基于自适应模糊PID的二级倒立摆控制方法

Based on Adaptive Fuzzy PID of Two-stage Inverted PendulumControl Method

为了提高平面二级倒立摆模型控制过程的动态、静态性能及对控制器参数的自适应整定能力和抗干扰能力,提出一种将PID控制与模糊控制相结合的自适应控制算法。应用拉格朗日方程建立平面二级倒立摆数学模型。根据实际经验确定模糊隶属度函数并建立模糊规则表。通过计算误差和误差变化率设计自适应模糊PID控制器。为设计的控制器建立仿真模型,并与PID、模糊、LQR等控制方法对比实验性能。仿真结果表明:建立的自适应模糊PID控制器的超调量、调节时间更小,上、下摆角及位移的摆动幅度低,控制精度更高,且系统抗噪能力强,鲁棒性良好。验证了所提方法的理论正确性和控制算法的有效性。

In order to improve the dynamic and static performance of the control process of the plane two-stage inverted pendulum,as well as the adaptive setting ability and anti-interference ability of the controller parameters,an adaptive control algorithm combining PID control and fuzzy control is proposed.Firstly,lagrange equation is used to estabilish the plane Two-stage inverted pendulum’s mathematical model.Secondly,according to the practical experience,the fuzzy membership function is determined and the fuzzy rule table is established.The adaptive fuzzy PID controller is designed by calculating error and error variation rate.A simulation model is established for the designed controller,and the experimental performance is compared with PID,fuzzy,LQR and other control methods.The simulation results show that the adaptive fuzzy PID controller has less overshoot and adjustment time,lower amplitude of swing of up and down angle and displacement,higher control precision,strong antinoise ability and good robustness.The theoretical correctness of the proposed method and the effectiveness of the control algorithm are verified.