This dissertation presents a set of general numerical tools for simulating feedforward active noise control in the frequency domain. Feedforward control is numerically similar to linear least squares regression, and can take advantage of various numerical techniques developed in the statistics literature for use with regression. Therefore, an important theme of this work is to look at the control problem from a statistical point of view, and explore the analogies between feedforward control and basic statistical principles of regression.
Motivating the numerical approach is the need to simulate active noise control for systems whose dynamics must be modeled numerically because analytical solutions do not exist, e.g., fluid-structure interaction problems. Plant dynamics for examples in the present work are modeled using a finite-element / boundary-element computer program, and the associated numerical methods are general enough for us with many types of problems. The derivation is presented in the context of active structural-acoustic control (ASAC), in which sound radiating from a vibrating structure is controlled by applying time-harmonic vibrational inputs directly on the structure.
First, a feedforward control simulation is developed for a submerged spherical shell using both analytical and numerical techniques; the numerical formulation is found by discretizing the integrations used in the analytical approach. ASAC is shown to be effective for controlling radiation from the spherical shell. For a point-force disturbance at low frequencies, a single control input can reduce the radiated power by up to 20 dB (ignoring the possibility of measurement noise). A more general numerical methodology is then developed based on weighted least-squares regression in the complex domain. It is shown that basic regression diagnostics, which are used in the statistics literature to describe the quality and reliability of a regression, can be used to model the effects of error sensor measurement noise to produce a more realistic simulation. Numerical results are presented for a finite-length, fluid-loaded cylindrical shell with clamped, rigid end closures. It is shown that when the controller reduces the radiated power by less than 2 dB, the control simulation is usually invalid for statistical reasons. Also developed are confidence intervals for the individual control input magnitudes, and prediction intervals which help evaluate the sensitivity to measurement noise for the regression as a whole.
Collinearity, a type of numerical ill-conditioning that can corrupt regression results, is demonstrated to occur in an example feedforward control simulation. The effects of collinearity are discussed, and a basic diagnostic is developed to detect and analyze collinearity. Subset selection, a numerical procedure for improving regressions, is shown to correspond to optimizing actuator locations for best control system performance. Exhaustive-search subset selection is used to optimize actuator locations for a sample structure. Finally, a convenient method is given for investigating alternate controller formulations, and examples of several alternate controllers are given including a wavenumber-domain controller. Numerical results for a cylindrical shell give insight to the mechanisms used by the control system, and a new visualization technique is used to relate farfield pressure distributions to surface velocity distributions using wavenumber analysis. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/38445 |
| Date | 06 June 2008 |
| Creators | Ruckman, Christopher E. |
| Contributors | Mechanical Engineering, Fuller, Chris R., Burdisso, Ricardo A., Liu, Yuan-Ning, Robertshaw, Harry H., Rogers, Craig A. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | xiii, 161 leaves, BTD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 30902031, LD5655.V856_1994.R835.pdf |
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