Abstract

This paper deals with the problem of PID design for continuous-time systems with time delays. The system is assumed to be free of parametric disturbances and affected by a time-invariant discrete delay of known magnitude. The robustness of the PID control with respect to structured uncertainties is investigated with the small-gain theorem and better performance is sought through the minimization of an upper bound to the closed-loop system H ? norm. A Lyapunov-Krasovskii type functional is used yielding delay-dependent design conditions. The controller design is accomplished by means of a convex optimization procedure formulated using linear matrix inequalities (LMIs). Numerical experiments are provided to illustrate the main characteristics of the proposed design method. The particular case of a recycle process controller is addressed. © 2011 IFAC.