Control of a class of nonlinear systems subject to periodic exogenous signals

This paper examines the control of Single-Input, Single-Output Feedback Linearizable nonlinear systems that are either (i) subject to periodic disturbances or (ii) tracking periodic reference trajectories. The key concept is the straightforward combination of well known Differential Geometric techniques with the Internal Model Principle resulting in a nonlinear repetitive control strategy. A formulation is presented for the case of Input-State Linearizable and Input-Output Linearizable systems in continuous time. The potential benefits of the nonlinear repetitive controller are given. It is shown that while the standard nonlinear control techniques can be made robust to known disturbances, the nonlinear repetitive technique has desirable characteristics in that it does not require knowledge of the disturbance magnitude and does not need an increased loop gain to accomplish robustness. The procedure is applied to a numerical simulation example with the resulting benefits being clearly shown.