Robust IDA-PBC for non-separable PCH systems under time-varying external disturbances

Authors

M. E. Guerrero-Sánchez, J. R. Montoya-Morales, G. Valencia-Palomo, O. Hernández-González

Abstract

This work tackles the time-varying matched external disturbances rejection problem of robust Interconnection and Damping Assignment-Passivity Based Control methodology. The main objective of this paper is the stabilization of under-actuated non-separable Port-controlled Hamiltonian (PCH) systems with an inertia matrix dependent of the unactuated coordinates, where the control input is affected by time-varying matched external disturbances. The proposed methodology adds an extension in the system coordinates, such that the system’s closed-loop stability and its PCH structure are preserved despite the presence of time-varying disturbances. The theoretical results are applied to an overhead crane and illustrated through numerical simulations.

Keywords

non-separable pch systems, overhead crane, perturbed pch systems, robust ida-pbc, time-varying disturbances

Citation

• Journal: Nonlinear Dynamics
• Year: 2025
• Volume: 113
• Issue: 4
• Pages: 3499–3510
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s11071-024-10380-w

BibTeX

@article{Guerrero_S_nchez_2024,
  title={{Robust IDA-PBC for non-separable PCH systems under time-varying external disturbances}},
  volume={113},
  ISSN={1573-269X},
  DOI={10.1007/s11071-024-10380-w},
  number={4},
  journal={Nonlinear Dynamics},
  publisher={Springer Science and Business Media LLC},
  author={Guerrero-Sánchez, M. E. and Montoya-Morales, J. R. and Valencia-Palomo, G. and Hernández-González, O.},
  year={2024},
  pages={3499--3510}
}

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References

• Ortega R, Spong MW, Gomez-Estern F, Blankenstein G (2002) Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans Automat Contr 47(8):1218–1233. https://doi.org/10.1109/tac.2002.80077 – 10.1109/tac.2002.800770
• Donaire A, Junco S (2009) On the addition of integral action to port-controlled Hamiltonian systems. Automatica 45(8):1910–1916. https://doi.org/10.1016/j.automatica.2009.04.00 – 10.1016/j.automatica.2009.04.006
• Ortega R, Romero JG (2012) Robust integral control of port-Hamiltonian systems: The case of non-passive outputs with unmatched disturbances. Systems & Control Letters 61(1):11–17. https://doi.org/10.1016/j.sysconle.2011.09.01 – 10.1016/j.sysconle.2011.09.015
• Deng M, Bu N (2012) Robust Control for Nonlinear Systems Using Passivity-Based Robust Right Coprime Factorization. IEEE Trans Automat Contr 57(10):2599–2604. https://doi.org/10.1109/tac.2012.218842 – 10.1109/tac.2012.2188426
• Romero JG, Donaire A, Ortega R (2013) Robust energy shaping control of mechanical systems. Systems & Control Letters 62(9):770–780. https://doi.org/10.1016/j.sysconle.2013.05.01 – 10.1016/j.sysconle.2013.05.011
• Ryalat M, Laila DS, Torbati MM (2015) Integral IDA-PBC and PID-like control for port-controlled Hamiltonian systems. 2015 American Control Conference (ACC) 5365–537 – 10.1109/acc.2015.7172178
• Ferguson J, Donaire A, Middleton RH (2017) Integral Control of Port-Hamiltonian Systems: Nonpassive Outputs Without Coordinate Transformation. IEEE Trans Automat Contr 62(11):5947–5953. https://doi.org/10.1109/tac.2017.270099 – 10.1109/tac.2017.2700995
• Kozlov VV (1983) Integrability and non-integrability in Hamiltonian mechanics. Russ Math Surv 38(1):1–76. https://doi.org/10.1070/rm1983v038n01abeh00333 – 10.1070/rm1983v038n01abeh003330
• Błaszak M (2019) Quantum versus Classical Mechanics and Integrability Problems. Springer International Publishin – 10.1007/978-3-030-18379-0
• Benenti G, Casati G, Veble G (2003) Decay of the classical Loschmidt echo in integrable systems. Phys Rev E 68(3). https://doi.org/10.1103/physreve.68.03621 – 10.1103/physreve.68.036212
• Donaire A, Romero JG, Ortega R, Siciliano B, Crespo M (2016) Robust IDA-PBC for underactuated mechanical systems subject to matched disturbances. Int J Robust Nonlinear Control 27(6):1000–1016. https://doi.org/10.1002/rnc.361 – 10.1002/rnc.3615
• Ryalat M, Laila DS (2018) A Robust IDA-PBC Approach for Handling Uncertainties in Underactuated Mechanical Systems. IEEE Trans Automat Contr 63(10):3495–3502. https://doi.org/10.1109/tac.2018.279719 – 10.1109/tac.2018.2797191
• Donaire A, Romero JG, Ortega R (2020) Correction to the Paper “A Robust IDA-PBC Approach for Handling Uncertainties in Underactuated Mechanical Systems” [Oct 18 3495-3502]. IEEE Trans Automat Contr 65(7):3223–3226. https://doi.org/10.1109/tac.2019.294987 – 10.1109/tac.2019.2949876
• Guerrero-Sánchez ME, Hernández-González O, Valencia-Palomo G, Mercado-Ravell DA, López-Estrada FR, Hoyo-Montaño JA (2021) Robust IDA-PBC for under-actuated systems with inertia matrix dependent of the unactuated coordinates: application to a UAV carrying a load. Nonlinear Dyn 105(4):3225–3238. https://doi.org/10.1007/s11071-021-06776- – 10.1007/s11071-021-06776-7
• Ferguson J, Donaire A, Ortega R, Middleton RH (2020) Matched Disturbance Rejection for a Class of Nonlinear Systems. IEEE Trans Automat Contr 65(4):1710–1715. https://doi.org/10.1109/tac.2019.293339 – 10.1109/tac.2019.2933398
• (2021) Disturbance Rejection in Port‐Hamiltonian Systems. PID Passivity‐Based Control of Nonlinear Systems with Applications 153–19 – 10.1002/9781119694199.ch8
• Kennedy JM, Donaire A, Ford JJ, Valentinis F (2019) Suppression of Wave Disturbances and Tracking Control for Marine Systems. 2019 IEEE 58th Conference on Decision and Control (CDC) 8296–830 – 10.1109/cdc40024.2019.9029664
• Schule J, Donaire A, Sawodny O (2020) Passivity-based control design for a continuum robotic manipulator with disturbances. 2020 IEEE/SICE International Symposium on System Integration (SII) 144–14 – 10.1109/sii46433.2020.9026249
• Gandarilla I, Santibáñez V, Sandoval J, Romero JG (2021) PID passivity-based control laws for joint position regulation of a self-balancing robot. Control Engineering Practice 116:104927. https://doi.org/10.1016/j.conengprac.2021.10492 – 10.1016/j.conengprac.2021.104927
• Zonetti D, Bergna‐Diaz G, Ortega R, Monshizadeh N (2021) PID passivity‐based droop control of power converters: Large‐signal stability, robustness and performance. Intl J Robust & Nonlinear 32(3):1769–1795. https://doi.org/10.1002/rnc.591 – 10.1002/rnc.5917
• Cisneros R, Gao R, Ortega R, Husain I (2020) A PI+passivity-based control of a wind energy conversion system enabled with a solid-state transformer. International Journal of Control 94(9):2453–2463. https://doi.org/10.1080/00207179.2019.171076 – 10.1080/00207179.2019.1710768
• Ferguson J, Wu D, Ortega R (2020) On Matched Disturbance Suppression for Port-Hamiltonian Systems. IEEE Control Syst Lett 4(4):892–897. https://doi.org/10.1109/lcsys.2020.299426 – 10.1109/lcsys.2020.2994262
• Ortega R, van der Schaft A, Maschke B, Escobar G (2002) Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38(4):585–596. https://doi.org/10.1016/s0005-1098(01)00278- – 10.1016/s0005-1098(01)00278-3