Nonlinear Partial Differential Equation Model-Based Coordination Control for a Master–Slave Two-Link Rigid–Flexible Manipulator With Vibration Repression

Abstract

In this study, vibration control problem is considered for a coordinative master–slave two-link rigid–flexible manipulator. By the help of Hamilton's principle, the dynamic model of the master–slave two-link rigid–flexible manipulator is expressed using nonlinear partial differential equations (PDEs). Based on the nonlinear PDE model, we propose a novel coordination controller for the master–slave system. The proposed controller can achieve the following three objectives: (1) making the master manipulator track the given angles; (2) making the slave manipulator track the angles of the master manipulator; and (3) repressing the deflection and vibration of both the master and the slave flexible manipulators. Stability analysis of the closed-loop system is proven by LaSalle's invariance principle. Two simulation cases are given to validate the effectiveness of the coordination controller.