Abstract This paper proposes a novel method for antiresonance assignment and regional pole placement in linear time-invariant vibrating systems, by means of state feedback control. The method also handles asymmetric systems and unstable ones too. Additionally, it works with both point and cross-receptances and handles the simultaneous assignment of more antiresonances in the same receptance. The method relies on two stages. In the first stage, the desired pairs of closed-loop zeros of a prescribed receptance are exactly assigned. In the second stage, all the closed-loop system poles are placed within the desired region of the complex plane. This feature allows the controller to impose the system stability and to feature the desired dynamic properties through a regional pole placement. Since the gain correction computed in the second stage is obtained as a solution of the homogeneous system related to the zero-assignment problem, it does not cause any spillover on the assigned zeros. The first step exploits the receptance method for gain computing, while the second step uses the first-order model formulation to exploit all the benefits of the Linear Matrix Inequality theory, by formulating a bilinear matrix problem solved as a semidefinite optimization aimed at reducing the control effort. The chief original contribution of the proposed method is that it embeds an a-priori imposition of both the closed-loop stability and the pole clustering in the desired regions, by overcoming the limitations of most of the methods appeared in the literature. The method effectiveness is demonstrated through five meaningful test cases.

中文翻译：

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具有区域极点布置的反共振分配的线性振动系统的主动控制

摘要 本文提出了一种利用状态反馈控制在线性时不变振动系统中进行反共振分配和区域极点布置的新方法。该方法还处理非对称系统和不稳定系统。此外，它适用于点和交叉接收，并在同一接收中处理更多反共振的同时分配。该方法依赖于两个阶段。在第一阶段，指定接收的所需闭环零点对被精确分配。在第二阶段，所有闭环系统极点都放置在复平面的所需区域内。此功能允许控制器通过区域极点放置来增强系统稳定性并具有所需的动态特性。由于在第二阶段计算的增益校正是作为与零分配问题相关的齐次系统的解决方案获得的，因此不会对分配的零造成任何溢出。第一步利用接收方法进行增益计算，而第二步利用一阶模型公式来利用线性矩阵不等式理论的所有优点，将双线性矩阵问题公式化为半定优化，旨在减少控制努力。所提出的方法的主要原始贡献是它通过克服文献中出现的大多数方法的局限性，在所需区域中嵌入了闭环稳定性和极点聚类的先验施加。该方法的有效性通过五个有意义的测试用例来证明。