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For System Dynamics & Control. By Dr. Hong Zhang. Start Matlab. Free Matlab Clones. Octave Very Similar commands Can run most M-files No built-in Simulink package Pure command line . Free Matlab Clones. Scilab

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For system dynamics control

For System Dynamics & Control

By Dr. Hong Zhang

Start matlab
Start Matlab

Free matlab clones
Free Matlab Clones

  • Octave


    • Very Similar commands

    • Can run most M-files

    • No built-in Simulink package

    • Pure command line

Free matlab clones1
Free Matlab Clones

  • Scilab


    • Some commands are different

    • Built-in Xcos to clone Simulink

    • Some Graphic interface

Transfer function
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
Plot Transient Response

  • Unit step response


  • Unit impulse response


  • 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
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
Partial Fractional Expansion

[r, p, k] = residue(num, den);


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
Start Simulink

Click the Simulink icon in Matlab window

Matlab main window

Simulink modeling window

Simulink library browser

Transfer function1
Transfer Function

  • Find, dragand drop following blocks to the window

    • Simulink Continuous  Transfer Function

    • Sources  Step

    • Sinks  Scope

      You will get



Except sources and sinks, every block should have an input and an output.

Building Blocks

Modify transfer function
Modify Transfer Function

  • Double click the Transfer function block.

  • Change Numerator to [1], denominator to [1 3 2]

Run simulation
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
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
Sinusoidal Response

  • Replace the source with a Sine wave with frequency =3

Hint: Double click the block name to change it.

Flowchart with feedback
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
Mass-Spring-Damper Modeling