Determination of all stabilizing fractional-order PID controllers that satisfy a weighted sensitivity constraint

Abstract

This paper presents a method for determining all stabilizing fractional-order (FO) proportional-integral-derivative (PID) controllers that satisfy an H∞ weighted-sensitivity constraint for a system of integer or non-integer order. All the parameters of such FO PID controllers are calculated in the frequency domain and are given in terms of the proportional gain Kp, integral gain Ki, and derivative gain Kd. In this paper, they will be plotted on the (Kp, Ki), (Kp, Kd), and (Ki, Kd) planes. In particular, this approach provides all the possible values of the gain parameters of the FO PID controllers that satisfy a given weighted-sensitivity condition even when the transfer function of a system is not available, as long as the frequency response thereof can be obtained. An example is given by way of illustrating the usefulness and effectiveness of the method.