Practical Synchronous Sliding Mode Control With Time Delay Estimation for a 4-DOF Parallel Manipulator With Unknown Dynamics and Variable Payload

This paper presents a practical synchronous sliding mode control (SSMC) using time-delay estimation (TDE) for trajectory tracking of a 4-DOF parallel robot with a variant payload, unknown dynamics, and actuator faults. The feature of the proposed control is its integration of the synchronous sliding mode control to synchronize joint motions using cross-coupling error in the 4-DOF parallel robot, which is often neglected in conventional control. Moreover, the TDE is employed to estimate lumped uncertainties including unknown dynamics, external disturbance, and internal uncertainty. By integrating these techniques, the controller achieves high tracking accuracy and robustness without requiring a precise dynamic model. Additionally, the stability analysis of the closed-loop system is proved using the Lyapunov theory. Furthermore, the proposed controller is evaluated through both simulations and the 4-DOF parallel robot experiment. In simulations, the proposed method achieved the lowest root mean squared error (RMSE) of 0.00063 rad among all joints for tracking error and 0.00049 rad for synchronous error, outperforming conventional controllers. Experimental results from the test bench demonstrate that the proposed controller maintained superior accuracy under a 2 kg payload and motor efficiency loss, reducing tracking RMSE by 12.1% and synchronous RMSE by 10.6% compared to synchronous PD time delay estimation.