Vipperman J S, Clark R L
Department of Mechanical Engineering, University of Pittsburgh, Pennsylvania 15261, USA.
J Acoust Soc Am. 1999 Sep;106(3 Pt 1):1392-9. doi: 10.1121/1.427142.
Piezoceramic transducers have become popular elements of smart structures that are used for active vibration control and active structural acoustic control. A spatial differentiation is performed by the piezoceramic transducers since they couple into the strain field of the piezostructure. This differentiation causes higher-frequency modes to be emphasized more heavily, causing the effective compliance of the structure as seen by the piezoceramic transducer to increase with frequency. This nonuniform compliance has significant impact on the performance that can be achieved through colocated direct rate feedback control. It is shown that the rectangular piezoceramic transducer is a low-pass wave number filter with a cutoff frequency inversely proportional to the aperture size. Thus DRFB performance can be greatly improved simply by making the size of the piezoceramic transducer large relative to the size of the structure. The resulting increase in coupling to the lower-frequency modes, which are generally targeted by the control system, results in a much reduced control effort. In the event that a large aperture is not practical, it is shown that dynamic compensation can be used to obtain good performance at the cost of much increased computational complexity. Analytical open and closed loop results for an acoustically radiating simply supported plate piezostructure are presented.
压电陶瓷换能器已成为智能结构中常用的元件，用于主动振动控制和主动结构声学控制。由于压电陶瓷换能器耦合到压电结构的应变场中，因此会进行空间微分。这种微分导致高频模态被更强烈地强调，使得压电陶瓷换能器所看到的结构的有效柔顺性随频率增加。这种不均匀的柔顺性对通过共置直接速率反馈控制所能实现的性能有重大影响。结果表明，矩形压电陶瓷换能器是一种低通波数滤波器，其截止频率与孔径大小成反比。因此，只需使压电陶瓷换能器的尺寸相对于结构尺寸足够大，就能大大提高直接速率反馈控制（DRFB）的性能。与通常由控制系统针对的低频模态的耦合增加，从而使控制努力大大降低。如果大孔径不可行，研究表明可以使用动态补偿以大大增加计算复杂度为代价来获得良好性能。给出了声学辐射简支板压电结构的解析开环和闭环结果。
