SPEED CONTROL OF DC MOTOR USING PID AND FUZZY CONTROLLER:
COMPARATIVE STUDY
Renin Ravindran
*1, Parag Nukte
*2, Pranav Waghmare
*3, Pooja Vhankhande
*4, Ashitosh Chavan
*5, Ravikumar Jadhav
*6*1,2,3,4
UG Students, E&TC, MIT Academy of Engineering, Alandi(D), Pune, Maharashtra, INDIA
*5
Assistant Professor, E&TC, MIT Academy of Engineering, Alandi(D), Pune, Maharashtra, INDIA
*6
Assistant Professor, Avantika University, Ujjain, MP, INDIA.
ABSTRACT
The paper explains an efficient method for controlling the speed of DC motor using various control laws. The PID and fuzzy control are used to simulate and evaluate the effects on the speed of the DC motor. The paper demonstrates a complete study of DC motor modeling, analysis and design using MATLAB and SIMULINK. The PID control demands plant knowledge while a fuzzy controller requires a rule-based knowledge.
Keywords: DC Motor, Defuzzification, FLC, Fuzzification, SIMULINK.
I. INTRODUCTION
DC Motors are popular in the industry [1] [2] due to high accuracy and fine increments while regulating its speed. Due to the simple structure and robust performance, controllers like Proportional-Integral-Derivative (PID) and Fuzzy Logic Controller (FLC) are used in a wide range of applications in industry. The design of PID control requires knowledge of proportional, integral and derivative gain. Since a long time to the present era, great effort was made to find ways of reducing time spent refining controller choices. Lots of optimizations are made in the PID controllers [3] [4]. The FLC can minimize the nonlinearity effect in DC motor efficiently as compared to standard control and enhances system performance [5] [6]. The paper illustrates the comparative analysis of speed control of DC motor using PID and FLC. The MATLAB-SIMULINK is used for performance analysis and modeling of the DC motor. The paper is structured as follows. Section-2 gives the mathematical model of the DC motor along with the specifications. Section-3 and Section 4 describes the PID and Fuzzy Logic Control law. Section-5 gives simulation result and discussion of PID and FLC. In Section-6 paper is concluded.
II. MATHEMATICAL MODEL OF DC MOTOR
The DC motor torque (τ) is proportional to the armature current (i ) and magnetic field strength and can be written as;
(1)
Where kt is a constant factor The back emf eb is written as;
̇ (2)
Where ̇ is angular velocity of the DC is motor and is constant factor.
The back emf constant and motor torque are equal and can be written as k which represent both the back emf constants and motor torque.
Figure 1 shows the electric circuit of the DC motor. The parameters in figure are explained in Table 1.
Figure 1: DC Motor Model
Table 1. DC Motor Parameter Parameters Description
R Resistance
L Inductance
J Moment of Inertia B Viscous Friction Constant
E Back EMF
By applying voltage law to Figure 1, we get;
̈ ̇ (3)
̇ (4)
Where; ̇ and ̈ are velocity and acceleration respectively.
By applying Laplace Transformation to equation (3) and (4), it can be expressed in the Laplace domain with the variable s. After simplification and removing I(s), we get the open-loop transfer function as;
( ) ( )( ) (5)
In the above open-loop transfer function the rotational velocity is taken into consideration as the output and the input is considered as the armature voltage.
The standard DC motor parameter values are given in Table 2.
Table 2. Specifications of DC Motor Parameters Values Resistance (R) 0.5 Ω Inductance (L) 0.02 H Motor Torque (k) 0.5 Moment of Inertia ( J) 0.01 kg m2 Viscous Friction Constant (b) 0.0089 N ms
By putting the values in Table 2 in equation (5), we get;
( ) ( ) (6)
III. PID CONTROLLER
A PID controller is a frequently used feedback mechanism for control loops in the industry. A PID is used to calculate an error based on measured process variable and the set point. The control law is attempting to minimize the error by changing the control input automatically to the plant. PID is used to calculate the control signal u(t) for a DC motor plant. The PID equation can be written as;
( ) ( ) ∫ ( ) ( ) (7)
Figure 2 clearly depicts the functionality of this PID controller. PID controller is used to achieving the control signal for the DC motor plant based on error e(t) which is calculated with the help of measured output and reference set point. The generated control signal u(t) in this case, the PWM signal which is directly applied to DC motor for controlling purpose.
Figure 2: PID Control
Table 3 explains the various control actions of PID control, estimates and use.
Table 3. Various Control Actions
Control Actions Estimates When to use
P Present Slow system response, offset tolerant systems
I Past Too slow to be used often
D Future Not used alone because of high sensitivity and no set point
PI Present and Future Most widely used
PID All Most Robust, can be noise sensitive, often used
IV. FUZZY CONTROLLER
Description
Fuzzy Controller is primarily a linguistic based control system that seeks to solve for human know-how on how a machine can be controlled without the need for a mathematical model. The fundamental structure of the FLC system is depicted in Figure 3. The Fuzzy Logic controller includes 4 primary additives like fuzzification, Rule base, Inference operation, and defuzzification.
Figure 3: Fuzzy Logic Control
1. Fuzzification: The step one in developing a fuzzy controller is to select a state variables act as the signal for input which serves the dynamic performance of the machine. Fuzzy logic makes use of language variables including big, small, high, low, positive, negative and so forth in place of numerical variables. The method of transforming a numerical variable into a linguistic variable which is the fuzzy number is referred to as fuzzification. An entire universe of discourse is characterized by fuzzy sets using its membership functions.
The fuzzy sets can take distinct shapes [5] along with Gaussian, triangular, trapezoidal, etc.
2. Rule Base: The rules are in If-Then fashion referred to as the conditions and the conclusion respectively.
The software is able to compute a control signal based on the measured inputs errors and difference in errors.
3. Inference Operation: The inference operation incorporates a data processing machine that consistently employs inference steps similar to that of a human brain. It evaluates the fuzzy policies and produces an output for each and every rule. There are various types of inference engines like, max-min method, max-dot product [7].
4. Defuzzification: Defuzzification is a reversal of Fuzzification. The defuzzification output is in the linguistic variable. It’s fuzzy number further the need for the linguistic variable to convert into crisp output [8],[9].
There are many defuzzification methods, but commonly used are Mean of maximum (MOM), Bisector of area (BOA) and Center of gravity (COG).
Figure 4: Rules for FLC
Figure 5: Surface view of FLC Rule based
Figure 4 shows the different rules of the fuzzy logic controller. Figure 5 depicts the surface viewer to view the output surface for your fuzzy system as per the input and output variables specified to the FIS editor, their corresponding membership functions, and the fuzzy rules for your system.
Designing procedure
Firstly, we have to design the Fuzzy Logic Controller using an editor called FIS editor. FIS file is generated using the toolset present in MATLAB for fuzzy logic. Select the appropriate Membership Functions, after selecting the membership function, a rule base is established as you can see in the Figure 4. The integral element of FLC is the compilation of linguistic rules. Looking at the block diagram of FLC, it consists of two inputs which are Speed Error and Change in Error and one output to control the response. Figure 6 and 7 shows the membership functions for the input respectively with the change in errors. The Figure 8 shows the membership function for output.
Figure 6: Input variable: Error
Figure 7: Input variable: Change in Error
Figure 8: Output variable: Change in Error
V. RESULTS ANDANALYSIS
The output responses of the system with PID and FLC are carried out in MATLAB and SIMULINK. The Response of the system is carried out by applying the step signal as an input to the DC motor transfer function in (5).
PID Controller
Figure 9 depicts PID controller designed in SIMULINK for DC motor plant, where parameters for the controller are adjusted using Runge-Kutta.
Figure 9: PID-SIMULINK Model
The step response for the 2nd order system using PID is shown in Figure 10. The figure shows that the system has large overshoot and higher Settling time. The get the optimum output response we can vary the PID controller gains, i.e. P, I and D.
Figure 10: Stem response using PID Fuzzy Logic Controller
The DC motor transfer function augmented with FLC is design in a SIMULINK as shown in Figure 11.
The output of the fuzzy logic controller in Figure 12 shows excellent results than the PID controller. It is observed from the figure that the overshoot has decreased significantly to an amount compared to the PID.
Figure 12: Step response using Fuzzy control
Figure 13: Step response using PID and FLC
Figure 13 illustrates the combined response of the system using both the controllers. As compared to PID the system overshoot of the system has been reduced drastically using FLC. Table IV shows the other system parameters like peak time and rise time.
Table 4. Output Parameter: Comparative Analysis
Parameter PID Controller Fuzzy Logic Controller
Rise Time (sec) 0.0286 0.1240
Peak Time (sec) 1.0763 0.2662
VI. CONCLUSION
The DC motor plant is modelled and simulated for the PID controller and for the Fuzzy logic controller in MATLAB and SIMULINK. The DC motor system performance has significantly improved after applying the control laws. Fuzzy controller produces a better output response than traditional PID control. The system shows a high steady-state and transient response, less response time, high precision and steady state error. The proposed Fuzzy Logic Controller has more similarities over traditional controls, such as greater stability, power and static reliability. Based on the results obtained, FLC is more effective and efficient than the PID controller with minimum transient and steady-state parameters in the fuzzy logic.
VII. REFERENCES
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[3] Safwan A. Hamoodi, Rasha A. Mohammed, Bashar M. Salih, “DC Motor Speed Control Using PID Controller Implementation by Simulink and Practical,” International Journal of Electrical Engineering. vol. 11, no. 1, pp. 39–49, 2018.
[4] Dr. Maan, M. Shaker- Yaareb, and M.B. Ismeal Al khashab, “Design and Implementation of Fuzzy Logic system for DC motor Speed Control,” Iraq J. Electrical and Electronic Engineering, vol. 6, 2010.
[5] Dr. Jamal A. Mohammed, “Modeling, Analysis and Speed Control Design Methods of a DC Motor,” Eng. &
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[6] Yasser Ali Almatheel and Ahmed Abdelrahman, “Speed Control of DC Motor Using Fuzzy Logic Controller,” International Conference on Communication, Control, Computing and Electronics Engineering (ICCCCEE), Khartoum, Sudan 2017.
[7] A.G. Aissaoui and A. Tahour, “Application of Fuzzy Logic in Control of Electrical Machines, Fuzzy Logic- Controls, Concepts, Theories and Applications”, Prof. Elmer Dadios (Ed.), ISBN: 978-953-51-0396-7.
[8] P. Vas (2001). “Artificial Intelligence Based Drives”, In: M.H. Rashid. Power Electronics Handbook.
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