On heat dissipation control of linear variable reluctance motors
Citation for published version (APA):Katalenic, A., & Lierop, van, C. M. M. (2011). On heat dissipation control of linear variable reluctance motors. In Abstract presented at the 30th Benelux Meeting on Systems and Control, 15 - 17 March 2011, Lommel, Belgium (pp. 186-). Universiteit Gent.
Document status and date: Published: 01/01/2011
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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: a.katalenic@tue.nl
1 Introduction
Many material 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= σ d2 12A2 g ( dΦ dt )2 +C √ σd A3/2g dΦ dt 3 2 , (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]:
m ¨g = F + Fd= 1 µ0Ag ( Φ2 1− 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
Φ2are 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 ddtΦ (e.g. sensing coil) andΦ (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 some heat dis-sipation which depends on the desired force profile and can be accurately calculated using available flux measurements and (1). The idea is to introduce additional dissipation in
i2 i1 F g0 g m u2 u1 1 1 d dt F é ù F ê ú ë û 2 2 d dt F é ù F ê ú ë û
Figure 1:Schematics of a linear variable reluctance motor.
order to meet temperature distribution objectives. Two ap-proaches are investigated:
• The heat dissipation is controlled by adding high-frequent sinusoidal components to the flux refer-ence signals, i.e. Φ∗1re f(t) =Φ1re f+ AΦ1sin(ωt) and
Φ∗
2re f(t) =Φ2re f+ AΦ2sin(ωt), whereω is an order
of magnitude larger then the motion control band-width, and AΦ1 and AΦ2 are additional control sig-nals of relatively small amplitudes used for dissipa-tion control. The inertia of the mass will further at-tenuate these components by -40 dB, so they will be neglectable in the motion control, but can create prob-lems for the power electronics since the available volt-age swing will be reduced.
• By investigating (2) it can be seen that there are infinitely many possible Φ1 and Φ2 that generate
the same net force on the translator. The con-troller has to choose the signals Φ1re f and Φ2re f,
so that equalities ( Φ2 1re f− Φ22re f ) =µ0AgFdesiredand Ptot ( dΦ1re f dt + dΦ2re f dt )
= Pdesired hold. This approach
requires no high frequent components in the control signal and is therefore preferred.
The applications of the introduced schemes include start-up transient temperature control and steady-state temperature fluctuation reduction in electromechanical machines.
References
[1] G. Bertotti, “General properties of power losses in soft ferromagnetic materials,” IEEE Trans. Magn., vol. 24, no. 1, Jan. 1988.
[2] D.L. Trumper, S.M. Olson, and P.K. Subrahmanyan, “Linearizing control of magnetic suspension systems,” IEEE Trans. Contr. Syst. Technol., vol. 5, no. 4, July. 1997.