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UDC 519.622
K.R. Aida-zade1, A.H. Bagirov2, V.A. Hashimov3


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

kamil_aydazade@rambler.ru

2 Institute of Control Systems, National Academy
of Sciences of Azerbaijan, Baku, Azerbaijan

arzu-bagirov@mail.ru

3 Institute of Control Systems, National Academy
of Sciences of Azerbaijan, Baku, Azerbaijan

vugarhashimov@gmail.com

FEEDBACK CONTROL OF THE POWER OF MOVING SOURCES
WHEN HEATING THE BAR

Abstract. The problem of synthesis of power control of the sources moving according to the given rules and trajectories when the rod is heated is considered. The current values of the controls are determined depending on the values of the temperature of the bar at the points of measurement. Formulas for the components of the gradient of the objective functional are obtained with respect to the feedback parameters and the coordinates of the measurement points, which are used to numerically solve the test problem using first-order numerical optimization methods. The results of computer experiments are presented.

Keywords: bar heating, feedback control, moving sources, temperature measuring points, feedback parameters.



FULL TEXT

REFERENCES

  1. Lions J.-L. Controle optimal de systemes gouvernes par des equations aux derivees partielles. Paris: Dunod Ganthier-Villars, 1969.

  2. Butkovsky A.G. Methods for controlling systems with distributed parameters [in Russian]. Moscow: Nauka, 1984. 568 p.

  3. Deineka V.S., Sergienko I.V. Optimal control of heterogeneous distributed systems [in Russian]. Kiev: Nauk. dumka, 2003. 506 p.

  4. Utkin V.I. Sliding modes in optimization and control problems [in Russian]. Moscow: Nauka, 1981. 368 p.

  5. Ray W.H. Advanced process control. McGraw-Hill Book Company, 1980. 376 p.

  6. Egorov A.I. Fundamentals of control theory [in Russian]. Moscow: Fizmatlit, 2004. 504 p.

  7. Butkovsky A.G., Pustylnikov L.M. The theory of mobile control of systems with distributed parameters [in Russian]. Moscow: Nauka, 1980. 384 p.

  8. Sirazetdinov T.K. Optimizing systems with distributed parameters [in Russian]. Moscow: Nauka, 1977. 420 p.

  9. Sergienko I.V., Deineka V.S. Optimal control of distributed systems with conjugation conditions. New York: Kluwer Acad. Publ., 2005. 383 p.

  10. Polyak B.T., Khlebnikov M.V., Rapoport L.B. Mathematical theory of automatic control [in Russian]. Moscow: LENAND, 2019. 504 p.

  11. Lions J.-L., Magenes E. ProblЩmes aux limites non homogЩnes at application. Vol. 1. Paris, 1968.

  12. Vasiliev F.P. Optimization methods [in Russian]. Moscow: Factorial Press, 2002. 824 p.

  13. Guliyev S.Z. Synthesis of zonal controls for a problem of heating with delay under nonseparated boundary conditions. Cybernetics and Systems Analysis. 2018. Vol. 54, N 1. P. 110–121.

  14. Aida-zade K.R., Abdullaev V.M. On an approach to designing control of the distributed-parameter processes. Automation and Remote Control. 2012. Vol. 73, N 9. P. 1443–1455.

  15. Nakhushev A.M. Loaded equations and their application [in Russian]. Moscow: Nauka, 2012. 232 p.

  16. Alikhanov A.A., Berezgov A.M., Shkhanukov-Lafishev M.X. Boundary value problems for certain classes of loaded differential equations and solving them by finite difference methods. Comp. Math. Math. Phys. 2008. Vol. 48, N 9. P. 1581–1590.

  17. Abdullaev V.M., Aida-zade K.R. Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations. Comp. Math. Math. Phys. 2014. Vol. 54, N 7. P. 1096–1109.

  18. Abdullayev V.M., Aida-zade K.R. Finite-difference methods for solving loaded parabolic equations. Comp. Math. Math. Phys. 2016. Vol. 56, N 1. P. 93–105.

  19. Aida-zade K.R., Bagirov A.G. On the problem of spacing of oil wells and control of their production rates. Automation and Remote Control. 2006. Vol. 67, N 1. P. 44–53.

  20. Samarskiy A.A. Difference scheme theory [in Russian]. Moscow: Nauka, 1989. 616 p.




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