Abstract

This paper deals with an optimal design of a new type Variable coefficient Fractional Order PID (V-FOPID) controller by using heuristic optimization algorithms. Although many studies have mainly paid attention to correct the performance of the system’s transient and steady state responses together, few studies are interested in both transient and steady state performances separately. It is obvious that handling these two cases independently will bring out a better control response. However, there are no studies using different controller parameters for the transient and steady state responses of the system in fractional order control systems. The major contribution of the paper is to fill this gap by presenting a novel approach. To justify the claimed efficiency of the proposed V-FOPID controller, variable coefficient controllers and classical ones are tested through a set of simulations which is about controlling of an Automatic Voltage Regulator (AVR) system. According to the obtained results, first of all it was observed that proposed V-FOPID controller has superiority to the classical PID, Variable coefficient PID (V-PID) and classical Fractional Order PID (FOPID) controllers. Secondly, Particle Swarm Optimization (PSO) algorithm has shown its advantage compared to the Artificial Immune System (AIS) algorithm for the controller design.

Highlights

  • Traditional PID controller and its offshoots are indispensable type of controllers for the industrial and academic studies

  • The optimal controller coefficients obtained with the Particle Swarm Optimization (PSO) and Artificial Immune System (AIS) algorithms are given in the Table II for PID and Fractional Order PID (FOPID) controller and the Table III for VFOPID controller

  • The Automatic Voltage Regulator (AVR) system is an important and challenging plant that is frequently used in control engineering applications and it is needed to adjust the terminal voltage

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Summary

INTRODUCTION

Traditional PID controller and its offshoots are indispensable type of controllers for the industrial and academic studies. Improved industrial and academic applications are in need of advanced control strategies, new controller types etc. With this idea, a new type of controller has been enhanced by Podlubny as the generalization of a traditional PID controller [3], [4]. This study mainly targets to fill these gaps and main contributions of this study to the literature are as follows: Presenting a new type of variable fractional PID controller, whose gains are dependent to the system error so that it is possible to improve the transient response and provide a robust control structure. A systematic design procedure for the determination of the fractional and traditional controllers by using heuristic optimization methods such as artificial immune and particle swarm optimization algorithms

FRACTIONAL CALCULUS
Grünwald Letnikov Direct Definition
IMPLEMENTED SYSTEM
Mathematical Model of the V-FOPID
Optimal Design of the Control Systems
EXPERIMENTAL RESULTS
CONCLUSIONS
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