Optimal Switching Time Control for Suppressing Residual Vibration in a High-Speed Macro-Micro Manipulator System

Abstract

This brief studies a novel residual vibration suppression problem arising in a high-speed macromicromanipulator system designed for various precision positioning tasks. First, the dynamic of the macromicrosystem is mathematically modeled by a nonlinear partial differential equation (PDE). Subsequently, a new nonlinear vibration suppression and trajectory planning problem governed by a couple of ordinary differential equations (ODEs) are successfully formulated by using the assumed mode method (AMM) and Hamilton’s principle. Based on the developed model, an optimal switching time control strategy combined with control parameterization is proposed to realize the residual vibration suppression by trajectory planning. The gradients of the cost functional with respect to the unknown control variables and switching time variables are derived analytically by the sensitivity analysis method. Both numerical simulations and real experiments in the laboratory verify that the proposed method is superior to the classical fifth-order polynomial (FOP) approach for the vibration suppression problem.