# For System Dynamics & Control

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For System Dynamics & Control
By Dr. Hong Zhang

Start Matlab

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

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

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);

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)

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)

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.

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

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

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

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

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

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

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

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

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