PID tuning under uncertain conditions: robust LMI design for second-order plus time-delay transfer functions*

This paper proposes a systematic method for design of PID controllers for continuous time systems subjected to time-delay. An appropriate Lyapunov-Krasovskii functional is proposed yielding delay dependent conditions that guarantee a prescribed H∞ performance for the closed-loop system. The controller design is carried out by means of convex optimization problems written in the form of linear matrix inequalities. The innovative aspect is that robustness issues associated with time-delay are investigated by assuming that it can vary within prescribed bounds. Numerical experiments are provided to illustrate the advantages.