Positive Real Zeros in Flexible Beams

Abstract

Feedback control of flexible structures naturally involves actuators and sensors that often cannot be placed at the same point in the structure. It has been widely recognized that this noncollocation can lead to difficult control problems and, in particular, difficulty in achieving high robustness to variation in the dynamic properties of the structure. This problem has previously been traced to transmission zeros in the dynamic transfer function between sensor location and actuator location, especially those lying on the positive real axis in the complex plane. In this artie/e, the physical significance of these zeros is explored and the dynamic properties of beams that give rise to real positive zeros are contrasted to those of torsional and compressive systems that do not.