Controlling the nonlinear dynamics of a beam system

Citation
Mf. Heertjes et Mjg. Van De Molengraft, Controlling the nonlinear dynamics of a beam system, CHAOS SOL F, 12(1), 2001, pp. 49-66
Citations number
24
Categorie Soggetti
Multidisciplinary
Journal title
CHAOS SOLITONS & FRACTALS
ISSN journal
09600779 → ACNP
Volume
12
Issue
1
Year of publication
2001
Pages
49 - 66
Database
ISI
SICI code
0960-0779(200101)12:1<49:CTNDOA>2.0.ZU;2-N
Abstract
Control based on linear error feedback is applied to reduce vibration ampli tudes in a piecewise linear beam system. Hereto small amplitude 1-periodic solutions are stabilized wherever they coexist with two or more long-term s olutions. In theory, no control effort is required to maintain the 1-period ic response once it has been stabilized. For the beam system, 1-periodic so lutions are stabilized by feedback at one location along the beam. Feedback is represented by servo-stiffness or servo-damping which results from incr easing two corresponding control parameters. At appropriate levels of these parameters local, or global, asymptotic stability (of the zero-equilibrium ) of the error dynamics, i.e. stability of the underlying 1-periodic soluti ons, can be guaranteed. Local asymptotic stability can be guaranteed for a large range of actuator locations and excitation frequencies and is indicat ed by bifurcations. Global asymptotic stability can only be guaranteed for a limited range of actuator locations on the basis of the well-known circle criterion. The difference between local and global asymptotic stability in terms of the required values for the control parameters can be significant , and may result in large differences in control performance. (C) 2000 Else vier Science Ltd. All rights reserved.