Huang-Jen Chiu

•
Linearization of the Power Stage
X = 0 = AX + BV
and Vo
= CX
~
~
d
V
⇒
V
o
d
= −CA
−1
B
•
~ ~
x = Ax+
A1
− A2
) X + ( B1
−B2
) Vd
Steady-state
[( ] d
⇒s
x(
s)
= Ax(
s)
+ [( A1
− A2
) X + ( B1
−B2
) Vd
] d(
s)
~
−1
⇒ x( s)
= [ sI − A]
[( A1
− A2
) X + ( B1
−B2
) Vd
] d(
s)
⇒
~
DC voltage transfer ratio
vo(
s)
−1
( s)
= = C[
sI − A]
[( A1
− A2
) X + ( B1
−B2
) V ] + ( C1
−C2)
X
~
d(
s)
Tp d
~
~
~
~
vo ~
=
Cx+
[( C −C
) X]
d
1
2
~