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 H1 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.
