Paper id 26201464

International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637

Tuning a PID controller for a Separately Excited DC Motor Shweta Choudhary1, Sushil Prashar2, Gagandeep Sharma3 ‫ ݐ݊݁݉ݐݎܽ݌݁ܦ ݈ܽܿ݅ݎݐ݈ܿ݁ܧ‬ଵ,ଶ,ଷ , ‫ܦ‬. ‫ܣ‬. ܸ. ‫ܿ݁ܶ & ݃݊݅ݎ݁​݁݊݅݃݊ܧ ݂݋ ݁ݐݑݐ݅ݐݏ݊ܫ‬ℎ݊‫݈݀݊ܽܽܬ ݕ݃݋݈݋‬ℎܽ‫ݎ‬, ‫ܽ݅݀݊ܫ‬ଵ,ଶ,ଷ ‫ݏ‬ℎ‫ܿܽݐ݁ݓ‬ℎ‫݀ݑ݋‬ℎܽ‫ݕݎ‬352@݈݃݉ܽ݅. ܿ‫݉݋‬ଵ , ‫ݏܽݎܽ݌‬ℎܽ‫ݏݑݏ_ݎ‬ℎ݈݅@‫ܽݕ‬ℎ‫݋݋‬. ܿ‫݉݋‬ଶ , ݃ܽ݃​݃‫ݑ‬246@݈݃݉ܽ݅. ܿ‫݉݋‬ଷ

Abstract-From the last decade, the need for electric driven vehicle has risen rapidly due to the global warming problem. The traditional Proportional-Integral-Derivative controller, which has been widely used for the speed control of dc motor drives, has been compared with the relatively new Integral-Proportional-Derivative controller which first discussed in the year of 1978. PID controller is used to control the speed of DC Motor. A model is developed and simulated using MATLAB/SIMULINK. This paper presents different speed controlling strategies for DC motor. These strategies are Proportional Controller, Proportional Integral Controller, Proportional Derivative Controller, Proportional Integral Derivative Controller. Mathematical model of separately excited DC motor is developed and speed of the motor is controlled by PID controller in MATLAB/SIMULINK environment. Tuning of the controller is done by using two different methods and results are compared.

Index Terms- MATLAB/SIMULINK, excited, tuning.

1. INTRODUCTION DC motor is the most common choice if wide range of adjustable speed drive operation is specified. Of the three kinds of DC motors – series shunt and separately excited DC motors, separately excited DC motors are most often used. Different speed can be obtained by changing the armature voltage and the field voltage. A common actuator in control systems is the DC motor. It directly provides the rotary motion and, coupled with wheels or drums and cables, can provide transitional motion. Today variant applications require more and more features such as speed applications to multipurpose accessories, user friendly interfaces, and security features. Different type of electric motor is shown in next figure.

[1]

Shunt Motor DC Motor

Series Motor Separately Excited Permanent Magnet

ELECTRIC MOTOR

AC Motor

Induction Motor Synchronous Motor Stepper Motor

Other Motors

Brushless DC Motor Hysteresis Motor Reluctance Motor

Fig.1.Types of electric motor DC machines continue to be widely used in industry. A major application for small DC electric motors is in automobiles. Large DC motors are used in power shovels, elevators, and some factories. Factories such as aluminum and steel rolling mills use large numbers of DC motors.

These applications require the precise control of speed and torque which the DC motors can provide. The higher maintenance cost of the DC motors is accepted because of their precise performance capabilities. The DC motors in rolling mills may be in sizes up to and even exceeding

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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 6000 horsepower. As the processes and requirements in industry become more complex the communications requirements both within the factory and outside the factory become more critical. Computer networks are now being used in factories because of their ability to carry more data and their lower cost. Many protocols on these computer networks allow delays to occur under high load conditions. Some protocol seven permit data to be lost under certain conditions. Control systems are sensitive to the delays in their associated communication systems. There are various techniques to attempt to mitigate the effect of time delays in control systems. This paper analyzes one of these methods which utilize a Proportional-Integral-Differential controller in a DC motor control system. Next figure shows different types of DC motors. [2]

DC MOTOR Separately Excited

Self Excited

Permanent Motor

performances more than other DC motor models.

The DC motor is driven by applied voltage.

The separately excited motor has independent voltage supplies to the field and rotor windings allowing more control over the motor performance.

The voltage on either the field or the rotor windings can be used to control the speed and torque of a separately excited motor. Application of separately excited motor is in train and automotive traction applications. [3] 3. DC MOTOR MATHEMATICAL MODEL This DC motor system is a separately excited DC motor, which is often used to the velocity tuning and the position adjustment. This paper focuses on the study of DC motor linear speed control, therefore, the separately excited DC motor is adopted. Make use of the armature voltage control method to control the DC motor velocity, the armature voltage controls the distinguishing feature of method as the flux fixed, is also a field current fixedly. [4] 3.1. Motor controlled by the stator

Shunt Excited

a. The rotor’s current ݅௔ (t) is constant, i.e., ݅௔ (t) = ‫ܫ‬ Compound ௔. b.

The magnetic flux Φ (t) between the stator and Excited Series the rotor is given by the linear relation: Excited Φ(t) = ‫ܭ‬௙ ݅௙ (t) (3.1) Cumulative Differential Where ‫ܭ‬௙ is a constant and if (t) is the stator’s Compound Compound current. c. The torque Tm (t) that is developed by the motor Fig.2. Types of DC motor. is given by the relation ܶ௠ (t) = ‫ܭ‬௠ ‫ܫ‬௔ Φ (t) 2. MODEL OF DC MOTOR (3.2) where ‫ܭ‬௠ is a constant.

DC machines are characterized by their versatility. d. The Kirchhoff’s voltage law for the stator By means of various combinations of shunt, series, network is ௗ௜ and separately-excited field windings they can be ‫ݒ‬௙ (t) = ೑ ‫ܮ‬௙ + ܴ௙ ݅௙ ௗ௧ designed to display a wide variety of volt-ampere (3.3) or speed-torque characteristics for both dynamic e. The rotor’s rotational motion is described by the and steady-state operation. Because of the ease differential equation with which they can be controlled systems of DC ௗ௪ ܶ௠ (t) = ‫ܬ‬௠ ೘ + ‫ܤ‬௠ ‫ݓ‬௠ machines have been frequently used in many ௗ௧ (3.4) applications requiring a wide range of motor speeds Where ‫ܬ‬௠ is the torque inertia, ‫ܤ‬௠ is the coefficient and a precise output motor control, In this paper, the separated excitation DC motor model is chosen of friction ߠ௠ (t) is the angular position or according to his good electrical and mechanical displacement, ‫ݓ‬௠ (‫ )ݐ‬and is the angular velocity of

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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 the motor. Substituting equation (3.1) into equation (3.2), Then ܶ௠ (t)= ‫ܭ‬௠ ‫ܭ‬௙ ‫ܫ‬௔ ݅௙ (t) (3.5) Also, if we substitute equation (3.5) into equation (3.4), we have ‫ܬ‬௠

ௗ௪೘ ௗ௧

+ ‫ܤ‬௠ ‫ݓ‬௠ =‫ܭ‬௠ ‫ܭ‬௙ ‫ܫ‬௔ ݅௙ (t) = ‫ݒ‬௙ (t)

(3.6)

The transfer function of DC motor controlled by the rotor is calculated as the follow:By applying the Laplace transform to equation (3.11) and equation (2.17): ‫ܮ ݏ‬௔ ‫ܫ‬௔ (‫ )ݏ‬+ ܴ௔ ‫ܫ‬௔ (‫)ݏ‬+ ‫ܭ‬௕ ߗ௠ (‫ܸ = )ݏ‬௔ (‫)ݏ‬ (3.13) ‫ܬ‬௕ ‫ߗݏ‬௠ (‫ )ݏ‬+ ‫ܤ‬௠ ߗ௠ (‫= )ݏ‬ ‫ܭ‬௜ ‫ܫ‬௔ (‫)ݏ‬, ߗ௠ (‫=)ݏ‬s ߆௠ (‫( )ݏ‬3.14)

The transfer function of DC motor controlled by the stator is calculated as the follow: Applying the Laplace transforms to equation (3.3) and equation (3.4) and after some algebraic manipulations is driven, then the following transfer function is driven as:G (s) =

ఏ೘ (௦) ௏೑ (௦)

=

1 ‫ܮݏ‬௔ + ܴ௔

‫݅ܭ‬ ‫ܬ‬௠ ‫ ݏ‬+ ‫ܤ‬௠

௄೘ ௄೑ ூೌ ௦(௃೘ ௦ା஻೘ ) (௅೑ ௦ାோ೑ )

(3.7) Where all initial conditions of the motor are assumed zero.

‫ܭ‬௕ ‫ݏ‬

2 Motors controlled by the rotor a. The rotor’s current ݅௙ (t) is constant, i.e., ݅௙ (t) = ‫ܫ‬௙ . b. The magnetic flux Φ (t) given by equation (3.1), will be constant since ݅௙ (t) is a constant, i.e. Φ (t) = ‫ܭ‬௙ ݅௙ (t) Φ c. The torque Tm (t), given by equation (3.2), now has the form ܶ௠ (t) = ‫ܭ‬௠ ݅௔ (‫ܭ =)ݐ‬௜ ݅௔ (t) (3.8) where ‫ܭ‬௜ = ‫ܭ‬௠ Φ d. The voltage ‫ݒ‬௕ (‫ )ݐ‬is proportional to the angular velocity of the motor, i.e. ‫ݒ‬௕ (t) =‫ܭ‬௕ ‫ݓ‬௠ (‫)ݐ‬ (3.9) e. The Kirchhoff’s law of voltages for the rotor network is ‫ܮ‬௔ =

ௗ௜ೌ ௗ௧

+ ܴ௔ ݅௔ + ‫ݒ‬௕ = ‫ݒ‬௔

(3.10) or ‫ܮ‬௔ =

ௗ௜ೌ ௗ௧

+ ܴ௔ ݅௔ + ‫ܭ‬௕ ‫ݓ‬௠ = ‫ݒ‬௔

(3.11) Where use was made of equation (3.8) f. The rotor’s rotational motion is described by the differential equation ‫ܬ‬௠

ௗ௪೘ ௗ௧

(3.12)

+ ‫ܤ‬௠ ‫ݓ‬௠ = ܶ௠ (‫ܭ)ݐ‬௜ ݅௔ , ‫ݓ‬௠ =

ௗఏ೘ ௗ௧

Fig.3. Transfer function form of DC motor All initial conditions are assumed zero. The transfer function will then be G (s) =

ఏ೘ (௦) ௏೑ (௦)

=

௄೔ ௦(௅ೌ ௦ାோೌ ) (௃೘ ௦ା஻೘ )ା௄೔ ௄್ ௦

(3.15) G (s) =

௄೔ ௅ೌ ௃೘ ௦ య ା (௃೘ ோೌ ା௅ೌ ஻೘ )ௌ మ ା (ோೌ ஻೘ ା ௄೔ ௄್ )௦

(3.16)

4. DIFFERENT CONTROLLER TECHNIQUES 4.1. Proportional Controller The Proportional, or “P”, controller is the most basic controller. The control law is simple: control is directly proportional to error. Proportional control is the easiest feedback control to implement, and simple proportional control is probably the most 18 common kind of control loop.

A proportional controller is just the error signal multiplied by a constant and fed out to the drive.

The chief shortcoming of the P-control law is that it allows DC offset error; it droops in the presence of fixed disturbances. Such disturbances are 139

International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 ubiquitous in controls: Ambient temperature drains heat, power supply loads draw DC current, and friction slows motion. DC offset error cannot be tolerated in many systems, but where it can, the modest P controller can suffice. [5] 4.2. Proportional Integral Controller The P-I controller has a proportional as well as an integral term in the forward path, the block diagram with a P-I controller for a dc motor drive is shown in Fig. 1. The integral controller has the property of making the steady state error zero for a step change, although a P-I controller makes the steadystate error zero, it may take a considerable amount of time to accomplish this.[6] 4.3. Proportional Derivative Controller The P controller is augmented with a ‘D’ term to allow the higher proportional gain. The ‘D’ gain advances the phase of the loop by virtue of the 90 degree phase lead of a derivative. Using the ‘D’ gain will usually allow the system responsiveness to increase. The differential term is the last value of the position minus the current value of the 19 position. This gives a rough estimate of these velocity (delta position/sample time), which predicts where the position will be in a while. The ‘PD’ controller is fast, powerful but more susceptible to stability problems, sampling irregularities, noise, and high frequency oscillations. Derivatives have high gain at high frequencies. So while some ‘D’ does help the phase margin, it affects the gain margin by adding gain at the phase crossover, typically at high frequency.

Also, the derivative gain is sensitive to noise. In case of a differential element, the output is proportional to the position change divided by the sample time. If the position is changing at a constant rate but the sample time varies from sample to sample, noise will be observed. Since the differential gain is usually high, this noise will be amplified a great deal. Differential control suffers from noise problems because noise is usually spread relatively evenly across the frequency spectrum. Control commands and plant outputs, however, usually have most of their content at lower frequencies. Proportional control passes noise. Integral control averages its input signal, which tends to eliminate noise. Differential control enhances high frequency signals, so it enhances

noise. The ‘D’ gain needs to be followed by a low pass filter to reduce the noise content. [7] 4.4. PID Controller Consider the characteristics parameters – proportional (P), integral (I), and derivative (D) controls, as applied to the diagram below in Fig.4.

A PID controller is simple three-term controller.

The letter P,I and D stand for P- Proportional, IIntegral, D- Derivative. The transfer function of the most basic form of PID controller is ‫ܭ = )ݏ(ܥ‬௣ + ݇௜ /‫ ݏ‬+ ‫ܭ‬ௗ ‫ݏ‬ Where ‫ܭ‬௣ = Proportional gain, ‫ܭ‬௜ = Integral gain and ‫ܭ‬ௗ = Derivative gain.

‫ܭ‬௣

1 ‫ݏ‬

‫ܭ‬௜

e

u

݀‫ݒ‬ ݀‫ݐ‬

‫ܭ‬ௗ

Fig.4. Simulation model of PID Controller The control u from the controller to the plant is equal to the Proportional gain (‫ܭ‬௣ ) times the magnitude of the error plus the Integral gain (‫ܭ‬௜ ) times the integral of the error plus the Derivative gain (‫ܭ‬ௗ ) times the derivative of the error. [8] The PID controller has the following form in the time domain: u(t)=

‫ܭ‬௣ e(t)

௧

+ ‫ܭ‬௜ ‫׬‬଴ ݁(‫)ݐ‬dt

+

‫ܭ‬ௗ

ௗ௘(௧) ௗ௧

(3.17) 140

International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 Table (1) Equation of controller in the time domain Proportional Control

u(t)= ‫ܭ‬௣ e(t)

Integral Control

u(t)= ‫ܭ‬௜ ‫׬‬଴ ݁(‫)ݐ‬dt

Derivative Control

u(t)= ‫ܭ‬ௗ

௧

ௗ௘(௧) ௗ௧

The PID controller has three principal control effects. The proportional (P) action gives a change in the input (manipulated variable) directly proportional to the control error. The integral (I) action gives a change in the input proportional to the integrated error, and its main purpose is to eliminate offset. The less commonly used derivative (D) action is used in some cases to speed up the response or to stabilize the system, and it gives a change in the input proportional to the derivative of the controlled variable. The overall controller output is the sum of the contributions from these three terms. The corresponding three adjustable PID parameters are most commonly selected to be (1) Controller gain- (increased value gives more proportional action and faster control) (2) Integral time- (decreased value gives more integral action and faster control) (3) Derivative time- (increased value gives more derivative action and faster control) Although the PID controller has only three parameters, it is not easy, without a systematic procedure, to find good values (tunings) for them.

In fact, a visit to a process plant will usually show that a large number of the PID controllers are poorly tuned. The objective of this paper is to provide simple model-based tuning rules that give insight into how the tuning depends on the process parameters based on very simple process information. These rules may then be used to assist in retuning the controller if, for example, the production rate is changed. Another related objective is that the rules should be so simple that they can be memorized. [9] 5. TUNING OF PID CONTROLLER The most critical step in application of PID controller is parameters tuning. Today self-tuning PID digital controller provides much convenience in engineering. [10] A very important step in the use of controllers is the controller parameters tuning process. In a PID

controller, each mode (proportional, integral and derivative mode) has a gain to be tuned, giving as a result three variables involved in the tuning process. [11] Due to its simplicity and excellent if not optimal performance in many applications, PID controllers are used in more than 95% of closed-loop industrial processes. We are most interested in four major characteristics of the closed-loop step response.

They are (1) Rise Time: the time it takes for the plant output Y to rise beyond 90% of the desired level for the first time.

(2) Overshoot: how much the peak level is higher than the steady state, normalized against the steady state.

(3) Settling Time: the time it takes for the system to converge to its steady state.

(4) Steady-state Error: the difference between the steady state output and the desired output.

Table (2) Effects of the Gains in the Response of the System Gai n

Rise Time

‫ܭ‬௣

Decreas e Small Change Decreas e

‫ܭ‬௜ ‫ܭ‬ௗ

Maximu m Overshoo t Increase Decrease Increase

Settling Time

Steady State Error

Small Change Increase

Decrease

Decreas e

Small Change Eliminat e

Typical steps for designing a PID controller are (1) Determine what characteristics of the system needs to be improved.

(2) Use KP to decrease the rise time.

(3) Use KD to reduce the overshoot and settling time.

(4) Use KI to eliminate the steady-state error.

A PID may have to be tuned when (1) Careful consideration was not given to the units of gains and other parameters.

(2) The process dynamics were not wellunderstood when the gains were first set, or the dynamics have (for any reason) changed.

(3) Some characteristics of the control system are direction-dependent (e.g. actuator piston area, heatup/cool-down of powerful heaters).

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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 (4) You (as designer or operator) think the controllers can perform better.

Always remember to check the hardware first because there are many conditions under which the PID may not have to be tuned. These conditions are when 1) A control valve sticks. Valves must be able to respond to commands.

2) A control valve is stripped out from highpressure flow where the valve’s response to a command must have some effect on the system.

3) Measurement taps are plugged, or sensors are disconnected. Bad measurements may have you correcting for errors that don’t exist. Once fix these hardware problems then depending on the responses we obtain an appropriate decision can be taken whether or not to tune a PID controller.

Fig.5. SIMULINK model of DC motor in MATLAB

6. SIMULINK MODEL AND RESULTS Previously shown figure 3 represents transfer function form of separately excited DC motor. The first transfer function shows stator of machine and second transfer function shows rotor or load of machine.

Figure 5 shows that simulink model with values of ܸ௙ = rotor voltage, ‫ܮ‬௔ =rotor inductance, ܴ௔ =rotor resistance, ܹ௠ (t) = angular velocity of the motor, ‫ܤ‬௠ = coefficient of friction, ‫ܬ‬௠ =torque inertia, ‫ܭ‬௜ and ‫ܭ‬௕ are constants.

Fig.6. Automatic tuning model in MATAB/SIMULINK Figure number 6 and 7 shows tuining methods in MATLAB/SIMULINK envirnoment named as automatic tuning and soft tuning respectively.

Figure 8 and 9 are shows the output of the system between time and voltage amplitude for speed of DC motor.

During tuning of PID controller with automatic tuning method and soft tuning method step response of both methods shows following result.

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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 Output During Soft Tuning

1

A m p litu d e

0.8 0.6 0.4 0.2 0 0

10

20

30

40

50

Time (sec) Fig.9. Soft tuning results

Fig.7. Soft tuning model in MATLAB/SIMLINK At the time of automatic tuning step responses shows .0253 sec rise time, 1.18 setting time, 8.33% overshoot.

At the time of soft tuning step responses shows 0.114 sec rise time, 5.2 setting time, 19.3% overshoot.

REFERENCE

That means automatic tuning gives better results as compare to soft tuning.

Output During Automatic Tuning 2.5

A m p lit u d e

2

1.5

1

0.5

0 0

5

10

15

20

25

30

35

40

Time (sec)

Fig.8. Automatic tuning results

45

7. CONCLUSION This paper gives a comparative study between tuning methods of PID controller for speed control of separately excited DC motor. As shown by previous results automatic tuning of the controller gives more accurate and stable results as compare to soft tuning.

50

[1] Aykut, K. (2011): Study on Fuzzy Logic Control of Electrical Machine, Association for Scientific Research, Mathematical and Computational applications, Vol.16,NO.1,pp.236-247.

[2] Kirkpatrick, K. P.; Chaudhry, G.M. (2009): DC Machine Control with Time Delay and a PID Controller, IEEE Conference on Automation Science and Engineering, pp.783-787.

[3] Dr. Kumar Jain, S; Senger, K.P. (2014): Setting up Adaptive Neuro Fuzzy Based Speed Control of DC Motor using Wavelet Transform Comparison with PID- Partical Swarm Optimization Strategy, International Journal of Research in Engineering Technology and Management, Vol. 02, pp.1-4.

[4] Huang, G; Lee, S. (2008): PC-based PID Speed Control in DC Motor, Audio, Language and Image Processing, International Conference IEEE, pp.400-407.

[5] Lotfi A. Z. (1999): Outline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on 143

International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 Systems, Man and cybernetics, SMC-3(1):2844.

[6] Mokrani, L.; Abdessemed, R. (2009): A Fuzzy Self Tuning PI Controller for Speed Control of Induction Motor Drive, Materials Laboratory, Electrical Engineering Department, Engineering Science Faculty, Laghouat University. Route de Ghardala B. P.37G. [7] Singh, Y. P.; Ahmed, A. (1996): Fuzzy linguistic control systems for process control applications, Journal of IETE, vol.42, no6, pp 363-376.

[8] Ang, K.; Chong, G.; Li, Y. (2005): PID control system analysis, design and technology, IEEE, vol. 13, pp. 559-576.

[9] Skogestad, S. (2001): Probably the best simple PID tuning rules in the world, Journal of Process Control, pp.1-27.

[10] Faieghi, M.R.; Azimi, S.M. (2010): Design an Optimized PID Controller for Brushless DC Motor by Using PSO and Based on NARMAX Identified Model with ANFIS, IEEE, 12th International Conference on Computer Modelling and Simulation, pp.16-21.

[11] Mallesham, G.; Rajani, A. (2006): Automatic Tuning of PID Controller Using Fuzzy Logic, 8th International Conference on Development and Application Systems Romania, pp.120127.

[12] El-Gammal, A. (2009): A Modified Design of PID Controller For DC Motor Drives Using Particle Swarm Optimization PSO, Power Engineering, Energy and Electrical Drives, International Conference IEEE, pp.419-424.

[13] Ilyas, A.; Jahan, A.; Mohammad, A. (2013): Tuning of Conventional PID and Fuzzy Logic Controller Using Different Defuzzification Techniques, International Journal of Scientific and Technology Reasarch, Vol.2, pp.138-142.

[14] Abhinav, R.; Sheel, S. (2012): An Adaptive, Robust control of DC motor Using Fuzzy-PID controller, IEEE International Conference on Power Electronics, Drives and Energy Systems, pp.1-5.

[15] Singh, A. R.; Giri, V. K. (2012): Compare and Simulation of Speed Control of DC Motor Using PID and Fuzzy Controller, International Journal of Electrical, Electronics & Communication Engineering, Vol. 2 No. 10, pp.814-817.

[16] Rai, J. N.; Singhal, M. (2012): Speed Control of DC Motor Using Fuzzy Logic Technique, Journal of Electrical and Electronics Engineering, Volume 3, PP 41-48.

[17] Ahmed, H. (2013): Controlling of D.C. Motor using Fuzzy Logic Controller, Conference on Advances in Communication and Control Systems, pp.666-670.

[18] Adewuyi, P.A. (2013): DC Motor Speed Control: A Case between PID Controller and

Fuzzy Logic Controller, International Journal of Multidisciplinary Science and Engineering, Vol. 4, pp.36-40.

[19] Ganguly, A.; Banerjee, A. (2013): Design of Tuning Methods of PID Controller Using Fuzzy Logic, International Journal of Emerging trends in Engineering and Development, Vol.5, pp.239-248.

[20] Kumar, K. R.; Dr. Choudhary, G.K. ; Kumar, C. (2011) "Speed Control of DC Motor using Fuzzy Technique" ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, pp.31-35

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