A loop shaping design using weighted generalized orthonormal basis functions

In the paper a robust control design method is proposed to obtain a compensator that realizes the required loop shape formed by nominal performance and robust stability specifications. First, a fictitious compensator is identified in such a way that the design loop transfer function tends toward the required loop transfer function. Since the compensator must be identified as accurately as possible in the frequency domains that are important in terms of the required loop shape, the identification is performed by a stable approximation using frequency-weighted generalized orthonormal basis functions (WGOBF). Second, a robust compensator is designed by using the H^∞/μ method taking into consideration the approximation error of the designed loop transfer function. The steps of the control design are illustrated to demonstrate the method on a numerical example.