Adaptive Asymtotic Tracking of Repetitive Signals - A Frequency Domain Approach

The problem of designing an adaptive tracking controller for repetitive reference signals is considered. It is assumed that the controlled plant is linear time invariant. The proposed controller, being able to identify the gain and phase of a plant at selected frequencies, adjusts the I/O map at frequencies contained in the reference signal so as to achieve zero steady state errors. Other control methods with the same goal like repetitive control usually have to know the system´s structure which, in the presence of unmodel dynamics, makes the robustness property less appealing. Since no structural knowledge has to be known in the proposed approach, it is robust as long as the phase and magnitude of the plant at those target frequencies are not drastically changed. However, the proposed controller does not alter the transient property of the plant, e.g., locations of poles. Thus, a combination of this controller and a feedback LTI controller is proposed also.