Basic feedback loop designecee.colorado.edu/~ecen5017/lectures/CU/L27_out.pdf · 6.7 16.5 dB....
22
Basic feedback loop design 1 i i ref L i T T i i G 1 ˆ ˆ s id M ci i R G V G T 1 Closed‐loop response Loop gain Design compensator transfer function G ci (s) to obtain: • Large ||T|| over wide range of frequencies, and high cross‐over f c • Sufficiently large phase margin Cross‐over frequency should be well below switching frequency, e.g. f c < f s /5 m
Transcript of Basic feedback loop designecee.colorado.edu/~ecen5017/lectures/CU/L27_out.pdf · 6.7 16.5 dB....
Basic feedback loop design
1
i
i
ref
Li T
TiiG
1ˆˆ
sidM
cii RGV
GT 1
Closed‐loop response
Loop gain
Design compensator transfer function Gci(s) to obtain: • Large ||T|| over wide range of frequencies, and high cross‐over fc• Sufficiently large phase margin Cross‐over frequency should be well below switching frequency, e.g. fc < fs/5
m
0
20
40
60
80
100
Mag
nitu
de (
dB)
100
101
102
103
104
-180
-135
-90
-45
0
45
90
135
180
Pha
se (
deg)
Bode Diagram
Frequency (Hz)
Start from uncompensated loop gain, Gci = 1
2
sidM
cii RGV
GT 1
ExampleConverter parametersfs = 20 kHzL = 150 HC = 500 FVM = 1Rs = 1
DC operating point:Vbus = 500 VIbus = 30 AVbat = 200 VD = 1‐Vbat/Vbus = 0.6IL = Ibus/D’ = 75 A
idsidM
i GRGV
T 1
uncomp,
)(log20 uncomp, jTi
)(uncomp, jTi
Loop gain with P compensator
3
-60
-40
-20
0
20
40
60
Mag
nitu
de (
dB)
100
101
102
103
104
-180
-90
0
90
180
Pha
se (
deg)
Bode Diagram
Frequency (Hz)
pici KsG )(
idpii
sidM
cii
GKT
RGV
GT
1
Closed‐loop response Gi with P compensator
4
pici KsG )(
i
i
ref
Li T
TiiG
1ˆˆ
-60
-40
-20
0
20
Mag
nitu
de (
dB)
100
101
102
103
104
-180
-90
0
90
180
Pha
se (
deg)
Bode Diagram
Frequency (Hz)
Proportional‐Integral (PI) Compensator
5
sK
sKKsG zc
piii
pici1)(
f
f
fzc
Loop gain with Proportional‐Integral (PI) compensator
6
sKsG zc
pici1)(
5/czc ff
-60
-40
-20
0
20
40
60
Mag
nitu
de (
dB)
100
101
102
103
104
-180
-90
0
90
180
Pha
se (
deg)
Bode Diagram
Frequency (Hz)
MATLAB code: find fc and
7
m% find phase margin and cross-over frequency[Gm,Pm,Wg,Wp] = margin(Ti);Pm % phase marginFc_actual = Wp/2/pi % cross-over frequency
Pm =78.3553
Fc_actual =2.0374e+03
Closed‐loop response Gi with PI compensator
8
i
i
ref
Li T
TiiG
1ˆˆ
sKsG zc
pici1)(
5/czc ff
-60
-40
-20
0
20
Mag
nitu
de (
dB)
100
101
102
103
104
-180
-90
0
90
180
Pha
se (
deg)
Bode Diagram
Frequency (Hz)
9
Voltage control loop• Incorporating the inner current control loop• Voltage loop gain Tv• Compensator design Gcv
+
vbat
_
+
vbus
_
iLL
S1
S2
Q1 D1
Q2 D2
ibat
Ibus
vs
+vge1_
+vge2_
C
ic
c1
c2
PWM
Pulse-widthmodulator c1
c2
cDead-timeGciGcv
currentsensing
voltagesensing
H
RsiL
Rsiref
HVref
Hvbus
+
_
+_
vc
Small‐signal AC equivalent circuit model
10
+–vbat
iL D’:1
ibus
+
vbus
_
L
C
Vbusd
IL d
Voltage control loop (outer loop), with embedded current control loop (inner loop)
11
GcvHvref
+
_Gi /Rs
vbus
H
Rsiref iL Gvi
Finding Gvi
12
0ˆ ,0ˆˆ
ˆ
busbat ivL
busvi i
vG
+–vbat
iL D’:1
ibus
+
vbus
_
L
C
Vbusd
IL d
Finding Gvi
13
14
zi
zvio
ivL
busvi s
s
Gi
vGbusbat
1
1
ˆˆ
0ˆ ,0ˆ
bus
busvio I
VDG '
bus
busz I
VL
Df2'
21
bus
buszi V
IC
f 121
2.8 kHz
19 Hz
Same numerical example
dB 5.167.6
Voltage control loop: loop gain
15
GcvHvref
+
_Gi /Rs
vbus
H
Rsiref iL Gvi
Closed‐loop response Gi with PI compensator
16
i
i
ref
Li T
TiiG
1ˆˆ
-60
-40
-20
0
20
Mag
nitu
de (
dB)
100
101
102
103
104
-180
-90
0
90
180
Pha
se (
deg)
Bode Diagram
Frequency (Hz)
ci
i sG
1
1
-120
-100
-80
-60
-40
-20
0
Mag
nitu
de (
dB)
100
101
102
103
104
0
90
180
270
360
Pha
se (
deg)
Bode Diagram
Frequency (Hz)
Voltage‐loop compensator Gcv designStart from uncompensated loop gain, Gcv = 1
17
vis
iv GR
HGT 1uncomp,
ExampleConverter parametersfs = 20 kHzL = 150 HC = 500 FVM = 1Rs = 1 H = 1/100
DC operating point:Vbus = 500 VIbus = 30 AVbat = 200 VD = 1‐Vbat/Vbus = 0.6IL = Ibus/D’ = 75 A
)(log20 uncomp, jTv
)(uncomp, jTv
0
‐90
‐180
‐270
‐360
Pha
se (
deg)
Loop gain with Proportional‐Integral (PI) compensator
18
sKsG zv
pvcp1)(
5/cvzv ff
-60
-40
-20
0
20
40
60
Mag
nitu
de (
dB)
100
101
102
103
104
0
90
180
270
360
Pha
se (
deg)
Bode Diagram
Frequency (Hz)
Hz 200cvfo
m 77
0
‐90
‐180
‐270
‐360
Pha
se (
deg)
Closed‐loop response Gv with PI compensator
19
v
v
ref
busv T
TvvG
1ˆˆ
-60
-40
-20
0
20
40
60
Mag
nitu
de (
dB)
100
101
102
103
104
0
90
180
270
360
Pha
se (
deg)
Bode Diagram
Frequency (Hz)
0
‐90
‐180
‐270
‐360
Pha
se (
deg)
Transient response
20
PID(s)
voltage-loopcompensator
Gcv
PID(s)
current-loopcompensator
Gci
Step
Scope
Inductor currentl imits
1/100
H
Duty cyclelimits
6
Bus voltagereference
250
Battery Voltage
ibus
Vbat
d
v bus
iL
Averaged Boost Converter Dynamic Model
Vbat iLv bus
d
‐30A to +30 step ibus(t) transient
Inductor(battery)
current limits‐200A, +200A
21
d
vbus
iL
22
d
vbus
iL
