单级倒立摆系统是一种广泛应用的物理模型，针对多变量、非线性、强耦合性的倒立摆系统，运用牛顿- 欧拉方法和拉格朗日方法分别建立了倒立摆的数学模型；然后对该模型进行闭环状态反馈控制,并在MATLAB环境下进行仿真；设计出该系统的降维观测器，并在 simulink上实现，实验结果证明了该降维观测器的有效性。

The simple inverted pendulum is a kind of physical model with broad application fields. According to multivariable, nonlinear and strong coupling inverted pendulum system. First, a mathematical model for the pendulum is set up by using the Newton-Euler method and Lagrange method respectively; then, the State feedback method is adopted to design the controllers, the simulation experiments were simulated by using the Matlab and its toolbox Simulink; at last, design the reduced-order observer of the system, by the simulation experiment through the Simulink in MATLAB results, not only the validity of the reduced-order observers were confirmed, but also their qualities and characteristics were shown fully.