Abstract
In this paper the variable structure control theory is utilized to derive a discontinuous controller to the magnetic levitation system. The magnetic levitation system model is considered uncertain, which subjected to the uncertainty in system parameters, also it is open-loop unstable and strongly nonlinear. The proposed variable structure control to magnetic levitation system is proved, and the area of attraction is determined. Additionally, the chattering, which induced due to the discontinuity in control law, is attenuated by using a non-smooth approximate. With this approximation the resulted controller is a continuous variable structure controller with a determined steady state error according to the selected control parameters. Finally the ability and the effectiveness of the proposed continuous variable structure controller to the magnetic levitation system are verified via numerical simulations. When state initiated inside the area of attraction, the results show that the ball position can be directed to follow various desired positions, with steady state error not exceeding . 
Highlights
Magnetic Levitation Systems (MLS) becoming popular in many applications
Matthew, et al, 2006 show that the MLS suffers from many problem, witch complicate the design task like the nonlinear and open loop instability nature, the uncertainty in system model and the external disturbance
A disturbance observer based control design methodology was introduced by Divyesh, et al, 2016, where a cascaded sliding mode control which use sliding mode controller disturbance-observer-based for the electrical loop and for the electromechanical loop
Summary
Magnetic Levitation Systems (MLS) becoming popular in many applications. They can be used for precise positioning such as frictionless bearings, magnetic levitation trains, wind tunnels, and conveyor systems. Matthew, et al, 2006 show that the MLS suffers from many problem, witch complicate the design task like the nonlinear and open loop instability nature, the uncertainty in system model and the external disturbance These challenges has led to a significant need for developing control technologies for magnetic levitation control systems. The control performance will be affected especially when the system model is uncertain and when the external disturbance is variable as was shown by Khalil, 2002 To solve this problem, a robust controller based on Lyapunov redesign approach was applied to MLS by Jinquan, et al, 2015 to eliminate perturbation. Variable Structure Control (VSC) recognized as an efficient tool to design of robust controllers for nonlinear, complex and high order linear plants and time-delay systems with parameter perturbations and external disturbances. The simulation results and discussion are found in sections five and six, respectively
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