Boundary Control Design for a Flexible Manipulator with Input Backlash * *This work was supported by the National Basic Research Program of China (973 Program) under Grant 2013CB733100, the National Natural Science Foundation of China under Grant 61522302, 6161101273, the Newton Advanced Fellowship from The Royal Society, UK, under Grant NA160436 the Beijing Natural Science Foundation under Grant 4172041, and

Abstract

Abstract Boundary control design for a class of flexible manipulator with input backlash is our uppermost work of this paper. The original infinite dimensional model of the manipulator is represented by a partial differential equation (PDE) and a set of ordinary differential equations (ODEs). Our control aims are: 1) moving the manipulator to the certain desired angle; 2) suppressing the vibration at the neighbourhood of the desired angle; 3) handling the backlash nonlinearity existing in the practical system. The stability of the system and the effectiveness of the designed controller are analysed by Lyapunov's direct method and numerical simulation.