Regulation control of underactuated mechanical systems based on a new matching equation of port-controlled hamiltonian systems
Authors
null Zheng Wang, P. Goldsmith, J. Gu
Abstract
We consider the control of Port-Controlled Hamiltonian (PCH) systems, which are a generalization of Euler-Lagrange Systems. A new matching equation for PCH systems is developed so that Interconnection Damping Assignment Passivity-Based Control (IDA-PBC) can be extended to the regulation of some underactuated PCH systems whose kinetic energy must be modified. A simple underactuated mechanical system (the inertial wheel pendulum) is used to demonstrate the effectiveness of the proposed method..
Citation
- Journal: 2009 IEEE International Conference on Robotics and Automation
- Year: 2009
- Volume:
- Issue:
- Pages: 992–997
- Publisher: IEEE
- DOI: 10.1109/robot.2009.5152627
BibTeX
@inproceedings{Zheng_Wang_2009,
title={{Regulation control of underactuated mechanical systems based on a new matching equation of port-controlled hamiltonian systems}},
DOI={10.1109/robot.2009.5152627},
booktitle={{2009 IEEE International Conference on Robotics and Automation}},
publisher={IEEE},
author={Zheng Wang and Goldsmith, P. and Gu, J.},
year={2009},
pages={992--997}
}
References
- ortega, output feedback stabilization of mass-balance systems. Output-Feedback Stabilization of Nonlinear Systems (1999)
- Maya‐Ortiz, P. & Espinosa‐Pérez, G. Output feedback excitation control of synchronous generators. Intl J Robust & Nonlinear 14, 879–890 (2004) – 10.1002/rnc.912
- ortega, some applications and extensions of interconnection and damping assignment passivity-based control. IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Systems (2003)
- maschke, port-controlled hamiltonian systems: modelling origins and system-theoretic properties. Proc 2nd IFAC NOLCOS (1992)
- Maschke, B. M., Van Der Schaft, A. J. & Breedveld, P. C. An intrinsic hamiltonian formulation of network dynamics: non-standard poisson structures and gyrators. Journal of the Franklin Institute 329, 923–966 (1992) – 10.1016/s0016-0032(92)90049-m
- Fujimoto, K. & Sugie, T. Stabilization of Hamiltonian systems with nonholonomic constraints based on time-varying generalized canonical transformations. Systems & Control Letters 44, 309–319 (2001) – 10.1016/s0167-6911(01)00150-5
- Galaz, M., Ortega, R., Bazanella, A. S. & Stankovic, A. M. An energy-shaping approach to the design of excitation control of synchronous generators. Automatica 39, 111–119 (2003) – 10.1016/s0005-1098(02)00177-2
- cheng, reducing the number of pdes in interconnection and damping assignment passivity-based control. Proceedings of 2005 IFAC World Congress (2005)
- Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems and its application to a magnetic levitation system. Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) 3388–3393 doi:10.1109/cdc.2001.980360 – 10.1109/cdc.2001.980360
- 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
- Ortega, R. & Mareels, I. Energy-balancing passivity-based control. Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334) 1265–1270 vol.2 (2000) doi:10.1109/acc.2000.876703 – 10.1109/acc.2000.876703
- Putting energy back in control. IEEE Control Syst. 21, 18–33 (2001) – 10.1109/37.915398
- ortega, energyshaping of port-controlled hamiltonian systems by interconnection. Proc of the 38th Conference on Decision and Control (1999)
- 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
- pasumarthy, on interconnections of infinite dimensional port-hamiltonian systems. Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS2004) (2004)
- Petrovic, V., Ortega, R. & Stankovi, A. M. Interconnection and damping assignment approach to control of PM synchronous motors. IEEE Trans. Contr. Syst. Technol. 9, 811–820 (2001) – 10.1109/87.960344
- Rodriguez, H., Ortega, R., Escobar, G. & Barabanov, N. A robustly stable output feedback saturated controller for the boost DC-to-DC converter. Systems & Control Letters 40, 1–8 (2000) – 10.1016/s0167-6911(99)00113-9
- Rodriguez, H., Ortega, R. & Escobar, G. A new family of energy-based non-linear controllers for switched power converters. ISIE 2001. 2001 IEEE International Symposium on Industrial Electronics Proceedings (Cat. No.01TH8570) vol. 2 723–727 – 10.1109/isie.2001.931555
- 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
- Astolfi, A., Chhabra, D. & Ortega, R. Asymptotic stabilization of some equilibria of an underactuated underwater vehicle. Systems & Control Letters 45, 193–206 (2002) – 10.1016/s0167-6911(01)00176-1
- aracil, a family of oscillating generalized hamiltonian systems. Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (2003)
- Cervera, J., van der Schaft, A. J. & Baños, A. Interconnection of port-Hamiltonian systems and composition of Dirac structures. Automatica 43, 212–225 (2007) – 10.1016/j.automatica.2006.08.014
- Acosta, J. A., Ortega, R., Astolfi, A. & Mahindrakar, A. D. Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one. IEEE Trans. Automat. Contr. 50, 1936–1955 (2005) – 10.1109/tac.2005.860292
- van der schaft, port-controlled hamiltonian systems: towards a theory for control and design of nonlinear physical systems. J Soc Instrument Contr Engineers Japan (2000)
- Blankenstein, G., Ortega, R. & Van Der Schaft, A. J. The matching conditions of controlled Lagrangians and IDA-passivity based control. International Journal of Control 75, 645–665 (2002) – 10.1080/00207170210135939
- Batlle, C., Doria-Cerezo, A. & Ortega, R. Power flow control of a doubly-fed induction machine coupled to a flywheel. Proceedings of the 2004 IEEE International Conference on Control Applications, 2004. vol. 2 1645–1650 – 10.1109/cca.2004.1387612
- Wang, Z. & Goldsmith, P. Modified energy-balancing-based control for the tracking problem. IET Control Theory Appl. 2, 310–322 (2008) – 10.1049/iet-cta:20070124
- – 10.1002/(sici)1097-0312(200003)53:3<354::aid-cpa3>3.3.co;2-l
- Viola, G., Ortega, R., Banavar, R., Acosta, J. A. & Astolfi, A. Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes. IEEE Trans. Automat. Contr. 52, 1093–1099 (2007) – 10.1109/tac.2007.899064
- Astolfi, A. & Ortega, R. Energy-Based Stabilization of Angular Velocity of Rigid Body in Failure Configuration. Journal of Guidance, Control, and Dynamics 25, 184a–1187 (2002) – 10.2514/2.4867
- Bupp, R. T., Bernstein, D. S. & Coppola, V. T. A benchmark problem for nonlinear control design: problem statement, experimental testbed, and passive nonlinear compensation. Proceedings of 1995 American Control Conference - ACC’95 vol. 6 4363–4367 – 10.1109/acc.1995.532759
- Bloch, A. M., Leonard, N. E. & Marsden, J. E. Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem. IEEE Trans. Automat. Contr. 45, 2253–2270 (2000) – 10.1109/9.895562