Integrated Optimal Design And Control Of High-speed And Light-weight Parallel Manipulator

With the advantages of high payload ratio, high stiffness and high accuracy, the parallel manipulator has been widely applied. And with the increasing demand of productivity, the parallel manipulator has been increasingly applied in high-speed grinding, pick-place and assembly. At the same time, to reduce the cost of product and the consumption of energy, the modern design method considering light weight has begun to be employed in the development of manipulators. However, in the high-speed operation, light-weight structure usually causes notable vibrations and deflections for existence of link flexibility and when the analysis method and control scheme for traditional rigid manipulators are utilized for this type of manipulators, the tracking accuracy and dynamic performances won’t be guaranteed. To solve the forementioned common problems of high-speed parallel manipulators, with the 3RRR parallel manipulator of typical structures as the research object, this thesis focuses on the following key issues, such as control system design oriented rigid-flexible coupling modeling of the parallel manipulator, integrated design incorporating structure optimization, driving and transmission parameters matching, control system parameters adjustment, and dynamic modeling based trajectory optimization and control system design. At the same time, the performance test and experiments are carried out.The kinematic and rigid dynamic model of the 3RRR parallel manipulator are built first, based on which, the flexible link is discretized with CFE(Curvature based finite element) considering the rigid ends from basic assumptions of the Euler beam, and models of commonly used cantilever beam and simply supported beam in the parallel manipulator are derived, so the ICFE(improved curvature based finite element) with the consideration of rigid ends is proposed. Then with the derived beam model and the small deformation assumption, the relationship between flexible motion of the links and rigid motion of the manipulator is thus established. With the forementioned models and Kane equation, the rigid-flexible model of the 3RRR parallel manipulator is derived. To validate the proposed model, modal analysis and acceleration analysis are studied respectively, and comparison studies with ABAQUS model are investigated. At the same time, the model simplification is conducted according to the modal analysis. The result shows that significant improvement on coincidence with the ABAQUS model for both modal analysis and acceleration analysis can be obtained with the account of rigid ends. For the proper simplification of the model and the avoidance of iteration of rigid and flexible constraint equations, the derived model can guarantee high accuracy and computation efficiency.To obtain excellent comprehensive performances for parallel manipulators, an integrated optimal design method is proposed, integrating mechanism optimization, driving and transmission parameter matching and control parameters adjustment. To adapt to high-speed motion, kinematic and dynamic performances of conditioning number, velocity index, acceleration capability, and base frequency are taken accounts into mechanism optimization. Then to match driving and transmission parameters and keep an economical cost, the constraint equations and the parameters library are built, and the cost is chosen as one of the optimization objectives. Also, to get high tracking accuracy, the dynamic foward plus PD control scheme is introduced, and the tracking error is chosen as one of the optimization objectives. Hence, the optimization model including mechanism parameters, driving and transmission parameters and control parameters is established, which is solved by the non-dominated sorting genetic algorithm II(NSGA-II). Finally, the high-speed parallel manipulator is optimized with the integrated optimal design. The result shows that comprehensive performances can be effectively promoted through the proposed integrated optimal design.To constrain flexible displacement(FD) and suppress the RV(Residue vibration) for high-speed parallel manipulator, from the perspective of trajectory planning, FD restriction and RV suppression are investigated for the given trajectory motion and point-to-point positioning considering link flexibility. For the given trajectory RV suppression problem, with the consideration of the characteristic of the frequency change with the position of the manipulator, the multi-mode input shaping(IS) method, Particle swarm optimization(PSO) and feedback control are integrated, and an optimization model with the RV as the optimization objective and the parameters of multi-mode shapers as optimization parameters is established, then the PSO is utilized for off-line optimization of the control model. The simulation result shows that the RV can be suppressed significantly with the optimized shapers, and with the increasing number of the shapers, the RV further lowers. For high-speed point-to-point motion, the time-optimal planning and multi-mode IS are integrated, and a two-step optimization method is proposed. The multi-segmented Gauss pseudospectral method(GPM) is introduced first for the solution of time optimal problem, then multi-mode IS is used for RV suppression of the obtained trajectory. The simulation result shows that the two-step optimization can realize FD constraint and RV suppression simultaneously with time-optimal motion.To solve the trajectory tracking problem of high-speed and light-weight parallel manipulators with flexible links, the integral manifold and high-gain observer based combined control scheme is proposed. The small parameter is introduced first according to the stiffness matrix, and the rigid-flexible coupling dynamic model is divided into slow and fast subsystems based on the integral manifold. Then the combined control scheme is devised for the two subsystems, in which the backstepping control was employed for the slow subsystem. Meanwhile corrective torques are derived to take flexible displacement of links into end-effector’s trajectory, and sliding variable structure control is adopted for the fast subsystem to guarantee the manifold invariant. To obtain the curvature velocity which is difficult to measure, the high-gain observer is designed and the stability is proven. Then stability of entire system with the combined control scheme is validated and the range of the small parameter is deduced. At last, comparison studies with singular perturbation based control and rigid model based backstepping controller are investigated to validate the proposed combined control. The simulation result shows that the proposed integral manifold and observer based combined control gives excellent performance in both vibration suppression and trajectory tracking.To validate the forementioned theoretical investigations, the mechanical design and selection of driving and transmission are carried out according to the result of integrated design, and the control structure of industrial computer, real-time operation system and high-speed communication bus is adopted. Then laser tracker is employed to test the repetitive positioning accuracy. To test the accuracy of the proposed dynamic model, the LMS vibration instrumentation is used to test the modes and accelerations. At last, multi-mode IS combined with PSO and feedback controller based planning for given trajectory motion and two-step planning for point-to-point motion are tested and validated in this thesis.