Robust design of standard controllers under plant parameters uncertainty

This note extends some results concerning the characterization of PID and lead/lag controllers satisfying given H-infinity closed–loop specifications. In particular, it is shown that: (i) the region of the plane of the free controller parameters where the considered H-infinity constraint is satisfied, is still formed by the union of (a bounded number of) disjoint convex sets even when the plant parameters are not fixed but belong to given intervals, and (ii) the determination of these sets entails the repeated solution of an optimization problem. The procedure is applied to find the parameters of a PID controller for an uncertain electric motor so as to ensure that the H1 norm of the sensitivity function is less than a prescribed value.