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Control Systems
Transfer Function from SSM
The transfer ...
Question
The transfer function for the state variable representation
X
=
A
X
+
B
U
,
Y
=
C
X
+
D
U
, is given by
A
D
+
C
(
s
I
−
A
)
−
1
B
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B
B
(
s
I
−
A
)
−
1
C
+
D
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C
D
(
s
I
−
A
)
−
1
B
+
C
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D
C
(
s
I
−
A
)
−
1
D
+
B
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Solution
The correct option is
A
D
+
C
(
s
I
−
A
)
−
1
B
T
.
F
.
=
C
[
s
I
−
A
]
−
1
B
+
D
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0
Similar questions
Q.
The state diagram of a system is shown below is described by the state -variable equations:
˙
x
=
A
X
+
B
u
;
y
=
C
X
+
D
u
The state -variable equations of the system in the figure above are
Q.
A single input single output linear system is a described by the equations
d
x
d
t
=
A
x
+
B
u
and
y
=
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x
+
d
u
, where A is an [n x n] matric and x and b are [n x 1] vectors. The transfer function is given by
Q.
The state space equation of a system is described by
˙
x
=
A
x
+
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u
,
y
=
C
x
where
x
is state vector,
u
is input,
y
is output and
A
=
[
0
1
0
−
2
]
,
B
=
[
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1
]
,
C
=
[
1
0
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Q.
A state space representation for the transfer function
y
(
s
)
u
(
s
)
=
s
+
6
s
2
+
5
s
+
6
is
˙
x
=
A
x
=
B
u
,
where
A
=
[
0
1
−
6
−
5
]
,
B
=
[
0
1
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Q.
Let the state- space representation of an LTI system be
˙
X
(
t
)
=
A
X
(
t
)
+
B
u
(
t
)
,
y
(
t
)
=
C
X
(
t
)
+
D
u
(
t
)
where
A
,
B
,
C
are matrices,
D
is a scalar,
u
(
t
)
is the input to the system, and
y
(
t
)
is its output. Let
B
=
[
0
0
1
]
T
and
d
=
0
. Which one of the following option for
A
and
C
will ensure that the transfer function ofthis LTI system is
H
(
s
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=
1
s
3
+
3
s
2
+
2
s
+
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