Trajectory Tracking Control of Parallel Manipulator with Integral Manifold and Observer

Abstract

In view of the problem that notable flexible displacement will occur for parallel manipulators when operating at high speed, the composite controller based on the integral manifold and high-gain observer is proposed for trajectory tracking and the 3RRR parallel manipulator is taken as the object. Based on the stiffness matrix, the small variable is introduced to decompose the rigid-flexible coupling dynamic model into slow and fast subsystem. For the slow subsystem, the backstepping control is applied for rigid motion tracking. In order to account for the links' flexible displacement the corrective torque is deduced, and the compensation for the flexible displacement is realized. For the fast subsystem, the sliding mode control is utilized to suppress the vibration. The high-gain observer is designed to avoid the measurement of the curvature rate of flexible links. Also, the stability of the overall system is proven with the Lyapunov stability theorem and the upper bound of the small variable is obtained. At last, the proposed composite controller together with the singular perturbation control and the rigid body model-based backstepping control are simulated, and vibration suppression and tracking performances are compared to validate the proposed control scheme.