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Speed Control of DC Motor at Variable Load Torque Using FLC

Kbrom Lbsu*, Selomone Fantaye and Fisseha Teklay

Mekell University, Ethiopia

Abstract

A DC motor is an electro-mechanical device which is used to drive different loads in many application areas such as industrial and home appliances. During operation, one of the basic parameters to be controlled is the speed of the motor, which is affected by the internal parameter of the motor and external load that is connected to it. Separately excited DC motors have been widely used in high performance applications and when a motor is desired to operate at constant speed, its speed varies due to variation of load torque. The objective of this thesis work is to control the speed of separately excited DC motors using a fuzzy logic controller considering different load torques. In order to control the speed of the DC motor we used a fuzzy logic controller in a MATLAB environment by varying load torque. First, an open loop system was designed and measured the speed, transient, and steady state error. Secondly, a PID controller was designed to control the speed of the motor by tuning (KP, KI, and KD) gains of the PID controller and measuring the speed, transient, and steady state error. On the other hand, a fuzzy logic controller was designed to control the speed of the motor by intelligent tuning, taking appropriate expert rules and comparing the result between a PID and fuzzy logic controller in the simulation result.

Finally, a fuzzy logic controller is a better controller than a PID controller by zero overshoot, reduction of 28.1% of settling, 27.87% of rise time, and 93.33% of steady state error. In addition to this, by solving nonlinear characteristics of the motor, it increases overall performance of the system.

Keywords: DC motor, PID controller, fuzzy controller

1.1 Introduction

The DC motor is an attractive piece of equipment in many industrial applications requiring variable speed and load characteristics for its ease of controllability. The speed control of a DC motor is very crucial in application where precision and protection are of the essence. The purpose of a motor speed controller is to take error correcting signals representing the required speed and to drive a motor at a fixed speed. DC motors have good speed control despondence and are widely used in speed control systems which need high control requirements, such as rolling mills, double-hulled tankers, high precision digital tools, etc. The speed of a DC motor can be varied by controlling the field flux, armature resistance, or terminal voltage that is applied to the armature circuit. Separately excited DC motors are mainly used as actuators in industrial applications. These motors have the advantage of having low friction, small size, high speed, low construction cost, and high torque.

1.2 Background of Thesis Work

DC motors used in many applications, such as still rolling mills, electric trains, electric vehicles, electric cranes, and robotic manipulators, require speed controllers to perform their tasks. The speed controller of DC motors was first carried out by means of voltage control in 1981 by Ward Leonard [2]. DC motors use feedback controllers to control the speed, position, or both. Today, the most famous and frequently used type of controller in the industry is a PID controller, but PID controllers do not offer satisfactory results when an adaptive algorithm is required [6]. Fuzzy logic control (FLC) is one of the most successful applications of fuzzy set theory, introduced by L.A Zadeh in 1973 and applied (Mamdani 1974) in an attempt to control systems that are structurally difficult to model. Since then, FLC has been an extremely active and fruitful research area with many industrial applications reported [3]. In the last three decades, FLC has evolved as an alternative complementary to the conventional control strategies in various engineering areas. Fuzzy control theory usually provides non-linear controllers that are capable of performing different complex non-linear control actions, even for uncertain nonlinear systems.

1.3 Statement of the Problem (Case Study)

Since DC motors have wide applications, the speed can be varied due to different condition. When a motor is desired to operate in a constant speed, its speed may be varied due to different loads; the speed of motor is decreased when the load is increased and the speed of the motor is increased when the load is decreased, so consequently the motor does not accurately work at the desired time. Machines are easily damaged without implementation of control methodology in the system and the conventional (PI, PD, PID) technique is widely used in DC motor speed and position control. It is not suitable for high performance cases because of the low robustness of PID controllers. Not only that, but the major problems in applying a conventional control system in a speed controller are the effects of nonlinear characteristics of a DC motor, such as saturations and fictions, that could degrade the performance of conventional controllers. This thesis work proposes a new ability of fuzzy logic control, whose approach offers a simpler, quicker, and more reliable solution that has clear advantages over conventional techniques and a control system that could give a faster response in order to maintain the speed of the DC motor at the desired value with minimum overshoot, minimum steady state error, minimum settling time, and fast rising time, all of which are very important and crucial in industrial application.

1.4 Research Methods

1.4.1 Fuzzy Logic Controller Theory

The fuzzy logic idea is similar to the human being's feeling and inference process, unlike the classical control strategy as shown in Figure 1.1.

Figure 1.1 Structure of fuzzy logic controller.

The principal elements of a fuzzy logic controller are:

1. A. Fuzzification
2. B. Rule Base and Inference Engine
3. C. Defuzzification

A. Fuzzification

This process converts the crisp input into the fuzzy linguistic values. Generally, fuzzy logic uses linguistic variables instead of any precise or numerical variables.

B. Rule Base and Inference Engine

A collection of rules is called a rule base. The rules are in an if/then format; formally, the "if" side is called the condition and the "then" side is called the conclusion.

• ? Fuzzy Inference Model
  1. (A). Mamdani Model: Mamdani-type inference, as defined for the toolbox, expects the output membership functions to be fuzzy sets. After the aggregation process, there is a fuzzy set for each output variable that needs defuzzification [4].
  2. (B). Segeno Model: The Segeno, or Takagi-Kang, Method of fuzzy inference is mostly similar to the Mamdani model, but the difference is Segeno output membership functions are either linear or constant and the rule base of the Segeno is: If x is A and y is B, then z is F(x, y). This model is mainly used if there is no expert knowledge about the system [5].

C. Defuzzification

The reverse of fuzzification is called defuzzification. It is the transformation of a fuzzy quantity into a precise quantity, just like fuzzification is the conversion of a precise quantity to a fuzzy quantity. The use of a fuzzy logic controller (FLC) produces the required output in a linguistic variable (fuzzy number). As per real world requirements, the linguistic variables should be transformed to a crisp output. We have been used the center of the area for the defuzzification process in this paper [1].

There are five basic defuzzification strategies and they are defined as follows:

1. Centroid of Area (COA): It is one of the most popular techniques used for defuzzification, as it is reminiscent of the calculation of expected values of probability distributions. It can be defined as follows: (1.1)

   where µA (Z) is the aggregated output MF.

2. Bisector of Area (BOA):
   It satisfies the equation: (1.2)

   where a = min {z/z ? z} and ß = max {z/z ? z}, that is the vertical line, and z = zBoA partitions the region between z = a, z = ß, y = 0, and y = µA into two regions with the same area.

3. Mean of Maximum (MOM):
   zmom is the average of the maximizing z at which the MF reaches a maximum µ*. It can be represented as follows: (1.3)

   where z' = {z | µA (z) = µ*}.

4. Smallest of Minimum (SOM):
   zSOM is the minimum of the maximizing z (in terms of magnitude).
5. Largest of Maximum (LOM):
   zLOM is the maximum of the maximizing z (in terms of magnitude).

Fuzzy Input:

1. i) Error of speed (5 membership)
2. ii) Change of speed error (5 membership)

Fuzzy Output:

1. i) Control output (5 memberships)

Fuzzy Inference System: Mamdani
Defuzzification Method: Centroid
Rules Base: 25 rules

Figure 1.2 Block diagram of DC motor with fuzzy logic controller.

1.5 Mathematical Model of DC Motor

Figure 1.3 Model of DC motor.

According to the Kirchhoff's voltage Law, the electrical equation of the DC motor is

where ia(t) is the armature current, Vb(t) is the...