Frequency Domain Stability Criterion for Vibration Control of the Bernoulli-Euler Beam

Abstract

A new single-input single-output frequency domain stability criterion for distributed parameter systems is illustrated by application to feedback control of a Bernoulli-Euler beam. The system is modeled using an infinite partial fraction expansion, while the control design is based on a truncated model. The Nyquist plot is shown to lie within a “tube of uncertainty” of the plot for the truncated model. Several numerical examples illustrate the power and simplicity of this criterion.