++

   uu(k)

   Teref

   +-

   dTe

   e(k)-e(k-1)

   Figure 5. Block diagram of FLC

   In the design of FLC, three membership functions

   Te were used for both error e(k), change of error e(k) and

   output u. Membership functions were constructed to

   1

   1

   +1

   -1

   Te

   +1

   -1

   Te

   Figure 3. Three-level torque hysteresis comparator

   sQ

   represent the inputs and output value. Fig. 5 and 6 show the fuzzy sets and corresponding triangular membership function description of each signal for

   V3 (010)

   V2 (110)

   input and output respectively. The fuzzy sets are as follows: z = Zero, p = Positive, n = Negative. The rule base of FLC system is given in Table 2. There may be 3×3=9 possible rules in the matrix.

   V4 (011)

   V7 (111)

   V1 (100)sD

   V0 (000)

   Table 1. Rule Base

   de e	N	Z	P
   N	N	N	Z
   Z	N	Z	P
   P	Z	P	P

   de e	N	Z	P
   N	N	N	Z
   Z	N	Z	P
   P	Z	P	P

   V5 (001) V6 (101)

   Figure 4. Voltage vectors

   Table 1. Switching Look-up Table

   1

   0.8

   0.6

   0.4

   0.2

   n z p

   Flux ()	Torque (Te)	SECTORS
   		S1	S2	S3	S4	S5	S6
   =1	Te=1	V2	V3	V4	V5	V6	V1
   	Te=-1	V6	V1	V2	V3	V4	V5
   =-1	Te=1	V3	V4	V5	V6	V1	V2
   	Te=-1	V5	V6	V1	V2	V3	V4

   Flux ()	Torque (Te)	SECTORS
   		S1	S2	S3	S4	S5	S6
   =1	Te=1	V2	V3	V4	V5	V6	V1
   	Te=-1	V6	V1	V2	V3	V4	V5
   =-1	Te=1	V3	V4	V5	V6	V1	V2
   	Te=-1	V5	V6	V1	V2	V3	V4

   0

   -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

   Figure 6. Membership functions for inputs and output

4. Simulation Results

   The study of DTC induction motor drive with implementing fuzzy logic controller with reduced rule base and PI controller is carried out in the MATLAB/Simulink environment. The simulations are performed for different reference speeds with load of 3N-m and no-load during 1sec. The parameters of the induction motor used in the simulation are given in Table 3.

   Table 3. Induction Motor Parameters

   Parameters	Values
   Stator resistance (Rs)	8.231
   Rotor resistance (Rr)	4.49
   Number of Poles (P)	2
   Stator self-inductance (Ls)	0.599H
   Rotor self-inductance (Lr)	0.599H
   Moment of inertia (J)	0.0019kg-m2
   Mutual inductance (Lm)	0.5787H
   Friction factor (B)	0.000263

   Fig. 7 shows the speed response of the induction motor with both PI and FLC at no-load and the output torque is given in Fig. 8. As it seen in fig. 8, the reference speed is 2000 rpm. The PI controller response reaches to reference speed after 150 ms with overshoot and the FLC response reaches to steady state after nearly 78 ms without overshoot. The simulation results show the proposed FLC provides good speed response over the PI controller. The output torques controlled by proposed FLC and PI controllers is illustrated in fig. 8 and 9.

   2500

   10

   8

   6

   Torque (N.m)

   Torque (N.m)

   4

   2

   0

   -2

   -4

   -6

   0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

   Time (sec)

   Figure 8. The output torque response(FLC)

   10

   8

   6

   Torque (N.m)

   Torque (N.m)

   4

   2

   0

   -2

   -4

   -6

   0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

   Time (sec)

   Figure 9. The output torque response(PI)

   Fig. 9 demonstrates the dynamic response of the proposed control technique. Firstly, DTC induction motor starts to operate in a steady state at 1500 rpm reference speed. Then, a sudden step speed command increasing, from 1500 rpm to 2250 rpm is performed. The FLC follows the reference speed without any overshoot and steady state error. As it can be seen from the simulation results, the performance of FLC is obviously superior to that of conventional PI control for all speed change cases. The torque responses of proposed FLC and PI controllers are given in fig. 11 and 12, respectively.

   2500

   2000 2000

   Speed (Rpm)

   Speed (Rpm)

   1500

   2080

   1500

   Speed (Rpm)

   Speed (Rpm)

   2350

   2060

   2300

   2040

   1580

   1000

   2020

   1000

   1560

   1540

   2250

   2000

   1520

   1980

   1500

   2200

   0.52 0.53 0.54 0.55 0.56 0.57

   500

   0

   1960

   1940

   0.1

   FLC PI

   Reference

   500

   0

   1480

   1460

   1440

   0.05 0.06 0.07 0.08 0.09 0.1

   PI FLC

   Reference

   0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

   Time (s)

   Figure 7. Speed response comparison at no-load

   0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

   Time (s)

   Figure 10. Speed response comparison at no-load

   10 10

   8 8

   6 6

   Torque (N.m)

   Torque (N.m)

   Torque (N.m)

   Torque (N.m)

   4 4

   2 2

   0 0

   -2 -2

   -4

   -6

   0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

   Time (sec)

   Figure 11. The output torque response(FLC)

   10

   8

   6

   Torque (N.m)

   Torque (N.m)

   4

   2

   0

   -2

   -4

   -6

   0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

   Time (sec)

   Figure 12. The output torque response(PI)

   Constant speed response with load of 3N-m at 0.5sec is given in fig. 13. The speed response with proposed FLC has no overshoot and settles faster in comparison with PI controller and there is no steady-state error in the speed response. When the load is applied there is sudden dip in speed. The speed falls from reference speed of 1750 rpm to nearly 1739 rpm and it takes 5 ms to reach the reference speed. As it seen, the proposed control technique gives better performance against the conventional PI controller with respect to overshoot, rise time and response time. The torque responses of proposed FLC and PI controllers are given in fig. 14 and 15, respectively.

   2000

   1500

   Speed (Rpm)

   Speed (Rpm)

   1000

   0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.48 0.49 0.5 0.51 0.52 0.53 0.54

   500

   PI

   FLC

   Reference

   0

   0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

   Time (s)

   Figure 13. Speed response comparison with load

   -4

   -6

   0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

   Time (sec)

   Figure 14. The output torque response(FLC)

   10

   8

   6

   Torque (N.m)

   Torque (N.m)

   4

   2

   0

   -2

   -4

   -6

   0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

   Time (sec)

   Figure 15. The output torque response(PI)

5. Conclusions

   In this paper, DTC induction motor drive system is presented and speed control of the induction motor is implemented. The motor drive system is carried out in MATLAB/Simulink environment using mathematical model of d-q of the induction motor. Then, the proposed FLC have been designed for speed control loop via MATLAB/Fuzzy Logic Toolbox. Afterwards, Compared simulation results with conventional PI controller are given. The responses obtained from the simulation esults, showed that the behavior with fuzzy logic control is advantageous compared with PI control for all speed change cases. In addition, the fuzzy logic controller with reduced rule base is easily designed and dont need the mathematical model of system to be controlled. Therefore, these features of the proposed fuzzy controller make it more attractive.

6. References

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3. Bose, B. K., 2002. Modern Power Electronics and AC Drivers, Prentice Hall, New Jersey.

4. Blaschke, F., May, The Principle of Field Orientation as Applied to the new Transvector Closed Loop Control System for Rotating-Field Machines, Siemens Review, vol. 34, pp 217-220, 1972.

5. Hasse, K., 1969: About the dynamics of adjustable-speed drives with converter-fed squirrel-cage induction motors (in German), Ph.D. Dissertation, Darmstadt Technische Hochschule.

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   Vol. 8: 338-353

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