Skip to main content
SpringerLink
Log in

Motion Control for Platforms Bearing Elastic Links with Unknown Phase States

  • CONTROL IN DETERMINISTIC SYSTEMS
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

Abstract

We consider the problem on the controlled motion of a platform such that a solid body bearing a dissipative oscillator is attached to it by means of a spring. The platform moves along a horizontal line under the action of the control force, undergoing the action of a bounded uncontrolled perturbation, e.g., the dry friction force, as well. It is assumed that the phase state of the oscillator is not accessible for measurement. We propose a control law leading the whole system to the prescribed rest state within a finite time period.

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

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Similar content being viewed by others

REFERENCES

  1. L. D. Akulenko, N. N. Bolotnik, A. E. Borisov, A. A. Gavrikov, and G. A. Emel’yanov, “Control of the apparent acceleration of a rigid body attached to a movable base by means of a two-degree-of-freedom gimbal,” J. Comput. Syst. Sci. Int. 51, 339 (2012).

    Article  MathSciNet  Google Scholar 

  2. I. M. Anan’evskii, “Control of a rigid body carrying an oscillator with incomplete information,” Dokl. Akad. Nauk 482, 23–27 (2018).

    Google Scholar 

  3. I. M. Anan’evskii and T. A. Ishkhanyan, “Control of a rigid body carrying dissipative oscillators under perturbations,” J. Comput. Syst. Sci. Int. 58, 40 (2019).

    Article  Google Scholar 

  4. A. Ovseevich, “A local feedback control bringing a linear system to equilibrium,” J. Optim. Theory Appl. 165, 532–544 (2015).

    Article  MathSciNet  Google Scholar 

  5. R. E. Kalman, P. L. Falb, and M. A. Arbib, Topics in Mathematical System Theory (McGraw-Hill, New York, 1969).

    MATH  Google Scholar 

  6. N. N. Krasovskii, Motion Control Theory (Nauka, Moscow, 1968) [in Russian].

    Google Scholar 

  7. E. D. Sontag, Mathematical Control Theory: Deterministic Finite-Dimensional Systems (Springer, New York, 1998).

    Book  Google Scholar 

  8. P. A. Brunovsky, “A classification of linear controllable systems,” Kybernetika 6, 173–188 (1970).

    MathSciNet  MATH  Google Scholar 

Download references

Funding

This work was supported by the Russian Foundation for Basic Research, project no. 17-01-00538 and is performed as part of the state-guaranteed order АААА-А17-117021310387-0.

Author information

Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia

    I. M. Anan’evskii

Authors
  1. I. M. Anan’evskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. M. Anan’evskii.

Additional information

Translated by A. Muravnik

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Anan’evskii, I.M. Motion Control for Platforms Bearing Elastic Links with Unknown Phase States. J. Comput. Syst. Sci. Int. 58, 844–851 (2019). https://doi.org/10.1134/S1064230719060030

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064230719060030

Search

Navigation