高阶系统时滞反馈的部分极点配置问题

Partial Pole Assignment Problem for High Order Systems with Time Delay

高阶系统部分极点配置问题是通过计算反馈矩阵将系统测得的不期望的特征值替换成想要的特征值,同时能够保持其余特征结构不变。这个问题常出现在动力结构主动控制系统中。在实际中,传感器测量、处理器计算等都需要一定的时间,导致控制力出现时间滞后现象,即高阶系统时滞反馈的部分极点配置问题。一般方法解决这个问题的过程会使用响应矩阵或解希尔维斯特方程,从而比较复杂,计算量大。文章提出一种明确的单输入算法解决这个问题,方法的优点是简单有效、易于实现,且在过程中没有使用响应矩阵等构成复杂的运算。实例验证了该方法的有效性和实用性。

The partial pole assignment problem for high order systems with time delay is considered,which the unwanted eigenvalues are moved to desired values and all other eigenpairs remain unchanged by calculation feedback matrix. The problem often appeared in the power structure in the active control system. In practice,these processes such as sensor,processor,calculation and so on take time,which lead to control time lag phenomenon. That was partial quadratic pole assignment problem with time delay. A general method to solve this problem is using the receptance matrix or solve the Sylvester,which is more complex and need large amount of calculation. A clear single input algorithm to solve this problem is presented in this paper. The advantage of this method is simple,effective,easy to implement,and have no complex calculations caused by response matrix. Finally,algorithm implementation and numerical examples show that the proposed method is effective and practical.