Fuzzy Logic : Application Of Fuzzy Logic In Adaptive Selecting Of Parameters Of PID Controller For Switched Reluctance Motor Drive

Fuzzy Logic : Application Of Fuzzy Logic In Adaptive Selecting Of Parameters Of PID Controller For Switched Reluctance Motor Drive

Abstract

Switched reluctance motor (SRM) is a form of stepper motor in which fewer number of poles are used. Thanks to its simple structure, it has the lowest construction cost of any industrial electric motor.  Common uses of SRM include applications where the rotor need to be held stationary for long periods. Moreover, it is utilized in potentially explosive environments such as mines and oil/gas industry because it does not incorporate a mechanical commutator (1). Bearing in mind the fact that the SRM drive (SRD) systems are multivariable, highly coupled and nonlinear, it is arduous to reach a satisfactory result by conventional control approach. Therefore, A fuzzy supervisor is used in this report to select parameters of a PID speed regulator. Furthermore, Simulink of MATLAB is used for simulation, which evinces that the response of the proposed system has a lower overshoot and steady state error compared with the conventional PID controller.

Introduction

Switched reluctance motor drive system (SRD) is a new type of electro-mechanical stepless speed regulation system with high reliability and wide range of speed regulation. Small starting current and large starting torque can also be realized .Therefore, it is suitable for frequent start-stop and positive & negative operation. However, due to its salient structure, the magnetic circuit of these motors are highly non-linear, which makes the SRD a multivariable, highly coupled and nonlinear system. The large ripple in torque and loud noise in the operation affect the SRD applications seriously  (2). As fuzzy control does not require an accurate mathematical model, it is suitable for nonlinear variable structure systems. In reference (2) a PID with a fuzzy supervisor is suggested which regulates only the proportional gain. Moreover in references (3), (4), (5) & (6) PID controller is replaced by a fuzzy controller. In (7) an adaptive fuzzy neural controller is used. In (8) a sensorless method is introduced. In this project a fuzzy supervisor is used along with a conventional PID controller. The fuzzy supervisor regulates proportional, integral and derivative parameters on the basis of speed error in order to achieve a better response compared with conventional PID controllers.

Lie Theory : Conversation with Leading Lie Theory Mind & Baylor University Math Department Chair Dr. Mark Sepanski & Professor

The Mathematical Model of SRM (2)

The model of SRM consists of the following electrical and mechanical parts

  1. Voltage equations

If the interaction effects of each phase are neglected, the balance equation of the phase k can be expressed as:


Where,,, &  represent the phase voltage, phase resistance, phase current and flux-linkage of the phase k windings respectively. Since flux is a function of the current and the rotor position, the above equation can be written as:

The above equation can be re-arranged as follows:

  1. Mechanical motion equations

Where is the electromagnetic torque , represents the rotational inertia , indicates the friction coefficient , shows the load torque , and represent the rotor angle and the angular velocity of the SRM respectively. The above equation can be rewritten in terms of angular velocity:

Fuzzification of input and output

For fuzzification, firstly, it is required to know the domain of each variable. Next, the linguistic variables of each variable are specified. Finally, the membership functions of each linguistic variable are selected. For all the aforementioned stages, we should use the knowledge of an experienced person. Here, using the database created by repeated simulation, the variables are sorted as in table 1. For all variables, (whether input or output) the linguistic variables are specified as in table 2  (2). Furthermore, membership functions are selected as in figures 2 & 3 for input and output variables (2).

Min.Max.Variable
-11Speed error (E)input
-11Changes of speed error (CE)
-11Kpoutput
-1010Ki
-0.0010.001Kd
signvariable
NBNegative big
NMNegative med.
NSNegative small
ZOzero
PSPositive small
PMPositive med.
PBPositive big

Table 2: Linguistic variables

Table 1: Domain of variables

E:\MS courses materials\Special subjects in instrumentation\My project\Kp,Ki,Kd.jpg

Figure 1: Membership functions of input variables

E:\MS courses materials\Special subjects in instrumentation\My project\E,CE.jpg

Figure 3: Membership functions of output variables

The membership functions of Ki and Kd are identical in shape to that of Kp, nevertheless, according to table 1, the horizontal axis ranges are different. In above figures, nearly all membership functions are triangular, except for NB & PB which are of the form of gauss2.

Fuzzy Rule Base

IFTHEN fuzzy rules connect inputs to outputs. Similar to membership functions, these rules need to be stated on the basis of the knowledge of an expert. The rules are given in Table 3  (2).

CE
Kp, Ki, KdNBNMNSZOPSPMPB
ENBPB, NB, PSPB, NB, NSPM, NM, NBPM, NM, NBPS, NS, NBPS, ZO, NMZO, ZO, PS
NMPB, NB, PSPB, NB, NSPM, NM, NBPS, NS, NMPS, NS, NMZO, ZO, NSNS, ZO, ZO
NSPM, NB, ZOPM, NM, NSPM, NS, NMPS, NS, NMZO, ZO, NSNS, PS, NSNS, PS, ZO
ZOPB, NM, ZOPM, NM, NSPS, NS, NSZO, ZO, NSNS, PS, NSNM, PM, NSNM, PM, ZO
PSPS, NM, ZOPS, NS, ZOZO, ZO, ZONS, PS, ZONS, PS, NSNM, PM, ZONM, PB, ZO
PMPS, ZO, PMZO, ZO, NSNS, PS, PSNS, PS, PSNM, PM, PSNM, PB, PSNB, PB, PB
PBZO, ZO, PBZO, ZO, PMNM, PS, PMNM, PM, PMNM, PM, PSNB, PB, PSNB, PB, PB

Table 3: Fuzzy rule base

Inside MATLAB Fuzzy Logic Toolbox, there is a part named Fuzzy Inference System (FIS), where Inputs and outputs of a fuzzy system can be introduced, the rule base written and a file with extension “.fis” created. This file can be invoked via MATLAB or Simulink. Here, this fis file is named “Fuzzy adaptive PID controller”. Once the fis file is completed, the following command is invoked in Command Window:

readfis (‘Fuzzy adaptive PID controller’)

This will make the following list be shown, which includes method used for fuzzy calculations.

       name: ‘Fuzzy adaptive PID controller’

       type: ‘mamdani’

       andMethod: ‘min’

       orMethod: ‘max’

       defuzzMethod: ‘centroid’

       impMethod: ‘min’

       aggMethod: ‘max’

       input: [1×2 struct]

       output: [1×3 struct]

       rule: [1×49 struct]

Simulink Silulation

In the MATLAB library, a model is represented for SRM as shown in figure 4, which is one of the MATLAB Demos for speed regulation of SRM  (9). By using this demo and adding feedback from speed, a PID controller and the fuzzy supervisor, the model in figure 5 is achieved.

E:\MS courses materials\Special subjects in instrumentation\My project\MATLA SRM.JPG

Figure 4: Simulink model of SRM in MATLAB Demos  (7)E:\MS courses materials\Special subjects in instrumentation\My project\Capture.JPG

Figure 5: Simulink model of SRM with PID controller and fuzzy supervisor

In this model, a 6/4-pole-three-phase SRM is used. DC voltage is 240 V. Rotor and stator resistors are both 0.05 ohm, inertia is 0.05 Kg.m2 and friction is 0.02 N.m.s . Finally, the model in figure 6 was created which contains another PID controlled SRM without fuzzy supervisor. The  Fuzzy Logic Controller block was connected to the aforementioned fis file.
E:\MS courses materials\Special subjects in instrumentation\My project\Capture3.JPG

Figure 6: the model used for comparison between solo PID controller and fuzzy-supervised PID controller

Two simulations were performed: response to load disturbance with a magnitude of 10 N.m in 0.3 s, and response to random disturbsnce. Results are shown in figures 7 & 8.

E:\MS courses materials\Special subjects in instrumentation\My project\Capture4.jpg

Figure 7: comparison between response of fuzzy-supervised PID controller and solo PID. Notice the effect of disturbance @ 0.3 s

E:\MS courses materials\Special subjects in instrumentation\My project\Capture2.JPG

Figure 8: response to random disturbance

Conclusion

The response of PID controller with fuzzy supervisor has no overshoot. The setteling time is very short too. Moreover, in fuzzy-PID controller, speed fluctuations are more reasonable in presense of random load disturbance. Therefore the fuzzy-PID system seems to achieve more stable results.

Fuzzy Logic : Application Of Fuzzy Logic In Adaptive Selecting Of Parameters Of PID Controller For Switched Reluctance Motor Drive Written by Hossein Osyani Khoozani

References

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4. FUZZY LOGIC CONTROL OF A SWITCHED RELUCTANCE MOTOR. L.G.B.Rolim, M..G.Rodrigues W. I. Suemitsu P.Branco J.A.Dente. 

5. Speed Control of Switched Reluctance Motor Based on Fuzzy Logic Controller. Hasanien, Gamal M. Hashem Hany M. s.l. : Cairo University, 2010.

6. Adaptive Neuro-Fuzzy Controller of Switched Reluctance Motor. Ahmed Tahour, Hamza Abid, Abdel Ghani Aissaoui. s.l. : SERBIAN JOURNAL OF ELECTRICAL ENGINEERING, 2007, Vol. 4.

7. A PRACTICAL APPROACH TO THE DESIGN AND IMPLEMENTATION OF SPEED CONTROLLER FOR SWITCHED RELUCTANCE MOTOR DRIVE USING FUZZY LOGIC CONTROLLER . Rengasamy, Subramanian Vijayan — Shanmugam Paramasivam —. s.l. : Journal of ELECTRICAL ENGINEERING, 2007, Vol. 58.

8. Sensorless Control of Switched Reluctance Motor Drive with Sensorless Control of Switched Reluctance Motor Drive with. Kumar, R. A. Gupta S.K.Bishnoi Rajesh. s.l. : International Journal of Computer Applications, 2010, Vol. 1.

9. MATLAB Help