Finite-time optimal control for MMCPS via a novel preassigned-time performance approach

Abstract

This paper studies the finite-time optimal stabilization problem of the macro–micro composite positioning stage (MMCPS). The dynamic model of the MMCPS is established as an interconnected system according to the Newton’s second law. Different from existing MMCPS control schemes, the convergence time of errors generated by control algorithms and coupling effects in the positioning process of the MMCPS is limited to the specific range depending on the initial value of the system, which is crucial for ensuring the cooperative work of macro and micro components. Meanwhile, the reinforcement learning strategy based on actor–critic neural networks is used to optimize the controller performance while ensuring the propulsion force on voice coil motor (VCM) and vibration reduction force on piezoelectric element actuator. Furthermore, a novel preassigned-time performance function is designed to guarantee that the displacements of the VCM axis and stage can be limited to the preassigned area in the preassigned time, thereby reducing vibration amplitude. All signals of the MMCPS system are proven to be semi-global practical finite-time stable. Finally, some simulation results demonstrate the feasibility of the designed algorithm.