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ABSTRACT
Fuzzy logic systems have recently been utilized in many control processes due to their ability to model uncertainty. This paper presents the design of a fuzzy control system to control the position of a DC motor. The motor was modeled and converted to a subsystem in Simulink. The entire system has been modeled using MATLAB 7.9/ Simulink toolbox. The fuzzy control was also designed using the Fuzzy Control Toolbox provided within Matlab, with each rule consisting of fuzzy sets conditioned to provide appropriate response times with regards to the limitations of our chosen motor.
First , a crisp Proportional-integral-derivative (PID) controller was designed and tuned using a Simulink block instead of conventional tuning methods such as hand-tuning or Ziegler-Nichols frequency response method. Then a Fuzzy Logic Controller (FLC) was designed. The performance of the proposed system is compared with that of its corresponding conventional Proportional-integral-derivative (PID) controller in terms of several performance measures such as rise time , peak overshoot , settling time and steady state error and in each case , the proposed scheme shows improved performance over its conventional counterpart.
INTRODUCTION
The use of DC shunt motors has increased tremendously since the day of its invention. They are being used in various industrial processes, robotics, house appliances and other similar applications. The reason for its day by day increasing popularity can be primarily attributed to its robust construction, simplicity in design and cost effectiveness. These have also proved to be more reliable. Apart from these advantages, they have some unfavorable features like their time varying and non-linear dynamics. Speed control is one of the various application imposed constraints for the choice of a motor. Hence, in the last few years it has been studied by many, and various methods for the same have been developed.
The controller types that are regularly used are: Proportional Integral (PI), Proportional Derivative (PD), Proportional Integral Derivative (PID), Fuzzy Logic Controller (FLC) or a blend between them. The PID controller offers a very efficient solution to numerous control problems in the real world. If PID controllers are tuned properly, they can provide a robust and reliable control. This very feature has made PID controllers exceedingly popular in industrial applications. The only problem associated with use of conventional PI, PD and PID controllers in speed control of DC shunt motor is the complexity in design arising due to the non-linearity of DC Shunt Motor dynamics. The conventional controllers have to linearize the non-linear systems in order to calculate the parameters. To obtain a perfect non-linear model is almost impossible and hence the values of the parameters that are obtained from it are thereby approximate. The conventional control methods possess the following difficulties:
Dependence on the exactness of the mathematical model of the system.
Expected performance not being met due to the load disturbance, motor saturation and thermal deviations.
Decent performance exhibited only at one operating speed when classical linear control is employed.
Adopting the right coefficients for acceptable results.
From the above, it can be deduced that in order to implement conventional control methodologies, it is necessary to have knowledge of the system’s model that is to be controlled. The usual method of computation of mathematical model of the induction motor is difficult, due to the non-linearity of motor dynamics. Whenever a variation in system or ambient parameters arises, the system’s behavior becomes non-pleasing. The conventional controllers designed to provide high performance increase the design complexity along with the cost.
Thus, to overcome the complexities of conventional controllers, fuzzy control has been implemented in many motor control applications. In the last three decades, fuzzy control has gained much popularity owing to its knowledge based algorithm, better non-linearity handling features and independence of plant modeling. The Fuzzy Logic Controller (FLC) owes its popularity to linguistic control. Here, an exact mathematical model for the system to be controlled is not required. Hence, Fuzzy logic basically tries to replicate the human thought process in its control algorithm. The FLC has thereby proven to be very beneficial in the industries as it has the proficiency to provide complex non-linear control to even the uncertain nonlinear systems. In addition to the aforementioned attributes, a fuzzy logic controller also makes good performance in terms of stability, precision, reliability and rapidity achievable.
ADVANTAGES OF FUZZY LOGIC CONTROLLER
The advantages provided by a FLC are listed below:
1. It is simple to design.
2. It provides a hint of human intelligence to the controller.
3. It is cost effective.
4. No mathematical modeling of the system is required.
5. Linguistic variables are used instead of numerical ones.
6. Non-linearity of the system can be handled easily.
7. System response is fast.
8. Reliability of the system is increased.
9. High degree of precision is achieved.
These advantages allow fuzzy controllers can be used in systems where description of the process and identification of the process parameters with precision is highly difficult. Hence it provides a fuzzy characteristic to the control mechanism.
1.1 PROJECT OBJECTIVE
The objectives of this project are as follows:
1. To design a fuzzy logic controller to control speed of the DC motor.
2. To analyze the performance comparison between PID and Fuzzy Logic Controller in order to control speed of the DC motor by simulation.
3. To implement the fuzzy logic controller using MATLAB Simulink.
SCOPE OF THE PROJECT
This project is to design a Fuzzy Logic Controller that can be used to control the speed of a DC shunt motor. As a machine’s performance is a vital factor for a big production line, this project will examine the efficiency and performance of a DC shunt motor with implementation of control methodology. Thus, the focuses of this project are as stated below:
1. Validate the performance of the PID and Fuzzy Logic Controller by simulation.
2. Perform simulation by using MATLAB-Simulink
3. The fine tuning for the each type of controller to optimize the result.
DC MOTOR
The electric motor is a motor that convert electrical energy into mechanical energy. There are two types of motor which are AC motor, and DC motor. A simple DC motor use electricity and magnetic field for producing torque which rotate the motor. Permanent magnet DC motor (PMDC) outperforms to AC motor because it provides better speed control on high torque loads and use in wide industrial application. DC motors are more usable as it designed to use with batteries and solar cells energy sources, which provide portability where we required it and thus provide cost effective solution, because it is not possible to have AC power supply in every place, DC motor show its response at both voltage and current. The applied voltage describes the speed of motor while current in the armature windings shows the torque. If applied load increased in the shaft of motor, then in order to sustain its speed motor draws more current from supply and if supply is not able to provide enough current then motor speed will be affected. Generally, it can be said that applied voltage affect speed while torque is controlled by current. DC motors provide more effective results if chopping circuit is used. Low power DC motor usually use in lifting and transportation purposes as low power AC motors do not have good torque capability. DC motor used in railway engines, electric cars, elevators, robotic applications, car windows and wide verify of small appliances and complex industrial mixing process where torque cannot be compromised. There are several types of DC motor but most common are brushed DC motor, brushless DC motor, stepper motor, and servo motor. These DC motors have three winding techniques such as shunt DC motor, series DC motor, and compound DC motor.
Field Resistance Control Method
In the field resistance control method, a series resistance is inserted in the shunt-field circuit of the motor in order to change the flux by controlling the field current. It is theoretically expected that an increase in the field resistance will result in an increase in the load speed of the motor and in the slope of torque speed curve.
Armature Voltage Control Method
In the armature voltage control method, the voltage applied to the armature circuit, is varied without changing the voltage applied to the field circuit of the motor. Therefore, the motor must be separately excited to use armature voltage control. When the armature voltage is increased, the no-load speed of the motor increases while the slope of torque speed curve remains unchanged since the flux is kept constant.
Armature Resistance Control Method
The armature resistance control is the less commonly used method for speed control in which an external resistance is inserted in series with the armature circuit. An increase in the armature resistance results in a significant increase in the slope of the torque speed characteristic of the motor while the no-load speed remains constant.
SPEED REGULATION AS A MEANS OF CONTROLLING A PROCESS
Let us consider the process of driving to work. Driving at the highest possible speed would probably cause an accident. And driving at a single speed that will be safe for every portion of the route will take long to reach to the destination. Hence adjusting the speed which goes well with the route minimizes the time to accomplish the objective of the process within limits of reliable operation. The process control benefits that may be provided by an adjustable speed drive are as follows:
1. Smoother operation.
2. Acceleration control as an added incentive.
3. Varying operating speed for each process.
4. Compensates for fluctuating process parameters.
5. Permits slow operation for setup purpose.
6. Allows accurate positioning.
7. Provides torque control.
CONTROL THEORY
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference. When one or more output variables of a system need to follow a certain reference over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system.
It is design to maintain the speed of the motor at a constant speed. In this case the system is the motor. The motor speed is the output and the control is the motor throttle which influences the engine torque output. One way to implement cruise control is by locking the throttle at the desired speed. In fact, any parameter different than what was assumed at design time will translate into a proportional error in the output velocity, including exact mass of the motor, etc., This type of controller is called an open-loop controller because there is no direct connection between the output of the system and the actual conditions encountered; that is to say, the system does not and cannot compensate for unexpected forces.
For a closed-loop control system, a sensor will monitor the motor speed and feedback the data to its computer and continuously adjusting its control input or the throttle as needed to ensure the control error to a minimum therefore maintaining the desired speed of the motor. Feedback on how the system is actually performing allows the controller to dynamically compensate for disturbances to the system, such as changes in slope of the ground. An ideal feedback control system cancels out all errors, effectively mitigating the effects of any forces that may or may not arise during operation and producing a response in the system that perfectly matches the user's wishes.
Closed-Loop Transfer Function
The output of the system y(t) is fed back through a sensor measurement F to the reference value r(t). The controller C then takes the error e (difference) between the reference and the output to change the inputs u to the system under control P. This is shown in the figure. This kind of controller is a closed-loop controller or feedback controller. This is called a single-input-single-output (SISO) control system; MIMO (i.e. Multi-Input-Multi-Output) systems, with more than one input/output, are common. In such cases variables are represented through vectors instead of simple scalar values. For some distributed parameter systems the vectors may be infinite-dimensional (typically functions).
PID CONTROLLER
Although the modern control technique has taken considerable attention during the last several years, PID controllers are still one of the best known controllers used in many industrial processes. Their important and impressive properties such as fast and efficient control action, simple but functional structure, ease of application and robust performance are among the reasons for their preferences.
During the design phase of PID controllers, there is a crucial and challenging task, in that, three controller parameter Kp, Ki and Kd which have a significant controller success, should be determined properly. Practically, this determination or say ‘tuning process’ is performed by an experienced operator based on trial and error method through the some practical rules. It is apparent that this method is time consuming and accordingly needs for relatively more time. Besides, once tuned, the controller performance may later deteriorate because of nonlinear or time varying characteristics of the process under control. In others word, a PID controller with fixed parameter set cannot provide a moderate performance over wide a range of operating condition. A proportional- integral- derivative controller (PID Controller) widely used in industrial control system. A PID controller attempts to correct the error between a measured process variable and a desired set point.
FUZZY LOGIC CONTROLLER
Fuzzy logic is a type of multi valued logic. It deals with approximate reasoning rather than precise. Fuzzy logic derived from fuzzy set theory. Fuzzy logic was first proposed by Lotfi Zadeh in 1965. Fuzzy controller is an innovative technology that modifies the design of systems with engineering expertise. Fuzzy logic use human knowledge to implement a system. It is mostly use in system where there are no mathematical equations for handling system. Common sense, human thinking and judgement are fuzzy rules. It helps engineers to solve non linear control problems. It mathematically emulates human knowledge for intelligent control system and complex application. Today, fuzzy logic are found in a variety of control applications like chemical process control, manufacturing and in such consumer products as washing machines, video cameras and automobiles.
The conventional Boolean logic has been extended to deal with the concept of partial truth – truth values which exist between “completely true" and "completely false", and what we shall be referring to as fuzzy logic. This is achieved through the concept of degree of membership. The essence of fuzzy logic rests on a set of linguistic if-then rules, like a human operator. It has met a growing interest in many motor control applications due to its non-linearity handling features and independence of plant modeling. Moreover, the fuzzy logic concepts play a vital role in developing controllers for the plant since it isn’t needy of the much complicated hardware and all it necessitates are only some set of rules.
There are two famous type of system currently used in fuzzy logic which are Mamdani fuzzy inference, and Sugeno fuzzy inference.Mamdani model is preferred here because it follows the Compositional Rule of Inference strictly in its fuzzy reasoning mechanism.
MAMDANI FUZZY INFERENCE
The most common method used currently is fuzzy inference system. In 1975, Professor Ebrahim Mamdani of London University introduced first time fuzzy systems to control a steam engine and boiler combination. He applied a set of fuzzy rules experienced human operators. The mamdani system usually done in four steps. The steps are fuzzification of the inputs, rule evaluation, aggregation of the rules, and defuzzification. Fuzzifications convert input data to degree of membership functions. In this process data is matched with condition of the rule and determined how well data is matched with rule at particular instance. Thus a degree of membership function is developed.
Fuzzification Block or Fuzzifier
The first step towards designing a Fuzzy Logic Controller is choosing appropriate inputs which will be fed to the same. These input variables should be such that, they represent the dynamical system completely. Then the function of the Fuzzifier comes into picture. Instead of using numerical variables, fuzzy logic uses linguistic variables for processing information. But since the inputs to the FLC are in the form of numerical variables (or in other words, crisp sets), they need to be converted into linguistic variables. This function of converting these crisp sets into fuzzy sets (linguistic variables) is performed by the Fuzzifier. The fuzzification technique involves outlining the membership functions for the inputs. These membership functions should cover the whole universe of discourse and each one represents a fuzzy set or a linguistic variable. The crisp inputs are thus transformed into fuzzy sets. Triangular MF, Trapezoidal MF, Bell MF, Generalized Bell MF or Sigmoidal MF can be used. Even a hybrid of any of the above Membership Functions can be used for fuzzification.
. Fuzzy Rule Base
Fuzzy logic has been centered on the point that it makes use of linguistic variables as its rule base. If a variable can take words in natural language as its values, it is called linguistic variable, where the words are characterized by fuzzy sets defined in the universe of discourse in which the variable is defined. Examples of these linguistic variables are slow, medium, high, young and thin. There could be combinations of this variable too, like “slow-young horse”, “a thin young female.” These characteristics are termed atomic terms while their combinations are called compounded terms. In the real world, words are often used to describe characteristics rather than numerical values. For example, one would say “the car was going at 100 miles per hour.” Terms such as slightly, very, more or less, etc. are called linguistic hedges since they add extra description to the variables, i.e. very – slow, more or less, slightly high, etc. At the heart of the fuzzy rule base are the IF-THEN rules.
A fuzzy IF-THEN rule is expressed as,
IF<fuzzy proposition>,
THEN <fuzzy proposition>.
Propositions are linguistic variables or atomic terms as described previously. This type of rule based system is different from the classical expert systems, In that, rules may not necessarily be derived from human expertise; they may also be derived from other sources. Three types of linguistic variable forms exist.
1. Assignment statements
2. Conditional statements
3. Unconditional statements
2. Database
It consists of the all the defined membership functions that are to be used by
the rules.
3. Reasoning Mechanism
It performs the inference procedure on the rules and the data given to provide a reasonable output. It is basically the codes of the software which are process the rules and the all the knowledge based on a particular situation. It exercises a human brain type of attribute to methodically carry out the inference steps for processing the information.
Defuzzification Block or Defuzzifier
A defuzzifier performs the exact opposite function of a fuzzifier. It transforms the fuzzyvariables (which are obtained as output after processing of the inputs) to crisp sets. The defuzzifier is necessary because in the real world the crisp values can only be taken as inputs to the other systems. Even though the fuzzy sets resemble the human thought process, their functionality is limited only to the above processes. A defuzzifier is generally required only when the Mamdani Fuzzy Model is used for designing a controller.