Integrated uncertainty model identification and robust control synthesis for linear time-invariant systems

Abstract

Given a nominal model, an integrated uncertainty model identification and mu-synthesis algorithm is presented for linear time-invariant (LTI) systems. The goal is 1) to construct an uncertainty model set characterized by parameterized weighting functions of dynamic perturbations and disturbances in the general linear fractional transformation (LFT) form - customary representation in modern robust control and 2) to select from this set according to closed-loop control objectives. The motivation is the simultaneous model validation and model optimization with respect to closed-loop requirements. The algorithm works on sampled, bounded-energy experimental data on the frequency-domain and integrates nominal model invalidation, uncertainty model construction and control synthesis in order to achieve robust performance. Standard D-K iteration steps are combined with an optimization step on a group of selected data. The method is demonstrated on a simple numerical example, where the results are comparable with analytic computations