Information Technology Reference
In-Depth Information
The following figures show both the original surface of the
Van der Pol
system
and it's piecewise bilinear representation for the vertex positions
d
1
and
d
2
.
The goal is to design a controller
C
so that the closed-loop system behaves like
the linear plant represented as,
x
1
=
˙
x
2
x
2
=
˙
ax
1
+
bx
2
+
u
where
a
=−
1 and
b
=−
3. The PB representation of
f
2
dp
for the linear plant is the
following (Table
8.2
).
With the controller calculated as
u
=
f
2
dp
−
f
2
p
, the following PB model of the
controller
C
is obtained (Table
8.3
).
Table 8.2
PB representation
of
f
2
dp
x
1
\
x
2
d
2
=−
4
d
2
=−
2
d
2
=
0
d
2
=
2
d
2
=
4
d
1
=−
4
16
10
4
−
2
−
8
d
1
=−
2
14
8
2
−
4
−
10
d
1
=
−
−
0
12
6
0
6
12
d
1
=
2
10
4
−
2
−
8
−
14
d
1
=
4
8
2
−
4
−
10
−
16
Table 8.3
PB model of
C
x
1
\
x
2
d
2
=−
4
d
2
=−
2
d
2
=
0
d
2
=
2
d
2
=
4
d
1
=−
4
-48
-24
0
24
48
d
1
=−
2
0
0
0
0
0
d
1
=
0
16
8
0
-8
-16
d
1
=
2
0
0
0
0
0
d
1
=
4
-48
-24
0
24
48
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