Vibration control of flexible beams using sensor averaging and actuator averaging methods

Techniques are developed for suspension of flexible elements for noncontact handling in manufacturing processes. In support of this work, a magnetic suspension test bed are constructed, using eight actuators and eight sensors to control the flexible modes of a 3-m-long, 6.35-mm-diameter steel tube with varying boundary conditions. A novel approach has been developed for the control of such noncontact suspensions through sensor averaging and actuator averaging. The difficult stability and robustness problems imposed by the flexible dynamics of the work piece can be overcome by taking a properly weighted average of the outputs of a distributed array of motion sensors (sensor averaging), and/or by applying a properly weighted distributed array of actuating forces (actuator averaging) to the work piece. These approaches generate spatial filters on a broad range of undesired resonance modes without adversely affecting phase, and the resulting modal gains are independent of the specific boundary conditions and longitudinal dimensions of the work piece. The averaging arrangement can also eliminate possible noncollocation problems. These approaches are thus generally applicable to a wide range of structural control problems. In this paper, the averaging methods applied to beams are presented in detail. The experimental results with a beam suspension confirm the value of the averaging techniques, and suggest the wide future application of these ideas in industrial processes that require noncontact handling of work pieces.