Robust design of PID controller for interval plants

We consider the problem of designing P, PI and PID controllers for interval plants. It is known from the area of parametric robust control that the stabilization problem for an interval plant are reduced to the equivalent problem of stabilizing either a finite set of certain extremal plants. This paper shows that under special conditions imposed on controller parameters and the order of plant, the number of extremal plants required for stabilization on PID controllers are reduced. Thereafter, using Ho's method, it allows one to obtain all the stabilizing set of PID gains for a interval plant family. We assure that the coefficient diagram method (CDM) is very useful for designing a controller because the design in CDM is not only carried out directly in the parameter space but also easy to meet the time domain specification, as shown in a numerical example.