Skip to main content
SpringerLink
Log in

Design of Controllers by Indices of Precision and Speed. III. Control-Stable Multidimensional Plants

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

Abstract

A method to design controllers satisfying the requirements on precision and speed of each controlled variable was proposed. Additionally, a way was indicated to attain the given radius of stability margins simultaneously for physical input and output of the control plant at opening the closed-loop system by individual loops. Solution of the problem relied on the diagonal dominance of the transfer matrix of the closed-loop system—from external perturbation to the controlled variable—provided by the controller.

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. Voznesenskii, I.N., On Control of Machines with Multiple Controllable Parameters, Avtom. Telemekh., 1938, no. 4–5, pp. 65–78.

    Google Scholar 

  2. Boksenbam, A.S. and Hood, R., General Algebraic Method Applied to Control Analysis of Complex Engine Types, NACA. Tech. Rept., 1950.

    Google Scholar 

  3. Meerov, M.V., Sistemy mnogosvyaznogo regulirovaniya (Systems of Multiply Connected Control), Moscow: Nauka, 1965.

    Google Scholar 

  4. Morozovskii, V.T., Mnogosvyaznye sistemy avtomaticheskogo regulirovaniya (Multiply Connnected Systems of Automatic Control), Moscow: Energiya, 1970.

    Google Scholar 

  5. Wolovich, W.A., Linear Multivariable System, New York: Springer, 1974.

    Book  MATH  Google Scholar 

  6. Rosenbrock, H.H., Computer-Aided Control System Design, London: Academic, 1974.

    MATH  Google Scholar 

  7. Bennet, W.H. and Baras, J.S., Decomposition and Decentralized System Design: A Review of Frequency Domain Methods, 24th IEEE Decision and Control Conf., 1985, pp. 1828–1835.

    Google Scholar 

  8. Wang, Q.-G., Decoupling Control, Berlin: Springer, 2003.

    MATH  Google Scholar 

  9. Aleksandrov, A.G., Metody postroeniya sistem avtomaticheskogo upravleniya (Methods of Designing Automatic Control Systems), Moscow: Fizmatlit, 2008.

    Google Scholar 

  10. Aleksandrov, A.G., On Analytical Design of Controllers, Autom. Remote Control, 2010, vol. 71, no. 6, pp. 977–992.

    Article  MathSciNet  MATH  Google Scholar 

  11. Agafonov, P.A. and Chestnov, V.N., H ∞-Control for Guaranteed Simultaneous Input and Output Stability Margins for a Multivariate System, Autom. Remote Control, 2004, vol. 65, no. 9, pp. 1452–1460.

    Article  MathSciNet  MATH  Google Scholar 

  12. Chestnov, V.N., Synthesizing H ∞-Controllers for Multidimensional Systems with Given Accuracy and Degree of Stability, Autom. Remote Control, 2011, vol. 72, no. 10, pp. 2161–2175.

    Article  MathSciNet  MATH  Google Scholar 

  13. Chestnov, V.N. and Zatsepilova, Zh.V., Design of Controllers of Multidimensional Systems by Engineering Indices of Preceision, Time of Control, and Margins of Stability, in Int. Conf. “Problems of Information Control, Transmission and Processing” (ATM-TKI-50)”, Saratov: SGTU, 2009, pp. 41–45.

    Google Scholar 

  14. Chestnov, V.N., Design of Multidimensional Systems of Desired Precision, Time of Control, and Radius of Margins of Stability, Differ. Uravn., 2014, vol. 50, no. 8, pp. 1138–1142.

    Google Scholar 

  15. Aleksandrov, A.G., Controller Design in Precision and Speed. I. Minimal Phase Onedimensional Plants, Autom. Remote Control, 2015, vol. 76, no. 5, pp. 749–761.

    Article  MathSciNet  MATH  Google Scholar 

  16. Aleksandrov, A.G., Design of Controllers by Indices of Precision and Speed. II. Nonminimal-Phase Plants, Autom. Remote Control, 2017, vol. 78, no. 6, pp. 961–973.

    Article  MathSciNet  MATH  Google Scholar 

  17. Aleksandrov, A.G., Chastotnaya teoriya avtomaticheskogo upravleniya (chastotnoe upravlenie) (Frequency Theory of Automatic Control (Frequency Control)), Elektrostal: EPI MISiS, 2010, Books 1 and 2.

    Google Scholar 

  18. Gantmakher, F.R., Teoriya matrits, Moscow: Nauka, 1988. Translated under the title The Theory of Matrices, New York: Chelsea, 1959.

    MATH  Google Scholar 

  19. Kurosh, A.G., Kurs vysshei algebry (Course of Higher Algebra), Moscow: Fizmatgiz, 1963.

    Google Scholar 

  20. Aleksandrov, A.G., Plotnikov, P.K., and Chelnokov, Yu.N., Design of Controllers of Two-component Gauge of Angular Velocity Based on Three-stage Gyro, Izv. Akad. Nauk SSSR, Mekh. Tverdogo Tela, 1974, no. 4, pp. 30–38.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    A. G. Aleksandrov

Authors
  1. A. G. Aleksandrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.G. Aleksandrov, 2018, published in Avtomatika i Telemekhanika, 2018, No. 2, pp. 51–70.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aleksandrov, A.G. Design of Controllers by Indices of Precision and Speed. III. Control-Stable Multidimensional Plants. Autom Remote Control 79, 241–257 (2018). https://doi.org/10.1134/S0005117918020042

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117918020042

Keywords

Search

Navigation