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首页> 外文期刊>Mechatronics, IEEE/ASME Transactions on >Spectral Conditions for Negative Imaginary Systems With Applications to Nanopositioning
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Spectral Conditions for Negative Imaginary Systems With Applications to Nanopositioning

机译：负虚构系统的光谱条件及其在纳米定位中的应用

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摘要

The negative imaginary (NI) property is exhibited by many systems such as flexible structures with force actuators and position sensors and can be used to prove the robust stability of flexible structure control systems. In this paper, we derive methods to check for the NI and strict negative imaginary (SNI) properties in both the single-input single-output as well as multi-input multi-output cases. The proposed methods are based on spectral conditions on a corresponding Hamiltonian matrix obtained for a given system transfer function matrix. Under certain conditions, a given transfer function matrix satisfies the NI property if and only if the corresponding Hamiltonian matrix has no pure imaginary eigenvalues with odd multiplicity. It is also shown that a given transfer function matrix satisfies the SNI property if and only if the corresponding Hamiltonian matrix has no eigenvalues on the imaginary axis, except at the origin. The results of this paper are applied to check the NI property in two nanopositioning applications.
机译：负虚数（NI）特性在诸如带有力致动器和位置传感器的柔性结构的许多系统中表现出来，可以用来证明柔性结构控制系统的鲁棒稳定性。在本文中，我们导出了在单输入单输出以及多输入多输出情况下检查NI和严格负虚数（SNI）属性的方法。所提出的方法基于给定系统传递函数矩阵所获得的相应汉密尔顿矩阵上的频谱条件。在一定条件下，给定的传递函数矩阵满足且仅当相应的哈密顿矩阵不具有纯奇偶数的虚部特征值时才满足NI特性。还表明，当且仅当相应的哈密顿矩阵在虚轴上除原点外没有特征值时，给定的传递函数矩阵才满足SNI属性。本文的结果用于检查两种纳米定位应用中的NI特性。

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