Abstract
In this paper, a parameter space design method of three term controller for a robust sensitivity minimization problem is proposed. Three term controller is a controller which contains two design parameters affinely, and PI controller or PID controller with one of the three gains fixed belong to this class. This method can be applied to a single-input single-output linear time-invariant system which may include time-delay elements. For this class of controllers, the solution of the robust sensitivity problem is given as a set on a parameter plane.
Since the design problem consists of an internal stability condition and a frequency domain condition on the jω axis, methods of computing the permissible sets for the two conditions are examined, independently. As for the computation of the latter set, first, permissible sets are obtained for a finite number of frequencies, and, next, they are drawn on a parameter plane. Then, the intersection includes the solution set. Namely, the set is obtained approximately as a necessary condition. The proposed method is applied to a first order system with a time delay element, and this result is compared with that of two disk type mixed sensitivity problem.
