Model reduction and robust controller design scheme for structural acoustics.

摘要

As science and technology progress, people seek a better quality of environment. Sound and vibration have become one of the important factors for determining such quality. Many engineers in acoustics, structures, electronics, materials and mathematics have explored control and structural acoustics to reduce the level of sound and vibration that surround our living and working environments. Structural acoustics explains the interaction between acoustic wave and structural vibration. This interaction involves either sound transmission or reflection from the structure. Proper control of structural vibration can control the reflection and/or transmission of the sound wave. There have been many research efforts to develop simple, reliable, high performance and wide operation frequency band control algorithms and control devices. Much progress and many achievements in this technology have been reported in related literature. Still, these reports show the need for further development in practical and commercially feasible application.; This thesis research was devoted to developing a feasible control system for structural acoustics. Simplicity and robustness of the system are the key issues in the controller design concept. This study was also devoted to building a bridge between state space based control theories with structural acoustics. Simplicity of structure models and controllers was realized by developing the concept of the Modal Hankel Singular Value (MHSV) based model reduction method and fabrication of analog controllers. The MHSV is a modified version of the Hankel Singular Value (HSV) that is popularly used for model reduction in many state space-based control applications. However, MHSV is developed for a modal coordinates system that is more useful in describing vibrating structures than state space. Analog controllers are designed from the transfer functions of controllers, which has great advantage over digital controllers in simplicity and cost.; Secondly, robust control theory is exploited for the design of controllers. In contrast to optimal control, which is designed to minimize the square norm of performance index variables, this control theory aims at reduction of the infinity norm of the variables. It delivers not only sufficient reduction of the variables in a specified frequency band, but also strong robustness in the control performance. In addition, the uncertainty of the vibrating structure model is included in the controller design in terms of modal parameters. This results in a control system that is robust to the uncertainty of modal parameters. Hence, the control system will be more reliable in a real application. Uncertainty analysis of the control systems was added to quantitatively describe the robustness of the control system. It identifies which parameter of the model is critical to the control performance. It is expected that this analysis can provide a guideline for further development of a more robust control system.; This simple and robust controller design for structural acoustics is applied for controls of sound transmission and sound reflection, numerically and experimentally. MHSV shows good model reduction of finite element based structure models. Numerical and experimental results of both transmission control and reflection control show good agreement, which supports the validity of the proposed control methods.; The analog control circuit is easier and cheaper to be miniaturized in a microchip than digital one. The proposed controller design method for structural acoustics application would be more practical if such a miniaturized chip were used as a controller.