Adaptive asymptotic 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 (like repetitive control) with the same goal usually have to know the system's structure, which, in the presence of unmodeled dynamics, makes the robustness property less appealing. Since no structural knowledge is needed 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.