A new viewpoint on the internal model principle and its application to periodic signal tracking

Periodic signal tracking is certainly easier than general signal tracking. This has been manifested for linear time-invariant systems by applying theories of repetitive control. However, because of the lack of corresponding theories, the difficulties in designing repetitive controllers for both periodic signal tracking and general signal tracking in nonlinear systems are similar or the same. In view of this, this paper proposes a new viewpoint on the internal model principle which is used to explain how the internal models work in the time domain when the desired signals are step signals, sine signals and general periodic signals, respectively. Guided by this viewpoint, the periodic signal tracking problem is considered as a stability problem for nonlinear systems. To demonstrate the effectiveness of this new viewpoint, a new method of designing repetitive controllers is proposed for periodic signal tracking of non-minimum phase nonlinear systems, where the internal dynamics are subject to a periodic disturbance. A simulation example illustrates the effectiveness of the new method.