By Dr. Hong Zhang

Octave
◦
◦
◦
◦
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http://www.gnu.org/software/octave/
Very Similar commands
Can run most M-files
No built-in Simulink package
Pure command line

Scilab
◦ http://www.scilab
.org/
◦ Some commands
are different
◦ Built-in Xcos to
clone Simulink
◦ Some Graphic
interface
Given a transfer function
a 2 s 2 + a 1 s + a0
b 2 s2 + b 1 s + b 0
We can define it in Matlab as
num = [a2, a1, a0];
den = [b2, b1, b0];
sys = tf(num, den);
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Unit step response
step(sys)
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Unit impulse response
impulse(sys)
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Arbitrary input response
t = tstart: tinterval : tfinish;
u = f(t); % u is a function of t, e.g. ramp is u=t;
lsim(sys, u, t)
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Just bring the output to a variable. E.g.
y1 = step(sys);
y2 = impule(sys);
y3 = lsim(sys, u, t);

Then we can use the variable. E.g.
plot(t,y1, t, y2)
plot(t, u, t, y3)
[r, p, k] = residue(num, den);
Where
r: root
p: pole
k: constant
If there are complex terms, we
can add the two conjugate ones
together to get a 2nd order real
term.
Click the Simulink
icon in Matlab
window
Matlab main window
Simulink modeling window
Simulink library browser

Find, drag and drop following blocks to
the window
◦ Simulink  Continuous  Transfer Function
◦ Sources  Step
◦ Sinks  Scope
You will get
Input
Building Blocks
Output
Except sources and
sinks, every block
should have an input
and an output.

Double click the Transfer function block.
Change Numerator to [1], denominator to
[1 3 2]


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Link the blocks by drag the output to input
Double click Scope to show Scope window
Click Ctrl+T or SimulationStart or button

Change the spring constant and damping
ratio, then you can have different response.
[1 2 1]
[1 2 12]
Hint: Hit the binocular to auto-scale the plot.

Replace the source with a Sine wave with
frequency =3
Hint: Double click the block name to
change it.

Hint:
◦ Hold Ctrl and click to tap an output line
◦ Right click a block and select Format to flip or rotate a block
Rewrite
as


Ý cxÝ kx  f (t)
mxÝ
Ý
xÝ
Assume
m=2kg
c=3NSec/m
k=3N/m
f(t)=1(t)N
1
m
[ f (t) cxÝ kx]