UFR Sciences Exactes et Naturelles
Moulin de la Housse
51687 Reims CEDEX 2
This talk deals with a prototype of a linear switched reluctance motor. Many manufacturing processes requiring high-precision linear position control, as pick-and-place machines, involve these kinds of machine. This motor present a highly nonlinear dynamic because the discrete nature of torque production mechanism. The hard nonlinearity is mainly due to the strong dependence between translator position and air-gap permeance. From this kind of machine, some works about step motors -  have detected many nonlinear phenomena. Because of this very complex dynamics nature, these motors are susceptible to exhibit different types of behaviors even in open loop operation. In addition to usual periodic orbits, quasi-periodic and chaotic behaviors have been reported. It has been shown , that a simplified dimensionless harmonic model, stemmed from a precise flux tubes model, gives results very similar to the exact model, especially in chaotic modes, because bifurcations and chaos arise from the main non linearities of the motor and do not result from some modeling details. This model has been successfully used to evaluate fractal properties of chaotic motions of the motor by the mean of intensive computations . The talk presented also some experimental result showing, for example, how to predict the experimental forecast horizon using a carefully computed Lyapunov spectrum.
 M. C. Pera, B. Robert & C. Goeldel, Nonlinear dynamics in electromechanical systems-application to a hybrid stepping motor, Electromotion, 7, 31-42, 2000.
 B. Robert, M.-C. Marion-Pera, & C. Goeldel, Dynamiques apériodiques et chaotiques du moteur pas à pas, Revue Internationale de Génie Electrique, 3, 375-410, 2000.
 M. R. De Castro, B. Robert, & C. Goeldel, Bifurcations and chaotic dynamics in a linear switched reluctance, 13th EPE-PEMC Conference, 2126-2133, 2008.
 M. R. De Castro, B. Robert & C. Goeldel, Strange Attractor and Fractal Dimension in a Linear Switched Reluctance Motor, 6th International Multi-Conference SSD 2009, Djerba, Tunisia.