H∞ Optimization of Fixed Structure Controllers

In this paper, the H∞ optimization problem of fixed structure linear controllers is considered. Applications of the problem include tuning of SISO (Single-Input Single-Output) PID (Proportional plus Integral plus Derivative) controller gains. The proposed algorithm starts with transformation of the original problems into a static output feedback controller synthesis problem, which does not impose any constraints on the controller structure except for its order. Unlike the full-order H∞ controller synthesis case, the H∞ optimization problem of static output feedback controllers cannot be reparameterized as a convex optimization problem. The cone complementarity linearization algorithm is used to overcome the nonconvexity problem due to the constraint on the controller order. The proposed algorithm is applied to the design of a SISO PID controller for head positioning of a magnetic hard disk drive.