# On heat dissipation control of linear variable reluctance motors

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## Abstract

On heat dissipation control of linear variable reluctance motors A. Katalenic and C.M.M. van Lierop Department of Electrical Engineering, Eindhoven University of Technology P.O. Box 513, 5600MB Eindhoven, The Netherlands Email: [email protected] 1 Introduction Manymaterial properties are temperature dependant. That is why the force actuators used in high-precision motion sys- tems are required, besides the high force predictability, to have predictable behavior with respect to heat dissipation. We investigate strategies on how to control heat dissipation of variable reluctance linear motors with flux feedback con- trol. 2 Physical principles A typical layout of a linear variable reluctance motor is shown in Fig. 1. If the magnetic cores are assumed to be made of a linear laminated ferromagnetic material, i.e. B = µH, then the total induction losses per unit volume of the material are given by [1]: Ptot ( dΦ dt ) = Pcl+Pex = σd2 12A2g ( dΦ dt )2 + C √ σd A3/2g ∣∣∣∣dΦdt ∣∣∣∣ 32 , (1) where Pcl are classical eddy current losses, Pex are excess losses, d is the lamination thickness, σ is the electric con- ductivity of the material, and C is a constant dependant on the material type. The hysteresis losses are neglected. Furthermore, the dynamics of the mass suspended by two variable reluctance actuators (Fig. 1) can be modeled as [2]: mg¨= F+Fd = 1 µ0Ag ( Φ21−Φ22 ) +Fd , (2) where m is the total mass of the translator, F is the net force on the translator, Fd is the disturbance force, and Φ1 and Φ2 are air gap magnetic fluxes entering the translator at the actuating direction. It is assumed that a high bandwidth, e.g. 10 kHz, flux feedback control loop is implemented for both actuators together with the measurements of dΦdt (e.g. sensing coil) and Φ (e.g. hall probe,observer). 3 Control design The heat dissipation in the translator is of interest. Since these actuators are primary used for tracking control and disturbance rejection, there will always be som

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