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Determination of Parametric Resonances in Distributed Parameter Systems Using Frequency Analysis

[+] Author Affiliations
Yong-Kwan Lee

Samsung Electro-Mechanics Company, Suwon, Gyunggi, South Korea

Leonid S. Chechurin

St. Petersburg State Polytechnic University, St. Petersburg, Russia

Paper No. DETC2007-34171, pp. 793-800; 8 pages
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME


Theoretical analysis of parametric instability for the control systems with distributed parameters shall be given. The approach to the solution of such systems can be composed of two parts, i.e. modeling and estimation of the distributed parameters and instability estimation of the periodical time-variant elements using parametric circumference. A control system with mechanical distributed parameters such as robot manipulators is introduced as an example. Theoretical analysis shows that the parametric instabilities occur by digital controllers or time-varying elements which excite the resonance regions of distributed parameters. An electro-mechanical transformer which consists of constant current motor and synchronous generator is applied as another example. Inductance between stator windings and rotor of the synchronous generator serves as a periodical time-varying parameter and long electrical line plays a role of an element with distributed parameters. Instability condition of the transformer rotation owing to the parametric resonance excitement was obtained.

Copyright © 2007 by ASME



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