Oscillation elimination of tip regulation for a single-link flexible manipulator

Abstract

Many existing variable structure control schemes for flexible manipulators use a conventional sliding surface, which is linear with respect to system states. It results in a reduced-order sliding motion, i.e. the closed-loop dynamics during ideal sliding has reduced number of eigenvalues to be assigned, and the fixed eigenvalue at the origin functions as integrator and may degrade system robustness. In this paper, an integral-type sliding surface is proposed which obtains a full-order sliding motion, such that all the eigenvalues of the closed-loop dynamics can be assigned. The integral-type sliding surface is derived from a reference model which does not have any finite zero but all negative real poles. In order to force the system to follow the reference model in the presence of the unstructured uncertainties, a variable structure controller is adopted. When in sliding mode, the system performs as the reference model. Hence there will be no vibration and the tip position regulation can be achieved when the system approaches steady-state. Simulation results demonstrate the effectiveness of the proposed approach.