lab1.md

Lab1 Slides can be found here

If you encounter the following error:

It is because the file name of script file is the same as the name of the model file. Changing the name of the script file to something different can solve the problem.

Why does $\frac{1}{s}$ represent the integrator? According to the Laplace transform of integral:

$$\mathscr{L}[\int g(t) d t]=\int_0^{+\infty}\int g(t)dt e^{-st}dt = \frac{G(s)+[\int g(t) d t]_{t=0}}{s}$$

where $G(s) = \mathscr{L}[g(t)]$

Simulink model with block labels

You can find more information here.

Matlab code running Simulink model

M=2;
K=16;
B=4;
fafinal = 8;
sim('lab1_simulink_model')
plot(t,x);
hold on
B=8; sim('lab1_simulink_model');plot(t,x)
B=12; sim('lab1_simulink_model');plot(t,x)
B=25; sim('lab1_simulink_model');plot(t,x)
legend('B=4','B=8','B=12','B=25');
hold off

You can find more information here.

Matlab code for simulation (Optional)

M=2;
K=16;
B=4
numeratorM=1;
denominatorM=[M 0];
sysM=tf(numeratorM,denominatorM) 
numeratorI=1;
denominatorI=[1 0];
sysI=tf(numeratorI,denominatorI)
sysMD=feedback(sysM,B)
sysMDS=feedback(series(sysMD,sysI),K)
subplot(1,2,1)
step(sysMDS,10)
subplot(1,2,2)
bode(sysMDS)

Detailed explanation:

The code "numeratorM=1;denominatorM=[M 0];sysM=tf(numeratorM,denominatorM)" builds the following blocks:

The code "sysMD=feedback(sysM,B)" builds the following blocks:

The code "numeratorI=1;denominatorI=[1 0];sysI=tf(numeratorI,denominatorI)" builds the second integrator block.

Finally, the code "sysMDS=feedback(series(sysMD,sysI),K)" builds the complete system.

Simscape model with block labels

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How plot velocity in scope