for system dynamics & control
Post on 22-Feb-2016
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For System Dynamics
& ControlBy Dr. Hong Zhang
Start Matlab
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
Free Matlab Clones
Given a transfer function a2s2 + a1s + a0
b2s2 + b1s + b0We can define it in Matlab as
num = [a2, a1, a0];den = [b2, b1, b0]; sys = tf(num, den);
Transfer Function
Unit step responsestep(sys)
Unit impulse responseimpulse(sys)
Arbitrary input responset = tstart: tinterval : tfinish;u = f(t); % u is a function of t, e.g. ramp is u=t;lsim(sys, u, t)
Plot Transient Response
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)
Response As a Variable
[r, p, k] = residue(num, den);Where
r: rootp: polek: constant
If there are complex terms, we can add the two conjugate ones together to get a 2nd order real term.
Partial Fractional Expansion
Click the Simulink icon in Matlab window
Start Simulink
Simulink library browserSimulink modeling window
Matlab main window
Find, drag and drop following blocks to the window◦ Simulink Continuous Transfer Function◦ Sources Step◦ Sinks ScopeYou will get
Transfer Function
Building Blocks
OutputInput
Except sources and sinks, every block should have an input and an output.
Double click the Transfer function block.
Modify Transfer Function
Change Numerator to [1], denominator to [1 3 2]
Link the blocks by drag the output to input Double click Scope to show Scope window Click Ctrl+T or SimulationStart or button
Run Simulation
Change the spring constant and damping ratio, then you can have different response.
Modify System
[1 2 12][1 2 1]Hint: Hit the binocular to auto-scale the plot.
Replace the source with a Sine wave with frequency =3
Sinusoidal Response
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
Flowchart with Feedback
Mass-Spring-Damper Modeling
€
m˙ ̇ x + c ˙ x + kx = f ( t)
€
˙ ̇ x = 1m [ f (t)− c ˙ x − kx]
Rewrite
as
Assumem=2kgc=3NSec/mk=3N/mf(t)=1(t)N
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