This thesis focuses on adaptive feedback control for low frequency acoustic energy absorption in acoustic enclosures. The specific application chosen for this work is the reduction of high interior sound pressure levels (SPL) experienced during launch within launch vehicle payload fairings. Two acoustic enclosures are used in the research: the first being a symmetric cylindrical duct and the other being a full scale model of a payload fairing. The symmetric cylindrical duct is used to validate the ability of the adaptive controller to compensate for large changes in the interior acoustical properties. The payload fairing is used to validate that feedback control, for a large geometry, does absorb acoustic energy. The feedback controller studied in this work is positive position feedback (PPF) used in conjunction with high and low pass Butterworth filters. An algorithm is formed from control experiments for setting the filter parameters of the PPF and Butterworth filters from non-adaptive control simulations and tests of the duct and payload fairing. This non-adaptive control shows internal SPL reductions of 2.2 dB in the cylindrical duct for the frequency range from 100 to 500 Hz and internal SPL reductions of 4.2 dB in the full scale fairing model for the frequency range from 50 to 250 Hz. The experimentally formed control algorithm is then used as the basis for an adaptive controller that uses the collocated feedback signal to actively tune the control parameters. The cylindrical duct enclosure with a movable end cap is used to test the adaptation properties of the controller. The movable end cap allows the frequencies of the acoustic modes to vary by more than 20 percent. Experiments show that a 10 percent change in the frequencies of the acoustic modes cause the closed-loop system to go unstable with a non-adaptive controller. The closed-loop system with the adaptive controller maintains stability and reduces the SPL throughout the 20 percent change of the acoustic modes' frequencies with a 2.3 dB SPL reduction before change and a 1.7 dB SPL reduction after the 20 percent change. / Master of Science

Increasing costs for space shuttle missions translate to smaller, lighter, and more flexible satellites that maintain or improve current dynamic requirements. This is especially true for optical systems and surfaces. Lightweight, inflatable structures, otherwise known as gossamer structures, are smaller, lighter, and more flexible than current satellite technology. Unfortunately, little research has been performed investigating cost effective and feasible methods of dynamic analysis and control of these structures due to their inherent, non-linear dynamic properties. Gossamer spacecraft have the potential of introducing lenses and membrane arrays in orbit on the order of 25 m in diameter. With such huge structures in space, imaging resolution and communication transmissibility will correspondingly increase in orders of magnitude. A daunting problem facing gossamer spacecraft is their highly flexible nature. Previous attempts at ground testing have produced only localized deformation of the structure's skin rather than excitation of the global (entire structure's) modes. Unfortunately, the global modes are necessary for model parameter verification. The motivation of this research is to find an effective and repeatable methodology for obtaining the dynamic response characteristics of a flexible, inflatable structure. By obtaining the dynamic response characteristics, a suitable control technique may be developed to effectively control the structure's vibration. Smart materials can be used for both active dynamic analysis as well as active control. In particular, piezoelectric materials, which demonstrate electro-mechanical coupling, are able to sense vibration and consequently can be integrated into a control scheme to reduce such vibration. Using smart materials to develop a vibration analysis and control algorithm for a gossamer space structure will fulfill the current requirements of space satellite systems. Smart materials will help spawn the next generation of space satellite technology. / Master of Science

The research presented in this thesis focuses on the use of feedback control for lowering acoustic levels within launch vehicle payload fairings. Due to the predominance of conical geometries within payload fairings, our work focused on the analytical modeling of conical shrouds using modal and impedance based models. Incorporating an actuating boundary condition within a sealed enclosure, resonant frequencies and mode shapes were developed as functions of geometric and mechanical parameters of the enclosure and the actuator. Using a set of modal approximations, a set of matrix equations have been developed describing the homogeneous form of the wave equation. Extending to impedance techniques, the resonant frequencies of the structure were again calculated, providing analytical validation of each model. Expanding this impedance model to first order form, the acoustic model has been coupled with actuator dynamics yielding a complete model of the system relating pressure to control voltage. Using this coupled state-space model, control design using Linear Quadratic Regulator and Positive Position Feedback techniques has also been presented. Using the properties of LQR analysis, an analytical study into the degree of coupling between actuator and cavity as a function of actuator resonance has been conducted. Constructing an experimetnal test-bed for model validation and control implementation, a small sealed enclosure was built and outfitted with sensors. Placing a control speaker at the small end of the cone the large opening was sealed with a rigid termination. An internal acoustic source was used to excite the system and pressure measurements were captured using an array of microphones located throughout the conic section. Using the parameters of this experimental test-bed, comparisons were made between LQR and PPF control designs. Using an impulse disturbance to excite the system, LQR simulations predicted reductions of 53.2% below those of the PPF design, while the control voltages corresponding to these reductions were 43.8% higher for LQR control. Actual application of these control designs showed that the ability to manually set PPF gains made this design technique much more convenient for actual implementation. Yielding overall attenuation of 38% with control voltages below 200 mV, single-channel low authority control was seen to be an effective solution for low frequency noise reduction. Control was then expanded to a larger geometry representative of Minotaur fairings. Designing strictly from experimental results, overall reductions of 38.5% were observed. Requiring slightly larger control voltages than those of the conical cavity, peak voltages were still found to be less than 306 mV. Extrapolating to higher excitation levels of 140 dB, overall power requirements for 38.5% pressure reductions were estimated to be less than 16 W. / Master of Science