Disturbance rejection in adaptive control for a class of nonlinear mechanical systems

This paper presents hybrid control strategy for robust trajectory tracking control for a class of uncertain nonlinear mechanical systems. The design combines adaptive fuzzy system with robust adaptive control algorithm. Adaptive fuzzy system approximates unknown nonlinear system dynamics while a robustifying adaptive control term is used to cope with uncertainties due to the presence of external disturbance, modeling error and other unmodeled dynamical effects. Using the Lyapunov method, we first develop a stable hybrid controller by assuming that the system output and its derivatives are available for feedback control design. Then, an output feedback form of the position-velocity (state feedback) hybrid controller is proposed where the unknown velocity signal is replaced by the output of a model-free linear estimator. We prove that the tracking error bound under output feedback design can converge asymptotically to the tracking error bound achieved under the state feedback control design. Finally, the proposed method is implemented and evaluated on a 3-DOF Phantom™ medical mechatronics system to demonstrate the theoretical development.