Parametric Control of Oscillations

  • Leonid ChechurinEmail author
  • Sergej Chechurin
  • Anton Mandrik
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 95)


Any oscillating system is described by certain parameters, and very often these parameters can be dynamically changed in a certain way to reach control goals. We overview a number of designs in which periodic variation of parameters in linear time-variant and nonlinear systems is the main control paradigm. We use frequency analysis and one-frequency approximation as the mathematical instrument. The approach that is also known as stationarization uses equivalent transfer functions for each time-variant and nonlinear element and reduces the stability analysis to classical Nyquist plot. The study presents in a unified framework several problems that have been solved in the last decades and new ideas, such as parametric synchronizing of oscillation. As the approach uses si mple mathematics, it can be used by field engineers for inventive oscillation control design for cranes, ships, rotors and many other vibrating systems.


Parametric control Oscillations 


  1. 1.
    Amer, Y.A., Ahmed, E.E.: Vibration control of a nonlinear dynamical system with time-varying stiffness subjected to multi external forces. Int. J. Eng. Appl. Sci. (IJEAS) 5(4), 50–64 (2014)Google Scholar
  2. 2.
    Chechurin, L., Chechurin, S.: Physical Fundamentals of Oscillations, p. 264. Springer, Cham (2018). Scholar
  3. 3.
    Eissa, M., Kamel, M., El-Sayed, A.T.: Vibration reduction of a nonlinear spring pendulum under multi external and parametric excitations via a longitudinal absorber. Mechanica 46, 325–340 (2011)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Insperger, T., Stépán, G.: Optimization of digital control with delay by periodic variation of the gain parameters. In: Proceedings of IFAC Workshop on Adaptation and Learning in Control and Signal Processing, and IFAC Workshop on Periodic Control Systems, Yokohama, Japan, pp. 145–150 (2004)Google Scholar
  5. 5.
    Mandrik, A.V., Chechurin, L.S., Chechurin, S.L.: Method for Stabilizing of Output Signal of Oscillating System. Patent RU2393520 (2010)Google Scholar
  6. 6.
    Mandrik, A.V., Chechurin, L.S., Chechurin, S.L.: Frequency analysis of parametrically controlled oscillating systems. IFAC-Papers OnLine. In: Proceedings of the 1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems MICNON. vol. 48, no. 11, pp. 651–655 (2015)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Leonid Chechurin
    • 1
    • 2
    Email author
  • Sergej Chechurin
    • 2
  • Anton Mandrik
    • 2
  1. 1.LUT UniversityLapeenrantaFinland
  2. 2.Peter the Great St. Petersburg Polytechnic UniversitySaint PetersburgRussia

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