Herbert Werner (UMIST)
Design methods based on the H-infinity norm of the closed-loop transfer function have gained popularity, because unlike H2 methods (best known as LQG), they offer a single framework in which to deal both with performance and robustness. On the other hand, since a H2 cost function offers a more natural way of representing certain aspects of the system performance, improving the robustness of H2 based design methods against perturbations of the nominal plant is a problem of considerable importance for practical applications.
In the robust H2 approach, the controller is designed to minimize an upper bound on the worst case H2 norm for a range of admissible plant perturbations. Both Riccati-based solutions and LMI-based solutions have been considered for this problem. In this presentation, the efficiency of an LMI-based design approach as a practical design tool is illustrated with case studies, including a well-known benchmark problem and an industrial application. It is shown that iterative scaling of the uncertainty representation leads to a significant improvement in performance. Two different ways of doing this in an LMI framework – based on the S-procedure and on Finsler's Lemma, respectively – are discussed. The achievable robust performance depends not only on the design method, but also on the representation of the parameter uncertainty. A systematic procedure for constructing an uncertainty representation from plant data in different operating conditions is also presented.