Determination of all stabilizing fractional-order PID controllers

Paper presented to the 6th Annual Symposium on Graduate Research and Scholarly Projects (GRASP) held at the Hughes Metropolitan Complex, Wichita State University, April 23, 2010.Research completed at the Department of Electrical Engineering and Computer Science, College of EngineeringA novel method for finding all fractional-order (FO) proportional-integral-derivative (PID) controllers that stabilize a given system of integer or non-integer order is proposed. The stability bounds 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) plane. A key advantage of this approach is that it provides the stability boundaries even when the transfer function of a system is not available, as long as the frequency response of the system can be obtained. An example is presented to illustrate the effectiveness of this method