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在控制理论及应用领域中,区域极点配置一直是控制系统设计的重要方法之一。该文针对线性连续及离散时间系统提出了一种统一的基于广义逆理论的圆形区域极点配置方法,即设计状态反馈控制器,使闭环极点位于给定的圆状区域中。文中给出了期望控制器存在的充要条件及其参数化代数表示。与已有结果相比,该文方法只需求解一线性矩阵方程,因而更易工程实现。数值算例验证的了该方法的有效性及直接性。
In the field of control theory and application, the regional pole assignment has been one of the most important methods to control system design. In this paper, we propose a uniform circular pole placement method based on generalized inverse theory for linear continuous and discrete time systems. The state feedback controller is designed so that the closed-loop poles lie in a given circular region. In this paper, the necessary and sufficient conditions for the existence of a desired controller and its parameterized algebraic representation are given. Compared with the existing results, the proposed method only needs to solve a linear matrix equation and is therefore easier to implement. Numerical examples demonstrate the effectiveness and immediacy of this method.