Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T07:12:26.022Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Doyle, J. C., Francis, B. A. and Tannenbaum, A., Feedback Control Theory (McMillan, New York, 1992).Google Scholar
2.Dwivedy, S. K. and Eberhard, P., “Dynamic analysis of flexible manipulators, a literature review,” Mech. Mach. Theory 41 (7), 749–777 (2006).CrossRefGoogle Scholar
3.Cannon, R. H. and Schmitz, E., “Initial experiments on end-point control of a flexible one-link robot,” J. Robot. Res. 3 (3), 62–75 (1984).CrossRefGoogle Scholar
4.Caracciolo, R., Richiedei, D., Trevisani, A. and Zanotto, V., “Robust mixed-norm position and vibration control of flexible link mechanisms,” Mechatronics 15 (7), 767–791 (2005).CrossRefGoogle Scholar
5.Lee, J. D., “Application of optimal control theory to flexible robotic manipulators,” Robot. Comput. Integr. Manuf. 3 (4), 327–355 (1990).CrossRefGoogle Scholar
6.Pal, S., Stephanou, H. E. and Cook, G., “Optimal control of a single-link flexible manipulator,” J. Intell. Robot. Syst. 2 (1), 187–199 (1989).CrossRefGoogle Scholar
7.Xuemin, S., Gourishankar, V. G. and Ming, R., “Near Optimum Control of Flexible Manipulators,” Canadian Conference on Electrical and Computer Engineering (1993) pp. 1073–1076.Google Scholar
8.Siciliano, B. and Book, W. J., “A singular perturbation approach to control of light weight flexible manipulator,” J. Robot. Res. 7 (4), 79–90 (1988).CrossRefGoogle Scholar
9.Chen, Y. P. and Yeung, K. S., “Regulation of a one link flexible robot arm using sliding mode technique,” J. Control 49 (6), 1965–1978 (1989).Google Scholar
10.Kotnik, P. T., Yurkovich, S. and Ozguner, U., “Acceleration Feedback Control for Flexible Manipulator Arm,” Proceedings of the IEEE International Conference on Robotics and Automation (1988) pp. 322–323.Google Scholar
11.Geniele, H., Patel, R. V. and Khorasani, K., “End-point control of a flexible manipulator: theory and experiments,” IEEE Trans. Control Syst. Technol. 5 (6), 556–570 (1997).CrossRefGoogle Scholar
12.Liu, K. P., You, W. and Li, Y. C., “Combining a Feedback Linearization Approach with Input Shaping for Flexible Manipulator Control,” Proceedings of the International Conference on Machine Learning and Cybernetics, Changchun University of Technology, China (2003) pp. 561–565.Google Scholar
13.Xu, W. L., Tso, S. K. and Wang, X. S., “Sensor-based deflection modeling and compensation control of flexible robotic manipulator,” Mech. Mach. Theory 33 (7), 909–924 (1998).CrossRefGoogle Scholar
14.Mohamed, Z. and Tokhi, M. O., “Command shaping techniques for vibration control of a flexible robot manipulator,” Mechatronics 14 (1), 69–90 (2004).CrossRefGoogle Scholar
15.Jalili, N., “An infinite dimensional distributed base controller for regulation of flexible robot arms,” ASME J. Dyn. Syst. Meas. Control 123 (4), 712–719 (2001).CrossRefGoogle Scholar
16.Sun, D. and Mills, J. K., “Combined PD Feedback and Distributed Piezoelectric-Polymer Vibration Control of a Single-Link Flexible Manipulator,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (1998) pp. 667–672.Google Scholar
17.Sun, D., Mills, J. K., Shan, J. and Tso, S. K., “A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement,” Mechatronics 14 (4), 381–401 (2004).CrossRefGoogle Scholar
18.Lin, S. H., Tosunoglu, S. and Tesar, D., “Control of a six-degree-of-freedom flexible industrial manipulator,” IEEE Control Syst. Mag. 11 (3), 24–30 (1991).Google Scholar
19.Jiang, Z. H., “Impedance control of flexible robot arms with parametric uncertainties,” J. Intell. Robot. Syst. 42 (2), 113–133 (2005).CrossRefGoogle Scholar
20.Kabamba, P. T., Meerkov, S. M. and Poh, E. K., “Youla parameterization in closed-loop vibrational control,” IEEE Trans. Autom. Control 39 (7), 1455–1459 (1994).CrossRefGoogle Scholar
21.Amirifar, R. and Sadati, N., “Stability and Performance Preserving Controller Order Reduction Via Youla Parameterization and LMIS,” Proceedings of the IEEE International Conference on Electronics, Circuits and Systems (2003) pp. 663–666.Google Scholar
22.Zandvliet, M. J., Scherer, C. W., Hol, C. W. J. and Van De Wal, M. M. J., “Multi-Objective H∞ Control Applied to a Wafer Stage Model,” Proceedings of the IEEE International Conference on Decision and Control, Netherlands796–802 (2004).Google Scholar
23.Saeks, R., Kaiser, J. and Cox, C., “Neuro Control and the Youla Parameterization,” Proceedings of the 4th International Conference on Systems, Man and Cybernetics (1993) pp. 115–118.Google Scholar
24.Nonaka, K., “Youla Parameterization of Output Feedback Sliding Mode Controller: Internal Stability and Disturbance Rejection,” American Control Conference (1999) pp. 553–539.Google Scholar
25.Mikles, J., Cirka, L. and Fikar, M., “Youla-Kucera parameterization self-tuning LQ control of a chemical reactor,” Department of Information Engineering and Process Control, Bratislava, Slovakia, grants No. 1/8108/01 and 1/135/03 (2002).Google Scholar
26.Landau, D., Airimitoaie, T. B. and Alma, M., “A Youla-Kucera parametrized adaptive Feedforward compensator for active vibration control with mechanical coupling,” Automatica 48 (9), 2152–2158 (2012).CrossRefGoogle Scholar
27.Niemann, H. and Poulsen, N. K., “Estimation of Model Uncertainties in Closed-Loop Systems,” American Control Conference, Denmark (2008) pp. 5186–5191.Google Scholar
28.Gazdos, F. and Dostal, P., “Adaptive control of a coupled drives apparatus using dual Youla-Kucera parameterization,” Triennial World Congress, Prague, Czech Republic16(1), 898–903 (2005).Google Scholar
29.Qi, X., Salapaka, M. V., Voulgaris, P. G. and Khammash, M., “Structured optimal and robust control with multiple criteria: aconvex solution,” IEEE Trans. Autom. Control 49 (10), 1623–1640 (2004).CrossRefGoogle Scholar
30.Nouri, B. M. and Zaidan, A., “Computer control of a powered two degree freedom reciprocating gait orthosis,” ISA Trans. 45 (2), 249–258 (2006).CrossRefGoogle ScholarPubMed
31.Hbaïeb, S., Font, S., Bendotti, P. and Falinower, C. M., “Finite dimensional q-parameterization for continuous time control design,” Proceedings of the 10th Mediterranean Conference on Control and Automation, Lisbon, Portugal (2002).Google Scholar
32.Esfandiar, H. and Daneshmand, S., “Closed loop control of the planar flexible manipulator via Youla-Kucera parameterization,” J. Mech. Sci. Technol. 27 (11), 3243–3252 (2013).CrossRefGoogle Scholar
33.Skogestad, S. and Postlethwaite, I., Multivariable Feedback Control: Analysis and Design, New York (John Wiley & Sons, 2005).Google Scholar
34.Doyle, J., Francis, B., and Tannenenbaum, A. R., Feedback Control Theory (Dover Publications, 2009).Google Scholar
35.Ninness, B. and Gustafsson, F., “A unifying construction of orthonormal bases for system identification,” IEEE Trans. Autom. Control 42 (4), 515–521 (1997).CrossRefGoogle Scholar
36.Szabo, Z., Bokor, J. and Schipp, F., “Identification of rational approximation models in H infinity using generalized orthonormal basis,” IEEE Trans. Autom. Control 44 (1), 153–158 (1999).CrossRefGoogle Scholar
37.Polak, E. and Salcudean, S. E., “On the design of linear multivariable feedback system via constrained nondifferentiable optimization in H/Sup infinity spaces,” IEEE Trans. Autom. Control 34 (3), 268–276 (1989).CrossRefGoogle Scholar
38.Esfandiar, H. and Daneshmand, S., “Complete dynamic modeling and approximate state space equations of the flexible link manipulator,” J. Mech. Sci. Technol. 26 (9), 2845–2856 (2012).CrossRefGoogle Scholar
39.Ferziger, J. H., Numerical Methods for Engineering Application 2nd ed. (John Wiley & Sons Publication, 1998).Google Scholar
40.Boyd, S. and Vandenberghe, L., Convex Optimization (Cambridge University Press, Cambridge, UK, 2004).CrossRefGoogle Scholar