State/Model-Free Variable-Gain Discrete Sliding Mode Control for an Ultraprecision Wafer Stage

Wafer stage is an important mechatronic unit of industrial lithography tool for manufacturing integrated circuits. This paper presents a novel state/model-free variable-gain discrete sliding mode control (DSMC) to suppress the unmolded position-dependent dynamics and disturbances in the nanopositioning wafer stage. The proposed DSMC is essentially composed of feedforward control term, linear feedback control term, and nonlinear switching control term, which can be designed separately. The gain of the switching control term is meaningfully designed to be variable to balance the tradeoff between the robustness and the chattering. Data-driven parameter optimization approach is employed to achieve the optimal controller parameters of the typically nonlinear controller, where off-line parameter updating is iteratively carried out based on the input/output data to minimize a predefined objective function. This scheme facilitates a rapid implementation without either a parameter model or a state observer, and excellent tracking performance with the optimal controller parameters. Moreover, the closed-loop stability is analyzed, and the proposed DSMC is finally implemented on an ultraprecision wafer stage developed in our lab. Comparative experimental results demonstrate that it not only achieves nanoscale tracking accuracy but also possesses promising robustness to position-dependent dynamics and disturbances.