基于LQR的环形一级倒立摆控制算法研究

Research on LQR Control Algorithm of Annular First-order Inverted Pendulum

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。

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 .