The Filtered-X Least-Mean-Square (FXLMS) algorithm is widely used in active noise control due to its robustness, simplicity, and ability to be implemented in real time. In a feedforward implementation of the FXLMS algorithm, a reference signal that is highly correlated with the noise to be controlled is filtered with an estimate of the transfer function of the secondary path. The convergence characteristics of the FXLMS algorithm have been well studied. A convergence parameter is used to optimize the convergence of the algorithm. However, the optimal value for the convergence parameter is frequency dependent. Thus for noise containing multiple tones at different frequencies the convergence parameter can only be optimized for one of those tones. Other tones will have slower convergence rates and in general less attenuation than they would have if they were treated singly and parameters could be optimized for those frequencies separately. A method is developed to modify the magnitude response of the secondary path estimate while maintaining the original phase response, which equalizes the convergence characteristics over multiple frequencies, giving more uniform convergence and attenuation for all tones being controlled. Stability of the algorithm is not compromised. The modification to the FXLMS algorithm is relatively simple to implement and has been shown to increase overall attenuation of a signal containing multiple tones by an additional 6-9 dB.

The properties of acoustic kinetic energy density and total energy density of sound fields in lightly damped enclosures have been explored thoroughly in the literature. Their increased spatial uniformity makes them more favorable measurement quantities for various applications than acoustic potential energy density (or squared pressure), which is most often used. In this dissertation, a new acoustic energy quantity, the generalized acoustic energy density (GED), will be introduced. It is defined by introducing weighting factors, α and 1 − α, in the formulation of total acoustic energy density. With the additional degree of freedom, the GED can conform to the traditional acoustic energy density quantities, or be optimized for different applications. The properties and applications of the GED are explored in this dissertation. For enclosed sound fields, it was found that GED with α = 1/4 is spatially more uniform than the acoustic potential energy density, acoustic kinetic energy density, and the total acoustic energy density, which makes it a more favorable measurement quantity than those traditional acoustic energy density quantities for many indoor measurement applications. For some other applications, such as active noise control in diffuse field, different values of α may be considered superior. The numerical verifications in this research are mainly based on a hybrid modal expansion developed for this work, which combines the free field Green's function and a modal expansion. The enclosed sound field is separated into the direct field and reverberant field, which have been treated together in traditional modal analysis. Studies on a point source in rectangular enclosures show that the hybrid modal expansion converges notably faster than the traditional modal expansions, especially in the region near the source, and introduces much smaller errors with a limited number of modes. The hybrid modal expansion can be easily applied to complex sound sources if the free field responses of the sources are known. Damped boundaries are also considered in this dissertation, and a set of modified modal functions is introduced, which is shown to be suitable for many damped boundary conditions.

Multiple fans are sometimes used in an array configuration to cool various types of electronic equipment. In addition to adding another noise source, using two fans with closely spaced blade passage frequencies (BPF) can create an annoying beat frequency. A two fan array with each fan having a different BPF was considered. The fans were theoretically modeled at the BPF and first harmonics. Each fan has two acoustic paths to the far field. Thus, each fan was modeled as a two source array. The first control configuration consisted of one control filter using six control sources and six error sensors in a fully coupled control system designed to control both fans simultaneously. The second configuration used two independent controllers with three control sources and three error sensors, one controller per fan. Experimentally, the averaged narrow band reduction of the BPFs and the second harmonic of the two independent controllers were 15.6 and 7.4 dB respectively, compared to a reduction of 14.4 and 5.7 dB at the two frequencies using a single control loop. The results suggest that independent controllers perform better than the single control loop for the fan array studied. Optimization of active noise control systems has increased performance but sometimes with decreased robustness. Two control source configurations for the sound power reduction of a simple source were analyzed by modeling the control systems. The two control source configurations were four symmetric control sources surrounding the noise source and an optimized linear array of four control sources. Simulation results show the linear array control source configuration is more sensitive to microphone placement errors, with a 20-33 dB reduction in attenuation for a microphone placement error of 2 mm compared to a 0.8 dB drop in attenuation for the symmetric case. The linear array configuration was found to be more sensitive to the microphone placement errors compared to the symmetric configuration. A 2.5 mm change in one microphone position causes an average of 6 dB loss in attenuation for the linear array configuration compared to a 0.6 dB loss for the symmetric configuration.

Noise from information technology (IT) equipment is a significant problem in today's modern society. Active Noise Control (ANC) has shown promise in reducing the effect of IT fan noise on users. Though ANC has been applied to axial fans (such as those found in desktop computers), it has not been applied to centrifugal fans, such as those found in laptop computers. This work applies an ANC method to a centrifugal fan mounted in a mock laptop enclosure. This method is applied in four steps. First, secondary sources are placed in the vicinity of the fan. Second, an accurate model of the radiation from the fan and secondary sources is constructed. Third, the total power radiated from this system is minimized. This creates nodal lines in the vicinity of the fan. Fourth, ANC error sensors are placed on the nodal lines predicted by the model. This creates these nodal lines experimentally, thus creating the minimum power condition. The noise from the exhaust and inlets of the fan will first be controlled individually. Then the method will be applied to the combined system. Global sound power radiation will be measured in all cases.

Active noise control (ANC) has been implemented using analog filters to reduce broadband noise from a small axial cooling fan. Previous work successfully attenuated narrow-band, tonal portions of the noise using a digital controller. The practical performance limits of this system were reached and it was desirable to attenuate the noise further. Additional research, therefore, sought to attenuate broadband noise from the fan using a digital controller, but performance was limited by the group delay inherent in the digital signal processor (DSP). Current research attempts to further attenuate broadband noise and improve performance of the system by combining the tonal controller with an analog feedback controller. An analog controller is implemented in parallel with the digital controller without degrading the performance of either individual controller. Broadband noise is attenuated in a certain frequency region, but at the expense of increasing noise in adjacent frequency regions. Results show that a single-input single-output (SISO) controller is preferable to a multiple-input multiple-output (MIMO) controller for this system.

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