bandwidth returns inf on transfer function

I have a tf object

tf1 =

From input "u1" to output "y1":

0.3645 s + 0.0003711

--------------------------

s^2 + 0.3928 s + 0.0003717

which gives me a bandwidth(tf1) = 0.3353

When I use a different tf object of lower order, but with almost the same impulse response

tf2 =

From input "u1" to output "y1":

0.9236 s + 0.001036

-------------------

s + 0.001038

bandwidth(tf2) = Inf

Also, If I look at the bode plots of both transfer functions, I can see that the left one (tf1) shows the full frequency range, while the plot for tf2 right on the right "stops" at 10e-2.

I am wondering, what is the reason for that and does it have other implications besides "bandwidth" is not working?

Answer 1

[Star Strider]

From the documentation —

‘fb = bandwidth(sys) returns the bandwidth of the SISO dynamic system model sys. The bandwidth is the first frequency where the gain drops below 70.79% (-3 dB) of its DC value.’

However it never gets to -3 dB. It is asymptotic at about -0.7 dB from about 0.1 to . I suspect that is the problem.

s = tf('s');
tf2 = (0.9236*s + 0.001036) / (s + 0.001038)

tf2 =
 
  0.9236 s + 0.001036
  -------------------
     s + 0.001038
 
Continuous-time transfer function.

win = logspace(-4,4,150);
figure
h = bodeplot(tf2,win);
opts = getoptions(h);
opts.Grid = 'on';
setoptions(h,opts)

.

[Michael Budach]

That is true, but why shows the bode plot only till 1e-2?

[Star Strider]

I am not certain of the reason it sets that limit (it chooses the limit based on the system characteristics, so it may set that on the basis of the system becoming asymptotic at about that frequency), however that can easily be overridden by providing the frequency vector as an additional argument, as my Answer demonstrates.

.