Linear stability analysis of model error control synthesis

Recently, a new approach for the robust control of nonlinear systems was presented. This approach, called Model Error Control Synthesis, employs an optimal real-time nonlinear estimator to determine model error corrections to the control input of a sliding mode controller using a one time-step ahead technique. Control compensation is achieved by using the estimated model error as a signal synthesis adaptive correction to the nominal control input so that maximum performance is achieved in the face of extreme model uncertainty and disturbance inputs. In this paper Model Error Control Synthesis is applied to a simple second order linear mass-spring-damper system and a higher order benchmark problem. A robustness analysis is performed for the mass-spring-damper system. The proof of the closed loop stability is derived using a Padé approximation for the time delay. It is shown that the weighting coefficient for the model error correction in the associated cost function cannot be set to zero since this gives a non-minimum phase system in the closed-loop response, and the control law itself is not asymptotically stable. Simulations are used to verify theoretical results.