论文标题
谐波放置
Harmonic Pole Placement
论文作者
论文摘要
在本文中，我们提出了一种设计状态反馈谐波控制定律的方法，该定律将线性谐波模型的闭环杆分配给某些所需的位置。该过程基于在不可逆转限制下的无限维谐波sylvester方程的解决方案。我们提供了足够的条件，以确保这种可逆性，并显示如何将这种无限二维的Sylvester方程求解到任意的小误差。结果在不稳定的线性周期系统上说明。我们还提供了反例，以说明以下事实：与经典有限的尺寸案例不同，在无限尺寸的情况下，即使满足可观察到的条件，Sylvester方程的解决方案也可能不可逆转。
In this paper, we propose a method to design state feedback harmonic control laws that assign the closed loop poles of a linear harmonic model to some desired locations. The procedure is based on the solution of an infinite-dimensional harmonic Sylvester equation under an invertibility constraint. We provide a sufficient condition to ensure this invertibility and show how this infinite-dimensional Sylvester equation can be solved up to an arbitrary small error. The results are illustrated on an unstable linear periodic system. We also provide a counterexample to illustrate the fact that, unlike the classical finite dimensional case, the solution of the Sylvester equation may not be invertible in the infinite dimensional case even if an observability condition is satisfied.
