倒立摆摆角全程控制的增益调度方法

Global control for the angle of inverted pendulum with gain scheduled

倒立摆摆角全程控制需要解决倒立摆摆角大范围变动以及倒立摆最低点和最高点之间不存在平衡点的大范围角度区域的控制问题。本文提出的增益调度方法在倒立摆最高点具有平衡点的邻域内使用了自抗扰控制器ADRC,在最低点及不存在平衡点的大范围角度区域使用基于Lyapunov理论的控制律。通过基于调度变量θ的插值算法协调这两种控制律的变换,避免了控制量的突变,实现了控制器参数在大范围角度下的选择。仿真结果说明了这种方法的有效性。基于Lyapunov的增益调度可以解决不存在平衡点的大范围变动工况内的非线性控制问题。

Global control for the angle of inverted pendulum has to deal with the control problem the angle changes in a large region which somewhere has no equilibrium points. In this proposed gain scheduled control method, Auto Disturbance Rejection Control(ADRC) is implemented in the region near the top with equilibrium points in it. The controller based on Lyapunov theory is applied in the region near the bottom and the region between the bottom and the top without equilibrium points. An interpolation based on scheduled variable is used to harmonize the above two controllers to obtain the controller parameters without jump through the large region. Simulation shows good effectiveness of the control system. The gain scheduled based on Lyapunov theory can solve the nonlinear control problem over a wide range without equilibrium points in it.