
Fundamentals of AC–DC–AC Converters Control and Applications 16-21
which, substituted in Equation 16.36, yields open-loop transfer function of the form:
G s
K K sT
sT s sT
U
OP
RL PP IP
IP p RL
L
( ) =
+
+
( )
+
( )
1
1 1
3
2
τ
Σ
(
16.40)
G s
T
K U
K s
s s sT
U
OP
RL
p RL L
RL p
p p RL
L
( ) =
+
+
( )
+
( )
≈
2
2 3
1 4
4 1 1
3
2τ
τ
τ τ
Σ
Σ Σ
TT
s
s s sT
s
s s
RL
i
p
p p RL
p
p p
2
1 4
4 1
1 4
8 8
2 2 3
τ
τ
τ τ
τ
τ τ
Σ
Σ
Σ Σ
Σ
Σ Σ
+
( )
+
( )
=
+
( )
+
33
.
(
16.41)
For the closed-loop transfer function:
G s
s
s s s
CP
p
p p p
( ) .=
+
+ + +
1 4
1 4 8 8
2 2 3 3
τ
τ τ
Σ
Σ Σ Σ
τ
(16.42)
Tuning of the regulators based on Equations 16.38 and 16.39 gives power tracking performance with
more then 40% overshoot, as shown in Figure 16.18 caused ...