Biomedical Engineering Reference
In-Depth Information
list of signs. For the first equation, we have four elements connected to the summer (a positive for
the input and three negative feedback elements), so the summer is modified by removing one pos-
+
itive sign and adding three negative signs, giving
.
-
-
-
The input is a pulse with magnitude 120 and duration of 10. To create a pulse, we use two step
inputs from the Library “Sources”. The step input block looks like
to enter the magnitude and
Step
duration, double-click on the block to open the “Block Parameters Step” and enter for the first
block 0 for “Step Time”, 10 for the “Initial value”, and 0 for the “Final value”. The second step
function uses the values 120 for the “Step Time”, 0 for the “Initial value”, and
120 for the “Final
value”. Another summer with line segments from the output of the step to the input of the sum-
mer is used to connect the two inputs. The output of the input summer is connected to the “
þ
”
input of the first summer.
After the summer, a gain of 1/3 is needed. The gain block looks like
1
, which is found in
Gain
the “Math Operations” library. After dragging it from the library, the magnitude is set by double-
clicking and entering a value of 1/3. The number inside the gain block is the value of the gain if it
can fit, otherwise “-k-” is used. A line segment is used to connect the summer to the gain.
Next, two integrators are dragged across to the workspace from the “Continuous” library. The
integrator has the symbol
1
s
in it that comes from the Laplace transform representation of integra-
tion. While not necessary in this example, integrators sometimes have nonzero initial conditions.
To enter the initial condition for an integrator, double-click on the integrator block, which opens
the “Block Parameters Integrator” window, where the initial condition can be entered. By default,
the initial conditions for the integrator are zero. The output of the summer is connected with a line
segment to the input of the first integrator, the output of the first integrator is connected to the
input of the second integrator, and the output of the second integrator is connected to the input
of the third integrator. It is generally good practice to label the output of each integrator. A label
can be entered by clicking anywhere in the open workspace. A convenient label for
¨
1
is “y1DDot”
(borrowed from the D-operator),
y
1
is “y1Dot”, and so on.
Three gain blocks are then dragged across to the workspace from the “Math Operations”
library. To rotate the gain block so that it is in the correct orientation, select it and press the “CTRL
and R” keys together twice for a 180
counterclockwise rotation (each click rotates 90
). The value
for each gain block is entered by double-clicking and entering 10, 60, and 5. Line segments are
used to connect the output of the integrators to the gain block by moving the mouse pointer over
the integrator output line segment, pressing “CTRL” and left-clicking the mouse (to break into the
line), and then moving the mouse pointer to the input of the gain block. The output of the gain
blocks are then connected to the summer. Note that the term
y
2
is not connected to the gain block
until the second equation is drawn.
The same steps are used to create the SIMULINK model for the second equation. Notice that
the input for the Gain2 block is
y
1
.
To view the output, two scopes are used from the “Sinks” library. For clarity the labels on each
scope are renamed to “y1” and “y2” by double-clicking on the labels below the scope and making
y
2
, and the input for Gain5 is
