For System Dynamics &amp; Control

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# For System Dynamics &amp; Control - PowerPoint PPT Presentation

For System Dynamics &amp; 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/

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### For System Dynamics & Control

By Dr. Hong Zhang

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

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.

Click the Simulink icon in Matlab window

Matlab main window

Transfer Function
• Find, dragand 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.

[1 2 1]

[1 2 12]

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