Design of discrete PID controllers for maximizing stability margins

The objective of this paper is to provide a discrete PID controller design procedure for maximizing stability margins. First, a new and complete characterization of the entire set of stabilizing discrete PID controllers for a given plant is presented. Then, based on this characterization, an efficient algorithm is developed for testing if, for a given plant, there exists a digital PID controller gain parameter space corresponding to closed-loop poles being inside the circle of radius rho centered at the origin. The developed algorithm is finally applied along with a bisection strategy to determine, for a specified small positive number epsilon, a minimum value rho(*)(epsilon) and the corresponding rho(*)(epsilon)- stabilizing discrete PID controller set for achieving at least 1-rho(*)(epsilon) of stability margin. To illustrate the features of our new characterization of stabilizing digital PID controller sets and the effectiveness of the presented algorithms to the maximum stability-margin discrete PID controller design, two numerical examples are provided.