Interconnection and damping assignment passivity-based control: towards a constructive procedure - Part I
Authors
Abstract
Interconnection and damping assignment passivity-based control is a technique that regulates the behavior of nonlinear systems assigning a desired (port-controlled Hamiltonian) structure to the closed-loop. Since the introduction of this controller design methodology five years ago (1999), many theoretical extensions and practical applications have been reported in the literature. The theoretical developments include some variations and shortcuts that are useful when dealing with particular classes of systems, and the incorporation of additional features to handle control scenarios other than just stabilization. On the application side the method has provided solutions to a wide variety of physical problems. The purpose of this paper is to review the fundamental theory of this control system design approach. Main new results and practical applications as well as current open problems and future directions are discussed in a companion paper.
Citation
- Journal: 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)
- Year: 2004
- Volume:
- Issue:
- Pages: 3412–3417 Vol.4
- Publisher: IEEE
- DOI: 10.1109/cdc.2004.1429236
BibTeX
@inproceedings{Ortega_2004,
title={{Interconnection and damping assignment passivity-based control: towards a constructive procedure - Part I}},
DOI={10.1109/cdc.2004.1429236},
booktitle={{2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)}},
publisher={IEEE},
author={Ortega, R. and Garcia-Canseco, E.},
year={2004},
pages={3412-3417 Vol.4}
}
References
- Garcia-Canseco, E., Astolfi, A. & Ortega, R. Interconnection and damping assignment passivity-based control: towards a constructive procedure - Part II. 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) 3418-3423 Vol.4 (2004) doi:10.1109/cdc.2004.1429237 – 10.1109/cdc.2004.1429237
- 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
- Prajna, S., van der Schaft, A. & Meinsma, G. An LMI approach to stabilization of linear port-controlled Hamiltonian systems. Systems & Control Letters 45, 371–385 (2002) – 10.1016/s0167-6911(01)00195-5
- 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
- Haddad, W. M., Nersesov, S. G. & Chellaboina, V. Energy-based control for hybrid port-controlled Hamiltonian systems. Proceedings of the 41st IEEE Conference on Decision and Control, 2002. vol. 2 1669–1674 – 10.1109/cdc.2002.1184760
- krstic, Nonlinear and Adaptive Control Design (1995)
- Rodríguez, H. & Ortega, R. Stabilization of electromechanical systems via interconnection and damping assignment. Intl J Robust & Nonlinear 13, 1095–1111 (2003) – 10.1002/rnc.804
- Escobar, G., van der Schaft, A. J. & Ortega, R. A Hamiltonian viewpoint in the modeling of switching power converters. Automatica 35, 445–452 (1999) – 10.1016/s0005-1098(98)00196-4
- 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
- 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
- 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
- Maithripala, D. H. S., Berg, J. M. & Dayawansa, W. P. Nonlinear dynamic output feedback stabilization of electrostatically actuated MEMS. 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475) vol. 1 61–66 – 10.1109/cdc.2003.1272536
- Putting energy back in control. IEEE Control Syst. 21, 18–33 (2001) – 10.1109/37.915398
- 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
- jeltsema, An energy-balancing perspective of IDA-PBC of nonlinear systems. IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Systems (2003)
- Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Euler-Lagrange systems. Communications and Control Engineering 15–37 (1998) doi:10.1007/978-1-4471-3603-3_2 – 10.1007/978-1-4471-3603-3_2
- Ortega, R. & Spong, M. W. Adaptive motion control of rigid robots: A tutorial. Automatica 25, 877–888 (1989) – 10.1016/0005-1098(89)90054-x
- 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
- Desoer, C. A., Vidyasagar, M. & Willson, A. N., Jr. Feedback Systems: Input-Output Properties. Journal of Dynamic Systems, Measurement, and Control 97, 453–454 (1975) – 10.1115/1.3426967
- ortega, Energy shaping of port-controlled Hamiltonian systems by interconnection. IEEE Conf Decision and Control (1999)
- Auckly, D., Kapitanski, L. & White, W. Control of nonlinear underactuated systems. Comm. Pure Appl. Math. 53, 354–369 (2000) – 10.1002/(sici)1097-0312(200003)53:3<354::aid-cpa3>3.3.co;2-l
- 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
- 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, L2-Gain and Passivity Techniques in Nonlinear Control (1999)