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On the control of a single flexible arm robot via Youla-Kucera parameterization

Published online by Cambridge University Press:  04 June 2014

Habib Esfandiar ,
Saeed Daneshmand  and
Roozbeh Dargahi Kermani
Habib Esfandiar
Affiliation:
Department of Mechanical Engineering, Firuzkooh Branch, Islamic Azad University, Firuzkooh, Iran
Saeed Daneshmand*
Affiliation:
Department of Mechanical Engineering, Majlesi Branch, Islamic Azad University, Isfahan, Iran
Roozbeh Dargahi Kermani
Affiliation:
Science & Technology Park, Semnan University, Semnan, Iran
*
*Corresponding author. E-mail: S.daneshmand@iaumajlesi.ac.ir
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Summary

In this paper, based on the Youla-Kucera (Y-K) parameterization, the control of a flexible beam acting as a flexible robotic manipulator is investigated. The method of Youla parameterization is the simple solution and proper method for describing the collection of all controllers that stabilize the closed-loop system. This collection comprises function of the Youla parameter which can be any proper transfer function that is stable. The main challenge in this approach is to obtain a Youla parameter with infinite dimension. This parameter is approximated by a subspace with finite dimensions, which makes the problem tractable. It is required to be generated from a finite number of bases within that space and the considered system can be approximated by an expansion of the orthonormal bases such as FIR, Laguerre, Kautz and generalized bases. To calculate the coefficients for each basis, it is necessary to define the problem in the form of an optimization problem that is solved by optimization techniques. The Linear Quadratic Regulator (LQR) optimization tool is employed in order to optimize the controller gains. The main aim in controller design is to merge the closed-loop system and the second order system with the desirable time response characteristic. The results of the Youla stabilizing controller for a planar flexible manipulator with lumped tip mass indicate that the proposed method is very efficient and robust for the time-continuous instances.

Keywords

Flexible manipulatorYoula-Kucera parameterizationOrthonormal basesOptimization problemLinear quadratic regulator
Type
Articles
Information
Robotica , Volume 34 , Issue 1 , January 2016 , pp. 150 - 172
Copyright
Copyright © Cambridge University Press 2014 

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