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Rejection of Nonharmonic Disturbances in Nonlinear Systems With Semi-Global Stability

An asymptotic rejection algorithm is proposed for nonlinear dynamic systems under nonharmonic periodic disturbances generated from nonlinear exosystems. The dynamic systems considered in this brief are in the normal form, a larger class of nonlinear dynamic systems than the output feedback systems. A new internal model design method is used to exploit the nonlinearities in the exosystem, together with high gain design to achieve asymptotic rejection of nonharmonic disturbances with the guaranteed semi-global stability of the overall system. An illustrative example demonstrates that the proposed algorithm can completely reject the nonharmonic periodic disturbances generated from a Van der Pol circuit.