Passivity-based Boundary Controls of Flexible Beams with Large Deformations

Authors

Gou Nishida, Kyosuke Yamaguchi, Noboru Sakamoto

Abstract

This paper discusses passivity-based boundary controls of flexible beams with large deformations in terms of a distributed parameter port-Hamiltonian system. Distributed parameter systems have been mainly studied from the viewpoint of analytical methods. However, analytical solutions cannot be always derived from nonlinear distributed parameter systems such as the flexible beam. A distributed parameter port-Hamiltonian system is a standard control representation that can be applied to such a complex system without model reductions. The passivity-based boundary controls consist of boundary damping assignment and boundary energy shaping. Inputs and outputs for the controls are systematically derived from the system representation. Finally, we illustrate numerical results of the controls for stabilizing the flexible beam and shaping its potential energy.

Citation

• Journal: Transactions of the Institute of Systems, Control and Information Engineers
• Year: 2013
• Volume: 26
• Issue: 7
• Pages: 288–296
• Publisher: The Institute of Systems, Control and Information Engineers
• DOI: 10.5687/iscie.26.288

BibTeX

@article{Nishida_2013,
  title={{Passivity-based Boundary Controls of Flexible Beams with Large Deformations}},
  volume={26},
  ISSN={2185-811X},
  DOI={10.5687/iscie.26.288},
  number={7},
  journal={Transactions of the Institute of Systems, Control and Information Engineers},
  publisher={The Institute of Systems, Control and Information Engineers},
  author={Nishida, Gou and Yamaguchi, Kyosuke and Sakamoto, Noboru},
  year={2013},
  pages={288--296}
}

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References

• Brogliato, B., Maschke, B., Lozano, R. & Egeland, O. Dissipative Systems Analysis and Control. Communications and Control Engineering (Springer London, 2007). doi:10.1007/978-1-84628-517-2 – 10.1007/978-1-84628-517-2
• Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Passivity-Based Control of Euler-Lagrange Systems. Communications and Control Engineering (Springer London, 1998). doi:10.1007/978-1-4471-3603-3 – 10.1007/978-1-4471-3603-3
• van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
• Duindam, V., Macchelli, A., Stramigioli, S. & Bruyninckx, H. Modeling and Control of Complex Physical Systems. (Springer Berlin Heidelberg, 2009). doi:10.1007/978-3-642-03196-0 – 10.1007/978-3-642-03196-0
• Simo, J. C. & Vu-Quoc, L. On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part I. Journal of Applied Mechanics 53, 849–854 (1986) – 10.1115/1.3171870
• Nishida, G., Takagi, K., Maschke, B. & Osada, T. Multi-scale distributed parameter modeling of ionic polymer-metal composite soft actuator. Control Engineering Practice 19, 321–334 (2011) – 10.1016/j.conengprac.2010.10.005
• Sepulchre, R., Janković, M. & Kokotović, P. V. Constructive Nonlinear Control. Communications and Control Engineering (Springer London, 1997). doi:10.1007/978-1-4471-0967-9 – 10.1007/978-1-4471-0967-9
• Simo, J. C. & Vu-Quoc, L. On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part II. Journal of Applied Mechanics 53, 855–863 (1986) – 10.1115/1.3171871