Robust PID Controller Design 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_∞-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_∞ PID synthesis are then used to devise a linear programming design procedure for determining the admissible PID gain values. One of the important features of the proposed method is that it constructively characterizes the entire set of admissible PID controllers. This characterization can facilitate the optimal design of any additional design requirements.