Nonlinear Q-filter in the learning of nano-positioning motion systems

To avoid an increased noise response under high-gain learning, a Q-filter with varying cut-off frequency is proposed. The Q-filter design is of particular interest in the wafer scanning industry where nano-position accuracy should be achieved under high-speed repetitive motion. In a lifted iterative learning control (ILC) setting, the nonlinear Q-filter is given state-dependent low-pass filter characteristics. Being induced by sufficiently large servo error signals, the Q-filter acts as a low-pass filter with sufficiently large cut-off frequency as to allow for a large learning gain, hence fast error convergence. For small error signals, i.e., the signal levels typically associated with noise, the Q-filter acts as a low-pass filter with a significantly reduced cut-off frequency. As a result, the amplification of noises through high-gain learning is kept limited. For a long-stroke wafer stage module of a wafer scanner, the effectiveness of the learning approach is assessed through experiment.