Modeling and adaptive control of acoustic noise.

Active noise control is a problem that receives significant attention in many areas including aerospace and manufacturing. The advent of inexpensive high performance processors has made it possible to implement real-time control algorithms to effect active noise control. Both fixed-gain and adaptive methods may be used to design controllers for this problem. For fixed-gain methods, it is necessary to obtain a mathematical model of the system to design controllers. In addition, models help us gain phenomenological insights into the dynamics of the system. Models are also necessary to perform numerical simulations. However, models are often inadequate for the purpose of controller design because they involve parameters that are difficult to determine and also because there are always unmodeled effects. This fact motivates the use of adaptive algorithms for control since adaptive methods usually require significantly less model information than fixed-gain methods. The first part of this dissertation deals with derivation of a state space model of a one-dimensional acoustic duct. Two types of actuation, namely, a side-mounted speaker (interior control) and an end-mounted speaker (boundary control) are considered. The techniques used to derive the model of the acoustic duct are extended to the problem of fluid surface wave control. A state space model of small amplitude surfaces waves of a fluid in a rectangular container is derived and two types of control methods, namely, surface pressure control and map actuator based control are proposed and analyzed. The second part of this dissertation deals with the development of an adaptive disturbance rejection algorithm that is applied to the problem of active noise control. ARMARKOV models which have the same structure as predictor models are used for system representation. The algorithm requires knowledge of only one path of the system, from control to performance, and does not require a measurement of the disturbance nor knowledge of its spectrum. The algorithm is multiple-input multiple-output. In addition, it is more robust to measurement noise by virtue of the fact that it operates on windows of data rather than instantaneous measurements. The algorithm can handle on tonal, narrowband and broadband disturbances. Experimental results on an acoustic duct which demonstrate the effectiveness of the algorithm are presented.PhDAerospace engineeringApplied SciencesElectrical engineeringMechanical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/130858/2/9811212.pd