A novel approach to suppression of oscillations

S. Zegzhda, M. Yushkov, Sh. Soltakhanov, N. Naumova, T. Shugaylo

Research output

Abstract

We propose a novel method of determining the control force that brings a mechanical system with finite degrees of freedom from one phase state into another one in a given time. When a system is brought from an available phase state into a prescribed state of rest we can speak about the oscillation suppression. Horizontal motion of a cart with s mathematical pendula is studied as an example. At first, a control by the Pontryagin maximum principle that minimizes the functional of the squared control force is suggested. This approach results in a nonholonomic constraint of order 2s+4. In order to develop a control we propose to employ the generalized Gauss principle which underlies the theory of motion of nonholonomic systems with high-order constraints. In this case, the motion is more smooth than the Pontryagin maximum principle suggests. In addition, by increasing the order of the generalized Gauss principle (when solving the extended boundary-value problem) one manages to get rid of jumps in the control at the beginning and end of motion which are characteristic for the Pontryagin maximum principle. We also discuss the singular points of solutions that appear when solving the extended boundary-value problems.

Original languageEnglish
Pages (from-to)781 - 788
Number of pages8
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume98
Issue number5
DOIs
Publication statusPublished - May 2018

Fingerprint

Maximum principle
Pontryagin Maximum Principle
Force control
Oscillation
Boundary value problems
Force Control
Motion
Gauss
Boundary Value Problem
Nonholonomic Constraints
Nonholonomic Systems
Singular Point
Mechanical Systems
Jump
Horizontal
Degree of freedom
Higher Order
Minimise

Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mechanics

Cite this

Zegzhda, S. ; Yushkov, M. ; Soltakhanov, Sh. ; Naumova, N. ; Shugaylo, T. / A novel approach to suppression of oscillations. In: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 2018 ; Vol. 98, No. 5. pp. 781 - 788.
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A novel approach to suppression of oscillations. / Zegzhda, S.; Yushkov, M.; Soltakhanov, Sh.; Naumova, N.; Shugaylo, T.

In: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 98, No. 5, 05.2018, p. 781 - 788.

Research output

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