Adaptive Control Of The Magnetic Levitation System

In recent years,although the existing control theories and methods of non-linear systems have developed rapidly,they still have their own limitations.Due to the inherent nonlinearity and open-loop instability of magnetic levitation systems,neither strict state feedback nor output feedback can be directly applied.However,as a high-tech,magnetic levitation technology has a broad application prospect in the fields of transportation,industry and aerospace.As the core content of the magnetic levitation system,the design of the controller has important theoretical significance and practical value.In this paper,the controller design,stability analysis,simulation and experiment of the third-order magnetic levitation system are studied.The main contents are as follows.1.Design of robust adaptive control of voltage-type magnetic levitation system based on K-filterAiming at the third-order magnetic levitation system with parameter uncertainty and bounded external interference,a robust adaptive controller for voltage-type magnetic levitation system based on K-filter is proposed.First,the mathematical model of the third-order magnetic levitation system is deduced to separate the unknown parameters from the available state variables of the system.Then K-filter observer is used to observe unmeasured speed state variables.Finally,combined with adaptive robust control technology,the backstepping design method is used to design the stability function and the overall controller.Lyapunov function is used to prove the stability of the entire nonlinear magnetic levitation system,and the stability of the system is analyzed strictly.Simulation and experimental results demonstrate that the designed controller has good tracking performance for complex reference trajectories.2.Design of robust adaptive control for voltage-type magnetic levitation system based on wavelet neural networkAiming at the third-order magnetic levitation system with model mismatch and bounded external disturbance,a robust adaptive controller for voltage-type magnetic levitation system based on wavelet neural network is proposed.First,the nonlinear magnetic levitation dynamic model in Content 1 is simplified by coordinate transformation.The speed signal can be obtained in the form of pseudo-differential,thus making the state of the entire magnetic levitation system available.Then combined with adaptive robust technology,the backstepping design method was used to divide the system into a position error signal subsystem,a speed error subsystem and an acceleration error subsystem,and a stability function is designed.Finally,the median theorem and Nussbaum function are used in the acceleration subsystem to deal with the implicit control input and unknown control direction of the nonlinear function.The wavelet neural network and Lyapunov function are used to realize the approximation of unknown nonlinear functions and the design of a real controller,respectively.Lyapunov function is used to prove the stability of the entire nonlinear magnetic levitation system,and the stability of the system is analyzed strictly.Simulation and experimental results show that the designed controller has good tracking performance for complex reference trajectories.