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Active sound control (ASC) based on surface potentials is one of two methods of noise control using potential-based method. The method does not require detailed knowledge of the noise source parameters, boundary conditions, characteristics of the acoustic medium or the transmission path. It allows significant volumetric noise cancellation inside the shielded region using only the knowledge of the total acoustic field which includes the wanted sound at the boundary of the shielded region(s) to obtain additional secondary sound sources known as controls which are distributed at the boundary of the shielded region. It allows the presence of a wanted sound inside the shielded region, which it preserves while canceling the noise. In contrast, other methods require various detailed knowledge. In many cases, they do not allow the wanted sound to be generated inside the protected region. The aim of this thesis is to implement numerically the ASC method in 3D bounded regions and confirm its theoretical predictions. The theoretical framework for the method has already been established in previous related literature. Experimental work in this area is mostly limited to laboratory experiments in one dimensional settings. The algorithm was tested in 3D numerical test cases in the frequency domain involving single and composite regions. The Helmholtz equation was used to model the wave propagation. In both single and composite regions, volumetric noise cancellation of over 20 dB was achieved at most areas of the shielded regions. Outside the shielded region, the field remained practically unchanged during noise cancellation. On the other hand, in test cases involving wanted sound, the noise inside the shielded region was canceled while the wanted sound was preserved. However, outside the shielded region, the field was amplified. Moreover in composite regions, the selective cancellation/propagation of the wanted sound was demonstrated successfully in regions having two and three sub-regions by allowing the wanted sound to propagate to one region but not to the other. To enforce selective propagation of the wanted sound, additional steps are required to obtain the separate field of the wanted sound in addition to the total field. A study on the effect of the number of controls on noise cancellation showed that in both single and composite regions, as the number of controls fell there was a corresponding decrease in the level of noise cancellation. A doubling of the number of controls yields about ~3 dB of noise cancellation, and vice versa. The independence of the operation of the algorithm on characteristics or number of noise sources, shape, size or position of shielded region is also demonstrated via further test cases. In all test cases considered, the results confirmed the theoretical predictions. However, at resonance modes the method did not provide noise cancellation, though at near-resonance modes a lower level of noise cancellation was obtained. Although this work considered only monochromatic waves, the method is applicable to broadband noise. In real-time application of the method, the assumption in the thesis that only the field of the noise source(s) is known does not hold and therefore its implementation is more complicated.

Several measurements may be used as error signals to determine how to appropriately control a sound field. These include pressure, particle velocity, energy density and intensity. In this thesis, numerical models are used to show which signals perform best in is free-field active noise control (ANC) using error sensors located in the near field of the sound sources. The second is equalization in a free field and a semi-free field. Minimized energy density total power output (MEDToPO) plots are developed; these indicate the maximum achievable attenuation for a chosen error sensor as a function of location. A global listening area equalization coefficient (GLAEC) is found to evaluate the performance of the equalization methods. It is calculated by finding the average of the spectral standard deviation of several frequency response measurements in a specified listening area. For free-field ANC employing error sensors located in the near field, pressure-based measurements perform the best. For free-field equalization over an extended listening region, total energy density performs best. Equalization of an extended listening region is more successful over a limited low-frequency bandwidth.

<p>In many practical multi-channel active sound control (ASC) applications, such as active noise control (ANC), various constraints need to be satisfied, such as the robust stability constraint, noise amplification constraint, controller output power constraints, etc. One way to enforce these constraints is to add a regularization term to the Wiener filter formulation, which, by tuning only a single parameter, can over-satisfy many constraints and degrade the ANC performance. Another approach for non-adaptive ANC filter design that can produce better ANC performance is to directly solve the constrained optimization problem formulated based on the <em>H</em>₂/<em>H</em>_inf control framework. However, such a formulation does not result in a convex optimization problem and its practicality can be limited by the significant computation time required in the solving process. In this dissertation, the traditional <em>H</em>₂/<em>H</em>_inf formulation is convexified and a global minimum is guaranteed. It is then further reformulated into a cone programming formulation and simplified by exploiting the problem structure in its dual form to obtain a more numerically efficient and stable formulation. A warmstarting strategy is also proposed to further reduce the required iterations. Results show that, compared with the traditional methods, the proposed method is more reliable and the computation time can be reduced from the order of days to seconds. When the acoustic feedback path is not strong enough to cause instability, then only constraints that prevent noise amplification outside the desired noise control band are needed. A singular vector filtering method is proposed to maintain satisfactory noise control performance in the desired noise reduction bands while mitigating noise amplification.</p> <p><br></p> <p>The proposed convex conic formulation can be used for a wide range of ASC applications. For example, the improvement in numerical efficiency and stability makes it possible to apply the proposed method to adaptive ANC filter design. Results also show that compared with the conventional constrained adaptive ANC method (leaky FxLMS), the proposed method can achieve a faster convergence rate and better steady-state noise control performance. The proposed conic method can also be used to design the room equalization filter for sound field reproduction and the hear-through filter design for earphones.</p> <p><br></p> <p>Besides efficient filter design methods, efficient filter implementation methods are also developed to reduce real-time computations in implementing designed control filters. A polyphase-structure-based filter design and implementation method is developed for ANC systems that can reduce the computation load for high sampling rate real-time filter implementation but does not introduce an additional time delay. Results show that, compared with various traditional low sampling rate implementations, the proposed method can significantly improve the noise control performance. Compared with the non-polyphase high-sampling rate method, the real-time computations that increase with the sampling rate are improved from quadratically to linearly. Another efficient filter implementation method is to use the infinite impulse response (IIR) filter structure instead of the finite impulse response (FIR) filter structure. A stable IIR filter design approach that does not need the computation and relocation of poles is improved to be applicable in the ANC applications. The result demonstrated that the proposed method can achieve better fitting accuracy and noise control performance in high-order applications.</p>