Robust Control and Uncertainty Set Shaping Obtained by System Identification

An important shortcoming about designing robust control for models generated from prediction error identification is that very few control design methods directly match the ellipsoidal parametric uncertainty regions that are generated by such identification methods. Models obtained from identification experiments in prediction error framework lie in an ellipsoid uncertainty region. In this contribution we present a joint robust control/input design procedure which guaranties stability and prescribed closed-loop performance using models identified from experimental data. Finite dimensional parameterization of the input spectrum is used to represent the input design problem as a convex optimization. A method for fixed-order H controller design for systems with ellipsoidal uncertainty is used and given H specifications on the closed-loop transfer function are translated into sufficient requirements on the input signal used to identify the system.