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An adaptive nonlinear output tracking control method is proposed to reject unmatched biased sinusoidal disturbances for nonlinear systems that are in the strict feedback form. The proposed method consists of a disturbance observer (DOB) and an adaptive nonlinear controller. The DOB is in the form of a high-pass filter, and it estimates biased sinusoidal disturbances with unknown frequencies. The performance of the DOB is investigated in the time and frequency domains. As the DOB cannot accurately estimate biased sinusoidal disturbances with unknown frequencies, an adaptive nonlinear controller is designed to compensate for the disturbance estimation errors and ensure output tracking. The adaptive nonlinear controller is developed via the backstepping procedure. Thus, matching conditions are not significant in this design. The discontinuous &#x201C;sgn&#x201D; function is applied to the controller to compensate for the disturbance estimation errors. An update law of the control gain of the discontinuous &#x201C;sgn&#x201D; function is proposed to suppress the disturbance estimation errors without the knowledge of their upper bounds. Low-pass filters are embedded in the controller to smooth the derivative of the discontinuous &#x201C;sgn&#x201D; function. Consequently, multiple unmatched biased sinusoidal disturbances are compensated by the proposed method without any knowledge of the disturbances. The proposed method can reject multiple biased sinusoidal disturbances while it guarantees the constraint of the tracking error in steady-state response. Furthermore, the proposed method can reject multiple biased sinusoidal disturbances.

Adaptive Nonlinear Output Tracking Control With Rejection of Unmatched Biased Sinusoidal Disturbances for Nonlinear Systems