Robustness of Feedback Systems with Several Modelling Errors

摘要

In this report we study robustness properties of linear multivariable feedbacksystems with several sources of modelling uncertainty. We assume that each source of uncertainty is modelled as a stable unstructured perturbation satisfying a frequency dependent norm bound. A stability margin for such an uncertainty description is furnished by the structured singular value. The structured singular value is obtained from a numerical optimization procedure. Consequently, it is difficult to obtain insight into the relation between its size and the plant, compensator, and design specifications upon which it depends. Our approach is to obtain such insight by deriving bounds and approximations to the structured singular value. The results we obtain are appealing in that they are both reasonably tight and in that they do provide the desired insight. We apply this insight first to understand the source of robustness difficulties associated with an ill-conditioned plant, and use the resulting information to develop a procedure for selecting weightings in LQG/LTR and H-infinity synthesis problems so that the structured singular value is minimized. (R.H.)