International Journal of Scientific & Engineering Research,Volume 3, Issue 6, June-2012 1 ISSN 2229-5518 IJSER © 2012 http://www.ijser.org Performance Analysis of Fractional Order PID Controller with the Conventional PID Controller for Bioreactor Control Shivaji Karad, Dr. S. Chatterji, Prasheel Suryawanshi Abstract— Despite the dramatic advancement of process control in recent decades, the proportional-integral-derivative (PID) controller contin- ues to be the most frequently used feedback controller today. PID control mechanism, the ubiquitous avail ability of reliable and cost effective commercial PID modules, and pervasive operator acceptance are among the reasons for the success of PID controllers. An elegant way of enhancing the performance of PID controllers is to use fractional-order controllers where I and D-actions have, in general, non-integer orders. In a PIλDδ controller, besides the proportional, integral and derivative constants, denoted by Kp, Ti and Td respectively, we have two more adjustable parameters: the powers of s in integral and derivative actions, viz. λ and δ respectively. This paper compares the performance of conventional PID and fractional PID controllers used for bio-reactor control. Index Terms — PID controller, Fractional Calculus, Fractional PID controller, Bio-reactor control ——————————  —————————— 1 INTRODUCTION he PID controllers have remained, by far; the most com- monly used in practically all industrial feedback control applications. The main reason is its relatively simple structure, which can be easily understood and implemented in practice. They are thus, more acceptable than advanced controllers in practical applications unless evidence shows that they are insufficient to meet specifications. Many techniques have been suggested for their parameters tuning. Although all the existing techniques for the PID controller parameter tuning perform well, a continuous and an intensive research work is still underway towards system control quality enhancement and performance improvements. On the other hand, in recent years, it is remarkable to note the increasing number of studies related with the application of fractional controllers in many areas of science and engineering. This fact is due to a better understanding of the fractional calculus potentialities. In the field of automatic con- trol, the fractional order controllers which are the generaliza- tion of classical integer order controllers would lead to more precise and robust control performances. Although it is reasonably true that the fractional order models require the fractional order controllers to achieve the best performance, in most cases the researchers consider the fractional order controllers applied to regular linear or non-linear dynamics to enhance the system control performances. This paper is organized as follows: In section 2, we present a brief introduction to fractional calculus. Section 3 deals with fractional order PID controller. Section 4 presents the application of proposed fractional PID controller for bio- reactor control system. Section 5 deals with simulation results of the system and section 6 discuss the conclusion. 2 FUNDAMENTALS OF FRACTIONAL CALCULUS 2.1 Definitions of Fractional Calculus Fractional calculus is an old mathematical topic since 17th century. Fractional calculus is a subdivision of calculus theory which generalizes the derivative or integral of a function to non-integer order. Fractional calculus helps evaluating (d n y/dt n ), n-fold integrals where n is fractional, irrational or complex. For fractional order systems n is considered to be fractional. The number of applications where fractional calculus has been used rapidly grows. These mathematical phenomena allow to describe a real object more accurately than the classical ―integer-order‖ methods. The real objects are generally fractional however, for many of them the fractionality is very low. The main reason for using the integer-order models was the absence of solution methods for fractional differential equations. At present there are lots of methods for approximation of fractional derivative and integral and fractional calculus can be easily used in wide areas of applications (e.g.: control theory - new fractional controllers and system models, electrical circuits theory - fractances, capacitor theory, etc.) [1], [2]. The generalized fundamental operator which includes the differentiation and integration is given as: T ———————————————— Shivaji Karad is currently pursuing Master of Engineering in Instrumen- tation & Control in NITTTR, Chandigarh, India. E-mail: shivaji.karad91@gmail.com Dr. S. Chatterji, Professor and Head, Electrical Engineering Department NITTTR, Chandigarh, India. Prasheel Suryawanshi, Associate Professor, Electronics & Tele Comm. Engineering Dept., MAE, Alandi, Pune, India.