Position Tracking Control Of Maglev System Based On LQR

The magnetic levitation system is widely used in high-speed maglev trains,dust-free factories and other fields because of its characteristics of no friction,no noise and no contact.In order to realize the position tracking control of maglev system,the linearized model of maglev system is established in this thesis.The characteristics of LQR(Linear Quadratic Regulator,LQR)second-order error feedback control and third-order error feedback control system are studied,and the basis for selecting LQR weighting matrix is given.At the same time,a LQR weighting matrix optimization method based on improved grey wolf optimization algorithm is designed.The specific research contents are as follows :Firstly,the linearized model of maglev system is established.Based on the analysis of the magnetic characteristics and sensor characteristics of the maglev system,the mathematical model of the maglev system is built,and the linearized model is designed by Taylor series expansion method.Finally,the Z-N(Ziegler-Nichols,Z-N)method is used to realize the tuning of the PID(Process Identifier,PID)regulator parameters.The simulation results show the effectiveness of the model linearization.Secondly,LQR second-order error feedback controller of maglev system is designed.For the position tracking control of the maglev system,the LQR second-order error feedback state equation is constructed,and the selection criteria of the proportional gain are determined according to the error dynamic range and input limit of the maglev system.Compared with the PID regulator,the LQR second-order error feedback controller has better performance.Thirdly,aiming at the problem of poor robustness of LQR second-order error feedback controller,a LQR third-order error feedback controller for maglev system is designed.Based on the state equation of the LQR third-order error feedback controller of the maglev system,the influence of the weighting matrix on the tracking performance is analyzed.The empirical formula for determining the weighting matrix is given through simulation.The simulation shows that the LQR third-order error feedback controller has stronger robustness than the PID and LQR second-order error feedback controllers,and the control signal changes slowly,which is more conducive to the hardware implementation of the controller.Fourthly,aiming at the subjectivity of weighting matrix selection in LQR,a LQR weighting matrix optimization method based on improved grey wolf optimization algorithm is proposed.In order to improve the performance of the traditional grey wolf optimization algorithm,the chaotic mapping initialization method is used to replace the random initialization method in the traditional GWO(Grey Wolf Optimization,GWO)to improve the distribution of population initialization.Secondly,the hunting behavior of grey wolves is improved.On the basis of linear random search,the spiral search method is added to increase the possibility of finding the potential optimal solution.Finally,the simulation results show that the proposed method has faster convergence speed and higher convergence accuracy than the traditional grey wolf optimization algorithm,whale optimization algorithm and particle swarm optimization algorithm.