Dual-loop ADRC–TS-ILC for contour error control of a two-degree-of-freedom parallel mechanism

To improve contour accuracy of two-degree-of-freedom parallel mechanisms for complex high-curvature trajectories under strong coupling, nonlinear friction, and nonrepetitive disturbances, a dual-loop contour error control method combining Active Disturbance Rejection Control (ADRC) and task-space-based iterative learning control (TS-ILC) is proposed. In the inner loop, a joint-space velocity-loop ADRC is designed to estimate and compensate lumped uncertainties, including inertial coupling, friction, and external disturbances, thereby enhancing disturbance rejection and weakening inter-joint coupling. In the outer loop, the shortest normal contour error is estimated in task space using the Newton iterative method and mapped into a joint-space learning error through the inverse Jacobian. A PD-type ILC with zero-phase filtering is then applied for repetitive error compensation. A MATLAB/Simulink and Simscape Multibody co-simulation platform is built to evaluate the method under white noise and random step load disturbances. Results on heart-shaped and five-leaf clover trajectories show that the proposed method achieves good robustness and convergence, reducing the maximum contour error by 74.15% and 54.48%, respectively, compared with the method that combines ADRC with joint-space tracking-error ILC. This study provides an effective solution for complex-trajectory contour control of high-speed, high-precision parallel mechanisms.