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.