COMPARATIVE STUDY OF INTEGER ORDER PI-PD CONTROLLER …

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Int. J. Elec&Electr.Eng&Telecoms. 2015 Swati Singh and Ankita Kosti, 2015

COMPARATIVE STUDY OF INTEGER ORDER PI-PDCONTROLLER AND FRACTIONAL ORDER PI-PDCONTROLLER OF A DC MOTOR FOR SPEED AND

POSITION CONTROL

Swati Singh1* and Ankita Kosti1

*Corresponding Author: Swati Singh,[email protected]

This paper includes the comparative study of fractional order PI and PD control system. In thispaper both controllers are used for the speed control and position control of the DC machine.Both these controllers are designed on time domain. The closed loop performances of PI andPD fractional order controllers are then compared with the classical integer PI and PD controllers’performance. The result shows that fractional order PI and PD controllers are better than classicalinteger order PI and PD controllers.

Keywords: Transfer function, Gain margin, Simulink

INTRODUCTIONControl of mechatronic systems is the biggestchallenge due to their interdisciplinary nature.PID controllers are simple in nature and robust,thus they are used for linear mechatronicsystems. Another method fractional ordercontrollers are also used for controllingpurpose. Speed Control of DC motors iscommon example of mechatronic domains.

The control strategies for DC motors havebeen ranged from simple PID controller toadvance fractional order controller. Fractionalorder PID controllers have extra tuning

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Int. J. Elec&Electr.Eng&Telecoms. 2015

1 Department of Electrical Engineering, Sri Ram Institute of Technology, Jabalpur, India.

parameters in comparison to classical PIDcontrollers because of which they have thecapacity to increase the closed loopperformance and robustness of the closed loopsystems.

In Fractional order controllers theperformance criteria are usually specified interms of gain crossover frequency, phasecrossover frequency, phase margin, gainmargin and robustness to open loop gainvariations.

This paper illustrates the basic time domainand frequency domain concepts. This paper

Research Paper

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Int. J. Elec&Electr.Eng&Telecoms. 2015 Swati Singh and Ankita Kosti, 2015

represents the tuning procedure for Fractionalorder PI controllers as well as tuning examplefor the speed control of DC motors. Also thetuning methods for Fractional order PDcontrollers and position control of DC motorsare represented in this paper.

Speed Control of DC MotorsFor the speed control, the controlled variableis the angular velocity.

In the first experimental set up, the speedcontrol DC motor using fractional order PIcontroller is done. The transfer function ofFractional order PI controller is given as:

...(4)

Equation (4) implies the following things:

• An imposed gain crossover frequency of theopen loop system is 1.

• An imposed phase margin of the open loopsystem is (– + m).

• Condition for robustness to gain variationsis zero.

The identification of a system was basedon a Pseudo Random Binary Signal(PRBS). To generate this followingcommand is used in MATLAB:

• idinput(127, ’PRBS’, [0 1/1], [-1 1])

By using Prediction Error Method (PEM) thesystem’s model is defined. The transferfunction of DC motor can be given as:

...(5)

Imposed performance specifications are,cg = 1.5, m = 50

The intersection of the two curves yieldssolution for ki and . Final values of ki = 2.26and = 0.79 are used to compute the value ofthird parameter kp.

Position Control of DC MotorsIn the second experimental set up, the positioncontrol DC motor using fractional order PDcontroller is done.

To design fractional order PD controllerfollowing equations are used:

Figure 1: General Model of DC Motor

...(1)

...(2)

Equation (2) represents a simplified modelwhere time constant of the armatureis taken as constant.

The transfer function from (t) as controlledvariable to armature voltage Va (manipulatedvariable) will be:

...(3)

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Int. J. Elec&Electr.Eng&Telecoms. 2015 Swati Singh and Ankita Kosti, 2015

...(6)

...(7)

In this next tuning parameters for fractionalorder PD controller is obtained, kp = 1.03, kd =1.1 and = 0.6.

RESULTS

...(8)

Above equation represents the identifiedmodel for DC Motor voltage-speed.

For position control discrete model is:

...(9)

Figure 3 represents a simulink model forfractional order PI controller. Result of thismodel is illustrated in Figure 4. Comparisonof Fractional order PI controller is done with

Integer order PI controller. The Integer orderPI controller has been designed using thesame specifications of Fractional order PIcontroller. In this case = 1 and tuningparameter are kp = 1.13 and ki = 2.23. Theseobservations indicate that fractional order PIcontrollers are much better than integer orderPI controllers.

In the second experimental set up, PDcontrollers are used to control the position ofthe DC motor.

Figure 4: Step Response of DC MotorSpeed Control

Figure 3: Simulink Diagram for DC MotorSpeed Control

Figure 2: Graphical selection forparameters ki and

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Int. J. Elec&Electr.Eng&Telecoms. 2015 Swati Singh and Ankita Kosti, 2015

Experimental parameters for fractionalorder PD controllers are kp = 0.85 and kd =1.15.

By comparing the experimental results forposition control it can be concluded that controleffort is similar for both PD controllers but forset point tracking, the fractional order PDcontroller outperforms than integer order PDcontrollers.

CONCLUSIONIn this paper, speed and position control of DCmotors by fractional order PI and PD controllersis done. By experimental and simulationresults, it is proved that fractional order PI andPD controllers outperforms the integer orderPI and PD controllers.

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Figure 5: Diagram for Position Controlof DC Motor

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Int. J. Elec&Electr.Eng&Telecoms. 2015 Swati Singh and Ankita Kosti, 2015

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