On robust PID control for time-delay plants

This paper presents an easily implementable method for determining the set of PID controllers that stabilize an LTI system with or without a time delay while satisfying certain robustness requirements. The adopted approach, which does not require approximating the time delay or solving complex non-algebraic equations, draws directly on the graphic approach suggested in [1], [2], [3] for PI controllers and first-order-plus-dead-time processes. In particular, it is shown that, on suitable cross sections of the parameter space, the boundary of the regions where a given H_∞ margin is ensured is the envelope of families of ellipses whose centres lie on the stability boundary. The loci of constant crossover frequencies, strictly related to the achievable passbands, are also displayed. The technique is applied to some benchmark examples with the aid of dedicated software.