Robust controller design for parametrized uncertain plants by synergizing QFT and Q-parametrization

Abstract

Based on the basic design methodology of quantitative feedback theory (QFT), Q parametrization is used to deal with the stability issue encountered. The set of all stabilizing controllers is first found for an arbitrarily chosen nominal plant using Q parametrization. To stabilize all the plants, a sufficient condition is developed to find the constraints on Q (s). The other requirements such as the uncertainties in performance specification and robust performance requirement are also converted into the same space as additional constraints. The loopshaping in Q -space is to find a feasible Q (s) to satisfy all the constraints. With a controller obtained through such a Q (s), one can derive the constraints posed on the controller C (s) due to all the requirements. The loopshaping directly in C -space then helps one to find a reduced-order controller. Numerical examples are used to illustrate the feasibility of the approach.