Skip to main content
SpringerLink
Log in

Control Synthesis for Temperature Maintaining Process in a Heat Supply Problem

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The paper studies the solution to an optimal control problem for the process of circulating coolant heating in the heat supply system. The amount of heat supplied for coolant heating in the steam furnace is defined by a linear dependence on the temperature measured in the sensing points. The problem involves optimization of linear feedback parameters, locations and number of sensing points. Formulas have been obtained for gradient of the functional being optimized, which are used in first-order optimization methods. The results of numerical experiments are presented.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W. H. Ray, Advanced Process Control, McGraw-Hill, New York (1981).

    Google Scholar 

  2. A. G. Butkovskii, Methods of Control of Distributed Parameter Systems [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  3. B. T. Polyak and P. S. Shcherbakov, Robust Stability and Control [in Russian], Nauka, Moscow (2002).

    Google Scholar 

  4. K. R. Aida-zade and V. A. Hashimov, “Optimizing the arrangement of lumped sources and measurement points of plate heating,” Cybern. Syst. Analysis, Vol. 55, No. 4, 605–615 (2019).

    Article  Google Scholar 

  5. S. Z. Guliyev, “Synthesis of zonal controls for a problem of heating with delay under nonseparated boundary conditions,” Cybern. Syst. Analysis, Vol. 54, No. 1, 110–121 (2018).

    Article  Google Scholar 

  6. H. Shang, J. F. Forbes, and M. Guay, “Feedback control of hyperbolic PDE systems,” in: IFAC Proceedings Volumes, Vol. 33, Iss. 10 (2000), pp. 533–538.

    Article  Google Scholar 

  7. J. M. Coron and Zh. Wang, “Output feedback stabilization for a scalar conservation law with a nonlocal velocity,” SIAM J. Math. Anal., Vol. 45, No. 5, 2646–2665 (2013).

    Article  MathSciNet  Google Scholar 

  8. L. Afifi, K. Lasri, M. Joundi, and N. Amimi, “Feedback controls for exact remediability in disturbed dynamical systems,” IMA J. of Mathematical Control and Information, Vol. 35, Iss. 2, 411–425 (2018).

  9. W. Mitkowski, W. Bauer, and M. Zagórowska, “Discrete-time feedback stabilization,” Archives of Control Sciences, Vol. 27, No. 2, 309–322 (2017).

    Article  MathSciNet  Google Scholar 

  10. I. V. Sergienko and V. S. Deineka, Optimal Control of Distributed Systems with Conjugation Conditions, Kluwer Acad. Publ., New York (2005).

    MATH  Google Scholar 

  11. K. R. Aida-zade and V. M. Abdullaev, “On an approach to designing control of the distributed-parameter processes,” Autom. Remote Control, Vol. 73, No. 9, 1443–1455 (2012).

    Article  MathSciNet  Google Scholar 

  12. K. R. Aida-zade and V. M. Abdullaev, “Optimizing placement of the control points at synthesis of the heating process control,” Autom. Remote Control, Vol. 78, No. 9, 1585–1599 (2017).

    Article  MathSciNet  Google Scholar 

  13. J. L. Lions, Controle Optimal des Systèmes Gouvernés par des Équations aux Derivés Partielles [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  14. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  15. M. T. Dzhenaliev, “Optimal control of linear loaded parabolic equations,” Differential Equations, Vol. 25, No. 4, 437–445 (1989).

    MathSciNet  MATH  Google Scholar 

  16. A. M. Nakhushev, Loaded Equations and Their Application [in Russian], Nauka, Moscow (2012).

    Google Scholar 

  17. A. A. Alikhanov, A. M. Berezgov, and M. Kh. Shkhanukov-Lafishev, “Boundary value problems for certain classes of loaded differential equations and solving them by finite difference methods,” Comput. Math. Math. Phys., Vol. 48, No. 9, 1581–1590 (2008).

    Article  MathSciNet  Google Scholar 

  18. K. R. Aida-zade, “An approach for solving nonlinearly loaded problems for linear ordinary differential equations,” Proc. of the Institute of Mathematics and Mechanics, Vol. 44, No. 2, 338–350 (2018).

    MathSciNet  MATH  Google Scholar 

  19. V. M. Abdullayev, “Numerical solution to optimal control problems with multipoint and integral conditions,” Proc. of the Institute of Mathematics and Mechanics, Vol. 44, No. 2, 171–186 (2018).

    MathSciNet  MATH  Google Scholar 

  20. V. M. Abdullayev, “Identification of the functions of response to loading for stationary systems,” Cybern. Syst. Analysis, Vol. 53, No. 3, 417–425 (2017).

    Article  Google Scholar 

  21. F. P. Vasil’ev, Optimization Methods [in Russian], Faktorial Press, Moscow (2002).

    Google Scholar 

  22. V. M. Abdullayev and K. R. Aida-zade, “Optimization of loading places and load response functions for stationary systems,” Comput. Math. Math. Phys., Vol. 57, No. 4, 634–644 (2017).

    Article  MathSciNet  Google Scholar 

  23. V. M. Abdullayev and K. R Aida-zade, “Finite-difference methods for solving loaded parabolic equation,” Comput. Math. Math. Phys., Vol. 56, No. 1, 93–105 (2016).

    Article  MathSciNet  Google Scholar 

  24. L. E. Elsgolts and S. B. Norkin, Introduction to the Theory and Application of Differential Equations with Deviating Arguments [in Russian], Nauka, Moscow (1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Control Systems, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan

    K. R. Aida-zade

  2. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan

    K. R. Aida-zade

  3. Azerbaijan State Oil and Industry University and Institute of Control Systems, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan

    V. M. Abdullayev

Authors
  1. K. R. Aida-zade
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. M. Abdullayev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to K. R. Aida-zade or V. M. Abdullayev.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2020, pp. 47–59.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aida-zade, K.R., Abdullayev, V.M. Control Synthesis for Temperature Maintaining Process in a Heat Supply Problem. Cybern Syst Anal 56, 380–391 (2020). https://doi.org/10.1007/s10559-020-00254-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-020-00254-5

Keywords

Search

Navigation