Adaptive Neural Preassigned-Time Control for Macro–Micro Composite Positioning Stage With Displacement Constraints

This article considers the rapid vibration reduction problem of macro–micro composite positioning stage (MMCPS) using an adaptive neural preassigned-time control strategy. Based on Newton's second law, the MMCPS is modeled as an interconnected system with unknown perturbations, and for the first time, the vibration reduction problem of MMCPS is transformed into a displacement constraint problem. Through adaptive neural network approximation and backstepping control, a preassigned-time controller with a novel performance function-related term is developed, which not only significantly improves the positioning accuracy and reduces the vibration amplitude but also ensures that the displacements of the voice coil motor axis and the stage are constrained to a predefined region in a finite time. Another distinguished feature of the proposed controller lies in the fact that the settling time of the displacement signals can be set as an arbitrary positive value. Moreover, all signals of the closed-loop system are proved to be semiglobally uniformly ultimately bounded. Finally, the feasibility of the designed control strategy is demonstrated via a simulation experiment.