A Nonconvex Quadratic SDP for Fixed Order H∞ Control and its Application to Generator Excitation System Design

Abstract

This paper proposes a computation method for fixed order controller synthesis which often arises in H∞ or robust control. With the motivation that the fixed order control problem can be casted to a non-convex quadratic objective function minimization subject to linear matrix inequality (LMI) constraints, a quadratic semidefinite programming (SDP) problem is solved by primal dual interior point method (IPM). The advantage of the proposed method is two-fold. First, the existing SDP solving method can be used with a slight modification. Second, since the method directly computes the solution of the problem, much faster results can be obtained than the existing successive LMI relaxation method such as cone complementarity linearization algorithm.In order to demonstrate the algorithm presented, an excitation system for a synchronous generator connected to an infinite bus is designed and simulated. A proportional-integral type automatic voltage regulator and a power system stabilizer considering H∞ performance are co-designed to provide appropriate damping for the system. The results show the practical applicability of the method.