Skip to main content
SpringerLink
Log in

Synthesis of Control Systems with Delay by the Embedding Theory on the Basis of Approximation of Delay

  • Published:
Journal of Control, Automation and Electrical Systems Aims and scope Submit manuscript

Abstract

The paper deals with the synthesis of control systems with deviating argument based on the embedding theory. It goes about the possibility of using of different types of expansions for the approximation of the pure delay units. In the paper, we show how to use algorithms for synthesis of control systems based on the desired dimension of the desired rate of overshoot and normalized transient time.

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

  • Asmykovich, I.K. (1999). Deat-beat control for discrete descriptor systems with delay Abstracts. In The third Russian–Korean international symposium on science and technology “KORUS’99 / Novosibirsk, (Vol. 1, p. 218).

  • Bukov, V. N. (2006). Embedding systems. In N. F. Botchkareva (Ed.), Analytic approach to the analysis and synthesis matrix systems. Kaluga: Publishing research of literature.

    Google Scholar 

  • Campbell, S. L., & Linh, Vu Hoang. (2009). Stability criteria for differential-algebraic equations with multiple delays and their numerical solutions. Applied Mathematics and Computation, 208, 397–415.

    Article  MathSciNet  MATH  Google Scholar 

  • Fridman, E. (2002). Stability of linear descriptor systems with delay: A Lyapunov-based approach. Journal of Mathematical Analysis and Applications, 273(1), 24–44.

    Article  MathSciNet  MATH  Google Scholar 

  • Gorecki, H. (1974). Analysis and synthesis of control systems with delay; per. with the floor. M: Engineering (p. 328) (in Russian).

  • Kuzmitsky, I. F., & Kulakov, G. T. (2010). Automatic control theory (p. 574). Minsk: Belarusian State Technological University (in Russian).

  • Lapeto, A.V. (2011). Analysis of methods of synthesis of automatic control systems with delay. In Proceedings BSTU, science and informatics (No. 6, pp. 78–80) (in Russian).

  • Ma, S., Cheng, Z., & Zhang, C. (2007). Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays. In IEEE Proceedings on control theory and applications (No. 1, pp. 1086–1095).

  • Marchenko, V. M., & Asmykovich, I. K. (2011). Representation of solutions of a handle-systems with delay. In Proceedings BSTU, Science and informatics (Vol. 6, No. 144, pp. 3–6) (in Russian).

  • Marchenko, V. M., Poddubnaya, O. N., & Zaczkiewicz, Z. (2006). On the observability of linear differential-algebraic systems with delays. IEEE Transactions on Automatic Control, 51(8), 1387–1392.

    Article  MathSciNet  Google Scholar 

  • Mishra, V. K., Tomar, N. K., & Gupta, M. K. (2016). On controllability and normalizability for linear descriptor systems. Journal of Control, Automation and Electrical Systems, 27(1), 19–28.

    Article  Google Scholar 

  • Vostrikov, A. (2010). The problem of synthesis of controllers for automation systems: State and prospects. Auto-meters, 12(46), 3–19. (in Russian).

    Google Scholar 

  • Wang, C.-J., & Liao, H.-E. (2001). Impulse observability and impulse controllability of linear time-varying singular systems. Automatica, 37(11), 1867–1872.

    Article  MATH  Google Scholar 

  • Wang, H., Liu, J., Yang, F., & Cai, T. (2015). Proportional-derivative controllers for stabilisation of first-order processes with time delay. International Journal of Systems Science, 46(6), 1065–1079.

    Article  MathSciNet  MATH  Google Scholar 

  • Yanusheuski, R. T. (1978). Facility management with delay. Moscow: Nauka, M (in Russian).

  • Yurkevich, V. D. (2015). MIMO tracking PI/PID controller design for nonlinear systems based on singular perturbation technique. IFAC-Papers, 48(22). In Proceedings of 1st IFAC conference on modelling, identification and control of nonlinear (MICNON 2015) (pp. 760–765).

  • Yurkevich, V. D. (2016). Multi-channel control system design for a robot manipulator based on the time-scale method. Optoelectronics, Instrumentation and Data Processing, 52(2), 196–202.

    Article  Google Scholar 

  • Zhong, R., & Yang, Z. (2006). Delay-dependent robust control of descriptor systems with time delay. Asian Journal of Control, 8(1), 36–44.

    Article  MathSciNet  Google Scholar 

  • Zhu, S., Zhang, C., Cheng, Z., & Feng, J. (2007). Delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems. IEEE Transactions on Automatic Control, 52, 880–885.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Belarussian State Technological University, Minsk, Belarus

    A. V. Lapeto, I. F. Kuzmicki & I. K. Asmykovich

Authors
  1. A. V. Lapeto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. F. Kuzmicki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. K. Asmykovich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Lapeto.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lapeto, A.V., Kuzmicki, I.F. & Asmykovich, I.K. Synthesis of Control Systems with Delay by the Embedding Theory on the Basis of Approximation of Delay. J Control Autom Electr Syst 28, 297–302 (2017). https://doi.org/10.1007/s40313-017-0306-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40313-017-0306-2

Keywords

Search

Navigation