MIN et al.: DSCM CONTROL BASED ON CBP AND DCEC FOR DC–DC CONVERTERS IN DCM 157
Fig. 2. Voltage regulation process based on CBP.
In order to control the output voltage, i
o
is regulated according
to v
ref
− v and i
ob
. By increasing (or decreasing) the charge
effect of i
o
in the (k +1)th switching cycle, v is regulated to
v
ref
at the beginning of the (k +2)th switching cycle.
Since capacitor voltage is determined by its charge current,
variation of v
C
in one switching cycle T is given by
v
C
z − v
C
=
T
C
i
C
=
T
C
(i
o
− i
load
). (1)
Although v ≈ v
C
, voltage on R
C
can be large, which is
dependent on R
C
and i
C
. It equals to −i
load
R
C
since i
C
=
−i
load
at the beginning of switching cycle (i.e., the sampling
point, where the diode is off). Therefore, the relationship be-
tween v
C
and v is v = v
C
− i
load
R
C
, and variation of v in one
switching cycle is given by
vz − v =
T
C
(i
o
− i
load
) − i
load
R
C
(z − 1)
=
T
C
i
o
−
v
R
−
R
C
v
R
(z − 1) (2)
where i
load
is substituted by v/R. In order to achieve the
voltage control strategy, the relationship between i
o
z and vz
2
should be derived. However, vz and R cannot appear in the
control strategy since they are unknown. Therefore, (2) is
multiplied by a differential factor (z +1− z
−1
− z
−2
) and is
given by
v(z
2
− 2+z
−2
)=
T
C
i
o
(z +1− z
−1
− z
−2
)
−
vT
RC
(z +1− z
−1
− z
−2
) −
R
C
v
R
(z
2
− 2+z
−2
). (3)
Supposing that T RC and R
C
R, then the relationship
between i
o
z and vz
2
is given by
v(z
2
− 2+z
−2
) ≈
T
C
i
o
(z +1− z
−1
− z
−2
). (4)
Finally, i
o
z and vz
2
are taken as the reference current and
the reference voltage, respectively. After replacing i
o
by i
ob
,
the voltage control strategy is given by
i
ref
=i
o
z = i
ob
(z
−1
+z
−2
−1)+
C
T
(v
ref
−2v+vz
−2
). (5)
Based on (5), the reference current is calculated by the
reference voltage, which can be used to regulate the output
Fig. 3. Current errors in the converter.
voltage. However, i
ob
must be acquired from the current ob-
server. Furthermore, i
ref
must be processed to d
1
to control the
output current.
B. Current Observer and Current Controller
Both the current observer and the current controller exploit
the energy conservation principle of inductor. For DCM con-
verters, charge and discharge energy of the inductor are equal in
one switching cycle since the inductor current must reach zero
before the end of the cycle. For an ideal boost converter, the
charge and discharge energy are v
2
g
d
2
1
T
2
/2L and i
o
(v − v
g
)T ,
respectively [23]. Therefore, the energy conservation equation
is given by
v
2
g
d
2
1
T
2
2L
= i
o
(v − v
g
)T. (6)
Based on (6), an output current is derived according to v
g
, v,
and d
1
, which obtains (7) for the current observer. That is,
i
ob
=
d
2
1
Tv
2
g
2(v − v
g
)L
. (7)
For the current controller, (8) is derived by substituting i
ref
for i
o
in (6). That is,
d
1
=
2(v − v
g
)Li
ref
Tv
2
g
. (8)
The basic CBP-DSCM controller is implemented with (5),
(7), and (8). According to Fig. 2, the output voltage can be
regulated to v
ref
in two switching cycles. However, parasitics
are not considered, which lead to errors in both i
ob
and i
ref
.
These errors degrade the dynamic response by decreasing cur-
rent regulation accuracy. Therefore, compensation is required
to reduce the errors.
III. DCEC
FOR CBP-DSCM CONTROL
As shown in Fig. 3, the voltage controller is designed to
regulate i
o
(k +1)through i
o
(k). However, parasitics v
F
, R
F
,
R
ds
,andR
L
are not considered in the energy conservation
equation (6). This causes errors in both observed current and
reference current. The observed current error Δi
ob
= i
ob
− i
o
is a deviation of i
ob
from i
o
, whereas the reference current error
Δi
ref
= i
ref
− i
o
is a deviation of i
ref
from i
o
.
Current errors occur in a basic CBP-DSCM controller. Con-
ventionally, Δi
ob
is compensated to increase current regulation
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