Page 74 - Modern Control of DC-Based Power Systems

Small-Signal Analysis of Cascaded Systems 39

T I
G i L c PICM 5 (2.51)
1 1 T I
where T PICM 5 G c I G i L d OL is the inner current control loop gain.
The PICM_FB converter model (2.52) is obtained from the PICM
^
converter model (2.42) by imposing a control current i c 52 G c V ^v.
1
2 3
^ G ii PICM FB

5 4 Z in PICM FB 5 (2.52)
i in ^ v g
^ v ^ i load
G vg PICM FB 2Z out PICM FB
The transfer functions of model (2.52) are given in (2.53) (2.56).
1 1 1 1 T PICM FB
5 1
Z in PICM FB Z in PICM 1 1 T PICM FB Z N vc PICM 1 1 T PICM FB
(2.53)

G vg PICM
G vg PICM FB 5 (2.54)
1 1 T PICM FB
G ic PICM Z out PICM T PICM FB
G ii PICM FB 5 G ii PICM 1 U (2.55)
G vc PICM 1 1 T PICM FB
Z out PICM
Z out PICM FB 5 (2.56)
1 1 T PICM FB
where
1 1 G ic PICM G vg PICM
5 2 (2.57)
Z N vc PICM Z in PICM G vc PICM
And T PICM FB 5 G c V G vc PICM is the voltage FB loop gain.
After having derived the modeling, the procedure to design both the
inner and outer PI controllers is presented hereafter. This procedure
requires first the inner current controller to be designed, and then the
outer voltage controller.
The inner current control loop gain is the following expression:
(2.58)
T PICM ðsÞ 5 G c I ðsÞ G i L d OL ðsÞ
It is required that the loop gain of T PICM ðsÞ has a certain phase margin
PM PICM at the control bandwidth ω c PICM . This imposes that the magni-
tude of the loop gain of T PICM ðsÞ is unitary at the control bandwidth