By Eure K.W.
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A piezo-electric transducer is mounted under the plate as the control actuator. The error, or plant output, is the signal read from the accelerometer. It is desired to reduce the amount of noise radiated from the plate. This is accomplished by reducing the vibration amplitude of the odd plate modes. Since the accelerometer is placed at the center of the plate, those modes with a node at the accelerometer are not observable. Even though even modes are poor radiators39, if it is desired to exercise control over them an additional piezo and accelerometer pair may be added.
23) where η( z ) = 1 − η1 z −1 − η 2 z −2 −−η nd z − nd Premultiplying Eq. 21) by η( z ) and using Eq. 24) where α~ ( z ) = η( z )α ( z ) = I m − α~1 z −1 − α~ 2 z −2 −−α~ p z − p − nd ~ ~ ~ ~ ~ β ( z ) = η( z )β ( z ) = β 0 − β 1 z −1 − β 2 z −2 −− β p z − p − nd In Eq. 24) the system order is p + nd rather than p. This is due to the fact that the model given by Eq. 24) has imbedded within the parameters an exact model of the disturbance41. The value of nd is twice the number of periodic disturbances acting on the system.
The feedback controller cannot reduce the level of uncorrelated noise at the sensor output. As can be seen from Fig. 6, the correlation has been mostly removed. The Fourier transform of the autocorrelation will give the spectrum. The spectra of the open- and closed-loop systems are shown in Fig. 7. 01. 5 KHz. 7 Generalized Predictive Control In Fig. 7, the gray line is the spectrum of the accelerometer output without control and the dotted black line is the output with control. The result is similar to that shown in Fig.
Adaptive predictive feedback techniques for vibration control by Eure K.W.