Speed Sensorless Control of a Long-Stator Linear Synchronous-Motor arranged by Multiple Sections

Transcription

1 Speed Sensorless Control of a Long-Stator Linear Synchronous-Motor arranged by Multiple Sections Roberto Leidhold Peter Mutschler Department of Power Electronics and Control of Drives Darmsta University of Technology Germany Page

2 Organization Introduction Motor Model Speed and position Experimental results Conclusions Linear motion Page

3 Introduction Linear Motion Usually: Rotative motors + rotative-to-linear transmission - belts and pulleys - racks and pinions - screw systems Alternative: Linear Motors -higher dynamic response -no backslash -higher efficiency -still more expensive (motor + control) Linear motor Page 3

4 Introduction Linear Motor Permanent Magnet (PM) synchronous motors. - 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 Stator arranged by several electrically independent sections - reduced reactive power and loses - several vehicles in the same carriageway - two inverters + power switching among sections - one inverter for each section Control Page 4

5 Introduction Control Field Orientation -> Mover position required to be known. Position sensors - expensive - reduce the reliability of the whole system - sensors are dispersed along the carriageway - very difficult to implement in curves Avoiding position sensors in linear motors is even more important than in rotative motors Sensorless methods - Position is derived from measured stator voltage and current. - Different constrains depending on the method used. Sensorless Page 5

6 Introduction Sensorless methods EMF based - loose performance as speed decreases - does not work at standstill - simple to implement. - non-periodic EMF - transition between sections Based on Magnetic Anisotropies. - Require detectable position dependent inductances. -More complex. - Difficult at high speed. - non-periodic anisotropies - transition between sections - higher leakage inductance (position independent) Motor scheme Page 6

7 Motor Model Scheme of one section of the linear synchronous motor Pole pitch Stator (one section) Mover x Pole pitch = 30 mm Stator: 3 poles arranged in 39 slots Mover: 3 poles Consecutive sections connected with a 80 phase shift. Model Page 7

8 Motor Model d u = i R + λ λ = λ + λ L PM ( x) d λ L = u i R e λ PM d e = = γ( θ ) λl = Li θ = x πτ p Model (Magnetic-Equivalent-Circuit) Normalized EMF space-vector γ( θ ) Experimental Several sections Page 8

9 d u = i R + λ λ = λ + λ λl L = Li PM ( x) d λ L Motor Model = u i R e λ PM d e = = γ( θ ) θ = x πτ p dx v = dv B = F v F M M 3 π T F = γ( θ ) i τ p L Normalized EMF space-vector γ( θ ) Waveform resulting from adding the EMF of three sections Magnitude reduction due to section transition EMF Page 9

10 Speed and position EMF - Speed is assumed constant - PM flux linkage sinusoidal sinθ e = f m cosθ Linear motor Section Section Mover t i t i d e cosθ = fm = sinθ J e 0 J= 0 v * - - v * d ˆ λ L d eˆ ( ˆ ) = u i R eˆ + G i L - λ L ( λˆ ) = J eˆ + G i L - L from current from current EMF Page 0

11 Speed and position Two EMF s (active sections i.e. where the mover is and the following) EMF - Speed is assumed constant - PM flux linkage sinusoidal sinθ e = f m cosθ Linear motor Mover Section Section t i t i d e cosθ = fm = sinθ J e d ˆ λ L ( ˆ ) = u i R eˆ + G i L - λ L 0 J= 0 v * from current EMF e - - v * from current EMF e d eˆ ( λˆ ) = J eˆ + G i L - L Speed and pos. Page

12 Speed and position Two EMF s (active sections i.e. where the mover is and the following) Addition of both EMF space vectors One speed and position Linear motor Mover EMF - Speed is assumed constant - PM flux linkage sinusoidal sinθ e = f m cosθ Section Section t i t i d e cosθ = fm = sinθ J e d ˆ λ L ( ˆ ) = u i R eˆ + G i L - λ L 0 J= 0 v * from current EMF - - v * from current EMF e d eˆ ( λˆ ) = J eˆ + G i L - L θ speed and position e +e Speed and pos. Page

13 Speed and position Two EMF s (active sections i.e. where the mover is and the following) Addition of both EMF space vectors One speed and position Linear motor Mover Speed and position Section Section c = cos ˆ θ sin ˆ θ ˆ e t i t i c = ˆ f sin( ˆ θ θ) ˆ f ( ˆ θ θ) m m v * EMF - - v * EMF d ˆ = K I c from current from current e d ˆ θ = ˆ KP c θ speed and position e +e Control Page 3

14 Speed and position Integration into the control loop Linear motor Data bus Mover Section Section Section 3 Section t i t i t 3 i 3 t 4 i 4 Controller addressing te ie ve* θ θ dq->αβ αβ->dq i v* Current even sections addressing to io vo* - - dq->αβ αβ->dq i v* Current odd sections iq* id*=0 iq* id*=0 Speed * θ Sections selector EMF Page 4

15 Speed and position Integration into the control loop Linear motor Data bus Mover Section Section Section 3 Section t i t i t 3 i 3 t 4 i 4 addressing te ie addressing to io Controller ve* EMF even θ θ dq->αβ αβ->dq i v* Current even sections e e vo* - - dq->αβ αβ->dq i v* Current odd sections EMF odd e o iq* id*=0 iq* id*=0 Speed * θ Sections selector Speed and pos. Page 5

16 Speed and position Integration into the control loop Linear motor Data bus Mover Section Section Section 3 Section t i t i t 3 i 3 t 4 i 4 addressing te ie addressing to io Controller θ ve* dq->αβ αβ->dq i v* Current even sections EMF even e e θ vo* - - dq->αβ αβ->dq i v* Current odd sections EMF odd e o iq* id*=0 iq* id*=0 Speed * θ speed and position θ Sections selector Section selector Page 6

17 Speed and position Integration into the control loop Linear motor Data bus Mover Section Section Section 3 Section t i t i t 3 i 3 t 4 i 4 addressing te ie addressing to io Controller θ ve* dq->αβ αβ->dq i v* Current even sections EMF even e e θ vo* - - dq->αβ αβ->dq i v* Current odd sections EMF odd e o iq* id*=0 iq* id*=0 Speed * θ speed and position θ e e Sections selector Exp. setup Page 7

18 Experimental results One section m Link to the load machine x Path Mover Parameters Page 8

19 Experimental results m Nominal current Peak current Nominal force Stator resist. Stator induct. Mover Mass Flux Load 5 Arms 04 Arms 900 N. Ω 6.4 mh.5 Kg Vs sin(θ/5) N Exp. results Page 9

20 Experimental results Speed.7 m/s Step to.95 m/s at t = s EMF in αβ EMF dq Page 0

21 Experimental results Speed.7 m/s Step to.95 m/s at t = s EMF in dq EMF dq Page

22 Experimental results Speed.7 m/s Step to.95 m/s at t = s EMF in dq Current Page

23 Experimental results Speed.7 m/s Step to.95 m/s at t = s EMF in dq q axis current Speed and pos. Page 3

24 Experimental results Speed.7 m/s Step to.95 m/s at t = s Linear Speed Position Error (electrical angle) Conclusions Page 4

25 Conclusions Control of Linear Synchronous-Motors without speed or position sensors. Speed control of the mover in a multi-section carriageway. Also provides the means to select the sections to be driven. Experimental tests in closed loop. High agreement between observed and actual values of speed and position, even when the mover is loaded. Validate the model simplifications introduced for the EMF as well as the overall proposal. Thanks Page 5

26 The speaker s attendance at this conference was sponsored by the Alexander von Humbol Foundation. humbol-foundation.de