This paper presents the design of a nonlinear control law for a typical electromagnetic actuator system. Electromagnetic actuators are widely implemented in industrial applications, and especially as linear positioning system. In this work, we aim at taking into account a magnetic phenomenon that is usually neglected: flux fringing. This issue is addressed with an uncertain modeling approach. The proposed control law consists of two steps, a backstepping control regulates the mechanical part and a sliding mode approach controls the coil current and the magnetic force implicitly. An illustrative example shows the effectiveness of the presented approach.

This paper presents the magnetic force modelling of a typical electromagnetic valve actuator system. In this work, the objective is to take into account two important features: the magnetic saturation phenomenon which is a physical problem and the positivity constraint of the magnetic force. Those issues are addressed with a switch modelling approach. The first proposed control law proves the stability in a limited set and the second one ensure the global stability of the closed loop system. For both controllers, the main part of the control consists of a two steps backstepping control, a first controller regulates the mechanical part depending on the expression of the magnetic force. And a second controller controls the coil current and the magnetic force implicitly. An illustrative example shows the effectiveness of the approach.

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