Robust energy shaping for mechanical systems with dissipative forces and disturbances

Authors

Ainoor Teimoorzadeh, Alejandro Donaire, Pierluigi Arpenti, Fabio Ruggiero

Abstract

This paper presents a novel energy shaping-based integral action for mechanical systems with unknown dissipative forces and matched disturbances. The proposed approach builds on the simultaneous interconnection and damping assignment method and takes advantage of the representation of the dissipative forces in the port-Hamiltonian dynamics. We consider dissipative forces that cannot be written in the classical dissipation structure of the port-Hamiltonian systems. We show that the proposed design ensures the stability of the equilibrium and is robust against dissipative force uncertainty, and rejects constant matched disturbances. Two case studies are presented, and simulation results show the closed-loop performance.

Citation

• Journal: 2022 European Control Conference (ECC)
• Year: 2022
• Volume:
• Issue:
• Pages: 1409–1414
• Publisher: IEEE
• DOI: 10.23919/ecc55457.2022.9838430

BibTeX

@inproceedings{Teimoorzadeh_2022,
  title={{Robust energy shaping for mechanical systems with dissipative forces and disturbances}},
  DOI={10.23919/ecc55457.2022.9838430},
  booktitle={{2022 European Control Conference (ECC)}},
  publisher={IEEE},
  author={Teimoorzadeh, Ainoor and Donaire, Alejandro and Arpenti, Pierluigi and Ruggiero, Fabio},
  year={2022},
  pages={1409--1414}
}

Download the bib file

References

• Ortega, R. & García-Canseco, E. Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control 10, 432–450 (2004) – 10.3166/ejc.10.432-450
• 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
• 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
• Ferguson, J., Donaire, A. & Middleton, R. H. Integral Control of Port-Hamiltonian Systems: Nonpassive Outputs Without Coordinate Transformation. IEEE Trans. Automat. Contr. 62, 5947–5953 (2017) – 10.1109/tac.2017.2700995
• Ferguson, J., Donaire, A., Ortega, R. & Middleton, R. H. Matched Disturbance Rejection for a Class of Nonlinear Systems. IEEE Trans. Automat. Contr. 65, 1710–1715 (2020) – 10.1109/tac.2019.2933398
• Ferguson, J., Donaire, A., Ortega, R. & Middleton, R. H. Matched disturbance rejection for energy-shaping controlled underactuated mechanical systems. 2017 IEEE 56th Annual Conference on Decision and Control (CDC) 1484–1489 (2017) doi:10.1109/cdc.2017.8263862 – 10.1109/cdc.2017.8263862
• 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, Port-Hamiltonian and power-based inte-gral type control of a manipulator system. IFAC World Congress (2011)
• Donaire, A. et al. Shaping the Energy of Mechanical Systems Without Solving Partial Differential Equations. IEEE Trans. Automat. Contr. 61, 1051–1056 (2016) – 10.1109/tac.2015.2458091
• Acosta, J. A., Ortega, R., Astolfi, A. & Mahindrakar, A. D. Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one. IEEE Trans. Automat. Contr. 50, 1936–1955 (2005) – 10.1109/tac.2005.860292
• Chang, D. E. On the method of interconnection and damping assignment passivity-based control for the stabilization of mechanical systems. Regul. Chaot. Dyn. 19, 556–575 (2014) – 10.1134/s1560354714050049
• Crasta, N., Ortega, R. & Pillai, H. K. On the matching equations of energy shaping controllers for mechanical systems. International Journal of Control 88, 1757–1765 (2015) – 10.1080/00207179.2015.1016453
• Donaire, A., Ortega, R. & Romero, J. G. Simultaneous interconnection and damping assignment passivity-based control of mechanical systems using dissipative forces. Systems & Control Letters 94, 118–126 (2016) – 10.1016/j.sysconle.2016.05.006
• Gómez-Estern, F. & Van der Schaft, A. J. Physical Damping in IDA-PBC Controlled Underactuated Mechanical Systems. European Journal of Control 10, 451–468 (2004) – 10.3166/ejc.10.451-468
• 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
• ortega, Passivity-Based Control of Mechanical Systems ser Feedback Stabilization of Controlled Dynamical Systems Lecture Notes in Electrical Engineering (2017)
• Donaire, A., Romero, J. G., Ortega, R., Siciliano, B. & Crespo, M. Robust IDA-PBC for underactuated mechanical systems subject to matched disturbances. Int. J. Robust. Nonlinear Control 27, 1000–1016 (2016) – 10.1002/rnc.3615