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

This paper examines the control of single-input feedback linearizable nonlinear systems that are either subject to periodic disturbances or tracking periodic reference trajectories with known periods. The key concept is the combination of 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 disturbances, the nonlinear repetitive technique is more robust to specific types of disturbances in that it does not require knowledge of the disturbance magnitude and does not need high gains to accomplish robustness. As a proof of concept, the procedure is experimentally applied to the active vibration isolation of a single degree of freedom (SDOF) magnetic levitation testbed with the resulting benefits being clearly shown.