Non-Integer Order Proportional Integral Control for Time Delay Plant with Single Fractional Order

Abstract

This paper studies the tuning of non-integer order proportional integral controller for time delay plants having one fractional order in its denominator polynomial. The well-known first order plus time delay plant is reorganized to have the order of the operator s to be an arbitrary real number. The main aim is to tune the parameters of the fractional order proportional integral controller to make the mentioned plant behavior to be stable and robust against unexpected changes in the gain of the system. The approach here is a graphical point of view on the Bode diagram. The two crossover points in the Bode diagram, the gain crossover frequency and the phase crossover frequency are tuned towards the desire of the researcher. This brought us to extend or to restrict the distance between these two crossover frequencies and thus, to provide the stability and robustness of the system. The design process is an analytical way from beginning to the end. Hence, the method is more reliable when compared with the methods based on optimization. This paper presents the findings of the first step in the research. The formulas to design the controller are found and the results are shown on an illustrative example.