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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 839105, 8 pages
http://dx.doi.org/10.1155/2015/839105
Research Article

Controlled Passage through Resonance for Flexible Vibration Units

1Institute of Problems in Mechanical Engineering, 61 Bolshoy Avenue V.O., Saint Petersburg 199178, Russia
2Saint Petersburg State University of Architecture and Civil Engineering (SPSUACE), 2nd Krasnoarmeiskaya Street 4, Saint Petersburg 190005, Russia
3University ITMO, St. Petersburg State University and Institute of Problems in Mechanical Engineering, 61 Bolshoy Avenue V.O., Saint Petersburg 199178, Russia

Received 28 December 2014; Revised 24 March 2015; Accepted 24 March 2015

Academic Editor: Tomasz Kapitaniak

Copyright © 2015 Dmitry A. Tomchin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The problem of controlled passage through resonance zone for mechanical systems with several degrees of freedom is studied. Control algorithm design is based on speed-gradient method and estimate for the frequency of the slow motion near resonance (Blekhman frequency). The simulation results for two-rotor flexible vibration units illustrating efficiency of the proposed algorithms and fractal dependence of the passage time on the initial conditions are presented. The novelty of the results is in demonstration of good behavior of the closed loop system if flexibility is taken into account.