Combining Sliding Mode and Passivity-Based Control for Manifold Design and Robustness Enhancement

Authors

Michele Cucuzzella, Pablo Borja, Edoardo Vacchini, Antonella Ferrara, Jacquelien Scherpen, Arjan van der Schaft

Abstract

The design of suitablesliding manifolds remains one of the main bottlenecks in sliding mode control. This article proposes a strategy to address this problem for a broad class of nonlinear systems. To this end, we develop an original, systematic methodology to design stabilizing sliding manifolds for a class of nonlinear port-Hamiltonian (pH) systems. In particular, we exploit the pH structure of the system to design a sliding manifold, where the system preserves the desired passivity properties that are useful to stabilize the dynamics of the system on the designed manifold. The proposed modular control design offers significant advantages compared to the individual application of sliding mode control and passivity-based control techniques, effectively simplifying the design and enhancing robustness. Finally, the applicability of the proposed strategy is assessed via simulations.

Citation

• Journal: IEEE Transactions on Automatic Control
• Year: 2026
• Volume: 71
• Issue: 7
• Pages: 4481–4495
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tac.2026.3661318

BibTeX

@article{Cucuzzella_2026,
  title={{Combining Sliding Mode and Passivity-Based Control for Manifold Design and Robustness Enhancement}},
  volume={71},
  ISSN={2334-3303},
  DOI={10.1109/tac.2026.3661318},
  number={7},
  journal={IEEE Transactions on Automatic Control},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Cucuzzella, Michele and Borja, Pablo and Vacchini, Edoardo and Ferrara, Antonella and Scherpen, Jacquelien and Schaft, Arjan van der},
  year={2026},
  pages={4481--4495}
}

Download the bib file

References

• Utkin, Sliding Modes in Control and Optimization, Series Communication and Control Engineering (1992)
• (1998) Sliding Mode Control. Sliding Mode Control 47–8 – 10.1201/9781498701822-10
• Bandyopadhyay B, Janardhanan S, Spurgeon SK (eds) (2013) Advances in Sliding Mode Control. Springer Berlin Heidelber – 10.1007/978-3-642-36986-5
• Shtessel Y, Edwards C, Fridman L, Levant A (2014) Sliding Mode Control and Observation. Springer New Yor – 10.1007/978-0-8176-4893-0
• Ferrara A, Incremona GP, Cucuzzella M (2019) Advanced and Optimization Based Sliding Mode Control: Theory and Application – 10.1137/1.9781611975840
• Choi HH (2007) LMI-Based Sliding Surface Design for Integral Sliding Mode Control of Mismatched Uncertain Systems. IEEE Trans Automat Contr 52(4):736–742. https://doi.org/10.1109/tac.2007.89454 – 10.1109/tac.2007.894543
• Yasuda K, Nakatsuji Y Robust sliding mode control of uncertain systems. Proceedings. 1996 IEEE International Workshop on Variable Structure Systems. - VSS’96 - 15–1 – 10.1109/vss.1996.578531
• Trip S, Cucuzzella M, De Persis C, van der Schaft A, Ferrara A (2019) Passivity-Based Design of Sliding Modes for Optimal Load Frequency Control. IEEE Trans Contr Syst Technol 27(5):1893–1906. https://doi.org/10.1109/tcst.2018.284184 – 10.1109/tcst.2018.2841844
• Trip S, Cucuzzella M, De Persis C, Ferrara A, Scherpen JMA (2018) Robust load frequency control of nonlinear power networks. International Journal of Control 93(2):346–359. https://doi.org/10.1080/00207179.2018.155733 – 10.1080/00207179.2018.1557338
• Duindam V, Macchelli A, Stramigioli S, Bruyninckx H (2009) Modeling and Control of Complex Physical Systems. Springer Berlin Heidelber – 10.1007/978-3-642-03196-0
• van der Schaft A, Jeltsema D (2014) Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control 1(2–3):173–378. https://doi.org/10.1561/260000000 – 10.1561/2600000002
• (2001) Putting energy back in control. IEEE Control Syst 21(2):18–33. https://doi.org/10.1109/37.91539 – 10.1109/37.915398
• Ortega R, García-Canseco E (2004) Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control 10(5):432–450. https://doi.org/10.3166/ejc.10.432-45 – 10.3166/ejc.10.432-450
• Ortega R, Romero JG, Borja P, Donaire A (2021) PID Passivity‐Based Control of Nonlinear Systems with Application – 10.1002/9781119694199
• Wang W-J, Chen J-Y (2005) Passivity-Based Sliding Mode Position Control for Induction Motor Drives. IEEE Trans On Energy Conversion 20(2):316–321. https://doi.org/10.1109/tec.2004.84150 – 10.1109/tec.2004.841504
• Macchelli A, Stramigioli S, Schaft A van der, Melchiorri C (2002) CONSIDERATIONS ON THE ZERO-DYNAMICS OF PORT HAMILTONIAN SYSTEMS AND APPLICATION TO PASSIVE IMPLEMENTATION OF SLIDING-MODE CONTROL. IFAC Proceedings Volumes 35(1):13–18. https://doi.org/10.3182/20020721-6-es-1901.0025 – 10.3182/20020721-6-es-1901.00252
• Koshkouei AJ (2008) Passivity‐based sliding mode control for nonlinear systems. Adaptive Control & Signal 22(9):859–874. https://doi.org/10.1002/acs.102 – 10.1002/acs.1028
• Fujimoto K, Sakata N, Maruta I, Ferguson J (2021) A Passivity Based Sliding Mode Controller for Simple Port-Hamiltonian Systems. IEEE Control Syst Lett 5(3):839–844. https://doi.org/10.1109/lcsys.2020.300532 – 10.1109/lcsys.2020.3005327
• Fujimoto K, Baba T, Sakata N, Maruta I (2022) A Passivity-Based Sliding Mode Controller for a Class of Electro-Mechanical Systems. IEEE Control Syst Lett 6:1208–1213. https://doi.org/10.1109/lcsys.2021.308954 – 10.1109/lcsys.2021.3089541
• Liu W, Wang Y (2022) Passivity-Based Sliding Mode Control for Lur’e Singularly Perturbed Time-Delay Systems with Input Nonlinearity. Circuits Syst Signal Process 41(11):6007–6030. https://doi.org/10.1007/s00034-022-02086- – 10.1007/s00034-022-02086-4
• Gutman S, Leitmann G (1976) Stabilizing feedback control for dynamical systems with bounded uncertainty. 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes 94–9 – 10.1109/cdc.1976.267709
• Krantz SG, Parks HR (2013) The Implicit Function Theorem. Springer New Yor – 10.1007/978-1-4614-5981-1
• Borja P, Ortega R, Scherpen JMA (2021) New Results on Stabilization of Port-Hamiltonian Systems via PID Passivity-Based Control. IEEE Trans Automat Contr 66(2):625–636. https://doi.org/10.1109/tac.2020.298673 – 10.1109/tac.2020.2986731
• Borja P, Chan-Zheng C, Scherpen JMA (2023) Stabilization of Physical Systems via Saturated Controllers With Partial State Measurements. IEEE Trans Contr Syst Technol 31(6):2405–2419. https://doi.org/10.1109/tcst.2023.325924 – 10.1109/tcst.2023.3259243
• Chan-Zheng C, Borja P, Scherpen JMA (2023) Dead-zone compensation via passivity-based control for a class of mechanical systems. IFAC-PapersOnLine 56(1):319–324. https://doi.org/10.1016/j.ifacol.2023.02.05 – 10.1016/j.ifacol.2023.02.054
• Ortega R, van der Schaft A, Castanos F, Astolfi A (2008) Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Trans Automat Contr 53(11):2527–2542. https://doi.org/10.1109/tac.2008.200693 – 10.1109/tac.2008.2006930
• Utkin V, Hoon Lee Chattering Problem in Sliding Mode Control Systems. International Workshop on Variable Structure Systems, 2006. VSS’06. 346–35 – 10.1109/vss.2006.1644542
• Levant A (2010) Chattering Analysis. IEEE Trans Automat Contr 55(6):1380–1389. https://doi.org/10.1109/tac.2010.204197 – 10.1109/tac.2010.2041973
• Moreno JA, Osorio M (2012) Strict Lyapunov Functions for the Super-Twisting Algorithm. IEEE Trans Automat Contr 57(4):1035–1040. https://doi.org/10.1109/tac.2012.218617 – 10.1109/tac.2012.2186179
• Nagesh I, Edwards C (2014) A multivariable super-twisting sliding mode approach. Automatica 50(3):984–988. https://doi.org/10.1016/j.automatica.2013.12.03 – 10.1016/j.automatica.2013.12.032
• Bartolini G, Ferrara A, Usai E (1998) Chattering avoidance by second-order sliding mode control. IEEE Trans Automat Contr 43(2):241–246. https://doi.org/10.1109/9.66107 – 10.1109/9.661074
• Dinuzzo F, Ferrara A (2009) Higher Order Sliding Mode Controllers With Optimal Reaching. IEEE Trans Automat Contr 54(9):2126–2136. https://doi.org/10.1109/tac.2009.202694 – 10.1109/tac.2009.2026940
• Astolfi A, Ortega R (2003) Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems. IEEE Trans Automat Contr 48(4):590–606. https://doi.org/10.1109/tac.2003.80982 – 10.1109/tac.2003.809820
• 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
• 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
• 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
• Ferguson J, Middleton RH, Donaire A (2015) Disturbance rejection via control by interconnection of port-Hamiltonian systems. 2015 54th IEEE Conference on Decision and Control (CDC) 507–51 – 10.1109/cdc.2015.7402279
• Sontag ED, Wang Y (1995) On characterizations of the input-to-state stability property. Systems & Control Letters 24(5):351–359. https://doi.org/10.1016/0167-6911(94)00050- – 10.1016/0167-6911(94)00050-6
• Ferguson J, Cucuzzella M, Scherpen JMA (2021) Exponential Stability and Local ISS for DC Networks. IEEE Control Syst Lett 5(3):893–898. https://doi.org/10.1109/lcsys.2020.300722 – 10.1109/lcsys.2020.3007222
• Cucuzzella M, Kosaraju KC, Scherpen JMA (2023) Voltage Control of DC Microgrids: Robustness for Unknown ZIP-Loads. IEEE Control Syst Lett 7:139–144. https://doi.org/10.1109/lcsys.2022.318792 – 10.1109/lcsys.2022.3187925
• Ferguson J, Cucuzzella M, Scherpen JMA (2023) Increasing the region of attraction in DC microgrids. Automatica 151:110883. https://doi.org/10.1016/j.automatica.2023.11088 – 10.1016/j.automatica.2023.110883
• Cucuzzella M, Rosti S, Cavallo A, Ferrara A (2017) Decentralized Sliding Mode voltage control in DC microgrids. 2017 American Control Conference (ACC) 3445–345 – 10.23919/acc.2017.7963479
• Vacchini E, Cucuzzella M, Borja P, Ferrara A (2024) Robust Voltage Regulation for DC Microgrids via Passivity-Based Sliding Mode Control. 2024 17th International Workshop on Variable Structure Systems (VSS) 273–27 – 10.1109/vss61690.2024.10753420
• Borja P (2024) Interconnection and Damping Assignment Passivity-Based Control Without Partial Differential Equations. 2024 UKACC 14th International Conference on Control (CONTROL) 131–13 – 10.1109/control60310.2024.10532055
• Chalupa, Comprehensive model of DTS200 three tank system in simulink. Int. J. Math. Models Methods Appl. Sci. (2012)