Modal analysis is a fundamental and important task for modeling and control of the flexible manipulator. However, almost all of the traditional modal analysis methods view the flexible manipulator as a pure mechanical...Modal analysis is a fundamental and important task for modeling and control of the flexible manipulator. However, almost all of the traditional modal analysis methods view the flexible manipulator as a pure mechanical structure and neglect feedback action of joint controller. In order to study the effects of joint controller on the modal analysis of rotational flexible manipulator, a closed-loop analytical modal analysis method is proposed. Firstly, two exact boundary constraints, namely servo feedback constraint and bending moment constraint, are derived to solve the vibration partial differential equation. It is found that the stiffness and damping gains of joint controller are both included in the boundary conditions, which lead to an unconventional secular term. Secondly, analytical algorithm based on Ritz approach is developed by using Laplace transform and complex modal approach to obtain the natural frequencies and mode shapes. And then, the numerical simulations are performed and the computational results show that joint controller has pronounced influence on the modal parameters： joint controller stiffness reduces the natural frequency, while joint controller damping makes the shape phase non-zero. Furthermore, the validity of the presented conclusion is confirmed through experimental studies. These findings are expected to improve the performance of dynamics simulation systems and model-based controllers.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.51305039)Specialized Research Fund for the Doctoral Program of Higher Education,China(Grant No.20110005120004)+1 种基金Fundamental Research Funds for the Central Universities,China(Grant No.2014PTB-00-01)National Basic Research Program of China(973 Program,Grant No.2013CB733000)
文摘Modal analysis is a fundamental and important task for modeling and control of the flexible manipulator. However, almost all of the traditional modal analysis methods view the flexible manipulator as a pure mechanical structure and neglect feedback action of joint controller. In order to study the effects of joint controller on the modal analysis of rotational flexible manipulator, a closed-loop analytical modal analysis method is proposed. Firstly, two exact boundary constraints, namely servo feedback constraint and bending moment constraint, are derived to solve the vibration partial differential equation. It is found that the stiffness and damping gains of joint controller are both included in the boundary conditions, which lead to an unconventional secular term. Secondly, analytical algorithm based on Ritz approach is developed by using Laplace transform and complex modal approach to obtain the natural frequencies and mode shapes. And then, the numerical simulations are performed and the computational results show that joint controller has pronounced influence on the modal parameters： joint controller stiffness reduces the natural frequency, while joint controller damping makes the shape phase non-zero. Furthermore, the validity of the presented conclusion is confirmed through experimental studies. These findings are expected to improve the performance of dynamics simulation systems and model-based controllers.
