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Dynamic model and input shaping control of a flexible link parallel manipulator considering the exact boundary conditions

Published online by Cambridge University Press:  01 April 2014

Quan Zhang ,
James K. Mills ,
William L. Cleghorn ,
Jiamei Jin  and
Zhijun Sun
Quan Zhang
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada
James K. Mills*
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada
William L. Cleghorn
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada
Jiamei Jin
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China
Zhijun Sun
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China
*
*Corresponding author. E-mail: mills@mie.utoronto.ca
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Summary

In this paper, a rigid–flexible planar parallel manipulator (PPM) actuated by three linear ultrasonic motors for high-accuracy positioning is proposed. Based on the extended Hamilton's principle, a rigid–flexible dynamic model of the proposed PPM is developed utilizing exact boundary conditions. To derive an appropriate low-order dynamic model for the design of the controller, the assumed modes method is employed to discretize elastic motion. Then to investigate the interaction between the rigid and elastic motions, a proportional derivative feedback controller combined with a feed-forward-computed torque controller is developed to achieve motion tracking while attenuating the residual vibration. Then the controller is extended to incorporate an input shaper for the further suppression of residual vibration of flexible linkages. Computer simulations are presented as well as experimental results to verify the proposed dynamic model and controller. The input shaping method is verified to be effective in attenuating residual vibration in a highly coupled rigid–flexible PPM. The procedure employed for dynamic modeling and control analysis provides a valuable contribution into the vibration suppression of such a PPM.

Keywords

Flexible parallel manipulatorDynamic modelExact boundary conditionsPD feedbackInput shaping
Type
Articles
Information
Robotica , Volume 33 , Issue 6 , July 2015 , pp. 1201 - 1230
Copyright
Copyright © Cambridge University Press 2014 

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