Information Technology Reference
In-Depth Information
In (2) and (3):
A
1
=
00
0
,C
=
10
,x
=
iv
0
,
t
on
means the time when the switch is on in one PWM period.
In one PWM period
T
s
, output current is controlled by changing duty cycle,
0
,A
2
=
0
1
L
,B
1
=
B
2
=
L
0
−
1
RC
1
1
RC
−
C
−
1.
In order to formulate an adequate boost converter model, which is of fun-
damental importance for the subsequent derivation and implementation of the
optimal control problem, it is necessary to construct the discrete model. To de-
scribe interaction between the switching dynamics and continuous dynamics, the
period of length
T
s
is divided in sub-periods of duration
τ
s
=
T
s
/N
with
N
≤
d
(
k
)=
t
on
/T
s
≤
2. N
subinterval could be divided into three categories of state: (i) the system in state
on; (ii) the system in state off; (iii) the system is in transition state.
ξ
(
n
) is state
of every sub-interval
τ
s
,
n
≥
∈
(0
,
1
,
···
,N
−
1),and
ξ
(0) =
x
(
k
)
,ξ
(
N
)=
x
(
k
+1),
define binary variables
δ
n
as
δ
n
=1
1, in which
δ
n
=1meanstheswitchSisonatthetimeof
nδ
s
, paper [8] has introduced the
detailed information.
↔
d
(
k
)
≥
n/N,n
=0
,
1
,
···
,N
−
4 Model Predictive Control for MPPT
Mixed Logic Dynamic (MLD) formulation captures the associated hybrid fea-
tures and allows the definition of the optimal control problem in a convenient
way. By introducing auxiliary logical variable and continuous variable, the state
variable can be expressed as linear state equations with constraints can be ex-
pressed as inequation:
x
(
k
+1)=
A
x
(
k
)+
b
d
(
k
)+
Rδ
(
k
)+
Gz
(
k
)
(4)
E
1
d
(
k
)+
E
2
δ
(
k
)+
E
3
z
(
k
)
≤
E
4
x
(
k
)+
E
5
(5)
which will act as predictive model and constraints respectively. For MLD model,
paper [9] has given a detailed introduction.
The main control objective in this work is to regulate the output current to its
reference
I
∗
.Let
Δd
(
k
) indicates the absolute value of the difference between two
consecutive duty cycle. This term is introduced in order to reduce the presence of
unwanted chattering in the input when the system has almost reached stationary
conditions. The objective of system optimization is finding the optimal control
sequence
D
∗
=[
d
∗
(
k
)
,d
∗
(
k
+1)
,
,d
∗
(
M
1)], which makes the system output
track expected reference trace and the performance function (4) least.
···
−
k
=0
||
P
k
=0
||
M
2
Qr
+
2
Qm
D,x,d
=
min
y
(
k
+
i/k
)
−
y
r
(
i
)
||
Δd
(
k
+
i
−
1
/k
)
||
(6)
P is prediction horizon, M is control horizon,
y
(
k
+
i/k
) is the predicted output
at instant k,
y
r
is reference signal,
2
Q
=
x
T
Qx,Q
=
Q
T
0,
Q
y
is weight-
ing coecient to penalize output signal error and
Q
m
is a weighting coecient
||
x
||
≥
Search WWH ::
Custom Search