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Small-Signal Analysis of Cascaded Systems 37

g v ˆ 1 + in i ˆ
(s ) +
_ OL
Z in +
G vg _OL (s ) + - + v ˆ
G (s ) + + L i ˆ
i L g _OL +
i ˆ load
G ii _OL (s )
Z (s )
out _OL
G (s )
i i L _OL
d ˆ
G (s )
id _OL
G (s )
vd _OL
G (s )
i L d _OL
Converter
G c_I
T PICM
+ - PICM Converter
T PICM_FB
c i ˆ
x ˆ
G c_V –1
Figure 2.14 Small-signal block diagram representation of a switching converter with
inner PI current loop and outer PI voltage loop.

Finally, the control design procedure for the inner current controller and
outer voltage controller is presented.

2.5.1.1 Modeling and Design Procedure of Current Mode Control
With PI Controllers
The small-signal linearized PICM converter model has three inputs and
three outputs, as shown in Fig. 2.15. The inputs are supply voltage per-
^
^
turbation ^ g , load current perturbation i load , and control current i c . The
v
first two inputs are disturbances and the third input is the control input.
The three outputs are input current perturbation ^ i in , output voltage per-
v
turbation ^, and inductor current perturbation ^ i L . The model is
1
2 3
^ G ii PICM G ic PICM
2 3 2 3
i in ^ v g
Z in PICM 7
6
^ v 5 7 ^ (2.42)
4 5 6 4 i load 5
G vg PICM 2 Z out PICM G vc PICM ^
4 5
^ i L i c
G i L g PICM G i L i PICM G i L c PICM