Improved potential energy-shaping for port-controlled Hamiltonian systems

Authors

Liangcheng Cai, Yong He, Min Wu, Jinhua She

Abstract

This paper investigates the asymptotical stabilization of port-controlled Hamiltonian (PCH) systems via the improved potential energy-shaping (IPES) method. First, a desired potential energy introduced by a transitive Hamiltonian function is added to the original kinetic energy to yield a desired Hamiltonian function. Second, an asymptotically stabilized controller is designed based on a new matching equation with the obtained Hamiltonian function. Finally, a numerical example is given to show the effectiveness of the proposed method.

Keywords

Port-controlled Hamiltonian (PCH) systems; Improved potential energy-shaping (IPES); Asymptotical stabilization

Citation

• Journal: Journal of Control Theory and Applications
• Year: 2012
• Volume: 10
• Issue: 3
• Pages: 385–390
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s11768-012-0282-9

BibTeX

@article{Cai_2012,
  title={{Improved potential energy-shaping for port-controlled Hamiltonian systems}},
  volume={10},
  ISSN={1993-0623},
  DOI={10.1007/s11768-012-0282-9},
  number={3},
  journal={Journal of Control Theory and Applications},
  publisher={Springer Science and Business Media LLC},
  author={Cai, Liangcheng and He, Yong and Wu, Min and She, Jinhua},
  year={2012},
  pages={385--390}
}

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References

• Dalsmo, M. & van der Schaft, A. On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems. SIAM J. Control Optim. 37, 54–91 (1998) – 10.1137/s0363012996312039
• 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
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38, 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• Ortega, R. & García-Canseco, E. Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control 10, 432–450 (2004) – 10.3166/ejc.10.432-450
• Ortega, R., van der Schaft, A., Castanos, F. & Astolfi, A. Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Trans. Automat. Contr. 53, 2527–2542 (2008) – 10.1109/tac.2008.2006930
• Castaños, F. & Ortega, R. Energy-balancing passivity-based control is equivalent to dissipation and output invariance. Systems & Control Letters 58, 553–560 (2009) – 10.1016/j.sysconle.2009.03.007
• Donaire, A. & Junco, S. Energy shaping, interconnection and damping assignment, and integral control in the bond graph domain. Simulation Modelling Practice and Theory 17, 152–174 (2009) – 10.1016/j.simpat.2008.02.012
• Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans. Automat. Contr. 47, 1218–1233 (2002) – 10.1109/tac.2002.800770
• Castaños, F., Ortega, R., van der Schaft, A. & Astolfi, A. Asymptotic stabilization via control by interconnection of port-Hamiltonian systems. Automatica 45, 1611–1618 (2009) – 10.1016/j.automatica.2009.03.015
• Donaire, A. & Junco, S. On the addition of integral action to port-controlled Hamiltonian systems. Automatica 45, 1910–1916 (2009) – 10.1016/j.automatica.2009.04.006
• Astolfi, A., Ortega, R. & Venkatraman, A. A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints. Automatica 46, 182–189 (2010) – 10.1016/j.automatica.2009.10.027
• Venkatraman, A., Ortega, R., Sarras, I. & van der Schaft, A. Speed Observation and Position Feedback Stabilization of Partially Linearizable Mechanical Systems. IEEE Trans. Automat. Contr. 55, 1059–1074 (2010) – 10.1109/tac.2010.2042010
• Jeltsema, D., Ortega, R. & M.A. Scherpen, J. An energy-balancing perspective of interconnection and damping assignment control of nonlinear systems. Automatica 40, 1643–1646 (2004) – 10.1016/j.automatica.2004.04.007
• Ramírez, H., Sbarbaro, D. & Ortega, R. On the control of non-linear processes: An IDA–PBC approach. Journal of Process Control 19, 405–414 (2009) – 10.1016/j.jprocont.2008.06.018
• Xi, Z. & Cheng, D. Passivity-based stabilization and H 8 control of the Hamiltonian control systems with dissipation and its applications to power systems. International Journal of Control 73, 1686–1691 (2000) – 10.1080/00207170050201762