Image Processing Reference
In-Depth Information
The resulting gain matrix is
K
11
K
12
K
21
K
22
00
:
037
K ¼
¼
(5
:
39)
1
:
50
The MATLAB pole placement yields
K
11
K
12
K
21
K
22
0
:
32
0
:
3
K ¼
¼
(5
:
40)
0
:
12
1
:
3
The MATLAB solution gives a more robust design with respect to variations in the
system parameters. For example consider slight perturbation of matrix A by
DA,
that is,
0
1
0
:
0039
0
:
0004
0
:
0039
0
:
9996
A ¼ A þ DA ¼
þ
¼
0
:
12
1
0
:
0026
0
:
0048
0
:
1174
1
:
0048
The closed-loop A matrix using the
first design (K matrix given by Equation 5.39) is
00
0
:
0039
0
:
9996
1
1
01
:
037
A
C
¼ A BK ¼
0
:
1174
1
:
0048
1
:
50
1
:
5039
0
:
9626
¼
1
:
6174
1
:
0048
T
.
The closed-loop poles are eigenvalues of A
C
which are p
1
¼
½
0
:
3784 0
:
1207
T
T
is
The percentage change from the desired poles p ¼ l
1
½
l
2
¼
½
0
:
30
:
2
Dl ¼
k
p
p
1
k
2
kpk
2
100
¼
30
:
92%
The closed-loop A matrix using the second design (K matrix given by Equation
5.40) is
0
:
0039
0
:
9996
1
1
01
0
:
32
0
:
3
A
C
¼
0
:
1174
1
:
0048
0
:
12
1
:
3
0
:
2039
0
:
0004
¼
0
:
0026
0
:
2952
T
and the percentage change is
The closed-loop poles are p
2
¼
½
0
:
2952 0
:
2039
Dl ¼
k
p
p
2
k
2
kpk
2
100
¼
1
:
72%
Therefore, the second design using the MATLAB pole-placement algorithm is less
sensitive to variations in system
s parameters.
'
Search WWH ::
Custom Search