DKL:2/16/07
HW 3
1/4
HW 3
ECE 3704
Due 21607
From Lindner’s notes
10.5.1
Consider the block diagram in Figure P10.5.1.
(10)
(a) Find the transfer function by block diagram reduction.
(10)
(b) Assign state variables to the block diagram and write the state equations.
(10)
(c) Enter the state space model into Matlab and computer the transfer function.
Show your code. Show that this answer match part (a).
1
s
1
s
1
s
4
3
+

+

+
+
X
(
s
)
Y
(
s
)
Figure P10.5.1
Solution
This problem illustrates block diagram reduction and the construction of state space
models from an allintegrator block diagram, Procedure 10.5.9.
(a) The first step is to reduce the inner feedback loop as shown in Figure P10.5.1a.
1
s
1
+
3
s
=
1
s
+
3
Figure P10.5.1a
Continuing, the next feedback loop is reduced as shown in Figure P10.5.1b.
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HW 3
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1
s
(
s
+
3)
1
+
(4)
1
s
(
s
+
3)
( )
=
1
s
(
s
+
3)
+
4
=
1
s
2
+
3
s
+
4
Figure P10.5.1b
Finally, the parallel combination is reduced to obtain the transfer function
Y
(
s
)
X
(
s
)
=
1
s
2
+
3
s
+
4
+
1
s
=
s
2
+
4
s
+
4
s s
2
+
3
s
+
4
(
)
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