Automation and Remote Control

, Volume 62, Issue 3, pp 343–355 | Cite as

Control of a Nonlinear Vibratory System of the Fourth Order with Unknown Parameters

  • I. M. Anan'evskii


A problem of control of a mechanical system is considered that represents two mass points connected by a spring and moving along parallel straight lines. It is assumed that masses of the points and the rigidity of the spring are unknown and the points are subject to forces of dry friction with unknown variable coefficients. A control law is built up by which a limited force applied to the first mass brings it into a prescribed position in a finite time. An algorithm is put forward that uses piecewise-linear feedback links whose gain factors tend to infinity as the system approaches a terminal set. The second Lyapunov method is used for substantiating the algorithm. The effectiveness of the suggested control law is shown with the aid of numerical modeling.


Numerical Modeling System Theory Mechanical System Unknown Parameter Fourth Order 
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  1. 1.
    Chernous'ko, F.L., Decomposition and Suboptimal Control in Dynamic Systems, Prikl. Mat. Mekh., 1990, vol. 54, issue 6, pp. 883–893.Google Scholar
  2. 2.
    Chernous'ko, F.L., Synthesis of Control of a Nonlinear Dynamic System, Prikl. Mat. Mekh., 1992, vol. 56, issue 2, pp. 179–191.Google Scholar
  3. 3.
    Pyatnitskii, E.S., The Principle of Decomposition in Control of Mechanical Systems, Dokl. Akad. Nauk SSSR, 1988, vol. 300, no. 2, pp. 300–304.Google Scholar
  4. 4.
    Pyatnitskii, E.S., Synthesis of Hierarchical Systems of Control of Mechanical Objects on the Principle of Decomposition, Avtom. Telemekh., 1989, no. 1, pp. 87–99; no. 2, pp. 71–86.Google Scholar
  5. 5.
    Matyukhin, V.I., Strong Stability of Motion of Mechanical Systems, Avtom. Telemekh., 1996, no. 1, pp. 37–56.Google Scholar
  6. 6.
    Anan'evskii, I.M., Control of a Mechanical System with Unknown Parameters by Means of a Limited Force, Prikl. Mat. Mekh., vol. 61, issue 1, pp. 52–62.Google Scholar
  7. 7.
    Anana'evskii, I.M., Control of a Linear Mechanical System with Elastic Elements under Uncertainty Conditions, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1997, no. 4, pp. 60–68.Google Scholar
  8. 8.
    Anan'evskii, I.M., Control of a Two-Mass System with Unknown Parameters, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1998, no. 2, pp. 72–82.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • I. M. Anan'evskii
    • 1
  1. 1.Institute for Mechanics ResearchRussian Academy of SciencesMoscowRussia

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