State and parameter estimation in solenoid nonlinear equations

We propose a model-based method that allows to estimate the magnetic force accurately, hence the armature displacement of linear solenoids. The nonlinear electrodynamical model of solenoids is used. The unscented Kalman filter is applied to analyze the current transient response, and the dynamics of the solenoid is estimated at each time instant. Furthermore, a new approach to estimate the varying internal solenoid reluctance, from the nonlinear model of solenoids, is proposed. The estimation is performed for each value of the current and predicted while the armature is moving. This leads to an accurate computation of the electromotive magnetic force related to the velocity of the moving actuator's component, thus permitting to know the system dynamics accurately.