Comparison of control oriented models for the LongStator Linear Synchronous Motor and their experimental validation Roberto Leidhold Rodrigo Benavides Peter Mutschler Department of Power Electronics and Control of Drives Darmstadt University of Technology Germany Page 1
Organization Introduction Motor Description Motor Models Results Conclusions Page 2
Linear Motors Introduction Replace rotative motors + rotativetolinear transmissions Possibility of new applications Characteristics higher dynamic response no backslash higher efficiency still more expensive (motor + control) Known since a long time (e.g. Laithwaite 1971) It is only recently that instances of application are found Due to the advances in: power electronics signal processing and control systems Page 3
Linear Motors Introduction One key for designing a control system is to have an adequate model Magnetic saturation Nonsinusoidal flux Nonperiodic characteristics (end effects) Cogging force Two approaches are analyzed for modeling a Linear Motor: Based on Finite Element Analysis (FEA) Based on Magnetic Equivalent Circuits (MEC) Model oriented for: Simulation of the drive (more features than the fundamental wave model) Design of the controllers Page 4
Motor Description Linear motor Permanent Magnet (PM) synchronous motor high efficiency high power density allows a higher air gap Long stator (carriageway) Short mover (vehicle) passive mover: no brushes or cables connected longer travel distance Page 5
Motor Description x Pole pitch τ = 30 mm Stator: 13 poles 39 slots Mover: 3 poles Nominal Force 500 N Nominal Current 54 A Page 6
Motor Description One segment 1 m Load machine Path Mover Page 7
Motor Model Geometry Magnetic characteristics B Fe H MEC FEA 0 0 R S φ S1 R S φ Sn F S1 R L a 1,1 a 1,2 R G F Sn a 1,(n1) R L a 1,n R L R G a 21 φ G1 φ Gn a 2 ( ) 0= f2 λ,, ia,x E (, ) F = f a x λ x i x Lookup Table 1 Lookup Table 2 i F E Electrical Mechanical dλ R dt = i+ u dv = 1 FE Bv F dt M dx = v dt ( ) L Stationary frame Model Page 8
Motor Model: Magnetic Equivalent Circuit 0 0 0 0 0 Stator (one segment) 0 A + C B + A C + B A + C B + A C + B B A + C B + a 11 a 12 a 1(n1) a 1n a 21 a 22 a 2(n1) a 2n a 1(n+1) a 2(n+1) a 140 a 3 a 3 a 3 a 3 Mover x a 3 a 3 R S 0 φ S1 R S 0 φ Sn R S 0 φ S40 ( F φ x ) 0,,,a,, ( ) = f 1 FS a 1 a 2 3 φs φ M F S1 R L a 1,1 a 1,2 F Sn F S40 a 1,(n1) R L a 1,n R L a 1,(n+1) a 1,39 R L a 1,40 R G R G R G a 2,1 a 2,n a 2,40 φ G1 φ Gn φ G40 λ = w T φs FS = w i ( i a a, λ, ( x ) 0,,,a,, ( ) = f 2 a1 a2 3 φ M φ M1 a 3 R φ Mn M a 3 Flux facing the tooth R M φ M40 a 3 Virtual Work F E ( a a 1 ) = 40 1 2 3 x T dφm( x) dx Page 9
Motor Model: Magnetic Equivalent Circuit Flux facing the tooth, due to the magnet φ ( x) = B l b ( x) M r S G b G (x) b S b S Stator tooth i Magnet 0.5 b S x b M 0.5b S 0.5b S b M +0.5b S 0 0.5(b M +b S ) b M +1.5b S x Page 10
Motor Model: Finite Element Analysis 2D Magnetostatic Simulation FE λβ λα Current iq Position x π/τ Current iq Position x π/τ Current iq Position x π/τ Page 11
MEC based model Results (Static) FEA based model Experimental test Force vs. Position Three Segments connected in series Fed with qcurrent in the field oriented frame Page 12
Results (Dynamic) Voltage step in the field oriented frame vq = 50V Page 13
Conclusions Model preparation Offline computations Simulations FEA based model Simple and Systematic Slow (days) Very fast (minutes) MEC based model Requires special skills More decisions must be taken by the developer Fast (minutes) Very fast (minutes) Slight differences between models and experimental tests High agreement between results of both models Future work: use of MEC based model for analysis of magnetic saliencies (for sensorless position detection). Page 14
The speaker s attendance at this conference was sponsored by the Alexander von Humboldt Foundation. http://www.humboldt humboldtfoundation.de