Research On Robust Adaptive Control Of Magnetic Levitation Systems

Magnetic levitation system makes the objects realize non-contact suspension by magnetic attraction force overcoming its own gravity.It has lots of advantages such as non-contact,high speed,low energy consumption,low pollution,high safety and so on.Because of the advantages of the magnetic levitation system,it has been widely used in different fields including traffic transportation industry,aeronautical and space technologies industry and industrial production etc.However,the magnetic levitation system is an open-loop unstable nonlinear system in nature and always subjected to various kinds of uncertainties and external disturbance,as a result,it is a challenge job to design the controller for it.In this thesis,the dynamic models of single-point and two-point magnetic levitation systems are built respectively,which possess the parametric uncertainties,external disturbance and mechanical coupling between different levitation points in the levitation systems.On this basis,the corresponding tracking control problems of two kinds of magnetic levitation systems are studied to achieve the tracking objective.The main research contents of this thesis are as follows:Firstly,taking magnetic levitation ball system as the research object of the singlepoint levitation system and based on its working principle,the single-point nonlinear dynamics model subjected to parametric uncertainty and mismatched external disturbance is built.Then a robust adaptive control based on the disturbance observer is designed.In the algorithm,the disturbance observer is used to estimate the external time-varying mismatched disturbance and its state is integrated into the proposed control law to realize the disturbance compensation effectively.The theoretical analysis and mathematical simulation show that the control law can effectively attenuate the influence of external disturbance and parametric uncertainties on the system performance,and the closed-loop system has satisfying tracking performance.Secondly,to deal with jump of unknown parameter and/or external disturbance largely variation during operating in single-point levitation system,the performanceoriented mathematical model is built by introducing system prescribed tracking performance into original system with the aid of certain output error transformation.On this basis,an Immersion and Invariance(I&I)adaptation law is adopted to recover the unknown parameter in system,which introduces an additional tuning function to shape the convergence procedure of the estimated parameter.And an extended disturbance observer is designed to deal with external disturbance of the system.Combined with the baseline dynamic surface controller with I&I adaptation law and disturbance observer,the control law for the prescribed tracking performance is obtained.Theoretical analysis shows that the control law can achieve satisfying tracking performance and steady-state accuracy.Finally,for the levitation system with two-point levitation modules,the corresponding mathematical model is built with consideration of the mechanical coupling between the two levitation points.Based on this model,a robust adaptive synchronization control law is proposed.The Barrier Lyapunov Functions is used to synthesize the baseline synchronization controller to achieve output constraint of the levitation module.An I&I adaptation law is adopted to recover the unknown parameters in levitation module and a disturbance observer is constructed to handle the external disturbance in the levitation module simultaneously,which are integrated into the controller with output constraint to obtain satisfying control performance of the closed-loop system.The theoretical analysis and numerical simulation results show that the designed control law makes the two-point magnetic levitation system achieve satisfying synchronization control performance and output constraints are not violated as well.There are 23 figures,6 tables and 61 references in this thesis.