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Effects of joint controller on analytical modal analysis of rotational flexible manipulator

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Abstract

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.

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References

  1. BIAN Yushu, GAO Zhihui. Impact vibration attenuation for a flexible robotic manipulator through transfer and dissipation of energy[J]. Shock and Vibration, 2013, 20(4): 665–680.

    Article  Google Scholar 

  2. BIAN Yushu, GAO Zhihui, YUN Chao. Study on vibration reduction and mobility improvement of the flexible manipulator via redundancy resolution[J]. Nonlinear Dynamics, 2011, 65(4): 359–368.

    Article  MathSciNet  Google Scholar 

  3. ZHANG Xuping, MILLS J K, CLEGHORN W L. Multi-mode vibration control and position error analysis of parallel manipulator with multiple flexible links[J]. Transactions of the Canadian Society for Mechanical Engineering, 2010, 34(2): 197–213.

    Google Scholar 

  4. BIAN Yushu, GAO Zhihui, YUN Chao. Motion control of the flexible manipulator via controllable local degrees of freedom[J]. Nonlinear Dynamics, 2009, 55(4): 373–384.

    Article  MATH  MathSciNet  Google Scholar 

  5. DI CASTRI C, MESSINA A. Exact modeling for control of flexible manipulators[J]. Journal of Vibration and Control, 2012, 18(10): 1526–1551.

    Article  MathSciNet  Google Scholar 

  6. REDDY M P P, JACOB J. Accurate modeling and nonlinear finite element analysis of a flexible-link manipulator[J]. International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering, 2014, 8(1): 165–170.

    Google Scholar 

  7. DI CASTRI C, MESSINA A. Vibration analysis of a planar multilink manipulator using a reduced-order matrix formulation[J]. Mechanics Research Communications, 2011, 38(3): 231–238.

    Article  MATH  Google Scholar 

  8. ZHU Chunxia, LUO Jiman, WANG Dan, et al. Research on modal parameters identification of parallel manipulator with flexible multi-body system[J]. Research Journal of Applied Sciences, Engineering and Technology, 2013, 5(10): 2974–2979.

    Google Scholar 

  9. XI F, FENTON R G. Exact modeling for control of flexible manipulators[J]. The International Journal of Robotics Research, 1994, 13(5): 443–453.

    Article  Google Scholar 

  10. GAO Zhihui, BIAN Yushu, YUN Chao. Coupling effect of flexible joint and flexible link on dynamic singularity of flexible manipulator [J]. Chinese Journal of Mechanical Engineering, 2008, 21(1): 9–12.

    Article  Google Scholar 

  11. VAKIL M, FOTOUHI R, NIKIFORUK P N, et al. A study of the free vibration of flexible-link flexible-joint manipulators[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2011, 225(6): 1361–1371.

    Google Scholar 

  12. MEHREZ M W, EL-BADAWY A A. Effect of the joint inertia on selection of under-actuated control algorithm for flexible-link manipulators[J]. Mechanism and Machine Theory, 2010, 45(7): 967–980.

    Article  MATH  Google Scholar 

  13. AL-BEDOOR B O, ALMUSALLAM A A. Dynamics of flexible-link and flexible-joint manipulator carrying a payload with rotary inertia[J]. Mechanism and Machine Theory, 2000, 35(6): 785–820.

    Article  MATH  Google Scholar 

  14. OGUAMANAM D C D, ARSHAD M. On the natural frequencies of a flexible manipulator with a tip payload[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2005, 219(11): 1199–1205.

    Google Scholar 

  15. KALYONCU M, BOTSALI F M. Vibration analysis of an elastic robot Manipulator with prismatic Joint and A time-varying end mass [J]. Arabian Journal for Science and Engineering, 2004, 29(1): 27–38.

    Google Scholar 

  16. TENG Youyou, CAI Guoping. Frequency characteristics of a flexible hub-beam system with arbitrary settling position of attached mass[J]. Journal of Vibration and Control, 2007, 13(6): 769–794.

    Article  MATH  Google Scholar 

  17. HUNG S C C, WENG C I. Modal analysis of controlled multilink systems with flexible links and joints[J]. Journal of Guidance, Control, and Dynamics, 1992, 15(3): 634–641.

    Article  MATH  Google Scholar 

  18. SETHI V, FRANCHEK M A, SONG G. Active multimodal vibration suppression of a flexible structure with piezoceramic sensor and actuator by using loop shaping[J]. Journal of Vibration and Control, 2011, 17(13): 1994–2006.

    Article  MATH  Google Scholar 

  19. RAJA S, SINHA P K, PRATHAP G. Active stiffening and active damping effects on closed loop vibration control of composite beams and plates[J]. Journal of Reinforced Plastics and Composites, 2003, 22(12): 1101–1121.

    Article  Google Scholar 

  20. MAXWELL N D, ASOKANTHAN S F. Modal characteristics of a flexible beam with multiple distributed actuators[J]. Journal of Sound and Vibration, 2004, 269(1): 19–31.

    Article  Google Scholar 

  21. KERMANI M R. Analytic modal analyses of a partially strengthened Timoshenko beam[J]. IEEE Transactions on Control Systems Technology, 2010, 18(4): 850–858.

    Article  Google Scholar 

  22. BENJEDDOU A. Advances in piezoelectric finite element modeling of adaptive structural elements: a survey[J]. Computers & Structures, 2000, 76(1): 347–363.

    Article  Google Scholar 

  23. BRATLAND M, HAUGEN B, ROLVAG T. Modal analysis of active flexible multibody systems[J]. Computers & Structures, 2011, 89(9): 750–761.

    Article  Google Scholar 

  24. CHEAH C C. Task-space PD control of robot manipulators: unified analysis and duality property[J]. The International Journal of Robotics Research, 2008, 27(10): 1152–1170.

    Article  MathSciNet  Google Scholar 

  25. ISLAM S, LIU P X. PD output feedback control design for industrial robotic manipulators[J]. IEEE-ASME Transactions on Mechatronics, 2011, 16(1): 187–197.

    Article  Google Scholar 

  26. HECKMANN A. On the choice of boundary conditions for mode shapes in flexible multibody systems[J]. Multibody System Dynamics, 2010, 23(2): 141–163.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Automation School, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Ming Chu, Yanheng Zhang, Gang Chen & Hanxu Sun

Authors
  1. Ming Chu
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  2. Yanheng Zhang
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  3. Gang Chen
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  4. Hanxu Sun
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Corresponding author

Correspondence to Ming Chu.

Additional information

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), and National Basic Research Program of China(973 Program, Grant No. 2013CB733000)

CHU Ming, born 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.

ZHANG Yanheng, born in 1978, is currently an associate professor at Automation School, Beijing 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.

CHEN 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.

SUN 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.

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Chu, M., Zhang, Y., Chen, G. et al. Effects of joint controller on analytical modal analysis of rotational flexible manipulator. Chin. J. Mech. Eng. 28, 460–469 (2015). https://doi.org/10.3901/CJME.2015.0121.017

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  • DOI: https://doi.org/10.3901/CJME.2015.0121.017

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