Research On Fractional-order Calculus-based Identification And Control Techniques For Magnetic Levitation System

When describing systems,fractional calculus can more fully reflect the characteris-tics of real systems.Compared with integer order controller,fractional order control has the advantage of order tunable.This paper takes the levitation system of medium-and-low speed maglev train as the research object,and proposes a magnetic levitation system mod-eling method based on fractional-order calculus for the problem of large gap fluctuations when the magnetic levitation train passes through the track steps,and designs a fractional-order PI^λD^μcontroller based on the model,so that the control performance can be better improved.The research content of this paper is as follows.1.To address the problem of inaccurate modeling of the suspension system of mag-netic levitation trains,a system identification method based on fractional order calculus is proposed.Most of the existing models are obtained by first establishing physical models based on the relevant theories of electromagnetism and dynamics,and then linearizing them at the equilibrium point.This modeling method makes the control algorithm suffer from the inaccuracy of the model,which leads to the lack of stability and robustness.In this paper,an identification method of magnetic levitation system based on fractional calculus is proposed.The input signal and output signal of Haar wavelet decomposition system are used to transform the fractional differential equation into fractional integral equation,and then the Haar wavelet integral operation matrix is introduced to transform the frac-tional integral equation into algebraic equation,so that the identification process can use the traditional method.The fractional-order system identification problem is transformed into a least-squares optimization problem by giving the order and letting the order vary within a certain range to avoid nonlinear optimization.2.The wavelet multi-resolution analysis theory is introduced to optimize the speed of levitation system identification.By discarding the high-frequency coefficients of the input and output signals and reducing the dimension of the matrix involved in the opera-tion,the acceleration of the recognition process is achieved.The method accelerates the recognition speed without increasing the error of recognition.In addition,the method has certain anti-interference ability,and can achieve good recognition results in the case of noise.Simulation and experiments verify the effectiveness of the proposed identification method,and the results show that the fractional order system can describe the suspension system more accurately.3.Based on the discriminative magnetic levitation system model,the effect of pa-rameter variation on the control performance in the fractional-order PI^λD^μcontroller is analyzed;the fractional-order PI^λD^μcontroller is designed based on the particle swarm optimization algorithm,and simulations and physical experiments are conducted.Simula-tion results show that the fractional order PI^lambdaD^mucontroller has better control effect than the traditional integer order PIDcontroller.The experimental results are in agree-ment with the simulation results,showing that the fractional-order PI^λD^μcontroller can reduce the amplitude of gap fluctuations and shorten the time required to return the system to the steady state than the integer-order PID controller under the condition of external disturbances in the system.