二级倒立摆的 LQG 最优控制研究

摘要

为实现二级倒立摆系统的稳摆控制，应用了线性二次高斯最优控制。根据LQG的分离原理，首先利用最优控制设计控制律，得到状态反馈；由于系统状态不能完全测得，而且系统也不可避免地会受到噪声的影响，在详细给出相应参数取值规则的基础上，采用了卡尔曼滤波对系统输出做出最优估计。最后的仿真结果表明，设计的控制器能够较好地对二级倒立摆进行稳定控制，且具有抑制噪声和抗干扰能力。%In order to achieve the stable control for a double inverted pendulum system ,linear quadratic Gauss optimization control was applied .Based on separation principle of LQG ,the control law was proposed by the optimal control firstly ,and then a state feedback was obtained .Whereas the states of a system can’t be measured completely ,and the system could be inevitably affected by the noise ,based on the rule of value of the corresponding parameters ,the optimal estimations of the system outputs were received by means of Kalman filtering . The conclusive experiment shows that the designed controller steadily dominates a double inverted pendulum system ,and the system has a good ability of noise abatement and anti-interference .