A Barrier Function-Based Variable Structure Control for Maglev System

Abstract

Magnetic levitation (Maglev) systems are widely employed in the industry especially in mechatronics systems for precise positioning and suspension. They are inherently unstable having nonlinear models with uncertain parameters and exposed to external disturbances. Therefore, high-performance robust control designs are recommended for these systems. An Adaptive Variable Structure Controller based on barrier function (AVSCbf) is designed for the first time in this work to control the displacement of the ball position of a disturbed Maglev system. This approach does not require prior knowledge of the disturbance upper bounds in the design procedure. The state space region defined by the barrier function is designed to be attractive and invariant. This feature is essential to reject disturbances and handle parametric uncertainties. The adaptive law is activated when the state trajectory is initiated outside the invariant set defined by the barrier function. The gain of the VSC is adapted according to an adaptation law, which considers the system input constraints. The control input is constrained to be a bounded positive quantity. The adaptive VSC is only applied during the reaching phase. Once the state reaches the invariant set, the barrier-function-based VSC is applied to confine the state inside it. The resulting overall controller is a chattering-free VSC since the barrier-function based VSC is continuous. The steady-state error is limited to a minimal value by only specifying the barrier function parameter. Numerical simulations are conducted to show the efficiency of the new approach. Three types of VSC controllers for the Maglev system are compared. AVSCbf is compared to the performance of adaptive only VSC without the barrier function (AVSC) and both are designed in this work. AVSCbf is also compared to the classical VSC performance from previous work in the literature. The results of the comparison showed the efficiency of the proposed controller.