Cascading Structure Linear Quadratic Tracking Control for Dual-stage Nanopositioning Systems

This paper investigates the design of a cascading linear quadratic tracking controller to improve the tracking performance of a dual-stage nanopositioning system. This approach separates the controller design between actuators, allowing for more flexibility in assigning actuator inputs. Specifically, the short-range actuator is given a reference dependent on the long range actuator’s residual tracking error compared to the full desired trajectory, effectively enabling more aggressive effort from the secondary actuator. This new control paradigm is validated in simulation on one axis of an experimental multi-axis dual-stage positioner, where individual actuator measurements are assumed to be available. Simulations are conducted with slow and fast triangular reference trajectories using the cascading design and a standard multi-input multi-output tracking controller. The plant is varied to include high-order dynamics and nonlinearities (specifically hysteresis) to further demonstrate performance. Results show a reduction of maximum and root-mean-square error by approximately 40% for plants with umodeled dynamics and hysteresis, while the root-mean-square error is reduced by nearly 90% for a model matching the plant’s dynamics.