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Repetitive control for nonlinear systems: an actuator-focussed design method

There exist at least two viewpoints on the internal model principle (IMP), namely the cancelation viewpoint and the geometrical viewpoint. However, neither of them is applicable to repetitive control (RC, or repetitive controller, also designated RC) of nonlinear systems directly. Because of this, error dynamics are often derived to transform a periodic signal tracking problem into a rejection problem. This not only fails to represent the special feature of periodic signals but also restricts the applications of RC. In view of this, this paper proposes a new viewpoint on IMP, namely the actuator-focussed viewpoint. With this, the periodic signal tracking problem can be converted into a stability problem without deriving error dynamics for linear periodic systems and nonlinear systems. In order to demonstrate its effectiveness, the proposed design approach is applied to RC problems for a linear periodic system, a minimum-phase nonlinear system and a nonminimum-phase nonlinear system.