Active noise control in finite length waveguides

James Dennis Stell, Purdue University

Abstract

This thesis discusses the performance of active noise control systems in rigid-walled, rectangular waveguides with reflective terminations. The theory is developed such that optimal secondary source strengths can be found to minimize three performance criteria; pressure at a selected set of points within the waveguide, potential energy in a selected volume of the waveguide, and power in the downstream region of the waveguide. Analytical results indicate that for control of a single mode the solution of the minimum pressure problem is identical to the solution of the minimum potential energy or minimum propagating power solutions. Simulation results indicate that by properly locating the secondary sources and the performance sensors the global performance of the minimum pressure solution approaches the optimal performance of the minimum potential energy or minimum power solutions. When these solutions are identical, or similar, a local control strategy is capable of obtaining global control. Guidelines are given for configuring an active control system that minimizes the pressure at a set of performance sensors such that the potential energy and propagating power are also minimized. To avoid the effects of evanescent energy the pressure sensors should be located as far downstream from the secondary sources as possible. The effects of evanescent energy can also be reduced by locating the performance sensors and secondary sources on the nodelines of the most significant evanescent mode. If the waveguide has reflective terminations then frequencies will exist at which the evanescent energy is more significant than at other frequencies. At these frequencies there will be reduced control of potential energy and power using pressure minimization. The number of frequencies of poor control can be reduced by locating the transducers properly; the secondary source should be located as close as possible to the reflecting upstream termination and the performance sensor should be located as close as possible to a reflecting downstream termination. The models used in this thesis are experimentally verified. Issues associated with implementing active noise controllers using digital filters are also discussed in this thesis. The reduction in sound pressure obtained over a frequency band increases logarithmically with filter size. The analytical predictions were also compared to the performance of a commercial active controller. The commercial controller did not perform consistently or as well as predicted due to the complex nature of the waveguide sound control problem.

Degree

Ph.D.

Advisors

Bernhard, Purdue University.

Subject Area

Mechanical engineering

COinS