Active control of multi-mode sound in waveguides

This thesis presents an analytical and experimental evaluation of a number of active control systems for plane-wave and higher-order modes in ducts. A plane-wave analysis of an active control system based upon harmonic steady-state response, with arbitrary end conditions and finite source impedance is derived. It is shown that the ideal controller depends only upon the controller component's dynamic response and the duct geometric and acoustic properties of the controller section. Off-optimum response is shown to depend upon duct termination conditions. It is shown that, as a consequence of the control system forcing a pressure release condition at the control source, the control source is effectively de-coupled from the duct.The control concepts derived for the plane wave are extended to the multi-mode case. Three adaptive controller configurations are derived based on different source and hardware conditions. An independent modal controller exerts control over each individual mode by implementing modal sensors and actuators. It is demonstrated that this permits generalized source(s) to be controlled, regardless of the coherence between modes. A hybrid modal controller reduces the sensor requirements while still retaining a modal character. Finally, a direct multi-channel controller is derived that does not consider the sound field to be composed of modes. Implementations of each of the three multi-mode controllers are described and their performance evaluated for bandlimited random noise sources. Overall reductions ranging from 16 to 20 dB were attained. The overall attenuation was limited to all cases by the reduction at mode cut-on frequencies. The frequency response function of the controller at these frequencies is shown to require high phase resolution and a long reverberation time.