中文摘要：

针对高阶次、不稳定、多变量、非线性、强耦合的两轮自平衡移动机器人系统，采用Lagrange方程推导出动力学模型，对其进行稳定性和可控性判断，并利用LQR和龙伯格极点配置的方法在此模型的基础上对两轮自平衡机器人的姿态和速度进行控制，可获得较为稳定的动态平衡过程。给出了数学模型推导的具体步骤，分别采用以上两种方法进行了仿真研究和比较。仿真实验结果表明，这两种控制方法对机器人的稳定性控制都是有效的。其中龙伯格极点配置控制方法使系统的跟踪速度更快、稳定性更高，具有较高的实际应用价值。

英文摘要：

Aiming to the two-wheeled self-balancing mobile robot system with high-rank, unstable, multi-variable, strongly coupling, complicated dynamic nonlinear property, this paper established the dynamic model applied Lagrange program, and carried on the stability and the controllability judgment to it. Based on this model, using LQR and the Dragon Bergh extreme disposition method carried on the control to the two-wheeled self-balancing mobile robot in the posture and the speed, and obtained the stable dynamical balance process. Listed some material steps at establishing the mathematics model, and used above two methods to do the simulation research and the comparison separately. It indicates through the simulation experiment that the two control method to the robot stable control all are effective. Dragon Bergh extreme disposition control method causes the system that the track speed to be quicker, the stability is higher, and it has the high practical application value.