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 ρ centered at the origin. The developed algorithm is finally applied along with a bisection strategy to determine, for a specified small positive number ε, a minimum value ρε* and the corresponding ρε*−stabilizing discrete PID controller set for achieving at least 1−ρε* 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.