Abstract: The inverted pendulum is one kind of ideal object for intelligent control.The Lagrangian equations are chosen to establish the nonlinear mathematical model of the triple inverted pendulum system，and then the model is linearized in its equilibrium point and the control law by using LQR（Linear Quadratic Regulator） optimal control theory is acquired.By analyzing the simulation curves obtained from a series of stabilizing swing and perturbation experiments on the triple inverted pendulum system，it makes clear the importance of the weight coefficients in the weight matrix Q for inverted pendulum stable control，which can therefore help to optimize the selection of these weight coefficients.The experimental results show that the system presents favorable robustness and dynamic property.

Key words: triple inverted pendulum system, Linear Quadratic Regulator（LQR） theory, optimal control, weight matrix

摘要： 倒立摆是智能控制的理想对象。使用拉格朗日方程建立三级倒立摆系统的非线性数学模型，在平衡点处对其线性化，利用LQR（Linear Quadratic Regulator）最优控制理论，导出控制规律。通过对三级倒立摆一系列稳定摆动和加扰实验仿真曲线的分析，明确了加权矩阵Q中各权系数对系统稳定性控制的重要性，由此来优化权系数的选择。实验表明，系统显示出较好的鲁棒性和动态性能。

关键词: 三级倒立摆系统, LQR理论, 最优控制, 权矩阵