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H_2 and H_∞ feedforward and feedback compensators for acoustic isolation

机译：H_2和H_∞前馈和反馈补偿器，用于隔声

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摘要

This paper investigates through numerical simulations the limits of performance for a class of feedforward and feedback compensators used for structural acoustic isolation, where the emphasis is on controlling the structural vibration that is responsible for the sound radiation. The proposed designs aim to attenuate the sound pressure transmitted through a double panel system filled with absorption material. The controller must reduce the noise radiated through the back panel when the front panel is excited by an external force that causes structural vibration. A point moment simulating a piezoelectric patch attached to the back panel is the actuator. In the feedforward setting, the pre-filter assumes full information of the exogenous disturbance. On the other hand, the feedback designs assume full information of the state. The H_2 and H_∞ norms are the optimally criteria used for both the filter design and the control design. All four designs are cast in the linear matrix inequality framework and incorporate parametric uncertainties described by a bounded convex polyhedral domain. It is shown that the performance of the feedforward and the feedback compensators are equivalent when model uncertainties are not taken into account. Otherwise, considering uncertainties, the feedback compensators have a more robust behavior.
机译：本文通过数值模拟研究了用于结构声隔离的一类前馈和反馈补偿器的性能极限，其中重点是控制引起声辐射的结构振动。提出的设计旨在衰减通过填充有吸收材料的双面板系统传输的声压。当前面板被引起结构振动的外力激发时，控制器必须降低通过后面板辐射的噪声。执行器是模拟安装在背面板上的压电片的点力矩。在前馈设置中，预滤波器假定外部干扰的全部信息。另一方面，反馈设计假定状态的完整信息。 H_2和H_∞范数是用于滤波器设计和控制设计的最佳准则。所有这四个设计都在线性矩阵不等式框架中进行转换，并包含由有界凸多面体域描述的参数不确定性。结果表明，当不考虑模型不确定性时，前馈和反馈补偿器的性能是等效的。否则，考虑到不确定性，反馈补偿器将具有更鲁棒的行为。

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