Modeling And Control Of Magnetic Levitation Ball Systems

In this thesis,the modeling of the magnetic suspension ball system and the design of the controller are considered.First,the nonlinear dynamic model of magnetic levitation ball system is established by using the Lagrange-Maxwell equation.Then,based on the model,three kinds of nonlinear tracking control strategies are given by selecting the appropriate Lyapunov function by using the nonlinear backstepping method:Displacement-velocity-flux feedback control When three states can be mea-sured,we directly use the Back-stepping control method and choose the appropriate Lyapunov function to design the controller,so that all the signals in the closed loop are bounded.By adjusting parameters,the trajectory of the model can be tracked as far as possible to the reference signal,so that the closed-loop system will achieve sta-bility.Considering that the accuracy of state measurement is limited by the measuring instrument in the measurement process,it is still a challenge to accurately measure the state in engineering.Therefore,we consider designing filters on this basis.Displacement-velocity feedback control Here we consider that when the cur-rent?or flux?is not measurable in the circuit,we design the corresponding filter ??? to overcome the difficulties caused by the precise measurement.At the same time,a displacement-velocity feedback tracking control scheme is designed for the magnetic levitation ball system by using backstepping control method.Displacement feedback control Further,on the basis of scheme two,we con-sider the design of an augmented filter???₁,???₂,when the current?or magnetic flux?and the velocity of the ball are not measurable.By using backstepping method,the third control method,namely,displacement feedback controller are designed.In the above three cases,we choose the appropriate initial value to ensure that all the signals in the closed loop system are bounded,and make the tracking errors small,and get the local stability results of the magnetic levitation ball system.Finally,the effectiveness of the three control strategies in this paper are proved by simulation experiments.