Optimal Switching Control of Motion Stages

To avoid the trade-off between improved disturbance rejection and deteriorated noise sensitivity under high-gain feedback, an optimal switching control design is presented. Using a deadzone-based switching gain, large servo error signals induce extra controller gain to improve low-frequency suppression. Small error signals induce no extra controller gain as to maintain a small-gain noise response. In a stability-invariant control context, the choice for the switching length is strictly performance-driven. With an iterative scheme based on the Gauss-Newton method, the optimal switching length is found by minimizing the servo error signals in a time-interval of interest. For a fast and nano-accurate wafer stage improved performance is demonstrated in terms of reduced settling times and improved scanning behavior. Robust stability of the switched system and the iterative scheme is assessed using Lyapunov arguments.