Active H-infinity control of sound radiation from thin plates

Abstract

The problem of active control of sound radiated by thin plates using arrays of spatially discrete piezoceramic sensors and actuators is addressed. A general methodology for the design of active structural acoustic controllers is presented. This methodology utilizes finite element modeling as a generic tool to perform structural discretization. The sound radiation mechanism is assumed to be that of structural bending waves in thin-walled structures. The discretized structure including the sensors and actuators is presented in state-space. The sound radiated by the structure into the far field is expressed as a quadratic form of the system states. This formulation is used to define the acoustic performance specification in a T^oo controller design setup. The methodology is applied to a plate equipped with three sensor/actuator pairs in a rigid baffle excited by a persistent external force. The controller performance is evaluated using numerical simulations. This performance is compared with controllers designed to attenuate structural vibrations. It is shown that the sound radiated by the plate into the farfield is more effectively controlled and reduced by dedicated acoustic controllers than by controllers designed to attenuate structural vibration. Introduction A Structural Acoustic Control (ASAC) has been extensively addressed in the literature. ASAC, as an application of intelligent structures technology, relies on the use of piezoelectric copolymers and ceramics (such as PVDF and PZT, respectively) both as sensors and actuators. The possibility of estimating the sound radiated by a vibrating structure into the far-field from measurements of the structural velocity field was investigated both 'Graduate Student, Student Member AIAA t Senior Lecturer, Member AIAA 'Professor, Associate Fellow AIAA analytically and experimentally by a number of researchers including Clark et al., Mathur and Iran, and others. The analytical formulation reported in these and other studies was performed exclusively on simple structures such as simply supported beams and plates, while neglecting the mass and stiffness of the sensors and actuators. The treatment of more complex structures, such as air plane fuselage and cylindrical shells, was restricted to laboratory experiments. Model based ASAC using state-space formulation and linear quadratic Gaussian (LQG) controller was presented by Baumann et al., who however did not include consistent sensing and actuation models in the design and evaluation of the controlled structure. Fuller et a/. summarized the state-ofthe-art in ASAC research and expanded the statespace based optimal control techniques for ASAC controller design. Their results, however, were limited to homogeneous structures for which both the mode shapes and the sound radiation mechanisms are assumed to be known. State-space models for active control of acoustic waves generated by a rigid piston were implemented by Wu et al., who also used LQ controller design. In summary, model-based ASAC designs reported in the literature are limited to structures for which the vibrational mode shapes and sound radiation mechanisms are assumed to be known analytically. Therefore, a methodology is needed for the design and analysis of general ASAC systems. This study attempts to address this need. The methodology developed herein utilizes the advanced capabilities of finite element (FE) software tools to obtain a discrete representation of the continuous structure dynamics. This allows the analysis of complex structural systems. In this study it is shown that the acoustic power radiated by the structure into the far-field can be approximately expressed in a quadratic form of system states. This forms the basis for a controller Copyright © 1997 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. American Institute of Aeronautics and Astronautics