Authors

Kenji Fujimoto, Kazunori Sakurama, Toshiharu Sugie

Abstract

This paper is devoted to trajectory tracking control of port-controlled Hamiltonian systems based on generalized canonical transformations. A general framework of tracking control utilizing the passivity property is proposed. Firstly, it is shown how to construct an error system, which describes the dynamics of the tracking error, by a passive port-controlled Hamiltonian system. Secondly, a practical procedure to construct tracking controllers of port-controlled Hamiltonian systems including nonholonomic systems is derived. Finally, a simple example of tracking control of a nonholonomic system demonstrates the effectiveness of the proposed method. This method is a natural extension of the conventional passivity based control and is expected to derive robustly stable control systems.

Keywords

nonlinear systems, physical models, tracking control

Citation

  • Journal: IFAC Proceedings Volumes
  • Year: 2001
  • Volume: 34
  • Issue: 6
  • Pages: 705–710
  • Publisher: Elsevier BV
  • DOI: 10.1016/s1474-6670(17)35261-8
  • Note: 5th IFAC Symposium on Nonlinear Control Systems 2001, St Petersburg, Russia, 4-6 July 2001

BibTeX

@article{Fujimoto_2001,
  title={{General Framework of Trajectory Tracking Control of Hamiltonian Systems via Generalized Canonical Transformations}},
  volume={34},
  ISSN={1474-6670},
  DOI={10.1016/s1474-6670(17)35261-8},
  number={6},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Fujimoto, Kenji and Sakurama, Kazunori and Sugie, Toshiharu},
  year={2001},
  pages={705--710}
}

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References

  • Flashner, Model tracking control of Hamiltonian systems. Trans. ASME (1989)
  • Fujimoto, Canonical transformation and stabilization of generalized Hamiltonian systems. Proc. 4th IFAc Symp. Nonlinear Control Systems (1998)
  • Fujimoto, Time-varying stabilization of nonholonomic Hamiltonian systems via canonical transformations. Proc. American Control Conference (2000)
  • Fujimoto, K. & Sugie, T. Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters 42, 217–227 (2001) – 10.1016/s0167-6911(00)00091-8
  • Fujimoto, Trajectory tracking control of port-controlled Hamiltonian systems and its application to a magnetic levitation system (2001)
  • Maschke, Portcontrolled Hamiltonian systems: modeling origins and system-theoretic properties. IFAC Symp. Nonlinear Control Systems (1992)
  • Maschke, A Hamiltonian approach to stabilization of nonholonomic mechanical systems. Proc. 33rd IEEE Conf. on Decision and Control (1994)
  • Maschke, An energy-based derivation of Lyapunov functions for forced systems with application to stabilizing control. Proc. IFAC World Congress (1999)
  • Ortega, Stabilization of port-controlled Hamiltonian systems: passivity and energy-balancing. To appear in Automatica (1999)
  • Takegaki, M. & Arimoto, S. A New Feedback Method for Dynamic Control of Manipulators. Journal of Dynamic Systems, Measurement, and Control 103, 119–125 (1981) – 10.1115/1.3139651
  • van der Schaft, Stabilization of Hamiltonian systems. Nonl. An. Th. Math. Appl. (1986)
  • van der Schaft, (2000)
  • Van Der Schaft, A. J. & Maschke, B. M. On the Hamiltonian formulation of nonholonomic mechanical systems. Reports on Mathematical Physics 34, 225–233 (1994) – 10.1016/0034-4877(94)90038-8