ece 595s ifoc aaron cramer carlos rodríguezsudhoff/ee595s/project1… · ·...
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ECE 595S
IFOC
Aaron CramerCarlos Rodríguez
Torque Command Performance
• Constant speed (1700 RPM)• Torque command stepped from 0.0 Nm to
3.0 Nm at 2.0 s• First with machine having “cold”
parameters• Then with machine having “warm”
parameters
“Cold” Performance
“Warm” Performance
Torque Command Performance
• When the machine has the “cold”parameters, IFOC effective
• When the machine has the “warm”parameters, steady-state torque error
• Also, steady-state error in the commanded flux linkages
Speed Control Performance
• Speed command stepped from 0.0 rad/s to 180.0 rad/s at 2.0 s
• Torque command limited to ±3.5 Nm• Simple PI loop around IFOC• First with “cold” parameters• Then with “warm” parameters
“Cold” Performance
“Warm” Performance
Speed Control Performance
• In both situations, the control is limited by the torque limit
• In both situations, the steady-state speed error is zero
• In both situations, the steady-state flux linkage error is zero
• In this situation the performance is acceptable• We will not consider the application of speed
control further in this discussion
IM model
• Consider the following representation of the IM in the stationary reference frame
( )
( )
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
+−
+
+−
+
++−
++−
=
+==
+=
Mlrlsrr
ssr
Mlrlsrr
Mr
Mlrlsrr
ssr
Mlrlsrr
Mr
Mlslrss
Ms
Mlslrss
rrs
Mlslrss
Ms
Mlslrss
rrs
rr
r
LLLLLr
LLLLLr
LLLLLr
LLLLLr
LLLLLr
LLLLLr
LLLLLr
LLLLLr
''
'
''
'
''
'
''
'
''
'
''
'
00
00
00
00
I
III
A
AAACxy
BuxAx
ωω
ω
IM model
[ ][ ][ ]Ts
dssqs
Tsds
sqs
Tsdr
sqr
sds
sqs
Mlrlsrr
M
Mlslrss
rr
Mlrlsrr
M
Mlslrss
rr
ii
vv
LLLLL
LLLLL
LLLLL
LLLLL
=
=
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
+−
+
+−
+=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−
=
y
u
x
C
B
AII
''
'''
'
'''
'
00
00
00001001
0100100000000000
λλλλ
TSK model
Stable if
( )
( )
min,max,
max,21
max,2
min,
1
1
1
1
rr
rr
r
r
K
kk
K
kk
ωωωω
αα
ωω
α
αα
α
−−
=−=
+=
+=
=
=
+=
∑
∑
=
=
III
III1
k
AAAAAA
AA
BuxAx
{ }0PAPA
0PP
kk <+
∈∀>=∃
T
T
Kk ,...,2,1
S.H. Żak, Systems and Control
G. Strang, Linear Algebra and its Applications
Observer design
Try placing poles very deep in the left half plane
{ }
( ) ( )xCyLBuxAx
ZPL
ZCZCPPAPA
Z0PP
kk
ˆˆˆ
2,...,2,1
1
−++=
=
+>++
∈∀∃
>=∃
−
α
α TTT
T
Kk
S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan,Linear Matrix Inequalities in System and Control Theory
M. Corless, AAE 666 Course Notes
[ ]( )2000Re −<λ
“Cold” Performance
“Cold” Performance
• Observer error is less than 5.0×10-5 Vs
• It takes longer to establish the flux
• No steady-state torque error
• Some steady-state flux linkage error
“Warm” Performance
“Warm” Performance
• Observer error is rather large (not decaying)
• There seems to be no convergence
• Torque actually becomes negative in response to a step command
What happened?
( )
( ) ( )
( ) ( )( ) ( ) ( )( )( ) ( )∫ −+=
−=
−=
−+−=
−=−++=
=+=
−−−−t
t
ttt detet0
0ˆˆˆ
0ˆˆˆ
ˆ
ˆ
ˆˆˆˆ
ˆˆˆˆˆ
τττ xL∆∆∆Aee
CC∆C
AA∆A
xL∆∆∆AeCLAe
xxexCyLBuxAx
CxyBuAxx
CLACLA
“Cold” Performance
“Cold” Performance
• Observer error is less than 5.0×10-5 Vs
• It takes longer to establish the flux
• No steady-state torque error
• Some steady-state flux linkage error
“Warm” Performance
“Warm” Performance
• Observer error is smaller than before
• No steady-state torque error
• Uses same input measurements as IFOC (± a voltage sensor or two)
Tr adaptation
( ) ( )
( .)
L L RMS RATED L L RMS EXPECTED
SYNC Rotor Mech slip
V Vω ω ω
− −=+
Tr offset adapted(wrm=1800 rpm)
Tr offset should be0.65 s
Warm performance(Tr)
At low speed(wrm=50 rpm)