Rejection of nonharmonic disturbances in nonlinear systems via the internal model approach

Abstract

This paper proposes an asymptotic rejection algorithm for rejecting exotic disturbances in nonlinear systems. Disturbances produced by nonlinear exosystems are nonharmonic and periodic. The proposed algorithm extends the rejection of nonlinear disturbances for nonlinear dynamic systems from systems in the strict feedback form and output feedback form to general nonlinear systems. A new nonlinear internal model is proposed to deal with these disturbances. Furthermore, a state feedback controller is designed to ensure that the system’s state variables asymptotically converge to zero, and disturbances can be completely rejected. The proposed algorithm has various applications, such as active vibration control. The proposed algorithm is demonstrated to completely reject the nonharmonic periodic disturbances produced by a van der Pol oscillator.