Dimensionality Reduction And Control Of Rigid-flexible Manipulator Model Based On Spectral Methods

With the development of science and technology,the requirements on speed and precision of mechanism become increasing in defense, industry and other fields. Lightweight and flexible structures have been widely used in engineering. Research in this area comes to flexible multibody dynamic system or rigid-flexible coupling dynamic system.The flexible manipulator is a typical application in this area. Since the flexible multibody dynamics system has lots of applications in defense industry such as aerospace,aviation and robot, the research about the dynamic modeling, model dimension reduction and active control have important theoretical and practical value.The dynamics model of flexible multi-body system obtained by space discretization methods was generally higher order. In order to facilitate dynamic characteristis and control, the high precision with low-dimensional approximate model was designed. A model dimension reduction method based on the time-space separation of spectral method and Galerkin truncation theory was proposed. An experimental platform of rigid-flexible manipulator was designed and built in this paper,and the rigid-flexible manipulator was employed to verificate the theory of model dimension reduction.The main research and achievements are as follows.1. An overall program of the rigid-flexible manipulator was designed according to the object and purpose of research. Then the 3D model and driver programs were established and determined, and the kinematics and workplaces of the manipulator were analyzed.2. The study of the article was focused on the rigid-flexible two-link arms of the manipulator, which was the infinite dimensional distributed parameter systems. The system dynamics equations, which was kind of partial differential equations, were obtained by Lagrange equation method. The low-dimensional approximate model,which contained main characteristics of the system, was derived basd on spectral method and reduction criterion of Galerkin method. Then Rigid-flexible coupling characteristics of the system were simulated and analyzed.3. The rigid-flexible two-link arms model is multiple-input-multi- ple-output (MIMO) system with property of non-minimum phase, nonlin-ear, time-varying parameters,etc characteristic. The output redefinition method was employed to eliminate the non-minimum phase of the system, and then two subsystems of the input-output subsystem and the internal dynamics subsystem were derived through input-output linearization method to partially linearize the dynamic model. A sliding controller with an index reaching law was designed to control the input-output subsystem, and a state feedback controller was employed to stabilize the internal dynamics subsystem. The simulation results illustrated that the control strategy has good dynamic and robust performance.4. The experiments were carried out in the experimental platform of rigid-flexible manipulator, and experimental results showed that the low-dimensional approximate model devided by spectral method and reduction criterion of Galerkin method was reasonable.Some references were provided to research of similar objects in engineering through this study. The topic of dynamics modeling, dimension reduction, control and other issues of the flexible multibody dynamic system are challenging, thus many aspects and issues need further study.