Global output regulation for a class of single input Port-controlled Hamiltonian disturbed systems

Authors

Baozeng Fu, Shihua Li, Jun Yang, Lei Guo

Abstract

The problem of global output regulation for a class of single input Port-controlled Hamiltonian disturbed systems is studied. A composite control method is developed by combining the damping injection and the nonlinear disturbance observer techniques together. A series of coordinate transformation is presented to transform the system with mismatched disturbance into matched disturbance system. By means of Lyapunov stability theorems, global stability analysis for the closed-loop Hamiltonian system is presented. It is shown that the system output is regulated to zero asymptotically in the presence of mismatched disturbance without larger overshoots and longer settling time caused by integral action. Study on two examples with simulation results demonstrates the effectiveness of the proposed control method.

Keywords

Global output regulation; Port-controlled Hamiltonian systems; Mismatched disturbances; Damping injection; Nonlinear disturbance observer; Coordinate transformation

Citation

• Journal: Applied Mathematics and Computation
• Year: 2018
• Volume: 325
• Issue:
• Pages: 322–331
• Publisher: Elsevier BV
• DOI: 10.1016/j.amc.2017.12.046

BibTeX

@article{Fu_2018,
  title={{Global output regulation for a class of single input Port-controlled Hamiltonian disturbed systems}},
  volume={325},
  ISSN={0096-3003},
  DOI={10.1016/j.amc.2017.12.046},
  journal={Applied Mathematics and Computation},
  publisher={Elsevier BV},
  author={Fu, Baozeng and Li, Shihua and Yang, Jun and Guo, Lei},
  year={2018},
  pages={322--331}
}

Download the bib file

References

• Maschke, Port-controlled Hamiltonian systems: modeling origins and system theoretic properties. (1992)
• Schaft, The Hamiltonian formulation of energy conserving physical systems with external ports. Arch. Elektronik bertragungstechnik (1995)
• Dalsmo, M. & van der Schaft, A. On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems. SIAM J. Control Optim. 37, 54–91 (1998) – 10.1137/s0363012996312039
• 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
• Li, Feedback control of fractional nonlinear differential algebraic systems with Hamiltonian function method. Appl. Math. Comput. (2008)
• 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
• 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
• 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
• 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
• 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
• Sun, Stabilization analysis of time-delay Hamiltonian systems in the presence of saturation. Appl. Math. Comput. (2011)
• 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
• He, Distributed finite-time leaderless consensus control for double-integrator multi-agent systems with external disturbances. Appl. Math. Comput. (2017)
• Jin, X.-Z., Wang, S.-F., Yang, G.-H. & Ye, D. Robust adaptive hierarchical insensitive tracking control of a class of leader-follower agents. Information Sciences 406–407, 234–247 (2017) – 10.1016/j.ins.2017.04.036
• Jin, X.-Z., Zhao, Z. & He, Y.-G. Insensitive leader-following consensus for a class of uncertain multi-agent systems against actuator faults. Neurocomputing 272, 189–196 (2018) – 10.1016/j.neucom.2017.06.072
• Lien, An efficient method to design robust observer-based control of uncertain linear systems. Appl. Math. Comput. (2004)
• Lin, Finite-time boundedness and L2-gain analysis for switched delay systems with norm-bounded disturbance. Appl. Math. Comput. (2011)
• Lin, Finite-time boundedness for switched systems with sector bounded nonlinearity and constant time delay. Appl. Math. Comput. (2016)
• 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
• Ferguson, Disturbance rejection via control by interconnection of port-Hamiltonian systems. (2015)
• 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
• Sun, L., Feng, G. & Wang, Y. Finite-time stabilization and H∞ 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
• 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
• 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
• Du, H., He, Y. & Cheng, Y. Finite-Time Synchronization of a Class of Second-Order Nonlinear Multi-Agent Systems Using Output Feedback Control. IEEE Trans. Circuits Syst. I 61, 1778–1788 (2014) – 10.1109/tcsi.2013.2295012
• Guo, (2013)
• Guo, L. & Cao, S. Anti-disturbance control theory for systems with multiple disturbances: A survey. ISA Transactions 53, 846–849 (2014) – 10.1016/j.isatra.2013.10.005
• 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
• Li, S., Yang, J., Chen, W.-H. & Chen, X. Generalized Extended State Observer Based Control for Systems With Mismatched Uncertainties. IEEE Trans. Ind. Electron. 59, 4792–4802 (2012) – 10.1109/tie.2011.2182011
• Li, (2014)
• 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
• Wang, Observer-based periodically intermittent control for linear systems via piecewise Lyapunov function method. Appl. Math. Comput. (2017)
• Wei, X. & Guo, L. Composite disturbance‐observer‐based control andH∞control for complex continuous models. Intl J Robust & Nonlinear 20, 106–118 (2009) – 10.1002/rnc.1425
• Yang, J., Chen, W.-H. & Li, S. Non-linear disturbance observer-based robust control for systems with mismatched disturbances/uncertainties. IET Control Theory Appl. 5, 2053–2062 (2011) – 10.1049/iet-cta.2010.0616
• Yang, J., Li, S., Su, J. & Yu, X. Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances. Automatica 49, 2287–2291 (2013) – 10.1016/j.automatica.2013.03.026
• Yang, J., Li, S. & Yu, X. Sliding-Mode Control for Systems With Mismatched Uncertainties via a Disturbance Observer. IEEE Trans. Ind. Electron. 60, 160–169 (2013) – 10.1109/tie.2012.2183841
• Wei, X. & Guo, L. Composite disturbance-observer-based control and terminal sliding mode control for non-linear systems with disturbances. International Journal of Control 82, 1082–1098 (2009) – 10.1080/00207170802455339
• Khalil, (2002)
• Wang, Finite-time stabilization of port-controlled Hamiltonian systems with application to nonlinear affine systems. (2008)
• Li, S., Sun, H., Yang, J. & Yu, X. Continuous Finite-Time Output Regulation for Disturbed Systems Under Mismatching Condition. IEEE Trans. Automat. Contr. 60, 277–282 (2015) – 10.1109/tac.2014.2324212
• Liu, H. & Li, S. Speed Control for PMSM Servo System Using Predictive Functional Control and Extended State Observer. IEEE Trans. Ind. Electron. 59, 1171–1183 (2012) – 10.1109/tie.2011.2162217
• 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