bode() yields wrong result

Hello,

I would like to plot the Bode diagram of the following transfer function:

If I use the following code, I do not get appropriate results:

s = tf('s');

f1 = 0.99 * 18.88;

f2 = (1 + s / (2 * 3.1415 * 10.58)) / (1 + s / (s / (2 * 3.1415 * 26.74)));

f3 = (s / (2 * 3.1415 * 23.17)) / (1 + s / (2 * 3.1415 * 23.17));

f4 = (s / (2 * 3.1415 * 25.21)) / (1 + s / (2 * 3.1415 * 25.21));

f5 = 1 / (1 + s / (2 * 3.1415 * 48000));

bode(f1 * f2 * f3 * f4 * f5); grid on;

However, if I only plot one factor of the transfer function, it seems to work properly.

I would really appreaciate any help regarding this problem.

[Paul]

s = tf('s');
f1 = 0.99 * 18.88;
f2 = (1 + s / (2 * 3.1415 * 10.58)) / (1 + s / (s / (2 * 3.1415 * 26.74)));
f3 = (s / (2 * 3.1415 * 23.17)) / (1 + s / (2 * 3.1415 * 23.17));
f4 = (s / (2 * 3.1415 * 25.21)) / (1 + s / (2 * 3.1415 * 25.21));
f5 = 1 / (1 + s / (2 * 3.1415 * 48000));
bode(f1 * f2 * f3 * f4 * f5); grid on;

What is your concern with the Bode plot?

[Pascal Warten]

This is not the Bode plot of the given transfer function. The last factor of the transfer function models a lowpass filter which cannot be seen in the Bode plot.

The amplitude frequency response should roughly look like this:

[Paul]

Most impportantly, correct the typo in f2 as indicated below by @Star Strider.

Also, bode() always works with frequencies in rad/TimeUnit. If you want to specify the frequency in Hz, you can do it manually.

s = tf('s');
f1 = 0.99 * 18.88;
f2 = (1 + s / (2 * 3.1415 * 10.58)) / (1 + s / (2 * 3.1415 * 26.74));
f3 = (s / (2 * 3.1415 * 23.17)) / (1 + s / (2 * 3.1415 * 23.17));
f4 = (s / (2 * 3.1415 * 25.21)) / (1 + s / (2 * 3.1415 * 25.21));
f5 = 1 / (1 + s / (2 * 3.1415 * 48000));
whz = logspace(0,6);
[m,p] = bode(f1 * f2 * f3 * f4 * f5,2*pi*whz);
semilogx(whz,db(squeeze(m)))

Or use bodeplot() to plot in Hz directly

opts = bodeoptions;
opts.FreqUnits = 'Hz';
bodeplot(f1*f2*f3*f4*f5,opts);

[Pascal Warten]

Thank you for your tips regarding the specifications of the units.

Answer 1

[Star Strider]

There is a typographical error in ‘f2’ and correcting it produces the desired result —

s = tf('s');
f1 = 0.99 * 18.88;
f2 = (1 + s / (10.58)) / (1 + s / (26.74));
f3 = (s / (23.17)) / (1 + s / (23.17));
f4 = (s / (25.21)) / (1 + s / (25.21));
f5 = 1 / (1 + s / (48000));

figure
bode(f1 * f2 * f3 * f4 * f5, {0 5E+7*2*pi})
grid on;

.

[Pascal Warten]

Thanks a lot!

[Star Strider]

As always, my pleasure!

.