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For System Dynamics & Control

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/

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For System Dynamics & Control

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  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 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, 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

  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. [1 2 1] [1 2 12] 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

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