Active modal control of sound fields by finite element modeling and H_∞ control theory

A new method of feedback control of sound fields that minimizes the total acoustic energy in a sound field of any shape excited by an unknown disturbance is presented. The proposed method is based on the finite element method and H_∞ control theory, and achieves both robust performance and high stability. The structure of the acoustic plant is formulated such that the H_∞ norm of the system transfer function expresses the total acoustic energy in the sound field. Computer simulations verify that the damping of a sound field can be increased without leading to instabilities of the closed loop system. It is also verified that the resonant peaks in the frequency spectrum of the total acoustic energy can be attenuated in the low-frequency range involved in the nominal model of the plant without exciting the residual mode dynamics in the high-frequency range. The control performance can be tuned by adjusting the weighting factor. Using this method, it is possible to dynamically alter the characteristics of a sound field.