二级倒立摆的奇异摄动分频控制

Singular Perturbed Frequency Dividing Control on Double Inverted Pendulum

首先分析了采用拉格朗日方法建模的二级倒立摆系统,并建立其奇异摄动系统模型,然后根据奇异摄动分频控制的特点,用奇异摄动快慢子系统的分解方法,得出二级倒立摆的快慢子系统。根据不同频段的频率特性采用合理的控制器设计,再进行恰当的组合得到整个系统的稳定控制器。最后,将其控制效果和传统的H∞控制器效果进行对比,得出奇异摄动分频控制应用在倒立摆系统上的有效性。

In this paper, firstly, the inverted pendulum system is analyzed by Lagrange modeling and the model of the inverted pendulum is built. Secondly, according to the characteristics of the singular perturbation frequency dividing control, by decomposing the singular perturbation slow and fast subsystem, the slow and fast subsystem of the double inverted pendulum has been obtained. According to the frequency characteristic of different frequency band, reasonable controller has been designed, and then the composite stable controller of the system is obtained by apt combination. At last, control effect of the singular perturbed frequency decomposition controller is compared with the H∞ controller, we can come to the conclusion that the validity of applying the method of singular perturbed frequency dividing control to the inverted pendulum system.