Nonlinear disturbance observer–based sliding mode control for double-driven parallel mechanism grinding

In this paper, a nonlinear disturbance observer (NDO) incorporating with a double hyperbolic sliding mode controller (DHSMC) based on the dynamic model of a double-driven parallel mechanism (DDPM) in joint space is proposed to solve the trajectory tracking problem of the end effector. The uncertainties, such as the unmodeled dynamics and random external disturbance, make the robustness of the trajectory tracking control a challenge that cannot be ignored, especially for the position-based impedance control. Therefore, first the dynamic model with the lumped disturbance of the DDPM in joint space is established. Then, the NDO and the DHSMC in joint space are designed to realize trajectory tracking and improve the robustness, where the double hyperbolic reaching law is used to reduce the chattering problem. The stability of the end effector is proofed using the proposed control protocol. Finally, the NDO-based DHSMC is utilized as the position controller in the force tracking of the end effector. Through quantitative simulation analysis, the root mean square error of DHSMC is 90% lower than that of constant rate and exponential rate sliding mode controller under lumped disturbance.