Authors

D. Vink, D. Ballance, P. Gawthrop

Abstract

Bond graphs are primarily used in the network modeling of lumped parameter physical systems, but controller design with this graphical technique is relatively unexplored. It is shown that bond graphs can be used as a tool for certain model matching control designs. Some basic facts on the nonlinear model matching problem are recalled. The model matching problem is then associated with a particular disturbance decoupling problem, and it is demonstrated that bicausal assignment methods for bond graphs can be applied to solve the disturbance decoupling problem as to meet the model matching objective. The adopted bond graph approach is presented through a detailed example, which shows that the obtained controller induces port-Hamiltonian error dynamics. As a result, the closed loop system has an associated standard bond graph representation, thereby rendering energy shaping and damping injection possible from within a graphical context.

Citation

  • Journal: Mathematical and Computer Modelling of Dynamical Systems
  • Year: 2006
  • Volume: 12
  • Issue: 2-3
  • Pages: 249–261
  • Publisher: Informa UK Limited
  • DOI: 10.1080/13873950500068278

BibTeX

@article{Vink_2006,
  title={{Bond graphs in model matching control}},
  volume={12},
  ISSN={1744-5051},
  DOI={10.1080/13873950500068278},
  number={2–3},
  journal={Mathematical and Computer Modelling of Dynamical Systems},
  publisher={Informa UK Limited},
  author={Vink, D. and Ballance, D. and Gawthrop, P.},
  year={2006},
  pages={249--261}
}

Download the bib file

References

  • Dalsmo, M. & van der Schaft, A. On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems. SIAM Journal on Control and Optimization vol. 37 54–91 (1998)10.1137/s0363012996312039
  • Gawthrop P. J.. Proceedings of the International Conference On Bond Graph Modelling and Simulation (ICBGM’95), SCS Publishing (1995)
  • Gawthrop, P. J. Physical interpretation of inverse dynamics using bicausal bond graphs. Journal of the Franklin Institute vol. 337 743–769 (2000) – 10.1016/s0016-0032(00)00051-x
  • P.J. Gawthrop. Proceedings of the 13th European Simulation Symposium: Simulation in Industry (2001)
  • Golo G.,. Nonlinear and Hybrid Systems in Automotive Control (2003)
  • Huijberts, H. J. C., Nijmeijer, H. & van der Wegen, L. L. M. Dynamic Disturbance Decoupling for Nonlinear Systems. SIAM Journal on Control and Optimization vol. 30 336–349 (1992) – 10.1137/0330021
  • Huijberts H. J.C.. Centrum voor Wiskunde en Informatica (CWI) (1994)
  • Sergio J.. International Conference on Bond Graph Modelling and Simulation (ICBGM’01), SCS Publishing (2001)
  • Karnopp D. C.. System dynamics, a unified approach, (1990)
  • Khalil H. K.. Nonlinear systems, (1996)
  • Nijmeijer, H. & van der Schaft, A. Nonlinear Dynamical Control Systems. (Springer New York, 1990). doi:10.1007/978-1-4757-2101-0 – 10.1007/978-1-4757-2101-0
  • 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
  • Yeh, T.-J. Backstepping control in the physical domain. Journal of the Franklin Institute vol. 338 455–479 (2001) – 10.1016/s0016-0032(01)00015-1