Nonlinear Disturbance Observer-Based Control for a Class of Port-Controlled Hamiltonian Disturbed Systems

Authors

Baozeng Fu, Qingzhi Wang, Wei He

Abstract

In this paper, a composite control scheme is presented to asymptotically stabilize a class of port-controlled Hamiltonian systems under nonvanishing disturbances. First, based on the damping injection method and the nonlinear disturbance observer (NDOB) technique, the robust composite control strategy is designed. The NDOB, as an effective observation tool, is developed to estimate the disturbances, and furthermore, the disturbances can be feedforward compensated using the estimates of disturbances. Then, for the augmented system, an asymptotic stability theorem is proposed via an input-to-state stability technique and Lyapunov stability theorems. The proposed control approach exhibits not only good robustness and disturbance rejection performances but also the property of nominal performance recovery. Finally, a simulation example on a circuit system is given to show the feasibility and advantage of the composite control method.

Citation

• Journal: IEEE Access
• Year: 2018
• Volume: 6
• Issue:
• Pages: 50299–50305
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/access.2018.2868919

BibTeX

@article{Fu_2018,
  title={{Nonlinear Disturbance Observer-Based Control for a Class of Port-Controlled Hamiltonian Disturbed Systems}},
  volume={6},
  ISSN={2169-3536},
  DOI={10.1109/access.2018.2868919},
  journal={IEEE Access},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Fu, Baozeng and Wang, Qingzhi and He, Wei},
  year={2018},
  pages={50299--50305}
}

Download the bib file

References

• wang, Finite-time stabilization of Port-controlled Hamiltonian systems with application to nonlinear affine systems. Proc Amer Control Conf (2008)
• khalil, Nonlinear Systems (2002)
• Yang, J., Cui, H., Li, S. & Zolotas, A. Optimized Active Disturbance Rejection Control for DC-DC Buck Converters With Uncertainties Using a Reduced-Order GPI Observer. IEEE Trans. Circuits Syst. I 65, 832–841 (2018) – 10.1109/tcsi.2017.2725386
• Sun, W. & Fu, B. Adaptive control of time‐varying uncertain non‐linear systems with input delay: a Hamiltonian approach. IET Control Theory & Appl 10, 1844–1858 (2016) – 10.1049/iet-cta.2015.1165
• Cao, Z., Hou, X. & Zhao, W. A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems. Asian Journal of Control 19, 151–163 (2016) – 10.1002/asjc.1341
• 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
• 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
• Zhao, Z., Yang, J., Li, S., Zhang, Z. & Guo, L. Finite-time super-twisting sliding mode control for Mars entry trajectory tracking. Journal of the Franklin Institute 352, 5226–5248 (2015) – 10.1016/j.jfranklin.2015.08.022
• Fu, B., Li, S., Yang, J. & Guo, L. Global output regulation for a class of single input Port-controlled Hamiltonian disturbed systems. Applied Mathematics and Computation 325, 322–331 (2018) – 10.1016/j.amc.2017.12.046
• Sun, W., Wang, Y. & Yang, R. L 2 disturbance attenuation for a class of time-delay Hamiltonian systems. J Syst Sci Complex 24, 672–682 (2011) – 10.1007/s11424-011-8368-x
• Wei, A. & Wang, Y. Stabilization and \(H_{\infty}\) control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Automatica 46, 2008–2013 (2010) – 10.1016/j.automatica.2010.08.001
• Sun, L., Feng, G. & Wang, Y. Finite-time stabilization and \(H_{\infty}\) control for a class of nonlinear Hamiltonian descriptor systems with application to affine nonlinear descriptor systems. Automatica 50, 2090–2097 (2014) – 10.1016/j.automatica.2014.05.031
• 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
• he, Incremental passivity based control for DC-DC boost converters under time-varying disturbances via a generalized proportional integral observer. J Power Electron (2018)
• Cheng, D. & Spurgeon, S. Stabilization of Hamiltonian systems with dissipation. International Journal of Control 74, 465–473 (2001) – 10.1080/00207170010010551
• Sun, H. & Guo, L. Composite adaptive disturbance observer based control and back-stepping method for nonlinear system with multiple mismatched disturbances. Journal of the Franklin Institute 351, 1027–1041 (2014) – 10.1016/j.jfranklin.2013.10.002
• Maschke, B., Ortega, R. & Van Der Schaft, A. J. Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Trans. Automat. Contr. 45, 1498–1502 (2000) – 10.1109/9.871758
• Xi, Z. Adaptive stabilization of generalized Hamiltonian systems with dissipation and its applications to power systems. International Journal of Systems Science 33, 839–846 (2002) – 10.1080/00207720210167113
• Yang, J., Chen, W.-H., Li, S., Guo, L. & Yan, Y. Disturbance/Uncertainty Estimation and Attenuation Techniques in PMSM Drives—A Survey. IEEE Trans. Ind. Electron. 64, 3273–3285 (2017) – 10.1109/tie.2016.2583412
• Wang, Y., Feng, G. & Cheng, D. Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems. Automatica 43, 403–415 (2007) – 10.1016/j.automatica.2006.09.008
• Sun, W., Wang, K., Nie, C. & Xie, X. Energy‐Based Controller Design of Stochastic Magnetic Levitation System. Mathematical Problems in Engineering 2017, (2017) – 10.1155/2017/7838431
• Yu, H., Yu, J., Liu, J. & Song, Q. Nonlinear control of induction motors based on state error PCH and energy-shaping principle. Nonlinear Dyn 72, 49–59 (2012) – 10.1007/s11071-012-0689-3
• van der schaft, The Hamiltonian formulation of energy conserving physical systems with external ports. AE&#x00DC Int J Electronics Comm (1995)
• Maschke, B. M. & van der Schaft, A. J. Port-Controlled Hamiltonian Systems: Modelling Origins and Systemtheoretic Properties. IFAC Proceedings Volumes 25, 359–365 (1992) – 10.1016/s1474-6670(17)52308-3
• Knorn, S., Donaire, A., Agüero, J. C. & Middleton, R. H. Passivity-based control for multi-vehicle systems subject to string constraints. Automatica 50, 3224–3230 (2014) – 10.1016/j.automatica.2014.10.038
• 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
• Chen, W.-H., Yang, J., Guo, L. & Li, S. Disturbance-Observer-Based Control and Related Methods—An Overview. IEEE Trans. Ind. Electron. 63, 1083–1095 (2016) – 10.1109/tie.2015.2478397
• 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
• Wu, C., Yang, J., Li, S., Li, Q. & Guo, L. Disturbance observer based model predictive control for accurate atmospheric entry of spacecraft. Advances in Space Research 61, 2457–2471 (2018) – 10.1016/j.asr.2018.02.010
• Guo, L. & Chen, W.-H. Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. Int. J. Robust Nonlinear Control 15, 109–125 (2005) – 10.1002/rnc.978
• Sun, J. & Li, S. Disturbance observer based iterative learning control method for a class of systems subject to mismatched disturbances. Transactions of the Institute of Measurement and Control 39, 1749–1760 (2016) – 10.1177/0142331216645173
• li, Disturbance Observer-based Control Methods and Applications (2014)