Development of a State-Space Observer for Active Noise Control Systems

Active noise control (ANC) is a method of reducing the unwanted sound. This is realized by artificially generating canceling (secondary) source(s) of sound through detecting the unwanted (primary) noise and processing it by an electronic controller, so that when the secondary wave is superimposed on the primary wave the two destructively interfere and cancellation occurs at the observation point. ANC system is an active research area for its high demand especially in the acoustic noise and vibration control systems. A lot of work in modeling an ANC system involves the transfer function approach, but unfortunately this method allows observation at a single point or mode. It is of interest to measure the level of cancellation not only at the observer but also around it. Therefore, a state space approach would allow observation at multi modes simultaneously and became the subject of this research. This thesis is concerned with the study and development of a state-space model (SSM) for ANC system in on dimensional free-field medium instead of Finite Impulse Response (FIR) Models. In this work, the derivation of the SSM of each propagation path of ANC system is presented and hence the system is termed Feedforward state space control system with feedback inclusion single input single output (SISO) architecture. The criterions of success considered the evaluation process are the length of the propagation path, level of cancellation, convergence rate, number of modes of each path, and destructive interferences occur at the cancellation path. The secondary path of the ANC system is modeled by using the LMS algorithm to complete the design of the Filtered-X Least Mean Square (FXLMS) controller. Then the adaptive FXLMS controller is presented and incorporated with the proposed model for both Feedforward with / without the acoustic Feedback cases. As a result, the comparisons between the two cases are presented by mean of level of cancellation and convergence rate. The simulation results of the proposed model show that the level of the disturbance signal at ten modes along the primary path is decreasing as much as the modes go away from the source indicating that this model is suitable to build the mechanism of the ANC system which satisfies the relation between the wave dissipation against the number of modes which are distributed along the length of path. The derivation of the SSM gives the opportunity to extend the work furthermore to involve the derivation of a state-space optimal observer which is named State Space Least Mean Square (SSLMS) observer. This observer is employed to observe and monitor the pressure modes along the propagation path through simulating it in an offline structure i.e. without controller, or to observe the modes at the cancellation path through simulating the SSLMS in an on-line structure i.e. while the controller is converging. The comparison results between the real and observed modes of the secondary propagation show an accurate observing. Finally, the comparisons of the observed pressures of three modes along the cancellation path while the controller is converging (on-line structure) are shown with the mode which is located at the observer achieving the best cancellation.

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