The purpose of this work is to reduce the transient operational vibration of the free end of a time-varying flexible beam when the beam is continually moving back and forth by a motor. At this time, the displacement signals at its free end are measured by two accelerometers mounted at the tip of the free end in the vertical and horizontal directions. The control device, a piezoelectric servo-damper mounted at the free end, consists of a sprung mass supported by two pairs of piezoelectric actuators, perpendicular to each other. The servo-damper system features that the device and control unit is made small and compact, and that the control force is imposed directly onto the free end of the beam.
Modeling of the system is achieved experimentally and analytically for the vertical and horizontal directions when the beam length takes the minimal, medium and maximal values. Using the model determined, I-control action is adopted such that the damping of the closed loop system is effectively increased. The upper limit of the I-gain, which maximizes the system damping within the theory of linear system, is found due to the saturation problem associated with the damper device.
Experimental results show that a fixed I-gain derived from a beam of medium length is effective for all beam lengths unless the time-varying property of system parameters is strong. And the control performances of the servo-damper system are compared which a damped vibration absorber. Finally, the servo-damper system is applied to a robot arm to confirm the effectiveness of the piezoelectric servo-damper system as an active vibration control device.
