中文摘要：

针对目前独轮机器人的侧向平衡控制问题，设计了一种基于飞轮的单级倒立摆系统。简单地介绍了目前有关倒立摆系统的研究现状，然后利用拉格朗日方法建立了基于飞轮的单级倒立摆系统的数学模型，同时，对所建立的数学模型（精确模型和线性化模型）在Matlab／Simulink中进行了仿真验证，仿真结果证实了所建立的模型是可信的，并用现代控制理论中的二次型最优调节器（LQR）实现对倒立摆的最优控制，仿真结果表明该方法对基于飞轮的单级倒立摆系统的平衡控制是有效的。

英文摘要：

To the lateral balance control problem of single wheel robot, a single inverted pendulum system based on flywheel is designed. The research status of inverted pendulum system is introduced simply. The mathematical model of a single inverted pendulum based on a flywheel is established by using the Lagrange equation. The simulation results using Matlab/Simulink tools show that the proposed mathematical model is believable. The LQR method in modern control theory is introduced to realize the optimal control of the inverted pendulum. The simulation results show that balance control of single inverted pendulum system based on flywheel is effective.