Modal Space Design And Control Of Considering Damping Effect For Six-degree-of-freedom Parallel Mechanisms

Parallel manipulators with six degrees of freedom have been widely used in industry owing to their high power-to-weight ratio, load carrying capacity, and stiffness. However, their intrinsic dynamic coupling manifests as strong coupling among each degree of freedom in the physical space of the system. Therefore, it is difficult to obtain ideal control quality using a controller that is designed based on traditional physical space. Recently, a novel modal-space control strategy was proposed by domestic and foreign scholars. Under the assumptions of proportional damping, employing modal decoupling theory, the highly coupled multiple-input multiple-output system in physical space is transformed into six independent single-input single-output systems in modal space, to get independent control in single degree-of-freedom system of each stage modality to improve the control quality and extend the bandwidth of the parallel manipulator.In industrial application, the joint damping of the parallel manipulator cannot be ignored, with this condition the phenomenon of the non-proportional damping coupling in the modal space will destroy the modal space decoupling condition, which seriously restricts the industrial application of modal-space control strategy. Therefore, in this paper, the mechanism of coupling nonlinear characteristic caused by the joint damping of parallel manipulator is in-depth analyzed, and then a new structural design method is proposed to eliminate modal space damping coupling effects to expand the scope of the modal-space control strategy, which has theoretical significance and engineering value. This paper researches in three aspects, including inertial parameters identification, structural design and control strategy.The manifestation of high control quality of modal-space control strategy is firstly affected by inertial parameters of the system, however, the existing inertial parameters identification method is flawed in identification principle due to without considering the coupling nonlinear caused by each joint damping of the parallel manipulator. To obtain accurate inertial parameters, this paper proposes a new inertial parameter identification method that eliminates the damping coupling effect. Based on the complete dynamic model involving damping characteristics of each joint of parallel manipulator, the relationship between damping coupling and inertial parameter identification is analyzed, and the identification equation is reconstructed, which includes phase difference information in each degree of freedom caused by damping coupling. On this base, errors in inertial parameters identification resulting from damping coupling effects are eliminated. Meanwhile, in view of the dry friction caused by the identification error, this paper establishes a quantitative evaluation index and modified method of identification error based on the waveform distortion. Simulation and experimental results verify the effectiveness of this proposed identification method.The design method based on modal decoupling provides an effective way to eliminate the system dynamics coupling characteristics from the aspect of structure, and the parallel manipulator with characteristics of mechanical decoupling lays the foundation for modal-space control strategy to play its superior control role. But the existing design method ignores the modal damping coupling characteristics caused by the joint damping of parallel manipulator, which thus cannot be an effective guidance for industrial parallel manipulator with low mechanical cost. To this end, the paper offers a universal analytic formula of modal parameters based on the modal analysis of vibration equation including system damping characteristics, in order to reveal the relationship between modal damping coupling characteristics and structural parameters, so a new way that makes modal-space control strategy still apply is proposed by means of changing the structure parameter to reduce the system non-proportional damping. Meanwhile, the paper analyzes the modal frequency coupling characteristics of parallel manipulator in the large workspace caused by pose, and puts forward a coupling evaluation index for global modal frequency coupling based on modal sensitivity. Finally, with the integrated optimized aim of reducing damping coupling characteristic and global frequency coupling feature, this paper proposes a global modal decoupling structure optimization method on the premise of eliminating the damping coupling effects.Finally, after the modal damping coupling influence has been eliminated by structural design, a new high frequency overdamping phenomena in modal space is brought out by joint damping characteristic of parallel manipulator, which can limit the further improving of system bandwidth. To this end, with the hydraulic control theory, this paper proposes a modal space control strategy to reduce the system damping by dynamic pressure feedback technique in order to extend the system bandwidth to the modal frequency, and next puts forward an analytical controller design method. Meanwhile for the purpose of applying the modal space control strategy to the large workspace parallel manipulator, this paper analyzes the modal coupling characteristics caused by pose, using modal parameters real-time solving algorithm which can eliminate the mode jumping phenomenon, finally realizes extending the modal space control strategy to the global modal space controller. The experimental results show that the controller can greatly improve the control performance and has advantages of a simple structure, a wide range of applications and design convenience, which provides a foundation for the engineering practice application of the modal space control strategy.