L1:1 436-459 Advanced Control and Automation Control of AC servo motors • 3-phase permanent magnet synchronous motors – “brushless DC” motor • trapezoidal back-EMF profile • rectangular pulse current profile • requires only 3 Hall-effect position sensors for electronic commutation – AC servo motor • sinusoidal back-EMF profile • balanced sinusoidal current profile • requires precise motor position measurement (resolver or encoder)
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Control of AC servo motors - University of Melbournepeople.eng.unimelb.edu.au/mcgood/436-459/motion_ctrl/AC...Source: P. Krause, O. Wasynczuk, S. Sudhoff, Analysis of Electric Machinery
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L1:1
436-459 Advanced Control and Automation
Control of AC servo motors
• 3-phase permanent magnet synchronous motors– “brushless DC” motor
• trapezoidal back-EMF profile• rectangular pulse current profile• requires only 3 Hall-effect position sensors for electronic
commutation– AC servo motor
• sinusoidal back-EMF profile• balanced sinusoidal current profile• requires precise motor position measurement (resolver or
2 2 2 23 3 3 3( ) ( ) ( ) ( ) ( ) ( ) ( )m e a e a e a e a e a e a eT k i k i k iπ π π πθ θ θ θ θ θ θ= + − − + + +
( ) cos( )a e p ek Kθ θ=
( ) cos( )a e p ei Iθ θ=• Sinusoidal phase current:
• Hence 2 2 22 23 3( ) cos cos ( ) cos ( )m e p p e e eT K I π πθ θ θ θ⎡ ⎤= + − + +⎣ ⎦
• Need precise measurement of rotor position to generate phase current with correct phase; i.e., encoder or resolver
3( )2m e p pT K Iθ =i.e.,
L1:9Mechanical and electrical position
• Balanced sinusoidally-distributed phase windings supplied with balanced 3-phase currents generate a spatially-sinusoidal MMF which rotates at angular speed ωm = (2/P)ωe radM/s(mechanical radians), where ωe is frequency of phase currents, P is number of motor poles:
Coil 1 ofphase a
Coil 2 ofphase a
3MMF cos2 2
ss p e s
N PI tP
ω φ⎛ ⎞ ⎛ ⎞= −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
4 pole motor
( ) cos( )a e p ei I tθ ω=
where φs = stator angular coordinate (radM)
o60 Eetω =
0etω =
o120 Eetω =
2
4
6
8
10
30
210
60
240
90
270
120
300
150
330
180 0
P = 4
o60 Eetω =
0etω =
o120 Eetω =
2
4
6
8
10
30
210
60
240
90
270
120
300
150
330
180 0
P = 4
2
4
6
8
10
30
210
60
240
90
270
120
300
150
330
180 0
P = 4
Ref: P. Krause, O. Wasynczuk, S. Sudhoff, Analysis of Electric Machinery and Drive Systems, Wiley (2002)
L1:10
Dynamics of AC servo motor• KVL for phases:
abcabc s abc s abc
ddt
= + +iv R i L e
[ ] [ ],T Tabc a b c abc a b cv v v i i i= =v i
3 3s phR ×=R I1 12 2
1 12 21 12 2
l ph ph ph
s ph l ph ph
ph ph l ph
L L L LL L L LL L L L
⎡ ⎤+ − −⎢ ⎥= − + −⎢ ⎥⎢ ⎥− − +⎣ ⎦
L
Ll , Lph = leakage and magnetising inductances of coils
23
23
cos2 cos( )
cos( )
r
abc r p r
r
KP
π
π
θω θ
θ
⎡ ⎤⎢ ⎥= −⎢ ⎥
+⎢ ⎥⎣ ⎦
e (sinusoidalback-EMF)
All this results in a very complex, nonlinear expression for the motor torque:
Tm = Tm(ia, ib, ic, θr)
L1:11Park transformation to qd0 variables• The equations are simplified by a transformation of variables from
the machine frame abc to a quadrature-direct-zero qd0 reference frame rotating with the rotor, at speed ωr = (P/2)ωm radE/s
• Transformation for voltage, current, flux linkage or charge variables: