Non-conservative robustness analysis for second-order systems

The problem of nonconservative robustness analysis is considered for second-order systems with uncertainty or changing parameters in the inertia matrix. Three different approaches are presented for putting such systems into a form suitable for analysis using existing control software. The importance of a well posed uncertainty representation which does not violate the physical constraints of the system is demonstrated and an algorithm is presented to avoid conservatism in the analysis/synthesis model. The approaches are applied to a two-link flexible manipulator which is highly nonlinear due to its variable configuration. The results show that a broad class of second-order systems can be analyzed by reformulating problems into ones that can be addressed using existing modern control and analysis techniques