Dynamical analysis and control of longitudinal electromagnetic levitation

Abstract

Electromagnetic levitation is a unique technique both for measurements of the thermophysical properties of metals and for producing homogeneous melt in material processing. To maintain stability of the levitated sample is one of the most notable difficulties observed in this technique. The longitudinal levitator developed by Bayazitoglu and Shampine overcomes most of the drawbacks that are inherent in currently used levitator and can support more massive samples than those that can be supported by existing devices. On the other hand, the undesired sample oscillations have been experienced unless the sample is released very near its equilibrium position as levitation is begun. To approach this problem, a dynamical model of the process is needed. This study addresses dynamical analysis and control of the longitudinal electromagnetic levitation. The levitation force is analytically derived considering the effect of the sample's motion. Based on the dynamical analysis, a nonlinear dynamical model of the process is derived. Using the numerical solution of the dynamical model, the influences of the system parameters on the dynamical behavior of the sample are illustrated. To achieve stable levitation the derived dynamical model has been linearized and implementing a linear control technique, the sample's undesired oscillations have been successfully eliminated at very beginning of the levitation