Modifying modal characteristics of sound fields by state feedback control

State feedback control of a sound field is investigated for improving the i rregular distribution of the natural frequencies at low frequencies. A stat e-space description of a sound field is derived from an inhomogeneous wave equation using the finite element method. The feedback control system is re alized as a feedback filter between sensor microphones and control sources using a state estimator for a linear dynamic system. Pole allocation is emp loyed for calculating the state feedback gain vector, such that the roots o f the closed-loop system have the desired modal distribution. Computer simu lations are performed to demonstrate the control achieved by distributing t he lowest undamped natural frequencies in a uniform manner. As a result, th e transfer functions with the state feedback control are modified so as to have peaks at identical intervals for the frequency range of interest. A co ntrol experiment in an enclosure is carried out with the same objective of control as modeled in the simulations. The experiment verifies that the des ired modal distribution can be achieved by introducing the proposed state f eedback control into a sound field. (C) 2001 Acoustical Society of America.