Skip to main content
Log in

Optimal control of nonlinear objects of engineering thermophysics

  • Automation Systems in Scientific Research and Industry
  • Published:
Optoelectronics, Instrumentation and Data Processing Aims and scope

Abstract

The piecewise continuous (relay) nature of lumped control actions in problems of timeand energy-optimal control of a wide range of distributed-parameter nonlinear objects of engineering thermophysics is established. On this basis, the required programmed controls in a number of practical situations can be found by the proposed algorithmically precise (alternance) method. As an example, which is of independent interest, the problem of optimal control of nonlinear models of induction heating of metal semi-products before subsequent pressure treatment is considered.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. Ya. Rapoport, Alternance Method in Applied Optimization Problems (Nauka, Moscow, 2000) [in Russian].

    MATH  Google Scholar 

  2. E. Ya. Rapoport, Optimal Control of Distributed-Parameter Systems (Vysshaya Shkola, Moscow, 2009) [in Russian].

    Google Scholar 

  3. Yu. E. Pleshivtseva, and E. Ya. Rapoport, “Consistent Parameterization of Control Actions in Boundary-Value Optimal Control Problems for Distributed-Parameter Systems,” Izv. Ros. Akad. Nauk. Ser. Teor. Sistemy Upravleniya, No. 3, 22–33 (2009).

  4. E. Ya. Rapoport and Yu. E. Pleshivtseva, “Algorithmically Precise Method of Parametric Optimization in Boundary-Value Optimal Control Problems for Distributed-Parameter Systems,” Avtometriya, 45(5), 103–112 (2009) [Optoelectr., Instrum. Data Process. 45 (5), 464–471 (2009)].

    Google Scholar 

  5. E. Ya. Rapoport, Optimization of Induction Heating of Metal (Metallurgiya, Moscow, 1993) [in Russian].

    Google Scholar 

  6. E. Rapoport and Yu. Pleshivtseva, Optimal Control of Induction Heating Processes (CRC Press, Taylor and Francis Group, Boca Raton, London-New York, 2007).

    Google Scholar 

  7. A. G. Butkovskii, Theory of Optimal Control of Distributed-Parameter Systems (Nauka, Moscow, 1965) [in Russian].

    Google Scholar 

  8. A. G. Butkovskii, S. A. Malyi, and Yu. N. Andreev, Metal Heating Control (Metallurgiya, Moscow, 1981) [in Russian].

    Google Scholar 

  9. W. H. Ray, Advanced Process Control (McGraw-Hill, 1983).

  10. A. A. Samarskii, The Theory of Difference Schemes (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  11. G. M. Fikhtengol’ts, A Course in Differential and Integral Calculus (Fizmatgiz, Vol. 1, 1962).

  12. A. V. Lykov, Heat and Mass Transfer (Energiya, Moscow, 1972) [in Russian].

    Google Scholar 

  13. E. Ya. Rapoport, Structural Modeling of Objects and Control Systems with Distributed Parameters (Vysshaya. Shkola, 2003) [in Russian].

  14. O. Yu. Sharapova, “Numerical Modeling of the Periodic Induction Heating Based on the FLUX Finite-Element Software Package,” Vestn. Samar. Gos. Tekh. Univers. Ser. Tekhnicheskie Nauki, No. 7, 180–185 (2010).

  15. O. Yu. Sharapova, “Optimal Control of Multidimensional Models of Periodic Processes of Induction Heating,” Nauchnye Vedomosti S. Peterburgskogo Gos. Politekhn. Univ. Ser. Informatika, Telekommun., Upravlenie, No. 5, 31–35 (2011).

  16. Yu. E. Pleshivtseva and O. Yu. Sharapova, “Energy-Efficient Algorithms for Optimal Control of Induction Heating Processes,” Vestn. Samar. Gos. Tekh. Univers. Ser. Tekh. Nauki, No. 4(32), 171–180 (2011).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. Ya. Rapoport.

Additional information

Original Russian Text © E.Ya. Rapoport, Yu.E. Pleshivtseva, 2012, published in Avtometriya, 2012, Vol. 48, No. 5, pp. 3–13.

About this article

Cite this article

Rapoport, E.Y., Pleshivtseva, Y.E. Optimal control of nonlinear objects of engineering thermophysics. Optoelectron.Instrument.Proc. 48, 429–437 (2012). https://doi.org/10.3103/S8756699012050019

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S8756699012050019

Keywords

Navigation