LMI-Based Sliding Mode Controller Design for an Uncertain Single-Link Flexible Robot Manipulator

A conventional (first order) sliding mode controller (SMC) is applied to an uncertain planar single-link flexible robot arm in the context of the regulator problem (disturbance rejection). The planar single-link flexible robot arm exhibits nonlinearities and uncertainties associated with Coulomb's friction, the payload, and viscous friction. A SMC design framework that takes into account matched and mismatched uncertainties is proposed in this paper. The design methodology involves linear matrix inequality (LMI) methods and polytopic models of the uncertain planar single-link flexible robot arm. Computer simulation results demonstrate the effectiveness of the proposed sliding mode approach.