Multivariable Fixed-Structural Controller Design Method Using Frequency Responses Guaranteeing Control Specifications by Convex Optimization

Abstract

In this paper, the stability condition and the robust performance condition are represented as a set of convex constraints with respect to the parameters of a linearly parameterized multivariable controller in the Nyquist diagram for the prespecified frequency points. This method can directly handle frequency-domain additive uncertainty without any modeling. Frequency-domain additive uncertainty can be minimized by appropriately selecting a nominal plant at each frequency point in the proposed approach. Moreover, this paper proposes the design constraints to assure the desired control bandwidth, phase margin and gain margin to satisfy desired control specifications. The effectiveness of the proposed method is verified by comparison with the model-based approach by using µ-synthesis with the D-K iteration algorithm and the case of the designed controller without proposed constraints through an experimental result.