中文摘要：

为了研究环形单级倒立摆的稳定控制,采用拉格朗日方法推导出环形单级倒立摆系统的数学模型,并设计1个线性二次型最优控制算法控制器（LQR）。在保持权重矩阵R=1的条件下,通过实验不断调整权重矩阵Q中的参数Q11和Q33,得到Q和R最优取值。然后,对环形单级倒立摆的稳定控制进行仿真和实物控制。研究结果表明：倒立摆起摆迅速,稳定控制性能优良。

英文摘要：

In orger to study the stability control for the system of the single link rotary inverted pendulum,the mathematical model was firstly derived from Lagrange Equation and then a LQR controller was designed.Under the weight matrix R was equal to 1,the optimum control weight matrix Q and R were achieved by adjusting the values of Q11 and Q33.Simulation study and control of inverted pendulum hardware system were made.The results show that this system is quickly swigged up,and the stability control performance is excellent.