This paper discusses the modelling of systems for active structural acoustic control. The finite element method is applied to model structures including the dynamics of piezoelectric sensors and actuators. A model reduction technique is presented to make the finite element model suitable for controller design. The reduced structural model is combined with an acoustic model which uses the radiation mode concept. For a test case consisting of a rectangular plate with one piezo patch the model reduction technique is validated. The results show that the an accurate prediction of both the structural and acoustic response is predicted by the reduced model. The model is compact requiring small simulation times, which makes it attractive for control system design. Finally the control performances for both structural and acoustic error criteria are presented.

most cases air, and cause pressure disturbances which are experienced as noise. This exchange of vibrational and acoustic energy is referred to as acoustoelastic interaction. Acousto-elastic interaction is described by time and space dependent disturbances, which propagate through the two media as waves, and are characterised by the wave propagation speed, frequency, wavelength and amplitude. The human ear is able to detect sound in the frequency range between 20 Hz and 20 kHz.Integration of noise and vibration issues in the design of consumer products, cars, machines, etc. can certainly improve the sound quality of such products, but it will not prevent noise problems. It is therefore common to tackle noise problems with additional means. The traditional way is to use passive methods, which are based on absorption and/or reflection of acoustic energy. Examples of absorption-based techniques are sound absorbing materials such as glasswool and foam and (coupled) tube resonators [1,2]. Sound can be reflected with single or double wall panels [3], for instance as shielding for noisy machinery. Passive methods provide an adequate solution to many noise problems, but have the drawback that they tend to be more attractive for the higher frequencies (> 1000 Hz). At low frequencies, passive methods often lead to an unacceptable increase in mass and volume.In contrast to passive methods, active control methods rely on an external energy source. Active control systems can take many forms, but such a system typically consists of sensors, to detect a response, an electronic controller, to suitably manipulate the sensor signals, and actuators, to influence the response. Active control is mainly suited for the low frequency range, where passive methods are less attractive [4]. The complementary use of active and passive methods is thus an attractive solution to noise (or vibration) problems. The subject of this thesis is an active control method for reducing the noise produced by vibrating structures. More precisely, the objective is to change the vibration of the structure in such a way that the sound radiation is reduced. Active control of sound and vibrationThe idea of active control of sound and vibration is not new. In 1936, Paul Lueg [5] patented a technique for controlling sound with additional sound. His idea is illustrated in Figure 1.1 for the control of a plane sound wave in a duct. An acoustic source A produces a sound wave s 1 , which propagates through the duct (from left to right). The components of the active control system are a microphone M , an electric controller V and a loudspeaker L. The • Smart aircraft wings [17]. The idea of using smart structures technology for shape control of aircraft wings is aimed at providing improved aerodynamic and aeroelastic performance compared to conventional wings. Researchers have for instance looked at hingeless trailing edge control surfaces ("flaps").• Active rotor blades [18,19,20]. During flight, helicopter rotor blades are exposed to unsteady aerodynamic loading con...