Finite-time Stable Robust Sliding Mode Dynamic Control for Parallel Robots

To address the tracking control problem for n -DOF parallel robots in presence of the lumped disturbance, including modeling errors, friction and external disturbance, a finite-time stable robust sliding mode dynamic control (FRSMDC) for parallel robots is explored. From the implementation condition of the FRSMDC for parallel robots, the limitation on the change rate of the lumped disturbance is relaxed for easy realization. From the results of the FRSMDC for parallel robots, the finite-time stability of the sliding variable is proved and the settling time is derived; the switching gain required is only larger than the upper bound of the disturbance estimation error, instead of the upper bound of the disturbance, due to the feed-forward compensation to the lumped disturbance via a disturbance observer. Consequently, the system robustness is improved and the chattering of FRSMDC is alleviated. The finite-time stability of the closed-loop system is confirmed with Lyapunov theory. Besides, the application of the proposed method is extended to a general multi-input multi-output nonlinear system with the relative degree m by analogy. Finally, the case of the dynamic control of a 6-DOF parallel robot for automobile electro-coating conveying is studied for simulation and experiment, so as to attest the validity of the FRSMDC for parallel robots.