Robust performance margins and robust controller design for systems with uncertain parameters

Abstract

The control of linear systems with uncertain parameters is considered and a method is presented for the computation of allowable parameter perturbations to maintain stability and performance conditions. Frequency bounds are placed on the sensitivity and the complementary sensitivity functions of the system in order to guarantee desired performance specifications such as input tracking and sensor noise attenuation. The algorithm makes use of Neimark's D-decomposition results on robust stability and extends the results to the case of robust performance. Explicit formulae are provided for performance measures that need to be minimized in a frequency range to compute the robust performance margin. The algorithm is then used in a controller synthesis procedure to design robust controllers in order to meet both stability and performance requirements. The details of the implementation of the procedure are illustrated through case studies.