Vibration control of a rotating Euler-Bernoulli beam

In this paper, vibration control of a rotating Euler-Bernoulli beam is considered. It is assumed that the fixed-free elastic beam is attached to the servomotor which uses PD control to achieve the desired angular rotation, at the same time, the shear force measured at the root of the beam is used as a feedback to control the beam tip vibration. Mode summation techniques and Laplace domain synthesis techniques are used to analyze the system. Parametric transfer functions relating beam tip motion to the desired rotation and beam rotation to the desired input rotation are obtained. One parameter is the frequency ratio between the natural frequency of the beam and the frequency of the control system, second parameter is the ratio between the shear force feedback gain and the control damping. Stability conditions with respect to these parameters are given. The effect of these parameters on the rotational motion and the beam tip vibration is discussed. Some values of these parameters that make possible desired rotational motion with suppressed tip vibration are suggested. Analysis and results of this work can also be applied to the bending strain feedback and tip velocity feedback control of a rotating Euler-Bernoulli beam. (C) 2000 Academic Press.