Study On Dynamic Modeling And Elastic Vibration Control Of Flexible Manipulator

The flexible manipulator is a typical representative of the rigid-flexible coupled multi-body dynamics system and is widely used in aerospace,robot and modern intelligent manufacturing.Compared with the traditional rigid manipulator,the flexible manipulator has the advantages of light weight,low energy consumption and large load mass ratio.In the actual operation,the movement of the flexible manipulator is often composed of a wide range of rigid body motion and elastic vibration caused by the elastic deformation of the flexible body.These two different forms of motion make the flexible manipulator system a rigid-flexible coupled and nonlinear time-varying system.Due to the presence of elastic vibration,the positioning accuracy of the flexible arm during the movement is reduced,and even the reliability of the system is reduced.In view of the vibration problem of flexible arm,this paper studies the dynamic characteristics and vibration control of single-link flexible manipulator based on the research results of dynamic system modeling and structural vibration control at home and abroad.The main research contents are as follows:Firstly,based on structural mechanics and mechanical vibration,a mathematical model of single-link flexible manipulator with concentrated mass at the end is established.Elastic deformation description and dynamic analysis of flexible manipulator are carried out by using hypothetical modal method.The Lagrange equation is used to establish the dynamic equation of the flexible arm and the expression of the state space is deduced to provide the basis for the subsequent vibration controller design and software simulation.The first six modes of the flexible arm are analyzed.Secondly,according to the basic principle and significance of the linear quadratic optimal control,the linear control of the flexible manipulator is carried out by using the linear quadratic optimal control.Different weighting matrices are selected.The experimental results show that the elastic vibration can be effectively suppressed.Genetic algorithm is used to search for the optimal weighting matrix.The optimized linear quadratic optimal control can attenuate the terminal vibration energy and improve the vibration suppression effect more quickly than before.Finally,the elastic vibration suppression problem of flexible manipulator is studied by feedforward control.The angular displacement and angular velocity of the manipulator under different trajectory planning functions are analyzed.Genetic algorithm is used to optimize the trajectory of flexible manipulator based on the fifth order polynomial function trajectory planning.The optimized optimal vibration control trajectory curve is obtained by using the fifth order polynomial function interpolation.Compared with the pre-optimized trajectory,the optimized flexible manipulator can effectively attenuate the residual residual vibration energy under the optimal trajectory control.The research contents and experimental results are not only practical for the dynamic modeling and vibration control of the single-pole flexible manipulator system,but also provide the methods and ideas for the more complex flexible system research.