Design of a simultaneous stabilizing controller for a resonance test-bed

The amplitude control of a resonance test-bed requires a robust performance controller which copes with complex structured uncertainties. Since the uncertainties cannot be modelled by linear fractional transformations the μ-synthesis method is not applicable. In this paper the structured uncertainties are described by N plant models and a general solution for the simultaneous stabilization problem is presented. The main idea behind our approach is-if using an appropriate controller parametrization-to approximate the cost function by a quadratic function in the unknown controller parameters. The resulting quadratic programming problem can be solved for the unknown parameters. It will be shown that the optimal controller has significant benefits over an H_∞ design