Bias Errors in Measurement of Vibratory Power and Implication for Active Control of Structural Vibration

Uncertainties in power measurements performed with piezoelectric accelerometers and force transducers are investigated. It is shown that the inherent structural damping of the transducers is responsible for a bias phase error, which typically is in the order of one degree. Fortunately, such bias errors can be largely compensated for by an absolute calibration of the transducers and inverse filtering that results in very small residual errors. Experimental results of this study indicate that these uncertainties will be in the order of one percent with respect to amplitude and two tenth of a degree for the phase. This implies that input power at a single point can be measured to within one dB in practical structures which possesses some damping. The uncertainty is increased, however, when sums of measured power contributions from more sources are to be minimised, as is the case in active control of vibratory power transmission into structures. This is demonstrated by computer simulations using a theoretical model of a beam structure which is driven by one primary source and two control sources. These simulations reveal the influence of residual errors on power measurements, and the limitations imposed in active control of structural vibration based upon a strategy of power minimisation.