基于 LQR 的环形一级倒立摆控制算法研究

摘要

In order to study the automatic swing -up of the first-order inverted pendulum ,and realize the stable control of it ,Lagrange method is used to establish mathematical modeling of the first -order inverted pendulum ,and design the LQR optimal controller ,then to analyze its performance .Under the condition of taking weight R = 1 ,constantly adjusting the weighting matrix Q ,it is concluded that the optimal values of Q and R .can be obtained .The experimental results show that the inverted pendulum can quickly swing up ,under stable control .%为了研究环形一级倒立摆的自动AA起摆及实现其稳定控制，采用拉格朗日方法推导建立环形一级倒立摆的数学建模，设计LQR最优控制器并对其性能进行分析。在取权重 R＝1的条件下，不断调整权重矩阵 Q ，得出最优 Q值和R值，并通过环形一级倒立摆进行实物控制。实验结果表明，倒立摆能快速起摆，并能稳定控制。