An exponentially convergent adaptive sliding mode control of robot manipulators

Abstract

Abstract A new robust adaptive algorithm for control of robot manipulators is proposed to account for a desired transient response with global exponential convergence of tracking errors without any persistent excitating assumption on the regressor. Its novelty lies in a new dynamic sliding surface that allows a systematic combination of adaptive control and variable structure control to yield a sliding mode inside an adaptive control loop. During sliding mode, parameter uncertainty appears in terms of known variables in such a manner that a new robust parameter estimator with enhanced stability properties is established. On the other hand, if the regressor meets the persistent exciting condition, the global uniform exponential stability of the equilibrium concerning the adaptive closed-loop error equation is easily established. The proposed controller from the VSS viewpoint relaxes the longstanding condition on a priori knowledge of the size of the parametric uncertainty to induce a sliding mode. On the other hand, from the adaptive control viewpoint it relaxes the standard assumption of the persistent excitation on the regressor to obtain the exponential convergence of tracking errors. Also, the stability against time-varying parameters is briefly discussed. Concluding remarks concerning its structural behaviour are given, and computer simulation data show a robust performance.