Modifying modal characteristics of sound fields by state feedback control.
State feedback control of a sound field is investigated for improving the irregular distribution of the natural frequencies at low frequencies. A state-space description of a sound field is derived from an inhomogeneous wave equation using the finite element method. The feedback control system is realized as a feedback filter between sensor microphones and control sources using a state estimator for a linear dynamic system. Pole allocation is employed for calculating the state feedback gain vector, such that the roots of the closed-loop system have the desired modal distribution. Computer simulations are performed to demonstrate the control achieved by distributing the lowest undamped natural frequencies in a uniform manner. As a result, the transfer functions with the state feedback control are modified so as to have peaks at identical intervals for the frequency range of interest. A control experiment in an enclosure is carried out with the same objective of control as modeled in the simulations. The experiment verifies that the desired modal distribution can be achieved by introducing the proposed state feedback control into a sound field.
Samejima
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Department of Acoustic Design, Kyushu Institute of Design, Fukuoka, Japan.