Stabilization and H∞ control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation

Authors

Airong Wei, Yuzhen Wang

Abstract

This paper investigates the stabilization and H ∞ control of nonlinear port-controlled Hamiltonian (PCH) systems subject to actuator saturation, and proposes a number of new results. First, the stabilization problem is studied, and a control design method is developed by using both the dissipative Hamiltonian structural and saturating actuator properties. Second, for the case that there are external disturbances in the systems, an H ∞ controller is designed to attenuate the disturbances. Finally, the results obtained for Hamiltonian systems are applied to the stabilization and H ∞ control of nonlinear affine systems subject to actuator saturation, and several interesting results are presented. Study of an example of power system with simulations shows that the controller proposed in this paper is effective.

Keywords

PCH system; Actuator saturation; Stabilization; \( H^\infty \)-control; Nonlinear affine system

Citation

• Journal: Automatica
• Year: 2010
• Volume: 46
• Issue: 12
• Pages: 2008–2013
• Publisher: Elsevier BV
• DOI: 10.1016/j.automatica.2010.08.001

BibTeX

@article{Wei_2010,
  title={{Stabilization and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation}},
  volume={46},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2010.08.001},
  number={12},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Wei, Airong and Wang, Yuzhen},
  year={2010},
  pages={2008--2013}
}

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References

• Bernstein, D. S. & Michel, A. N. A chronological bibliography on saturating actuators. Intl J Robust & Nonlinear 5, 375–380 (1995) – 10.1002/rnc.4590050502
• Castelan, E. B., Tarbouriech, S. & Queinnec, I. Control design for a class of nonlinear continuous-time systems. Automatica 44, 2034–2039 (2008) – 10.1016/j.automatica.2007.11.013
• Coutinho, D. F. & Gomes da Silva, J. M., Jr. Computing estimates of the region of attraction for rational control systems with saturating actuators. IET Control Theory Appl. 4, 315–325 (2010) – 10.1049/iet-cta.2008.0314
• 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 via generalized canonical transformations. Automatica 39, 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005
• Gomes da Silva, Antiwindup design with guaranteed regions of stability: an LMI-based approach. IEEE Transactions on Automatic Control (2005)
• Hu, (2001)
• Lu, (1993)
• McLachlan, R. I., Quispel, G. R. W. & Robidoux, N. Unified Approach to Hamiltonian Systems, Poisson Systems, Gradient Systems, and Systems with Lyapunov Functions or First Integrals. Phys. Rev. Lett. 81, 2399–2403 (1998) – 10.1103/physrevlett.81.2399
• Transient stabilization of multimachine power systems with nontrivial transfer conductances. IEEE Trans. Automat. Contr. 50, 60–75 (2005) – 10.1109/tac.2004.840477
• 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
• Saberi, A., Zongli Lin & Teel, A. R. Control of linear systems with saturating actuators. IEEE Trans. Automat. Contr. 41, 368–378 (1996) – 10.1109/9.486638
• Shen, T., Mei, S., Lu, Q., Hu, W. & Tamura, K. Adaptive nonlinear excitation control with L2 disturbance attenuation for power systems. Automatica 39, 81–89 (2003) – 10.1016/s0005-1098(02)00175-9
• Stoorvogel, A. A., Saberi, A. & Weiland, S. On external semi-global stochastic stabilization of linear systems with input saturation. 2007 American Control Conference 5845–5850 (2007) doi:10.1109/acc.2007.4282930 – 10.1109/acc.2007.4282930
• Sun, W., Lin, Z. & Wang, Y. Global asymptotic and finite-gain L<inf>2</inf> stabilization of port-controlled Hamiltonian systems subject to actuator saturation. 2009 American Control Conference 1894–1898 (2009) doi:10.1109/acc.2009.5160232 – 10.1109/acc.2009.5160232
• Sussmann, H. J., Sontag, E. D. & Yang, Y. A general result on the stabilization of linear systems using bounded controls. IEEE Trans. Automat. Contr. 39, 2411–2425 (1994) – 10.1109/9.362853
• Tarbouriech, (2007)
• Teel, A. R. Linear systems with input nonlinearities: Global stabilization by scheduling a family ofH∞‐type controllers. Intl J Robust & Nonlinear 5, 399–411 (1995) – 10.1002/rnc.4590050504
• Van der Schaft, (1999)
• Wang, Y., Cheng, D. & Hu, X. Problems on time-varying port-controlled Hamiltonian systems: geometric structure and dissipative realization. Automatica 41, 717–723 (2005) – 10.1016/j.automatica.2004.11.006
• Yuzhen Wang, Daizhan Cheng, Chunwen Li & You Ge. Dissipative hamiltonian realization and energy-based L/sub 2/-disturbance attenuation control of multimachine power systems. IEEE Trans. Automat. Contr. 48, 1428–1433 (2003) – 10.1109/tac.2003.815037
• Zairong Xi, Feng, G., Daizhan Cheng & Qiang Lu. Nonlinear decentralized saturated controller design for power systems. IEEE Trans. Contr. Syst. Technol. 11, 539–547 (2003) – 10.1109/tcst.2003.813404