基于RBF神经网络的磁悬浮时滞系统Backstepping控制与仿真

Backstepping Control and Simulation of Magnetic Suspension Time Delay System Based on RBF Neural Network

摘要: 磁悬浮系统能使铁磁性物体悬浮在空中，可以应用于科研、医疗、娱乐、交通等多个领域。为了解决非线性、不稳定磁悬浮系统的控制问题，建立了磁悬浮时滞系统的数学模型，采用了Backstepping控制以及RBF神经网络和Backstepping控制结合的方法进行研究，采用李雅普诺夫稳定性理论分别设计非线性控制器，保证闭环系统的理论稳定。在此基础上，利用Radial basis function (RBF)神经网络的逼近特性，设计了自适应律，研究了对系统中未知函数的拟合。最后，通过MATLAB对两种控制方法的效果进行对比，仿真结果表明，两种方法均能使系统稳定，RBF神经网络与Backstepping控制结合的方法能较快实现稳定，效果更好，且RBF神经网络对未知函数的拟合效果也良好。

Abstract: The magnetic levitation system can levitate ferromagnetic objects in the air, which can be used in scientific research, medical treatment, entertainment, transportation and other fields. In order to solve the control problem of nonlinear and unstable maglev system, a mathematical model of the maglev delay system is established, the backstepping control and the combination of RBF neural network and Backstepping control are used to study, and the nonlinear controller is designed by using the Lyapunov stability theory to ensure the theoretical stability of the closed-loop system. On this basis, the adaptive law is designed by using the approximation characteristics of the Radial basis function (RBF) neural network, and the fitting of the unknown functions in the system is studied. Finally, the results of the two control methods are compared by MATLAB, and the simulation results show that the two methods can make the system stable, and the combination of RBF neural network and Backstepping control can achieve stability quickly and better, and the RBF neural network has a good fitting effect on the unknown function.