PID Passivity-Based Control of Port-Hamiltonian Systems
Authors
Meng Zhang, Pablo Borja, Romeo Ortega, Zhitao Liu, Hongye Su
Abstract
In this note, we address the problem of stabilization of
Citation
- Journal: IEEE Transactions on Automatic Control
- Year: 2018
- Volume: 63
- Issue: 4
- Pages: 1032–1044
- Publisher: Institute of Electrical and Electronics Engineers (IEEE)
- DOI: 10.1109/tac.2017.2732283
BibTeX
@article{Zhang_2018,
title={{PID Passivity-Based Control of Port-Hamiltonian Systems}},
volume={63},
ISSN={1558-2523},
DOI={10.1109/tac.2017.2732283},
number={4},
journal={IEEE Transactions on Automatic Control},
publisher={Institute of Electrical and Electronics Engineers (IEEE)},
author={Zhang, Meng and Borja, Pablo and Ortega, Romeo and Liu, Zhitao and Su, Hongye},
year={2018},
pages={1032--1044}
}
References
- venkatraman, Energy shaping of port-Hamiltonian systems by using alternate passive outputs. Proc Eur Control Conf (2009)
- van der Schaft, A. Interconnections of input-output Hamiltonian systems with dissipation. 2016 IEEE 55th Conference on Decision and Control (CDC) 4686–4691 (2016) doi:10.1109/cdc.2016.7798983 – 10.1109/cdc.2016.7798983
- van der schaft, Port-Hamiltonian Systems Theory An Introductory Overview (2014)
- van der schaft, Gain and Passivity Techniques in Nonlinear Control (2016)
- Zhang, M., Ortega, R., Jeltsema, D. & Su, H. Further deleterious effects of the dissipation obstacle in control-by-interconnection of port-Hamiltonian systems. Automatica vol. 61 227–231 (2015) – 10.1016/j.automatica.2015.08.010
- Zhang, F., Trentelman, H. L. & Scherpen, J. M. A. Robust cooperative output regulation of heterogeneous Lur’e networks. International Journal of Robust and Nonlinear Control vol. 27 3061–3078 (2016) – 10.1002/rnc.3725
- vidyasagar, Nonlinear Systems Analysis (1993)
- Ferguson, J., Middleton, R. H. & Donaire, A. Disturbance rejection via control by interconnection of port-Hamiltonian systems. 2015 54th IEEE Conference on Decision and Control (CDC) 507–512 (2015) doi:10.1109/cdc.2015.7402279 – 10.1109/cdc.2015.7402279
- Duindam, V., Macchelli, A., Stramigioli, S. & Bruyninckx, H. Modeling and Control of Complex Physical Systems. (Springer Berlin Heidelberg, 2009). doi:10.1007/978-3-642-03196-0 – 10.1007/978-3-642-03196-0
- Hernandez-Gomez, M., Ortega, R., Lamnabhi-Lagarrigue, F. & Escobar, G. Adaptive PI Stabilization of Switched Power Converters. IEEE Transactions on Control Systems Technology vol. 18 688–698 (2010) – 10.1109/tcst.2009.2023669
- Horn, R. A. & Johnson, C. R. Matrix Analysis. (1985) doi:10.1017/cbo9780511810817 – 10.1017/cbo9780511810817
- Jayawardhana, B., Ortega, R., García-Canseco, E. & Castaños, F. Passivity of nonlinear incremental systems: Application to PI stabilization of nonlinear RLC circuits. Systems & Control Letters vol. 56 618–622 (2007) – 10.1016/j.sysconle.2007.03.011
- khalil, Nonlinear Systems (2002)
- Maschke, B., Ortega, R. & Van Der Schaft, A. J. Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Transactions on Automatic Control vol. 45 1498–1502 (2000) – 10.1109/9.871758
- Meza, C., Biel, D., Jeltsema, D. & Scherpen, J. M. A. Lyapunov-Based Control Scheme for Single-Phase Grid-Connected PV Central Inverters. IEEE Transactions on Control Systems Technology vol. 20 520–529 (2012) – 10.1109/tcst.2011.2114348
- Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
- Ortega, R., Jeltsema, D. & Scherpen, J. M. A. Power shaping: A new paradigm for stabilization of nonlinear RLC circuits. IEEE Transactions on Automatic Control vol. 48 1762–1767 (2003) – 10.1109/tac.2003.817918
- Sepulchre, R., Janković, M. & Kokotović, P. V. Constructive Nonlinear Control. Communications and Control Engineering (Springer London, 1997). doi:10.1007/978-1-4471-0967-9 – 10.1007/978-1-4471-0967-9
- Castaños, F., Jayawardhana, B., Ortega, R. & García-Canseco, E. Proportional Plus Integral Control for Set-Point Regulation of a Class of Nonlinear RLC Circuits. Circuits, Systems, and Signal Processing vol. 28 609–623 (2009) – 10.1007/s00034-009-9103-x
- Sanders, S. R. & Verghese, G. C. Lyapunov-based control for switched power converters. IEEE Transactions on Power Electronics vol. 7 17–24 (1992) – 10.1109/63.124573
- Castaños, F. & Ortega, R. Energy-balancing passivity-based control is equivalent to dissipation and output invariance. Systems & Control Letters vol. 58 553–560 (2009) – 10.1016/j.sysconle.2009.03.007
- Donaire, A. & Junco, S. On the addition of integral action to port-controlled Hamiltonian systems. Automatica vol. 45 1910–1916 (2009) – 10.1016/j.automatica.2009.04.006
- spivak, A Comprehensive Introduction to Differential Geometry (1999)
- Cisneros, R. et al. Global tracking passivity-based PI control of bilinear systems: Application to the interleaved boost and modular multilevel converters. Control Engineering Practice vol. 43 109–119 (2015) – 10.1016/j.conengprac.2015.07.002
- Donaire, A., Ortega, R. & Romero, J. G. Simultaneous interconnection and damping assignment passivity-based control of mechanical systems using dissipative forces. Systems & Control Letters vol. 94 118–126 (2016) – 10.1016/j.sysconle.2016.05.006
- Donaire, A. et al. Shaping the Energy of Mechanical Systems Without Solving Partial Differential Equations. IEEE Transactions on Automatic Control vol. 61 1051–1056 (2016) – 10.1109/tac.2015.2458091
- Borja, P., Cisneros, R. & Ortega, R. A constructive procedure for energy shaping of port—Hamiltonian systems. Automatica vol. 72 230–234 (2016) – 10.1016/j.automatica.2016.05.028
- desoer, Feedback Systems Input–Output Properties (1975)
- Åström, K. J. & Hägglund, T. The future of PID control. Control Engineering Practice vol. 9 1163–1175 (2001) – 10.1016/s0967-0661(01)00062-4
- Ortega, R., van der Schaft, A., Castanos, F. & Astolfi, A. Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 53 2527–2542 (2008) – 10.1109/tac.2008.2006930
- Ortega, R. & Romero, J. G. Robust integral control of port-Hamiltonian systems: The case of non-passive outputs with unmatched disturbances. Systems & Control Letters vol. 61 11–17 (2012) – 10.1016/j.sysconle.2011.09.015
- Ortega, R. & García-Canseco, E. Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control vol. 10 432–450 (2004) – 10.3166/ejc.10.432-450
- rao, Generalized Inverse of Matrices and its Applications (1971)
- Adaptation Is Unnecessary in L1-Adaptive Control: What Makes an Adaptive Controller ‘Adaptive’? IEEE Control Systems vol. 36 47–52 (2016) – 10.1109/mcs.2015.2495023
- Romero, J. G., Ortega, R. & Donaire, A. Energy Shaping of Mechanical Systems via PID Control and Extension to Constant Speed Tracking. IEEE Transactions on Automatic Control vol. 61 3551–3556 (2016) – 10.1109/tac.2016.2521725
- Romero, J. G., Donaire, A. & Ortega, R. Robust energy shaping control of mechanical systems. Systems & Control Letters vol. 62 770–780 (2013) – 10.1016/j.sysconle.2013.05.011