High frequency spatial vibration control using H_∞ method

A general feedback control approach has been developed to reduce the amplitude of high-frequency structural vibration modes without spending any control effort on reducing the vibration level of low-frequency modes. A procedure is outlined for developing a truncated structural model, which only includes the vibration modes of interest and takes account of the contributions of lower and higher-order modes in the frequency band of interest. Procedures for calculating the lower and higher order mode contributions are outlined, and a better model for estimating the contributions from the lower-order modes is developed by introducing a second-order term. The new controller so obtained has a lower order than standard feedback controllers and is also able to concentrate all the control energy on the modes resonant in the frequency band of interest. The control approach is further developed by using spatial output control to achieve a global attenuation of the structure for the desired frequencies and to allow the distribution of control energy among the controlled frequencies in any desired way. The general theory developed in this paper is validated experimentally using a cantilevered beam as a representative structure and controlling the fourth to the seventh-order vibration modes over a frequency range from 342 to 1125 Hz. Piezoelectric patches are used as a sensor and actuator and the global attenuation is measured using a scanning laser vibrometer.