Date of Award


Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy


Electronic Engineering

First Advisor

Dr. Patrick Pratt


The theory and application of Active Noise Control to remove irritating acoustic pollution from a variety of sources has and continues to receive significant attention from both theoreticians and practitioners.

While a classical acoustic noise problem is the rejection of acoustic tonal disturbances with the most common solution employed being the celebrated filtered-X LMS algorithm, this thesis shows that the presence of non-linearly induced harmonics at multiple frequencies of the original tone often results in poor performance of this algorithm. It is further found that the noise reduction at these problematic harmonics can be improved in a number of ways, with the most effective strategy involving the introduction of a nonlinear block to the existing algorithm. The resultant solution is then termed the nonlinear filtered-XLMS algorithm.

One of the key requirements of any feedback controller is robustness, i.e. the maintenance of stability and performance in the presence of plant uncertainty. While recent developments in H control theory provide the platform upon which such robust feedback systems are developed, this thesis highlights that for certain configurations a noise cancellation problem is equivalent to disturbance rejection in either a classical feedback or internal model control arrangement. It is further observed that uncertainty is implicitly present in acoustic plant models, making Hoc control the ideal approach for such a feedback Active Noise Control system. The efficacy of Hoo control theory relative to conventional approaches in controlling acoustic noise systems is reviewed, developed and extended. Moreover, a number of related Hoo solvers are employed to evaluate candidate controllers followed by a comprehensive comparison of their respective performances. One particular solver involving the innovative application of optimisation theory to reformulate and solve the robust control problem is presented. Some novel applications of the internal model principle are explored to reject acoustic tonal disturbances. Specifically, one original technique is presented that combines the internal model principle with optimisation theory, and a Hoo robustly stabilising cost function. Furthermore, it was found that the introduction of damping into the internal model of the disturbance enhances the forward path stability, with only a slight trade-off occurring in performance. As non-minimum phase dynamics are synonymous with acoustic systems, the closed loop sensitivity reduction capabilities of plants with such dynamics will be reviewed for the case of low frequency attenuation. Noting that unwanted acoustic disturbances are generally present at intermediate frequencies, this theory is extended to quantify the maximum sensitivity reduction capabilities over such a frequency range. In compliance with theory, experiments indicate that tonal noises can be cancelled using these robust feedback techniques, but satisfactory reduction in broadband noise is not possible.

Furthermore, a comprehensive comparison is made between the various adaptive feedforward and robust feedback Active Noise Controllers. This comparison indicates clearly which solutions are best suited to specific Active Noise Control applications.


Active Noise Control using Adaptive and Advanced Control Techniques By Michael O' Brien, B.Eng., M.Eng,

Submitted in partial fulfilment for a Doctor of Philosophy.

Submitted to HETAC, 2002

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