Integral IDA-PBC and PID-like control for port-controlled Hamiltonian systems
Authors
Mutaz Ryalat, Dina Shona Laila, Mohamed M. Torbati
Abstract
Interconnection and damping assignment passivity based control (IDA-PBC) has gained increasing popularity. In this paper, we propose constructive results on integral IDA-PBC and PID-type controllers for a class of port-controlled Hamiltonian (PCH) systems. The results extend some existing methods and address a new framework that allows the implementation of integral action control to under-actuated PCH systems that are quite commonly found in practice. Application of the results to control a Quanser inertia wheel pendulum is provided.
Citation
- Journal: 2015 American Control Conference (ACC)
- Year: 2015
- Volume:
- Issue:
- Pages: 5365–5370
- Publisher: IEEE
- DOI: 10.1109/acc.2015.7172178
BibTeX
@inproceedings{Ryalat_2015,
title={{Integral IDA-PBC and PID-like control for port-controlled Hamiltonian systems}},
DOI={10.1109/acc.2015.7172178},
booktitle={{2015 American Control Conference (ACC)}},
publisher={IEEE},
author={Ryalat, Mutaz and Laila, Dina Shona and Torbati, Mohamed M.},
year={2015},
pages={5365--5370}
}
References
- Ortega, R. & Romero, J. G. Robust integral control of port-Hamiltonian systems: The case of non-passive outputs with unmatched disturbances. Systems & Control Letters 61, 11–17 (2012) – 10.1016/j.sysconle.2011.09.015
- 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
- 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
- Gómez-Estern, F. & Van der Schaft, A. J. Physical Damping in IDA-PBC Controlled Underactuated Mechanical Systems. European Journal of Control 10, 451–468 (2004) – 10.3166/ejc.10.451-468
- sarras, On the modeling, linearization and energy shaping control of mechanical systems. Proceedings of the 4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control (2012)
- zhou, Essential of Robust Control (1998)
- Dirksz, D. A. & Scherpen, J. M. A. Power-based control: Canonical coordinate transformations, integral and adaptive control. Automatica 48, 1045–1056 (2012) – 10.1016/j.automatica.2012.03.003
- block, The Reaction Wheel Pendulum (2007)
- 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
- 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
- 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
- Ryalat, M. & Laila, D. S. IDA-PBC for a class of underactuated mechanical systems with application to a rotary inverted pendulum. 52nd IEEE Conference on Decision and Control 5240–5245 (2013) doi:10.1109/cdc.2013.6760713 – 10.1109/cdc.2013.6760713
- Romero, J. G., Donaire, A. & Ortega, R. Robust energy shaping control of mechanical systems. Systems & Control Letters 62, 770–780 (2013) – 10.1016/j.sysconle.2013.05.011
- khalil, Nonlinear Systems (2002)
- 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
- Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica 39, 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005