Application of the Udwadia-Kalaba methodology to the active control of shaft vibration.

Rotating shafts are prone to vibration and it is necessary to mitigate these vibrations to ensure proper operation of the machine. Such mitigation can be performed by active control. Among the available control strategies, one can apply the methodology proposed by Udwadia and Kalaba for trajectory control of nonlinear systems. In this work, such methodology is analyzed for controlling the lateral vibrations of a rotating shaft. First, this control technique is evaluated by placing the sensor-actuator pair in the point of interest for control (disc position of the shaft). Results show that the kinematic constraints applied by the control strategy are exactly tracked and lateral vibration of the shaft is significantly reduced. Second, the control technique is evaluated by placing the sensor-actuator pair at the bearing position of the shaft, thus far from the point of interest for control (disc position). In this case, vibration is reduced at the point of actuation, but not at the point of interest for control. However, the application of the methodology in an on/off strategy resulted in a successful reduction of the lateral vibrations of the shaft at the point of interest for control when crossing the first critical speeds. [ABSTRACT FROM AUTHOR]