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The close-loop transfer function is shown in
G (s)
=
cs
1 G (s) G
+
where
•
GM(s) is the control plant transfer function
For example, GM(s) is the transfer function associated to the phase-shifted full-bridge power-modulator
circuit.
The parameters are calculated with the assumption that the sensor-sampling cycle, T
than the time constant in relation to the converter-voltage feedback-loop bandwidth, TLC. As a general
rule, choose the sampling frequency as shown in
T
≤ 0.05 × T
s
LC
When the above assumption is true, the delayed effect from the sampling is ignored and the parameters
are determined after the position of the poles and zeros is known.
zeros in a form relating the z-domain to the s-domain.
(
K
´ w ´ w + w ´ w
0
p1
K
=
P
K
T
´
0
s
K
=
I
2
2 K
´
´ w - w
0
K
=
D
w ´ w ´ w
p1
2 T
-
´ w
s
a =
2 T
+
´ w
s
System Name
Complex Zeros
(K
, ƒ
, Q
, ƒ
)
0
z
z
p
Real Zeros
(K
, ƒ
, ƒ
, ƒ
)
0
z1
z2
p
Device PID
(K
, K
, K
, α)
p
i
d
SLUUAK4 – August 2013
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G (s) G
(s)
´
M
PID
(s) H (s)
´
´
M
PID
cs
- w ´ w
z1
p1
z2
z1
w ´ w ´ w
p1
z1
z2
(
) (
)
´ w - w
p1
z1
p1
z2
(
)
T
´ w +
2
z1
z2
s
p1
p1
p1
Table 8. Poles and Zeros from PID Coefficients
æ
+
1 z
´
+
´
ç
1000
K
K
ç
p
i
-
è
1 z
Copyright © 2013, Texas Instruments Incorporated
Description of the Digital Phase-Shifted Full-Bridge Converter
Equation
8.
Equation
9.
Table 8
)
z2
Transfer Functions
2
s
+
(
)
´ p ´
2
2
´ p ´
2
ƒ
z
æ
s
´
ç
ç
´ p ´
´ p ´
2
K
2
è
0
æ
ö æ
s
+
´
ç
1
÷ ç
´ p ´
2
ƒ
2
è
ø è
z1
æ
s
´
ç
ç
´ p ´
´ p ´
2
K
2
è
0
-
-
ö
1
1
-
1 z
+
´
÷
K
÷
d
-
-
-
1
8
1
- a ´
´
1
2
z
ø
, is much smaller
s
summarizes the poles and
s
+
1
´
ƒ
Q
z
z
ö
s
+
÷
1
÷
ƒ
ø
p
ö
s
+
1
÷
´ p ´
ƒ
ø
z2
ö
s
+
÷
1
÷
ƒ
ø
p
-
-
sc
19
´
´
´
´
2
KCOMP 2
4
2
Using the UCD3138PSFBEVM-027
(8)
(9)
(10)
(11)
(12)
(13)
1
(
)
´
+
PRD 1
43
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