Robust Design of Low Order Controllers via Uncertainty Model Identification

Abstract

In this paper an integrated robust identification and control design procedure is proposed. It is supposed that the plant to be controlled is linear, time invariant, stable, possibly infinite dimensional and that input-output noise-corrupted measurements are available, together with some general information on the plant and on the characteristics of the noise. The emphasis is placed on the design of controllers guaranteeing robust stability and robust performances, and on the trade off between controller complexity and achievable robust performances. First, an uncertainty model set is identified, consisting of a parametric model and a bound on the modeling error, accounting for the dynamics not modeled by the parametric model. Second, a robustly stable controller satisfying given H performance specifications is found using H optimization techniques. Third, the robust performances of the designed controller are computed, allowing to determine which level of model complexity is needed to guarantee desired closed loop performances. A numerical example illustrates the effectiveness of the proposed design procedure.