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Taylor series and adaptive passivity-based control for conical tanks level regulation

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Abstract

This manuscript proposes using a finite Taylor series (TS) and normalized adaptive passivity-based control (NAPBC) for nonlinear systems encompassing the level regulation of conical tanks. TS-NAPBC is as effective and robust as the traditional proportional integer control, and NAPBC. However, these latest techniques assume the existence of the input–output dynamical model obtained after computing a coordinates transformation of the original state-space representation, which takes time and is problematic. In contrast, the proposed TS-NAPNC exceeds them by having a faster and more straightforward design and commissioning, avoiding an input–output transformation, and not needing to know the plant parameters value. The TS-NAPBC deals with the unknown parameters and control direction of the TS. Moreover, it has adaptive law modifications due to the presence of a time-varying parameter associated with the TS rest term. The second Lyapunov stability method and Barbalat Lemma theoretically validate the proposition. Comparative experimental results show the effectiveness of TS-NAPBC and its robustness in front of plant parameter variations.

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References

  1. Byrnes, C.I., Isidori, A., Willems, J.C.: Feedback equivalence to passive nonlinear systems. In: Analysis of Controlled Dynamical Systems, pp. 118–135 (1991)

  2. Guerrero-Sánchez, M., Hernández-González, O., Valencia-Palomo, G., Mercado-Ravell, D., López-Estrada, F., Hoyo-Montaño, J.: 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 (2021)

    Article  Google Scholar 

  3. Mohammadi, K., Sirouspour, S., Grivani, A.: Passivity-based control of multiple quad-rotors carrying a cable-suspended payload. IEEE/ASME Trans. Mechatron. 27(4), 2390–2400 (2021)

    Article  Google Scholar 

  4. Feliu-Talegon, D., Feliu-Batlle, V.: Passivity-based control of a single-link flexible manipulator using fractional controllers. Nonlinear Dyn. 95(3), 2415–2441 (2019)

    Article  Google Scholar 

  5. Zhang, S., Zhu, H., He, X., Feng, Y., Pang, C.K.: Passivity-based coupling control for underactuated three-dimensional overhead cranes. ISA Trans. 126, 352–360 (2022)

    Article  Google Scholar 

  6. Zhao, E., Han, Y., Liu, Y., Yang, P., Zalhaf, A.S., Blaabjerg, F.: An optimized parameter design of passivity-based controller for single-phase voltage source inverters. Int. J. Electr. Power Energy Syst. 145, 108627 (2023)

    Article  Google Scholar 

  7. Moeini, N., Bahrami-Fard, M., Shahabadini, M., Azimi, S.M., Iman-Eini, H.: Passivity-based control of single-phase cascaded h-bridge grid-connected photovoltaic inverter. IEEE Trans. Ind. Electron. 70(2), 1512–1520 (2022)

    Article  Google Scholar 

  8. Chandrasekar, P., Ponnusamy, L.: Passivity based level controller design applied to a nonlinear SISO system. In: 2013 International Conference on Green Computing, Communication and Conservation of Energy (ICGCE), pp. 392–396 (2013)

  9. Chandrasekar, P., Ponnusamy, L.: Comparative study of controller for a variable area MIMO interacting nonlinear system. Int. J. Eng. Technol. 6(1), 227–235 (2014)

    Google Scholar 

  10. Travieso-Torres, J.C., Duarte-Mermoud, M.A., Beytía, O.: Experimental comparison of passivity-based controllers for the level regulation of a conical tank. In: 2016 IEEE International Conference on Automatica (ICA-ACCA), pp. 1–6 (2016)

  11. Travieso-Torres, J.C., Duarte-Mermoud, M.A., Gutierrez-Osorio, A., Beytía, O.: Passivity based control of a class of nonlinear systems and its application to the level regulation of a conical tank. RIAI-Revista Iberoamericana de Automatica e Informatica Industrial 15(2), 167–173 (2018)

    Article  Google Scholar 

  12. Travieso-Torres, J.C., Duarte-Mermoud, M.A., Sepuleveda, D.I.: Passivity-based control for stabilization, regulation and tracking purposes of a class of nonlinear systems. Int. J. Adapt. Control Signal Process. 21(7), 582–602 (2007)

    Article  MathSciNet  Google Scholar 

  13. Fan, B., Fu, Z., Sun, L.: Passive-based adaptive control with the full-order observer for induction motor without speed sensor. Nonlinear Dyn. 104(1), 483–495 (2021)

    Article  Google Scholar 

  14. Travieso-Torres, J.C., Contreras-Jara, C., Diaz, M., Aguila-Camacho, N., Duarte-Mermoud, M.A.: New adaptive starting scalar control scheme for induction motor variable speed drives. IEEE Trans. Energy Convers. 37(1), 729–736 (2021)

    Article  Google Scholar 

  15. Hassan, M.A., Li, E.-P., Li, X., Li, T., Duan, C., Chi, S.: Adaptive passivity-based control of DC–DC buck power converter with constant power load in DC microgrid systems. IEEE J. Emerg. Sel. Top. Power Electron. 7(3), 2029–2040 (2018)

    Article  Google Scholar 

  16. Soriano-Rangel, C., He, W., Mancilla-David, F., Ortega, R.: Voltage regulation in buck–boost converters feeding an unknown constant power load: an adaptive passivity-based control. IEEE Trans. Control Syst. Technol. 29(1), 395–402 (2021)

    Article  Google Scholar 

  17. Hassan, M.A., Su, C.L., Chen, F.Z., Lo, K.Y.: Adaptive passivity-based control of a DC–DC boost power converter supplying constant power and constant voltage loads. IEEE Trans. Ind. Electron. 69(6), 6204–6214 (2021)

    Article  Google Scholar 

  18. Keymasikhalaji, A., Haghjoo, M.: Adaptive passivity-based control of an autonomous underwater vehicle. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 236(20), 10563–10572 (2022)

    Article  Google Scholar 

  19. Zhao, J., Wang, X., Liang, Z., Li, W., Wang, X., Wong, P.: Adaptive event-based robust passive fault tolerant control for nonlinear lateral stability of autonomous electric vehicles with asynchronous constraints. ISA Trans. 127, 310–323 (2022)

    Article  Google Scholar 

  20. Mohammed, S., Alsofyani, I., Lee, K.B.: Improved adaptive CCS-MPCC for distorted model parameters mitigation of IPMSM drives. IEEE Trans. Ind. Electron. 71(4), 3483–3493 (2023)

    Article  Google Scholar 

  21. Hollweg, G., Evald, P., Mattos, E., Borin, L.: A direct adaptive controller with harmonic compensation for grid-connected converters. IEEE Trans. Ind. Electron. 71(3), 2978–2989 (2023)

    Article  Google Scholar 

  22. Isidori, A.: Nonlinear Control Systems: An Introduction. Springer, Berlin (1995)

    Book  Google Scholar 

  23. Travieso-Torres, J.C., Duarte-Mermoud, M.A., Beytia-Cancino, O.: Taylor polynomial approximation and adaptive passivity-based control applied to the level regulation of a conical tank. Asian J Control 19(5), 1722–1730 (2017)

    Article  MathSciNet  Google Scholar 

  24. Thomas, G.B., Weir, M.D., Hass, J., Giordano, F.R.: Thomas' calculus (2005)

  25. Nussbaum, R.: Some remarks on a conjecture in parameter adaptive-control. Syst. Control Lett. 3(5), 243–246 (1983)

    Article  MathSciNet  Google Scholar 

  26. Zheng, X., Yu, X., Jiang, J., Yang, X.: Time command filtered backstepping with its application to DC motor control systems. IEEE Trans. Ind. Electron. 71(3), 2955–2964 (2023)

    Article  Google Scholar 

  27. Zhang, J., Mu, X., Liu, Y.: Global adaptive regulation of stochastic high-order systems with unknown control direction. J. Franklin Inst. Eng. 354(15), 6630–6650 (2017)

    Article  MathSciNet  Google Scholar 

  28. Liu, Z., Huang, J., Wen, C., Su, X.: Distributed control of nonlinear systems with unknown time-varying control coefficients: a novel Nussbaum function approac. IEEE Trans. Autom. Control 68(7), 4191–4203 (2022)

    Google Scholar 

  29. Heinbockel, J.H.: Introduction to Finite and Infinite Series and Related Topics. Trafford Publishing, New York (2010)

    Google Scholar 

  30. Travieso-Torres, J.C., Contreras, C., Hernandez, F., Duarte-Mermoud, M.A., Aguila-Camacho, N., Orchard, M.E.: Adaptive passivity-based control extended for unknown control direction. ISA Trans. 122, 398–408 (2022)

    Article  Google Scholar 

  31. Narendra, K., Annaswamy, A.: A new adaptive law for robust adaptation without persistent excitation. IEEE Trans. Autom. Control 32(2), 134–145 (1987)

    Article  MathSciNet  Google Scholar 

  32. Narendra, K.S., Annaswamy, A.M.: Stable Adaptive Systems. Courier Corporation, New York (2012)

    Google Scholar 

  33. Prasad, G.M., Kedia, V., Rao, A.S.: Multi-model predictive control (MMPC) for non-linear systems with time delay: an experimental investigation. In: 2020 First IEEE International Conference on Measurement, Instrumentation, Control and Automation (ICMICA), Kurukshetra, India, pp. 1–5 (2020)

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Acknowledgements

The National Research and Development Agency supported This work through the research grant FONDEF ID17I20338. Also, by the University of Santiago of Chile via the research grant 2022 of the Industrial Technologies Department and the research grant 2022 of the Technological Faculty.

Funding

Author Abdiel Ricaldi-Morales has received support from the research grant 2022 of the Industrial Technologies Department, USACH. Author Adolfo Veliz-Tejo has received support from the research grant 2022 of the Technological Faculty, USACH. Authors Juan Carlos Travieso-Torres and Felipe Leiva-Silva have received support from the research grant FONDEF ID17I20338, ANID.

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Authors and Affiliations

  1. Department of Industrial Technologies, Universidad de Santiago de Chile, El Belloto 3735, 9170125, Estación Central, Santiago, Chile

    Abdiel Ricaldi-Morales & Juan Carlos Travieso-Torres

  2. Department of Electrical Engineering, Universidad Técnica Federico Santa María, Vicuña Mackenna 3939, 8940572, San Joaquín, Santiago, Chile

    Adolfo Véliz-Tejo & Felipe Leiva-Silva

Authors
  1. Abdiel Ricaldi-Morales
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  2. Juan Carlos Travieso-Torres
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  3. Adolfo Véliz-Tejo
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  4. Felipe Leiva-Silva
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Contributions

Unknown control direction theoretical analysis and experimental validation was developed by Abdiel Ricaldi-Morales. Material preparation, data collection and analysis were performed by Adolfo Veliz-Tejo and Felipe Leiva-Silva. The study conception, design, and first draft of the manuscript was written by Juan Carlos Travieso-Torres and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Juan Carlos Travieso-Torres.

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Ricaldi-Morales, A., Travieso-Torres, J.C., Véliz-Tejo, A. et al. Taylor series and adaptive passivity-based control for conical tanks level regulation. Nonlinear Dyn 112, 10081–10093 (2024). https://doi.org/10.1007/s11071-024-09596-7

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