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首页> 外文期刊>Mechanical systems and signal processing >Pole assignment in vibrating systems with time delay: An approach embedding an a-priori stability condition based on Linear Matrix Inequality
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Pole assignment in vibrating systems with time delay: An approach embedding an a-priori stability condition based on Linear Matrix Inequality

机译：时滞振动系统中的极点分配：一种基于线性矩阵不等式的先验稳定性条件嵌入方法

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摘要

The assignment of the poles of a second order vibrating system through state feedback is a problem that has been widely investigated and for which asymptotic stability has been precisely characterized. In the presence of time delayed input or output, however, the available methods often address the issue of stability only by a-posteriori verification, which is made difficult by the characteristic equation of the system being transcendent. A convenient way to characterize delay-independent stability of time delayed linear systems makes use of Linear Matrix Inequalities, which are advantageous also from the computational point of view, given the reliability that algorithms for semi-definite optimization have acquired over the recent years. In this paper, a method for the assignment of a subset of closed-loop poles, while the remaining ones are constrained in the left half of the complex plane, is presented. The method is numerically validated in four meaningful test-cases, comparable to the ones that are used in the current literature. The obtained results demonstrate that the proposed method can accurately assign the desired subset of poles and guarantee asymptotic stability in the presence of bounded time delay.
机译：通过状态反馈对二阶振动系统的极点进行分配是一个已经广泛研究的问题，并且已针对该问题精确表征了渐近稳定性。但是，在存在延时的输入或输出的情况下，可用的方法通常仅通过后验验证来解决稳定性问题，而后验验证则使系统的特性方程式难以实现。表征时滞线性系统的与延迟无关的稳定性的简便方法是利用线性矩阵不等式，鉴于近年来半定优化算法所获得的可靠性，线性不等式从计算的角度来看也是有利的。本文提出了一种闭环极子子集的分配方法，而其余子极则约束在复平面的左半部。该方法在四个有意义的测试案例中得到了数值验证，与当前文献中使用的测试案例相当。获得的结果表明，所提出的方法可以精确地分配期望的极点子集，并在存在有界时间延迟的情况下保证渐近稳定性。

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