Feed-forward control of non-minimum phase XY table system using Trajectory Fuzzy-RLS Hybrid ZPETC

A tracking control for non-minimum phase (NMP) XY Table could not use directly the inverse closed-loop transfer function as the feed-forward controller. This is due to unstable zeros of the closed-loop transfer function will become unstable poles at the feed-forward controller. Thus, ZPETC was introduced to encounter this unstable zeros problem. The ZPETC that was introduced by Tomizuka has unity gain for low frequencies, but not at high frequencies. Hence, this paper proposed a scheme called Trajectory Fuzzy-RLS Hybrid ZPETC without factorization of zeros polynomial where the optimum controller parameters are obtained offline using recursive least square (RLS) method and further retune online through fuzzy inference system (FIS). The tracking performance was compared with the design using Trajectory-Adaptive ZPETC. The simulation and real-time controls of the NMP XY Table show that the tracking performances for circular movement are significantly improved.