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Assignment of eigenvalue sensitivities from receptance measurements

机译：从接受度测量中分配特征值灵敏度

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The paper addresses the problem of eigenvalue assignment in active vibration control by the receptance method using single-input state feedback. It is demonstrated that not only can assignment be applied to the poles of the system but also to the sensitivities of the poles. The approach described has applications particularly in vibration absorption and the detuning of structures to avoid resonance. Insensitivity of the poles to perturbations in the system gains is desirable from the point of view of robust dynamical performance. The perturbation method is applied to a characteristic equation resulting in expressions for the derivatives of the pole eigenvalues with respect to the control gains. The method is based entirely upon measured vibration data in the form of receptances, there being no need to determine or to know the M, C, K matrices. The closed-loop sensitivities are expressed as linear functions of the control gains, thereby making accessible the assignment of the sensitivities to chosen values. For the case of the open-loop system, the method is shown to produce identical results to established eigenvalue sensitivity procedures. It is demonstrated that chosen eigenvalues may be rendered insensitive to all the control gain terms by choice of the distribution vector b. Numerical examples are provided to illustrate the working of the technique.
机译：本文通过采用单输入状态反馈的接受方法解决了主动振动控制中的特征值分配问题。事实证明，分配不仅可以应用于系统的极点，而且可以应用于极点的灵敏度。所描述的方法尤其在振动吸收和结构失谐以避免共振方面具有应用。从鲁棒的动态性能的观点来看，极点对系统增益的扰动不敏感是理想的。将扰动方法应用于特征方程，从而得出极特征值相对于控制增益的导数表达式。该方法完全基于接收形式的测得的振动数据，无需确定或知道M，C，K矩阵。闭环灵敏度表示为控制增益的线性函数，从而可以将灵敏度分配给所选值。对于开环系统，该方法显示出与已建立的特征值敏感度程序相同的结果。已经证明，通过选择分布矢量b，可以使所选择的特征值对所有控制增益项不敏感。提供了数字示例来说明该技术的工作。

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