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

Abstract

This paper presents a method for finding all fractional-order (FO) proportional-integral-derivative (PID) controllers that stabilize a given system and at the same time satisfy an H∞ weighted-sensitivity constraint. All the values of the gain parameters of such FO PID controllers are determined 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 were be calculated and plotted on the (Kp, Ki) plane with a fixed value of Kd. This approach can be used even when the transfer function of a system is not available, so long as the frequency response thereof can be obtained.