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We investigate the dynamic mode of a 3-degree of freedom (DOF) redundantly actuated parallel manipulator by taking the flexible deformation of the limbs into account. The dynamic model is derived using Newton-Euler formulation. Since the number of equations derived from the force and moment equilibrium of the parallel manipulator components is less than the number of unknown variables, the flexible deformation of the limbs is treated as an inequality constraint to find the solution of the dynamic model. The errors of moving platform caused by the flexible deformation of limbs are discussed, and a control strategy is given. To validate the model, the dynamic model is integrated with the control system and compared with the traditional method to minimize the normal driving forces.

Flexure-based micro-motion mechanisms have been widely utilized in modern precision industry due to their inherent merits, while model uncertainty, uncertain nonlinearity, and cross-coupling effect will obviously deteriorate their contour accuracy, especially in the high-speed application. This paper aims at improving the contouring performance of a flexure-based micro-motion stage utilized for tracking repetitive trajectories. The dynamic characteristic of the micro-motion stage is first studied and modeled as a second-order system, which is identified through an open-loop sinusoidal sweeping test. Then the iterative learning control (ILC) scheme is utilized to improve the tracking performance of individual axis of the stage. A nonlinear cross-coupled iterative learning control (CCILC) scheme is proposed to reduce the coupling effect among each axis, and thus improves contour accuracy of the stage. The nonlinear gain function incorporated into the CCILC controller can effectively avoid amplifying the non-recurring disturbances and noises in the iterations, which can further improve the stage’s contour accuracy in high-speed motion. Comparative experiments between traditional PID, ILC, ILC & CCILC, and the proposed ILC & nonlinear CCILC are carried out on the micro-motion stage to track circular and square trajectories. The results demonstrate that the proposed control scheme outperforms other control schemes much in improving the stage’s contour accuracy in high-speed motion. The study in this paper provides a practically effective technique for the flexure-based micro-motion stage in high-speed contouring motion.

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