Novel finite-time adaptive sliding mode tracking control for disturbed mechanical systems

Abstract

In this paper, the finite-time tracking control problem of mechanical systems subject to model uncertainties and external disturbances is investigated. A new type of finite-time adaptive sliding mode control approach is proposed based on a novel integral sliding mode surface and a novel parametric adaptation mechanism. The integral sliding mode surface is originally designed by utilizing the adding a power integrator technique. The parametric adaptation mechanism is developed by using a single adaptive updating law to estimate the square of the upper bound of the lumped uncertain term. As compared with the most existing studies, the distinctive features of the proposed controller are threefold. (1) Benefiting from the novel integral sliding mode surface, the proposed controller has no singularity problem inherently existing in the terminal sliding mode control. (2) Owing to the use of novel parametric adaptation mechanism, the proposed controller is smooth and the unexpected chattering phenomenon is significantly attenuated. Moreover, the proposed controller is structurally simple and requires relatively few online calculations, which makes it affordable for practical applications. (3) The practical finite-time stability of the overall closed-loop system is strictly proved. The proposed controller can ensure the position and velocity tracking errors stabilize to the adjustable small neighborhoods around the origin in finite time. Lastly, the effectiveness and advantages of the proposed control approach are illustrated through simulations and comparisons.