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Description of the Digital Phase-Shifted Full-Bridge Converter
12.6 Loop Compensation Using PID Control
Proportional, integral, and derivative (PID) control is usually used in the feedback-loop compensation in
digitally-controlled power converters. This section describes several aspects of how to use PID control.
12.6.1
Transformation of Digital-PID Coefficients to Poles and Zeros in the s-Domain
PID control in the UCD3138 control-law algorithm (CLA) for control loop is formed in the z-domain using
Equation
1.
( )
G z
=
K
+
c
P
Converting
Equation 1
form is with two real zeros and one real pole as shown in
æ
ç
è
( )
=
G
s
K
cz
0
K
is the gain of the frequency domain pole at the origin, and K
0
frequency when the integrator Bode-plot gain crosses over with 0 dB. K
initially designing feedback-loop compensation (see reference 5 in
The second form is when the two zeros are presented with complex conjugates as shown in
æ
ç
ç
è
( )
=
G
s
K
cz
0
Two complex conjugate zeros are expressed as,
w
r
w
=
z1, z2
2 Q
´
w = w ´ w
r
z1
w ´ w
z1
z2
Q
=
w + w
z1
z2
The factor of Q is in the range of 0 to infinite. The two complex conjugate zeros become the two real zeros
when Q is less than or equal to 0.5 (Q ≤ 0.5). Therefore,
sense,
Equation 3
A low-pass filter usually exists in a control loop of its feedback path. The low-pass filter adds a pole to the
loop as shown in
Equation
H (s) K
=
cs
cs
w
42
Using the UCD3138PSFBEVM-027
-
1
-
1
1 z
1 z
+
-
K
+
K
I
D
-
1
-
1
1 z
1
z
-
- a ´
to the s-domain equivalent using the bilinear transform results in two forms. One
ö æ
ö
s
s
+
+
1
÷ ç
1
÷
w
w
ø è
ø
z1
z2
æ
ö
s
+
ç
÷
s
1
ç
÷
w
è
ø
p1
ö
2
s
s
+
+
÷
1
÷
´ w
2
w
Q
ø
r
r
æ
ö
s
+
ç
÷
s
1
ç
÷
w
è
ø
p1
(
)
2
1 j 4 Q
1
and j
±
´
-
z2
can be used in either case across the range of Q.
7.
1
s
1
+
pcs
Copyright © 2013, Texas Instruments Incorporated
Equation
2.
is also represented as the angular
0
Section 15
1
= -
Equation 2
is a unique form of
is also used as a method for
0
for more details).
Equation
Equation
SLUUAK4 – August 2013
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(1)
(2)
3.
(3)
(4)
(5)
(6)
3. In this
(7)
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