Research On Predictive Control Of Magnetic Levitation Ball System Based On LSTM-ARX Model

Due to the uneven distribution of the magnetic field excited by the electromagnet in the magnetic levitation ball system,the nonlinear motion of the steel ball,and the nonlinear relationship between the voltage and current of the electromagnet coil,as well as other factors,the magnetic levitation ball control system has open-loop instability,timevarying,susceptible to interference and other strong nonlinear characteristics.Therefore,it is of great significance to study the characteristics analysis,modeling and control methods of the magnetic levitation ball system.Aiming at the strong nonlinearity in the magnetic levitation ball control system,this paper analyzes and deduces two important nonlinear factors.One is the relationship between the electromagnetic force on the steel ball in the control system and the distance from the magnetic pole surface;The other is the relationship between the electromagnet terminal voltage and the coil current.On this basis,this paper proposes the LSTMARX model based on the excellent function fitting ability of the long short-term memory(LSTM)network and the nonlinear description ability of the state-dependent autoregressive(SD-ARX)model,and introduces its model structure and parameter identification method in detail.The identification results of the magnetic levitation ball system verify the excellent modeling performance of the LSTM-ARX model.At the same time,this paper designs the model predictive controllers ARX-MPC,RBF-AXR-MPC and LSTM-ARX-MPC,and further designs the predictive function controller LSTM-ARX-PBC based on the Bernstein function and the LSTM-ARX model to reduce the online computation time of the model predictive controller.On this basis,this paper carry out a detailed and comprehensive physical control experiment study,and conducts step response control experiments and anti-interference experiments with different amplitudes at the high,medium and low operating points of the magnetic levitation ball system.Analyze and compare the dynamic tracking performance of the magnetic levitation ball under the regulation of PID,ARX-MPC,RBF-ARX-MPC,LSTM-ARXMPC and LSTM-ARX-PBC controllers.The physical control results of the magnetic levitation ball show that the adjustment effect of LSTM-ARX-MPC is far better than that of PID and ARX-MPC,and the control effect of LSTM-ARX-MPC is also significantly improved which compared to RBF-ARX-MPC;the prediction function controller LSTM-ARX-PBC greatly reduces the online computation time of the controller without increasing overshoot.The experimental results demonstrate the effectiveness of the predictive control algorithm based on the LSTM-ARX model and the function predictive controller based on the Bernstein function in the control of the magnetic levitation ball system.