Skip to main content

Advertisement

Log in

Stability conditions for a heat transfer object control system with Schipanov controller under imperfections in the controller

  • Nonlinear Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We study stability conditions for a control system over a linear one-side bounded heat transfer object with the so-called “Schipanov controller”; this controller under perfect implementation must ensure invariant behavior of the object’s output related to the input influence. We study the behavior of the output of a closed system under such possible imperfections in controller implementation as pure delay and inertia; we find classes of influences with respect to which one can ensure stability of the closed system, and find estimates of its output’s response levels to influences from these classes.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Schipanov, G.V., Theory, Computation, and Design Methods for Automated Controllers, in G.V. Schipanov i teoriya invariantnosti (G.V. Schipanov and Invariance Theory), Moscow: Fizmatlit, 2004, pp. 20–140.

    Google Scholar 

  2. Schipanov, G.V., Theory and Design Methods for Automated Controllers, in G.V. Schipanov i teoriya invariantnosti (G.V. Schipanov and Invariance Theory), Moscow: Fizmatlit, 2004, pp. 141–164.

    Google Scholar 

  3. Petrov, B.N., Izbrannye trudy (Selected Works), vol. 1, Teoriya avtomaticheskogo upravleniya (Automated Control Theory), Moscow: Nauka, 1983.

    Google Scholar 

  4. Solnechnyi, E.M, Vyrozhdennye sistemy i ikh ispol’zovanie v zadache sinteza zadannogo povedeniya (Degenerate Systems and Their Use in the Behavior Synthesis Problem), Moscow: Nauka, 1989.

    Google Scholar 

  5. Gaiduk, A.R., Teoriya i metody analiticheskogo sinteza sistem avtomaticheskogo upravleniya (polinomial’nyi podkhod) (Theory and Methods of Analytical Synthesis for Automated Control Systems: Polynomial Approach), Moscow: Fizmatlit, 2012.

    Google Scholar 

  6. Solnechnyi, E.M., Using G.V. Shchipanov’s Ideas to Provide Perturbation-Invariance of the Output of a Distributed Linear Plant, Autom. Remote Control, 2014, vol. 75, no. 1, pp. 75–86.

    Article  MathSciNet  MATH  Google Scholar 

  7. Lavrent’ev, M.A. and Shabat, B.V., Metody teorii funktsii kompleksnogo peremennogo (Methods of the Theory of Functions of Complex Variable), Moscow: Fizmatgiz, 1958.

    MATH  Google Scholar 

  8. Vladimirov, V.S., Obobshchennye funktsii v matematicheskoi fizike (Generalized Functions in Mathematical Physics), Moscow: Nauka, 1976.

    Google Scholar 

  9. Solnechnyi, E.M. and Cheremushkina, L.A., On Stability Conditions of a Control System for a Linear Heat Transfer Object Bounded from One Side, Autom. Remote Control, 2011, vol. 72, no. 4, pp. 684–698.

    Article  MathSciNet  MATH  Google Scholar 

  10. Bronstein, I.N. and Semendyaev, K.A., Spravochnik po matematike dlya inzhenerov i uchashchikhsya vtuzov (Handbook of Mathematics for Engineers and Technical Students), Leipzig: Toibner, Moscow: Nauka, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. M. Solnechnyi.

Additional information

Original Russian Text © E.M. Solnechnyi, 2016, published in Avtomatika i Telemekhanika, 2016, No. 12, pp. 70–88.

This paper was recommended for publication by L.B. Rapoport, a member of the Editorial Board

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Solnechnyi, E.M. Stability conditions for a heat transfer object control system with Schipanov controller under imperfections in the controller. Autom Remote Control 77, 2159–2174 (2016). https://doi.org/10.1134/S0005117916120067

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117916120067

Navigation