摘要
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.
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.
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)
Fundamental Research Funds for the Central Universities,China(Grant No.2014PTB-00-01)
National Basic Research Program of China(973 Program,Grant No.2013CB733000)
作者简介
CHU Ming, bom in 1983, is currently an associate professor at Automation School, Beijing University of Posts and Telecommunications, China. He received his PhD degree from Beijing University of Posts and Telecommunications, China, in 2010. His research interests include flexible dynamics modeling, vibration control and intelligent robotics. Tel： ＋86-10-61198259; Corresponding author. E-mail： chuming bupt@bupt.edu.cnZHANG Yanheng, born in 1978, is currently an associate professor at Automation School, Beo＇ing University of Posts and Telecommunications, China. He received his PhD degree from Beihang University, China, in 2008. His research interests include robot structure design and pipeline robot. Tel： ＋86-10-62281368; E-mail： zyh620@bupt.edu.cnCHEN Gang, born in 1982, is currently an associate professor at Automation School Beijing University of Posts and Telecommunications, China. He received his PhD degree from Beijing University of Posts and Telecommunications, China, in 2011. His research interests include robot motion planning. Tel： ＋86-10-61198259; E-mail： chengang_zdh@bupt.edu.cnSUN Hanxu, born in 1960, is currently a professor at Automation School, Beijing University of Posts and Telecommunications, China. He received his PhD degree from Beihang Universtiy, China, in 1989. His research interests include space robotics. Tel： ＋86-10-62281011; E-mail： hxsun@bupt.edu.cn
