Semi-modal active vibration control of plates using discrete piezoelectric modal filters

Abstract

Modal sensors and actuators working in closed loop enable to observe and control independently specific vibration modes, reducing the apparent dynamical complexity of the system and the necessary energy to control them. Modal sensors may be obtained by a properly designed weighted sum of the output signals of an array of sensors distributed on the host structure. Although some works found in the literature present techniques for designing and implementing modal filters based on a given array of sensors, the effect of the sensors’ distribution on the modal filter performance has received little attention. Recent studies have shown that some parameters, such as size, shape and location of the sensors, are very important for the performance of the resulting modal filters. This work presents a methodology for the design of semi-modal active vibration control of a rectangular plate using modal filters based on arrays of piezoelectric sensors. The geometric distribution of the array of piezoelectric sensors bonded to a rectangular plate is numerically optimized to improve the effectiveness and frequency range of a set of modal filters. An experimental implementation of the modal filters is carried out in order to validate their performance. It is shown that proper setup of weighting coefficients is an important requirement. Then, two simple control laws, namely direct velocity feedback and positive position feedback, using the modal filter output are designed and implemented. It is shown that modal filtering allows to effectively control selected vibration modes with quite simple signal processing requirements.