Discrete Input-Output Sliding-Mode Control with Range Compensation: Application in High-Speed Nanopositioning

In this work, a discrete sliding-mode control scheme is presented for dual-stage nanopositioning systems. The dual-stage structure consists of a long-range, low-speed actuator that displaces a short-range, high-speed, high-precision actuator. A discrete trajectory-tracking sliding-mode control law based on an input-output model is derived for dual-input, single-output nanopositioning systems. A difference equation formulation for the sliding surface is chosen to mitigate trajectory frequency transmission from the sliding variable to the error signal. The short-range actuator control effort is calculated based on this sliding variable, filtered based on its range characteristics, and the change in reference trajectory. The long-range actuator control law is formulated to account for this additional effort while satisfying the discrete reaching law condition. Simulations are conducted on linear and nonlinear models of a dual-stage positioner for low- and high-speed triangular reference trajectories. Results show approximately 30% improvement in the maximum error and an 18.8% root-mean-square error reduction over a long-range actuator sliding-mode control formulation for trajectories well beyond the typical closed-loop bandwidth of the device’s long-range actuator.