1. For System Dynamics & Control
By Dr. Hong Zhang

2. Start Matlab

3. Free Matlab Clones Octave http://www.gnu.org/software/octave/
Very Similar commands
Can run most M-files
No built-in Simulink package
Pure command line

4. Free Matlab Clones Scilab http://www.scilab .org/
Some commands are different
Built-in Xcos to clone Simulink
Some Graphic interface

5. Transfer Function a2s2 + a1s + a0 b2s2 + b1s + b0
Given a transfer function
a2s2 + a1s + a0
b2s2 + b1s + b0
We can define it in Matlab as
num = [a2, a1, a0];
den = [b2, b1, b0];
sys = tf(num, den);

6. Plot Transient Response
Unit step response
step(sys)
Unit impulse response
impulse(sys)
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)

7. Response As a Variable 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)

8. Partial Fractional Expansion
[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.

9. Start Simulink Click the Simulink icon in Matlab window
Matlab main window
Simulink modeling window
Simulink library browser

10. Transfer Function Find, drag and drop following blocks to the window
Simulink  Continuous  Transfer Function
Sources  Step
Sinks  Scope
You will get
Output
Input
Except sources and sinks, every block should have an input and an output.
Building Blocks

11. Modify Transfer Function
Double click the Transfer function block.
Change Numerator to [1], denominator to [1 3 2]

12. Run Simulation Link the blocks by drag the output to input
Double click Scope to show Scope window
Click Ctrl+T or SimulationStart or button

13. Modify System
Change the spring constant and damping ratio, then you can have different response.
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Hint: Hit the binocular to auto-scale the plot.

14. Sinusoidal Response
Replace the source with a Sine wave with frequency =3
Hint: Double click the block name to change it.

15. Flowchart with Feedback
Hint:
Hold Ctrl and click to tap an output line
Right click a block and select Format to flip or rotate a block

16. Mass-Spring-Damper Modeling
Rewrite as
Assume
m=2kg
c=3NSec/m
k=3N/m
f(t)=1(t)N