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A pole-zero based criterion for optimal placement of collocated sensor-actuator pair

机译：基于极零的基于零零的合并传感器致动器对的标准

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摘要

A new and computationally efficient criterion is developed concerning the optimal placement of a collocated sensor-actuator pair for active control of structural vibrations with a low authority controller. The basic idea behind the proposed criterion is based on the maximization of the pole-zero distance in open-loop which has a direct link with the maximum achievable damping ratio once in closed-loop. Unlike poles, the determination of transmission zeros is computationally tedious because it depends upon the placement of the sensor-actuator pair. Therefore, a new approximation to reliably estimate the transmission zeros is also introduced which remarkably enhances the computational efficiency of the proposed optimization criterion. The effectiveness of the proposed criterion is demonstrated on a cantilever beam and a simply supported plate and is also compared with two other widely used criteria: the Gramian controllability and the spatial H_2 norm. It is shown that the proposed criterion is pertinent and ensures higher damping values for the cantilever beam compared to the other two criteria. Nonetheless, the criterion requires adaptations to improve its reliability for structure with large modal density such as a simply supported plate.
机译：关于具有低权限控制器的结构振动的主动控制的连接传感器致动器对的最佳放置，开发了一种新的和计算上有效的标准。所提出的标准背后的基本思想基于开环中的极零距离的最大化，其具有与闭环中的最大可实现的阻尼比的直接链路。与杆不同，传输零的确定是计算乏味的，因为它取决于传感器致动器对的放置。因此，还引入了可靠地估计传输零的新近似，这显着提高了所提出的优化标准的计算效率。在悬臂梁和简单的支撑板上证明了所提出的标准的有效性，并且还与另外两个广泛使用的标准进行比较：克甘头可控性和空间H_2规范。结果表明，与其他两个标准相比，所提出的标准是相关的，并确保悬臂梁的更高阻尼值。尽管如此，标准需要适应，以改善其具有大型模态密度的结构的可靠性，例如简单的支撑板。

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