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Study of the Design and Tuning Methods of Pid Controller Based on Fuzzy Logic and Genetic Algorithm

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Study of the Design and Tuning Methods of Pid Controller Based on Fuzzy Logic and Genetic Algorithm STUDY OF THE DESIGN AND TUNING METHODS OF PID CONTROLLER BASED ON FUZZY LOGIC AND GENETIC ALGORITHM A thesis submitted in partial fulfillment of the requirements for the degree of Bachelor in Technology in Electronics and Instrumentation Engineering by Sangram Keshari Mallick and Mehetab Alam Khan Department of Electronics and Communication Engineering National Institute of Technology, Rourkela May, 2011 STUDY OF THE DESIGN AND TUNING METHODS OF PID CONTROLLER BASED ON FUZZY LOGIC AND GENETIC ALGORITHM A thesis submitted in partial fulfillment of the requirements for the degree of Bachelor in Technology in Electronics and Instrumentation Engineering by Sangram Keshari Mallick and Mehetab Alam Khan under the guidance of Prof. G. S. Rath Department of Electronics and Communication Engineering National Institute of Technology, Rourkela May, 2011 CERTIFICATE This is to certify that the thesis entitled “Study of the design and tuning methods of PID controller based on fuzzy logic and genetic algorithm” submitted by Sangram Keshari Mallick (107EI027) and Mehetab Alam Khan (107EI028) in partial fulfillment of the requirements for the award of Bachelor of Technology Degree in Electronics and Instrumentation Engineering at National Institute of Technology, Rourkela is an authentic work carried out by them under my supervision and guidance. To the best of my knowledge, the matter embodied in thesis has not been submitted to any other university/ Institute for the award of any degree or Diploma. Place: Rourkela Date: Prof. G. S. Rath Dept. of Electronics & Communication Engineering National Institute of Technology Rourkela – 769008 ABSTRACT This project tries to explore the potential of using soft computing methodologies in controllers and their advantages over conventional methods. PID controller, being the most widely used controller in industrial applications, needs efficient methods to control the different parameters of the plant. This thesis asserts that the conventional approach of PID tuning is not very efficient due to the presence of non-linearity in the system of the plant. The output of the conventional PID system has a quite high overshoot and settling time. The main focus of this project is to apply two specific soft-computing techniques viz. fuzzy logic and genetic algorithm to design and tuning of PID controller to get an output with better dynamic and static performance. The application of fuzzy logic to the PID controller imparts it the ability of tuning itself automatically in an on-line process while the application of genetic algorithm to the PID controller makes it give an optimum output by searching for the best set of solutions for the PID parameters. The project also discusses the benefits and the short-comings of both the methods. The simulation outputs are the MATLAB results obtained for a step input to a third-order plant. Page | iv ACKNOWLEDGEMENT We would like to express our gratitude and sincere thanks to Prof. G. S. Rath whose guidance, support and continuous encouragement helped us being motivated towards excellence throughout the course of this work. We wish to extend our gratitude to Prof. T. K. Dan for his timely suggestions and guidance during the project work. Finally, we would like to thank all of them who have been helpful and were associated with us directly and indirectly throughout the course of our work. Sangram Keshari Mallick Mehetab Alam Khan 107EI027 107EI028 Page | v TABLE OF CONTENTS CERTIFICATE iii ABSTRACT iv ACKNOWLEDGMENT v TABLE OF CONTENTS vi LIST OF FIGURES viii INTRODUCTION 1 1.1 Conventional PID controllers 2 1.1.1 Preliminary and background 2 1.1.2 Tuning of PID parameters 3 1.2 PID controller tuning using various soft-computing techniques 5 1.3 Thesis organization 5 FUZZY SELF-TUNING PID CONTROLLER 6 2.1 Fuzzy logic background 7 2.2 A self-tuning fuzzy PID controller 9 2.2.1 Self-tuning principle of fuzzy PID controller 9 2.2.2 Design and structure of the self-tuning fuzzy PID controller 10 2.2.3 Simulation results 13 2.3 Advantages of fuzzy self-tuning PID controller 20 2.4 Shortcomings of fuzzy self-tuning PID controller 21 GENETIC ALGORITHM BASED PID CONTROLLER 22 3.1 Genetic algorithm based PID controller 23 3.1.1 Preliminary and background of Genetic Algorithm 23 3.2 A GA-PID controller 23 3.2.1 Principles of GA-PID controller 23 3.2.2 Structure and design of GA-PID controller 24 Page | vi 3.2.3 Simulation results 30 3.2.4 Advantages of GA-PID controller 32 3.2.5 Shortcomings of GA-PID controller 32 CONCLUSION 33 4.1 Conclusion 34 4.2 Future scope 34 REFERENCES 35 Page | vii LIST OF FIGURES Fig. 1.1. Basic block diagram of a conventional PID controller 2 Fig. 1.2. Block diagram of the example system 4 Fig. 1.3. MATLAB simulation result for a conventional PID controller 4 Fig. 2.1. A pure fuzzy system 7 Fig. 2.2. min and max Mamdani fuzzy inference system 9 Fig. 2.3. Basic structure of a fuzzy PID controller 11 Fig. 2.4. Fuzzy rule tables for the PID parameters 11 Fig. 2.5. Mamdani fuzzy system 13 Fig. 2.6. Plots for the membership functions 15 Fig. 2.7. MATLAB simulation results for a step input for a fuzzy self-tuning PID 19 controller Fig. 3.1. Structure of GA-PID controller 25 Fig. 3.2. Simluation flowchart for auto-tuning GA-PID controller 29 Fig. 3.3. Fitness function plot 30 Fig. 3.4. PID parameters (Optimized values) 31 Fig. 3.5. Output response of the GA-PID controller 31 LIST OF TABLES Table 2.1 Fuzzy rules for Kp 11 Table 2.2 Fuzzy rules for Ki 12 Table 2.3 Fuzzy rules for Kd 13 Page | viii CHAPTER 1 INTRODUCTION 1.1 Conventional PID controllers 1.1.1 Preliminary and background PID controllers are the most widely-used type of controller for industrial applications. They are structurally simple and exhibit robust performance over a wide range of operating conditions. In the absence of the complete knowledge of the process these types of controllers are the most efficient of choices. The three main parameters involved are Proportional (P), Integral (I) and Derivative (D). The proportional part is responsible for following the desired set-point, while the integral and derivative part account for the accumulation of past errors and the rate of change of error in the process respectively. Kp e(t) Setpoint Error Output 푡 ( ) Plant Ki ∫ 푒 푥 푑푥 푑푒 Kd 푑푡 Fig. 1.1 Basic block diagram of a conventional PID controller For the PID controller presented in Fig. 1.1, ( ) Output of the PID controller, u(t) = Kp e(t) + Ki ∫ ( ) + Kd ……1.1 Where, Error, e(t) =Setpoint- Plant output Kp = proportional gain, Ki = integral gain, Kd = derivative gain Page | 2 1.1.2 Tuning of PID parameters Tuning of a PID controller refers to the tuning of its various parameters (P, I and D) to achieve an optimized value of the desired response. The basic requirements of the output will be the stability, desired rise time, peak time and overshoot. Different processes have different requirements of these parameters which can be achieved by meaningful tuning of the PID parameters. If the system can be taken offline, the tuning method involves analysis of the step- input response of the system to obtain different PID parameters. But in most of the industrial applications, the system must be online and tuning is achieved manually which requires very experienced personnel and there is always uncertainty due to human error. Another method of tuning can be Ziegler-Nichols method[8]. While this method is good for online calculations, it involves some trial-and-error which is not very desirable. The transfer function describing the plant for our example is as follows: G(s) = ……1.2 The above transfer function will be used for the study and comparison of the output response of conventional PID, fuzzy PID and PID using genetic algorithm. Following is an example of a conventional PID controller and its output to a step input response as achieved with some particular control parameter values. The output is the simulation result obtained with the help of MATLAB. PID 500 Controller 푠 + 30푠2 + 1000푠 Fig. 1.2 Block diagram of the example system Page | 3 Kp = 0.6 Ki=0.5 Kd = 0.001 Fig. 1.3 MATLAB simulation result for a conventional PID controller Here, the output response of the given third order system has an overshoot of more than 40%. Settling time is also close to 20 seconds. For practical applications in industry these values are too high to be tolerated. An output response having a minimum overshoot and fastest response is required. Page | 4 1.2 PID controller tuning using various soft-computing techniques PID controller model structure needs to be very precise. But in practical applications, to a different extent, most of the industrial processes exist to be nonlinear, the variability of parameters and the uncertainty of model are very high, thus using conventional PID control the precise control of the process cannot be achieved.The common methods known for tuning require the process model to be of a certain type, for example as in the case of a ‘First order plus dead time’ model. These methods require the process model to be reduced if it’s too complicated originally. The above problems can be well addressed by the application of soft-computing methods for tuning of the PID controller. These are specially useful for solving problems of computationally complicated and mathematically intraceable. This is due to the convenience of combining natural systems with intelligent machines effectively with the help of soft-computing methods.
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