二阶控制系统部分特征值配置及其敏感度分析

Partial eigenvalue assignment and sensitivity analysis ofsecond order control system

基于响应矩阵法,研究了二阶控制系统的部分特征值配置问题并对闭环系统的敏感度进行分析。部分特征值配置时,借助系统矩阵与特征矩阵的正交关系,建立了部分特征值配置的无溢出算法。该算法不需要求解Sylvester方程,通过少部分信息即可实现目标特征值的配置。另外还建立了特征值和特征向量的敏感度配置的响应矩阵法。最后通过算例展示了算法的有效性。

Based on the receptance matrix method,the partial eigenvalue assignment of second-order control systems was studied,and the sensitivity of closed-loop systems was analyzed.In partial eigenvalue assignment,a no spill-over algorithm for partial eigenvalue assignment was established by using the orthogonal relationship between system matrix and eigenvalue matrix.The algorithm did not need to solve Sylvester equation,and the configuration of target eigenvalues can be realized through a small part of information.In addition,the response matrix method for the sensitivity assignment of eigenvalues and eigenvectors was also established.Finally,an example showed the effectiveness of the algorithm.