Simultaneous stabilization of Port-Hamiltonian systems subject to actuation saturation and input delay
Authors
Abstract
This paper investigates the simultaneous stabilization of Port-Hamiltonian (PH) systems subject to actuation saturation (AS) and input delay. Firstly, two parallel connecting PH systems subject to the AS and input delay are proposed. Secondly, a simultaneous stabilization control law is designed by a difference between the two feedback control laws containing the input delay. Thirdly, computing a Lyapunov-Krasovskii function assures the simultaneous stabilization of the above systems. Finally, simulation is given to show the correctness of the proposed contents.
Keywords
Port-Hamiltonian system (PH); simultaneous stabilization; actuator saturation; input delay; Lyapunov-Krasovskii function
Citation
- Journal: International Journal of Automation and Computing
- Year: 2021
- Volume: 18
- Issue: 5
- Pages: 849–854
- Publisher: Springer Science and Business Media LLC
- DOI: 10.1007/s11633-015-0928-4
BibTeX
@article{Cai_2015,
title={{Simultaneous stabilization of Port-Hamiltonian systems subject to actuation saturation and input delay}},
volume={18},
ISSN={1751-8520},
DOI={10.1007/s11633-015-0928-4},
number={5},
journal={International Journal of Automation and Computing},
publisher={Springer Science and Business Media LLC},
author={Cai, Liang-Cheng},
year={2015},
pages={849--854}
}
References
- 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
- Dirksz, D. A. & Scherpen, J. M. A. Power-based control: Canonical coordinate transformations, integral and adaptive control. Automatica vol. 48 1045–1056 (2012) – 10.1016/j.automatica.2012.03.003
- Castaños, F., Gromov, D., Hayward, V. & Michalska, H. Implicit and explicit representations of continuous-time port-Hamiltonian systems. Systems & Control Letters vol. 62 324–330 (2013) – 10.1016/j.sysconle.2013.01.007
- Ionescu, T. C. & Astolfi, A. Families of moment matching based, structure preserving approximations for linear port Hamiltonian systems. Automatica vol. 49 2424–2434 (2013) – 10.1016/j.automatica.2013.05.006
- Cai, L., He, Y. & Wu, M. On the effects of desired damping matrix and desired Hamiltonian function in the matching equation for Port–Hamiltonian systems. Nonlinear Dynamics vol. 72 91–99 (2012) – 10.1007/s11071-012-0693-7
- Schöberl, M. & Siuka, A. Jet bundle formulation of infinite-dimensional port-Hamiltonian systems using differential operators. Automatica vol. 50 607–613 (2014) – 10.1016/j.automatica.2013.11.035
- Seslija, M., Scherpen, J. M. A. & van der Schaft, A. Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems. Automatica vol. 50 369–377 (2014) – 10.1016/j.automatica.2013.11.020
- Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
- 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
- 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
- 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
- Astolfi, A., Ortega, R. & Venkatraman, A. A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints. Automatica vol. 46 182–189 (2010) – 10.1016/j.automatica.2009.10.027
- Venkatraman, A., Ortega, R., Sarras, I. & van der Schaft, A. Speed Observation and Position Feedback Stabilization of Partially Linearizable Mechanical Systems. IEEE Transactions on Automatic Control vol. 55 1059–1074 (2010) – 10.1109/tac.2010.2042010
- Donaire, A. & Perez, T. Dynamic positioning of marine craft using a port-Hamiltonian framework. Automatica vol. 48 851–856 (2012) – 10.1016/j.automatica.2012.02.022
- Hu, T. & Lin, Z. Control Systems with Actuator Saturation. (Birkhäuser Boston, 2001). doi:10.1007/978-1-4612-0205-9 – 10.1007/978-1-4612-0205-9
- Zairong Xi, Feng, G., Daizhan Cheng & Qiang Lu. Nonlinear decentralized saturated controller design for power systems. IEEE Transactions on Control Systems Technology vol. 11 539–547 (2003) – 10.1109/tcst.2003.813404
- Wei, A. & Wang, Y. Stabilization and $H^\infty$ control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Automatica vol. 46 2008–2013 (2010) – 10.1016/j.automatica.2010.08.001
- R. Pasumarthy. R. Pasumarthy, C. Y. Kao. On stability of time-delay Hamiltonian systems. In Proceeding of the American Control Conference, IEEE, St. Louis, USA, pp. 4909–4914, 2009. (2009)
- Sun, W. W. Stabilization analysis of time-delay Hamiltonian systems in the presence of saturation. Applied Mathematics and Computation vol. 217 9625–9634 (2011) – 10.1016/j.amc.2011.04.044
- Yang, R. & Wang, Y. Finite-time stability analysis and $H^\infty$ control for a class of nonlinear time-delay Hamiltonian systems. Automatica vol. 49 390–401 (2013) – 10.1016/j.automatica.2012.11.034
- Cai, L., He, Y. & Wu, M. Energy-shaping for Hamiltonian control systems with time delay. Journal of Control Theory and Applications vol. 11 436–441 (2013) – 10.1007/s11768-013-2164-1
- Wang, Y., Feng, G. & Cheng, D. Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems. Automatica vol. 43 403–415 (2007) – 10.1016/j.automatica.2006.09.008
- Wei, A., Wang, Y. & Hu, X. Parallel simultaneous stabilization of a set of Port-Controlled Hamiltonian systems subject to actuator saturation. Journal of Systems Science and Complexity vol. 24 120–139 (2011) – 10.1007/s11424-011-8177-2
- Xi, Z. & Cheng, D. Passivity-based stabilization and H 8 control of the Hamiltonian control systems with dissipation and its applications to power systems. International Journal of Control vol. 73 1686–1691 (2000) – 10.1080/00207170050201762
- Q. Lu. Q. Lu, Y. Sun. Nonlinear Control and Power Systems, Beijing, China: Scientific Press, 1993. (1993)