Information Technology Reference
In-Depth Information
>
where
a
0 is the CP radius for CPs considered as charged spheres with uniform
volume charge density.
The new position of
j
th CP,
X
i
(
k
+
1
)
, and the new velocity of
j
th CP,
V
i
(
k
+
1
)
,
are obtained by means of the following equations that are similar to Eq. (
8.22
):
2
X
j
(
k
+
1
)
=
r
j
1
k
a
(
F
j
/
m
j
)(
t
)
+
r
j
2
k
V
j
(
k
)
t
+
X
j
(
k
),
v
)
=
X
j
(
)
/
(8.35)
V
j
(
k
+
1
k
+
1
)
−
X
j
(
k
t
,
where
k
a
is the acceleration parameter,
k
is the velocity parameter,
r
j
1
and
r
j
2
are
two uniformly distributed random numbers, 0
v
<
r
j
1
<
1, 0
<
r
j
2
<
1,
m
j
is the
mass of
j
th CP, it is considered as follows that
m
j
=
q
j
, and
t
is the time step set
to
1s for simplicity.
Using the similarity between Eq. (
8.22
) and (
8.35
), the first version of adaptive
CSS algorithm is based on the following adaptation of the parameters
k
a
and
k
t
=
:
v
k
a
=
3
(
1
−
k
/
k
max
),
k
v
=
0
.
5
(
1
+
k
/
k
max
).
(8.36)
With this regard the first version of adaptive CSS algorithm, with fixed length
stages, is similar to the adaptive GSA with fixed length stages given in Fig.
8.3
.
However, the following modifications occur: stage II uses the default parameter
values in the search process, and stage III employs the values of
k
a
and
k
v
that are
adapted according to Eq. (
8.36
), and the parameters in Eq. (
8.23
) can be modified.
The second adaptive CSS algorithm is similar to the second adaptive GSA but with
the above modifications in the stages II and III.
8.5 Case Study and Experimental Results
The design approach presented in Sect.
8.2
and supported by the adaptive GSAs
given in Sect.
8.3
are applied in a case study dedicated to the design and tuning of TS
PI-FLCs for the angular position control of a laboratory nonlinear DC servo system.
The parameters of the process are (Precup et al.
2012b
)
k
P
1
=
121
.
6956
,
T
=
0
.
9198 s
,
k
u
,
m
=
1
.
149
,
u
a
=
0
.
13
,
u
b
=
1
,
k
P
=
139
.
(8.37)
.
88
01 s that is accepted by the
laboratory equipment and by the quasi-continuous digital control requirements for
this process. The weighting parameter was set to
The sampling period was set to the value
T
s
=
0
.
5 in order to ensure two
equal terms that result from the sum in Eq. (
8.5
). The parameters of the two adaptive
GSAs and of the non-adaptive GSA (for the sake of comparison) were set to the
values
N
γ
=
1129
.
=
20,
k
max
=
100,
ψ
=
0
.
009,
ζ
=
30,
ε
0
=
0
.
01 and
g
0
=
100; these
values ensure a good convergence of the three algorithms.
Search WWH ::
Custom Search