Modeling and Control of Sound and Vibration for Smart Structures

by Oliver Janda

Institution: Technische Universit├Ąt Darmstadt
Department: Regelungstechnik und Mechatronik
Degree: PhD
Year: 2014
Record ID: 1099587
Full text PDF: http://tuprints.ulb.tu-darmstadt.de/4154/


This thesis presents a contribution to the improvement of modeling and control methodologies for smart structures. It is focused on comfort-compromising, sound- and vibration-related problems, which can be successfully handled by the concepts developed within the interdisciplinary field of adaptronics. As far as modeling of smart structures is concerned, it is advocated in this thesis to employ theoretical modeling to gather an understanding of the fundamental system properties and of the characteristics that are relevant for control design. Theoretical modeling of a generic smart structure with electromechanical as well as mechanical-acoustical coupling is illustrated at the beginning of this thesis. However, pure theoretical modeling of complex systems generally lacks sufficient accuracy for subsequent control design. For that reason, data-driven modeling is one of the key aspects of this work. A modeling procedure is developed that is capable of identifying models for linear time-invariant systems with many resonances from measurement data along with their associated model uncertainty. A minimum of prior assumptions is needed. Based on these models and their uncertainty descriptions, a straightforward yet powerful design methodology for multi-input multi-output active vibration control is presented. The resulting control design employs the well-developed machinery of H2 optimal control, and the resulting control loops are robustly stable with respect to the a-priori identified model uncertainty. This robust optimal design methodology for multi-input multi-output controllers offers both better performance and more degrees of freedom compared to the dominating design of single-input single-output controllers for active vibration control. These additional degrees of freedom especially pay off when not only vibration amplitudes but also vibration mode shapes in closed-loop are relevant. This is for example the case when acoustic radiation shall be controlled. Active acoustic control with structural measurements and control inputs is known as active structural acoustic control, which is the second key aspect of this work. A powerful tool for describing structure-borne sound radiation is the so-called power transfer matrix. This frequency-dependent matrix allows for the computation of structure-borne sound power from knowledge of structural motion. Here, a novel experimental modeling procedure for power transfer matrices is introduced which does not impose any restrictions on the geometry of the radiating structure or the acoustic environment whatsoever. With the help of this matrix, the robust optimal control design scheme for active vibration control can be extended to the control of structure-borne sound power in a straightforward manner. It is also shown that sound radiation into enclosed spaces can be handled with minor modifications of the control scheme for free-field radiation. All modeling and control design methods presented in this thesis are validated by simulation as well as experimental results.