非线性倒立摆起摆和稳定控制研究

该文深入研究了直线倒立摆的摆起和稳定控制。通过两种方法对倒立摆非线性模型进行线性化得到线性化模型。第一种方法是利用微分几何李导数理论，对坐标和输入输出进行变换，然后在局部进行线性化得到一个线性化模型；另一种方法直接在平衡点附近进行线性化得到线性化模型。最后用MATLAB仿真和实物控制分别证明了能量反馈理论和稳定控制理论具有良好的控制效果，且通过Lie理论对系统进行坐标变换得到线性化模型比略去高阶项得到的线性化模型具有更好的鲁棒性和控制效果。

Control of Swing-up and Stabilization of an Inverted Pendulum

In this paper , the swing-up and stabilization problems of an inverted pendulum are studied in detail . Two linear models are elicited by linearizing the nonlinear model of an inverted pendulum. The first model is presented by using the coordinate change and input transformation via the Lie theoretic approach. And the second model is presented by discarding high order approximation of the nonlinear system. The result of simulation and effect on control prove that the theories of energy feedback and stability control are effective. At the same time an conclusion can be drawn that the model using the coordinate change and input is closer to the real model than the model without the high order of nonlinear system.