一阶倒立摆的LQR稳定控制研究

倒立摆是一个典型的快速、多变量、非线性、绝对不稳定系统,对倒立摆系统的稳定性研究在理论上和方法上具有深远的意义。本文首先叙述了对倒立摆系统稳定性研究的意义,综述了倒立摆的研究现状。其次着重介绍了LQR控制的相关理论,设计出一阶倒立摆系统的控制器。然后,对设计出的控制器进行Matlab/Simulink仿真并将仿真结果应用于固高倒立摆实时控制系统中,比较实验结果,最后得出结论。

Study of LQR Stability Control in an Inverted Pendulum

The inverted pendulum is a kind of typical fast system with multi-variables, non-linearity, strong couoling and instinct instability. It＇ s very important for the profound significance of stability study of the inverted pendulum both in theory and practice. In this paper, the significance of there searching on the stability and the study on current conditions of inverted pendulum has been described generally at the first. After that, it introduces the theory of LQR control in details and designs the controller for the inverted pendulum system . Then, according to the controller designed by the controlling theories, do Matlab/Simulink. At last the result is used in the real-time controlling on the Googol inverted pendulum experiment equipment and the final conclusion can be made after the real-time experiment results.