Abstract

We consider the control design problem for a linear time-invariant plant. A linear controller is found that minimizes some system performance index, for example, the ratio of the plant output to the external disturbance, as the \(H_{\infty }\)-norm of the corresponding function, provided that the requirements for the system performance are satisfied, namely, those on the stability margin radius, the ratio of the control signal to the noise in measurements of the plant output, the damping ratio, and speed of response. The well-known control design methods from the Matlab Robust Control Toolbox package are considered for solving such a problem. A control design method is proposed that uses the roots of the characteristic polynomial of the closed-loop system as the variables to be varied in the standard optimization procedure and the standard pole placement procedure for obtaining the values of the controller coefficients.

中文翻译：

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SISO控制系统的极点布局优化

摘要

我们考虑线性时不变设备的控制设计问题。发现一个线性控制器可以最小化一些系统性能指标，例如，工厂输出与外部干扰的比率，如\(H_{\infty }\)- 相应函数的范数，前提是满足系统性能的要求，即稳定裕度半径、控制信号与设备输出测量中的噪声比、阻尼比和速度的要求回复。Matlab Robust Control Toolbox 软件包中众所周知的控制设计方法被认为可以解决此类问题。提出了一种控制设计方法，它使用闭环系统特征多项式的根作为标准优化程序和标准极点放置程序中的变量，以获得控制器系数的值。