Biomedical Engineering Reference
In-Depth Information
ÿ
y
y
Σ
∫
dt
∫
dt
3
y
−
−
4
y
Finally, the block diagram is completed by connecting
y
and
y
to the summer via a gain block
as shown in the following figure.
ÿ
y
y
Σ
∫
dt
∫
dt
−
−
4
y
4
3
y
3
A block diagram can also be drawn for a set of simultaneous differential equations using the
same approach as in Example A.6, drawing a block diagram for each equation and connecting
the output variables and its derivatives to the appropriate summer.
EXAMPLE PROBLEM A.7
Draw a block diagram for the following set of simultaneous differential equations.
3
y
1
þ
10
y
1
þ
60
y
1
þ
5
y
2
¼
f
(
t
Þ
5
y
1
þ
4
y
2
þ
5
y
2
þ
40
y
2
¼
0
where
f
(
t
) is an unspecified input function.
Solution
We begin by solving for the highest order derivative in each equation.
1
3
(
y
1
¼
10
y
1
60
y
1
5
y
2
þ
f
(
t
ÞÞ
1
4
(
y
2
¼
5
y
2
5
y
1
40
y
2
Þ
¨
2
as the output of each
summer, followed by two integrators for each output variable. Next, we complete the diagram by
including the terms on the right-hand side of the previous equations as the input to each summer
with appropriate gain elements, giving us the following figure.
The block diagram is drawn by first using two summers, with
¨
1
and
