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首页> 外文期刊>IEEE Transactions on Automatic Control >Analytic expressions of transfer function responses and choice ofnumerator coefficients (zeros)
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Analytic expressions of transfer function responses and choice ofnumerator coefficients (zeros)

机译：传递函数响应的解析表达式和分子系数的选择（零）

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General analytic expressions of transfer function responses are derived in this paper. The analytic forms include the numerator coefficients of the transfer function, a Vandermonde-like matrix, and a vector containing the transfer function eigenresponses, the latter two only depending on the eigenvalues. Several characteristics of basic transient responses are derived, e.g., their exact number of zeros. An upper bound on the number of extrema of the step response is obtained. An algorithm is suggested for the selection of the numerator coefficients, assuming fixed eigenvalues, using the derived characteristics of the basic transient responses, effectively leading to a suboptimal choice. Furthermore, the analytic formulas are used to calculate the numerator coefficients optimally, by minimizing the step transient, the ramp transient, the parabolic transient, etc. Simulations are presented indicating the properties of the basic transient responses and the transfer function response properties based on optimal and suboptimal choices of the numerator coefficients
机译：本文推导了传递函数响应的一般解析表达式。解析形式包括传递函数的分子系数，范德蒙德式矩阵和包含传递函数特征响应的向量，后两个仅取决于特征值。得出了基本瞬态响应的几个特征，例如它们的确切零个数。获得阶跃响应的极值个数的上限。建议使用假定的特征值固定的特征值，利用基本瞬态响应的导出特性，选择分子系数，从而有效地导致次优选择。此外，通过最小化阶跃瞬变，斜坡瞬变，抛物线瞬变等，使用解析公式来优化计算分子系数。仿真表明基本瞬态响应的特性和基于最优值的传递函数响应特性和分子系数的次优选择

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