On the synthesis of robust PID controllers for plants with structured and unstructured uncertainty

In this paper, we consider the problems of synthesizing PID controllers for robust stability and performance for a given linear time-invariant plant subject to both parametric and H-infinity-norm-bounded perturbations. Using results from the area of parametric robust control, synthesis problems are converted into simultaneous stabilization of a family of complex segment polynomials. The results on H-infinity PID synthesis are then used to devise a design procedure for determining the admissible PID gain values. One of the important features of the proposed method is that it constructively characterizes the approximated set of all admissible PID controllers. This characterization can facilitate the optimal design of any additional design requirements. Copyright (c) 2005 John Wiley & Sons, Ltd.