Skip to main content

A Multi-model Based Centralized MPC on the Quadruple-tank with Guaranteed Stability

  • Conference paper
  • First Online:
Informatics in Control, Automation and Robotics (ICINCO 2020)

Abstract

Applying a stabilizing model predictive control to a non-linear system is presented in this work. For this purpose, the quadruple-tank system has been considered for which a precise control benchmark was available and worked on previously. We could design a multi-model for the mentioned benchmark and to ensure the asymptotic stability of this non-linear system, we made a discretized linearized model and applied a centralized MPC controller with terminal cost constraint. Simulations depict the efficiency of the presented strategy.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alvarado, I., et al.: A comparative analysis of distributed MPC techniques applied to the HD-MPC four-tank benchmark. J. Process Control 5, 800–815 (2011)

    Article  Google Scholar 

  2. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  3. Cueli, J.R., Bordons, C.: Iterative nonlinear model predictive control. stability, robustness and applications. Control Eng. Pract. 16(9), 1023–1034 (2008). https://doi.org/10.1016/j.conengprac.2007.11.003. http://www.sciencedirect.com/science/article/pii/S0967066107001918

  4. Dua, P., Doyle, F.J., Pistikopoulos, E.N.: Model-based blood glucose control for type 1 diabetes via parametric programming. IEEE Trans. Bio-medical Eng. 53, 1478–1491 (2006)

    Article  Google Scholar 

  5. Garegnani, G., Rosatti, G., Bonaventura, L.: Free surface flows over mobile bed: mathematical analysis and numerical modeling of coupled and decoupled approaches. Commun. Appl. Ind. Math. 2(1) (2011)

    Google Scholar 

  6. Herrera, M., Pérez-Hernández, M., Kumar Parlikad, A., Izquierdo, J.: Multi-agent systems and complex networks: review and applications in systems engineering. Processes 8(3), 312 (2020)

    Article  Google Scholar 

  7. Huang, Y., Wang, H., Khajepour, A., He, H., Ji, J.: Model predictive control power management strategies for HEVs: a review. J. Power Sources 341, 91–106 (2017)

    Article  Google Scholar 

  8. Johansen, T.A., Murray-Smith, R.: The operating regime approach to nonlinear modelling and control. Multiple Model Approaches Model. Control 1, 3–72 (1997)

    Google Scholar 

  9. Johansson, K.H.: The quadruple-tank process: a multivariable laboratory process with an adjustable zero. IEEE Trans. Control Syst. Technol. 8, 456–465 (2000)

    Article  Google Scholar 

  10. Kalman, R.E., et al.: Contributions to the theory of optimal control. Bol. soc. mat. mexicana 5(2), 102–119 (1960)

    MathSciNet  Google Scholar 

  11. Maiworm, M., Bäthge, T., Findeisen, R.: Scenario-based model predictive control: recursive feasibility and stability. IFAC-PapersOnLine 48(8), 50–56 (2015)

    Article  Google Scholar 

  12. Pannocchia, G.: Course on model predictive control. Bio-engineering Rob. Res. Center 1–33 (2012)

    Google Scholar 

  13. Qin, S.J., Badgwell, T.A.: A survey of industrial model predictive control technology. Control Eng. Pract. 11(7), 733–764 (2003)

    Article  Google Scholar 

  14. Ranjbar, R., Etienne, L., Duviella, E., Maestre, J.M.: Implementation of centralized MPC on the quadruple-tank process with guaranteeing stability. In: Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics, ICINCO, vol. 1, pp. 56–62. INSTICC, SciTePress (2020). https://doi.org/10.5220/0009827700560062

  15. Rawlings, J.B., Mayne, D.Q.: Model Predictive Control: Theory and Design. Nob Hill Publication, Madison (2009)

    Google Scholar 

  16. Richter, S., Jones, C.N., Morari, M.: Real-time input-constrained MPC using fast gradient methods. In: Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, pp. 7387–7393. IEEE (2009)

    Google Scholar 

  17. Scokaert, P.O., Rawlings, J.B.: Constrained linear quadratic regulation. IEEE Trans. Autom. Control 43(8), 1163–1169 (1998)

    Article  MathSciNet  Google Scholar 

  18. Jeong, S.C.: PooGyeon park: constrained MPC algorithm for uncertain time-varying systems with state-delay. IEEE Trans. Autom. Control 50(2), 257–263 (2005). https://doi.org/10.1109/TAC.2004.841920

    Article  Google Scholar 

  19. Van Breemen, A.: Agent-based multi-controller systems-a design framework for complex control problems (2001)

    Google Scholar 

  20. Velázquez, J., Anctil, F., Perrin, C.: Performance and reliability of multimodel hydrological ensemble simulations based on seventeen lumped models and a thousand catchments. Hydrol. Earth Syst. Sci. 14(11), 2303 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Roza Ranjbar .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ranjbar, R., Etienne, L., Duviella, E., Maestre, J.M. (2022). A Multi-model Based Centralized MPC on the Quadruple-tank with Guaranteed Stability. In: Gusikhin, O., Madani, K., Zaytoon, J. (eds) Informatics in Control, Automation and Robotics. ICINCO 2020. Lecture Notes in Electrical Engineering, vol 793. Springer, Cham. https://doi.org/10.1007/978-3-030-92442-3_5

Download citation

Publish with us

Policies and ethics