Post on 03-Jun-2018
8/11/2019 ALSTOM Observer Report Vfinal
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1
Z1 Z2 Z3 Z4
Z1 Z4
Z2 Z3
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Z1 Z2
Z3 Z4
Vcc
D1
D3
D2
D4
qr
Cr Lr
r
qw
Cw
Lm
mA B
Rr
TR
qL
CL Load
Z1 Z2
Z3 Z4
Vcc
D1
D3
D2
D4
qr
Cr Lr
r
qw
Cw
Lm
mA B
Rr
TR
qL
CL Load
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x(t) = (J(s) R)Dx(t) + BuAB(t)
J(s) =
0 0 0 10 0 0 1 s2I0 0 0 sI1 (1 s2I) sI 0
, R=
0 0 0 00 0 0 00 0 0 00 0 0 Rr
B=
0001
s = {1, 0, 1}
x(k+ 1) = Fx(k) + GuAB(k) + K[y(k) Cx(k)]
F= G= K= y(k)=Cx(k)=
(ur) (uw) (ul) (ir)
ul uw ir J(s)R A0 A1
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2
Physical System Output
1
Fr_Phy
x' = Ax+Bu
y = Cx+Du
State-SpaceMultiport
Switch
In1Out1
Logic Unit
K*u
D
-K-
B
Add
K*u
A1
K*u
A0
K*u
A-1
1
Uab
A1 D M
M=diag(Cr Cw Cl Lr)
ur uw ul ir
D A0 A1 A1 gama0 phi0 gama1 phi1 gama1 phi1
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Fr_Obs
1
Discrete Observer Output
K*u
phimin1
K*u
phi1
K*u
phi0
K*u
gamamin1
K*u
gama1
K*u
gama0
Multiport
Switch
In1Out1
Logic Unit
K*u
K_C
y(n)=Cx(n)+Du(n)
x(n+1)=Ax(n)+Bu(n)
Discrete State-Space
K*u
D
Add4
Add3
Add2
Add1
Add
2
Fr_Phy
1
Uab
Discrete Observer
2
Physical System Output
1
Discrete Observer Output
Uab
Fr_Phy
Discrete Observer Output
Uab
Fr_Phy
Physical Syst em Output
Physical System
Uab
Controller
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0 1 2 3 4 5 6
x 10-4
-150
-100
-50
0
50
100
150
200Physical System
Time(sec)
Ur(V)
Uw(V)Ul(V)
Ir(A)
0 1 2 3 4 5 6
x 10-4
-150
-100
-50
0
50
100
150
200Discrete Observer
Time(sec)
Ur(V)
Uw(V)
Ul(V)
Ir(A)
Uab
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-50
0
50
100Xilinx Observer Model Output
Time(sec)
Ur(V)
Uw(V)
Ul(V)
Ir(A)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-50
0
50
100Discrete Observer Model Output
Time(sec)
Ur(V)
Uw(V)
Ul(V)
Ir(A)
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5
Xilinx Observer Output
4
ir
3
ul
2
uw
1
ur
sel
d1(min1)
d1(0)
d1(1)
d2(min1)
d2(0)
d2(1)
d3(min1)
d3(0)
d3(1)
d4(min1)
d4(0)
d4(1)
ur
uw
ul
Fr
switch
Uab
x1
x2
x3
x4
gamamin1
Uab
x1
x2
x3
x4
gama1
Uab
x1
x2
x3
x4
gama0
a1
a2
a3
a4
x1
x2
x3
x4
Phimin1
a1
a2
a3
a4
x1
x2
x3
x4
Phi1
a1
a2
a3
a4
x1
x2
x3
x4
Phi0
uw
ul
ir
Out1
Logic Unit
Gateway Out3
Gateway Out2
Gateway Out1
Gateway Out
Gateway In1
Gateway In
In1
In2
In3
In4
ur
uw
ul
Fr
Discrete State Space
a1
a2
a3
a4
ur
uw
ul
ir
D
Fr_Phy
Fr_Obs
K_C
Adjustment
a
b
a + b
Add3
In1
In2
In3
In4
In5
In6
In7
In8
Out1
Out2
Out3
Out4
Add2
In1
In2
In3
In4
In5
In6
In7
In8
Out1
Out2
Out3
Out4
Add1
In1
In2
In3
In4
In5
In6
In7
In8
Out1
Out2
Out3
Out4
Add
System
Generator
2
Uab
1 Fr_Phy
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Discrete Observer
3
Xili nx Observer Output
2
Physical System Output
1
Discrete Observer Output
Fr_Phy
Uab
Xilinx Observer Output
Xili nx ObserverUab
Fr_Phy
Discret e Observ er Output
Uab
Fr_Phy
Physical System Output
Physical System
Uab
Controller
0 5 10 15 20 25 300
20
40
60
80
100
120
140
160
180
200Xilinx Observer Wordlength Calculation
Decrease in Wordlength
Maximumd
ifferencebetweenPhysicalsystemandObserver
Ur(V)Uw(V)
Ul(V)
Ir(A)
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Tscaling = diag(2xUr 2xUw 2xUl 2xIr ) xUr , xUw , xUl xIr
2
xUr Ur
Ur2
xUr
= 1log(Ur) + xUr log(2)=log(1)xUr log(2) =log(Ur)xUr=log(Ur)/log(2)
Tscaling
Tscaling
x(k+ 1)=F x(k) + Gu(k)
y(k) = Cx(k) + Du(k)
xscaled(k+ 1)=T F T1x(k) + T Gu(k)
yscaled(k) = C T1x(k)+Du(k)
xscaled(k+ 1)=Tx(k+ 1)=T F T1x(k) + T Gu(k)+T K[y(k)yscaled(k)]
yscaled(k)=Ty(k) = C T1x(k)+Du(k)
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y(k)
xscaled(k+ 1)=Tx(k+ 1)=T F T1x(k) + T Gu(k)+T K[y(k)yscaled(k)]
xscaled(k+ 1)=Tx(k+ 1)=T F T1x(k) + T Gu(k)+T K[Cx(k) + Du(k) CT1x(k) Du(k)]
xscaled(k+ 1)=Tx(k+ 1)=T F T1
x(k) + T Gu(k)+T K[Cx(k) CT1
x(k)]xscaled(k+ 1)=Tx(k+ 1)=T F T
1x(k) + T Gu(k)+TKCT1[T x(k)x(k)]
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4x 10
-3 States of Unscaled Observer
Time(sec)
Ur(V)
Uw(V)Ul(V)
Fr(Wb)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-1.5
-1
-0.5
0
0.5
1States of Scaled Observer
Time(sec)
Ur(V)
Uw(V)
Ul(V)
Fr(Wb)
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0 5 10 15 20 25 300
20
40
60
80
100
120
140
160
180
Decrease in Wordlength
Maximumd
ifferencebetweenPhysicalsystemandObserver
Scaled Xilinx Observer Wordlength Calculation
Ur(V)
Uw(V)
Ul(V)
Ir(A)
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0 1 2 3 4 5 6
x 104
-1
-0.5
0
0.5
1
1.5
2
2.5
3Error (Xilinx observer at F=25 MHz)
Time(sec)
Ur(V)
Uw(V)
Ul(V)
Ir(A)
0 1 2 3 4 5 6
x 104
-2
0
2
4
6
8
10Error (Xilinx observer at F=80 MHz)
Time(sec)
Ur(V)
Uw(V)
Ul(V)
Ir(A)
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uw
0 1 2 3 4 5 6
x 10-4
-1
0
1
2
3
4
5Error
Time(sec)
Ur(V)
Uw(V)
Ul(V)
Ir(A)
0 1 2 3 4 5 6
x 10-4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4Error
Time(sec)
Ur(V)
Uw(V)
Ul(V)
Ir(A)
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ur= 0, uw = 0, ul = 0, ir = 0 ur = 0, uw = 0, ul= 0, ir= 0
ur= 50, uw = 0, ul= 300, ir = 20 ur = 50, uw= 0, ul = 300, ir= 20
ur= 0, uw = 0, ul = 300, ir= 0 ur = 0, uw = 0, ul= 300, ir = 0
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1
Xilinx Ob server Output
sel
d1(min1)
d1(0)
d1(1)
d2(min1)
d2(0)
d2(1)
d3(min1)
d3(0)
d3(1)
ur
ul
Fr
switch
Uab
x1
x2
x3
gamamin1
Uab
x1
x2
x3
gama1
Uab
x1
x2
x3
gama0
x 1
Tscaling
a1
a2
a3
x1
x2
x3
Phimin1
a1
a2
a3
x1
x2
x3
Phi1
a1
a2
a3
x1
x2
x3
Phi0
i r O ut 1
Logic Unit
Gateway Out2
Gateway Out1
Gateway Out
Gateway In1
Gateway In
In1
In2
In3
ur
ul
Fr
Discrete State Space
a1
a2
a3
ur
ul
ir
D
Fr_Phy
Fr_Obs
K_C
Adjustment
a
b
a + b
Add3
In1
In2
In3
In4
In5
In6
Out1
Out2
Out3
Add2
In1
In2
In3
In4
In5
In6
Out1
Out2
Out3
Add1
In1
In2
In3
In4
In5
In6
Out1
Out2
Out3
Add
System
Generator
2
Uab
1 Fr_Phy
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0 1 2 3 4 5 6
x 10
-4
-60
-40
-20
0
20
40
60
80
1003rd Order Scaled Xilinx Observer
Time(sec)
Ur(V)
Ul(V)
Ir(A)
0 1 2 3 4 5 6
x 10-4
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4Error
Time(sec)
Ur(V)
Ul(V)
Ir(A)
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ir ur
ir ur
0 2 4 6 8 10 12
x 104
-2
0
2
4
6
8
10
12
14
16
18
Samples
Error
Ur(V)
Ul(V)
Ir(A)
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R9
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uw
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1
Xilinx Observer Output
sel
d1(min1)
d1(0)
d1(1)
d2(min1)
d2(0)
d2(1)
d3(min1)
d3(0)
d3(1)
ur
ul
Fr
switch
Uab
x1
x2
x3
gamamin1
Uab
x1
x2
x3
gama1
Uab
x1
x2
x3
gama0
x 1
Tscaling
uab
Square Wave Generator
a1
a2
a3
x1
x2
x3
Phimin1
a1
a2
a3
x1
x2
x3
Phi1
a1
a2
a3
x1
x2
x3
Phi0
i r Out1
Logic Unit
Gateway Out2
Gateway Out1
Gateway Out
In1
In2
In3
ur
ul
Fr
Discrete State Space
a1
a2
a3
ur
ul
ir
D
cast
Convert1
castConvert
Fr_Phy
Fr_Obs
K_C
Adjustment
a
b
a + b
Add3
In1
In2
In3
In4
In5
In6
Out1
Out2
Out3
Add2
In1
In2
In3
In4
In5
In6
Out1
Out2
Out3
Add1
In1
In2
In3
In4
In5
In6
Out1
Out2
Out3
Add
SystemGenerator
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1
uab
a
b
a0
a
b
a0
a
b
a
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68_67
24_0
59_57
5_5
Gama0/1/min1
Phi0/1/-1
D
Adder Switch AddSub1
Logic Unit
61_60 4
51_50 4
45_374
16 3
1 1
1
7_0
State Space
81_80
85_84 AddSubK_C
4
4
1
11
1
Fr_Phy
Uab
48_47
7_0
59_57
5_5
Gama0/1/min1
Phi0/1/-1
D
Adder Switch AddSub1
Logic Unit
41_40 4
42_40 4
45_37 4
16 3
1 1
1
7_0
State Space
75_74 AddSubK_C
4
4
1
11
1
Fr_Phy
Uab
11_0 Tscaling
72_70
81_80