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ss2tf() Acting Oddly

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Daniel Gelman
Daniel Gelman on 24 Aug 2016
Answered: Jose Lara on 31 Aug 2016
I am constructing a few transfer functions and I believe this the output is very wrong. I am not expecting the numerator and denominator to be the same. As expected B is a 'tf' (transfer function) but for some reason F defaulted to 'ss' (solid-state representation).
s = tf('s');
B = 0.05/(0.0303*s+1);
F = (1+B)/(1+(B*exp(-0.1*s)));
[num,den] = ss2tf(F.a,F.b,F.c,F.d)
Fsys = tf(num,den)
Output:
num =
1.0e+03 *
0.001000000000000 0.067656765676568 1.143678724308074
den =
1.0e+03 *
0.001000000000000 0.067656765676568 1.143678724308074
Fsys =
s^2 + 67.66 s + 1144
--------------------
s^2 + 67.66 s + 1144
Continuous-time transfer function.

Answers (1)

Jose Lara
Jose Lara on 31 Aug 2016
You are trying to create an irrational transfer function. System interconnections using internal delays can only be represented in state-space, that is why F is defaulted to state-space. Try creating the system using only one equation by simplifying F and then using Pade approximation for the transport delays. Try the following steps:
s = tf('s');
Fs = ((0.0303*s + 1.05)/(0.0303*s+1+0.05*exp(-0.1*s)));
F = pade(Fs, 0);
[num,den] = ss2tf(F.a,F.b,F.c,F.d);
Fsys = tf(num,den);
Check out this other answer that uses transport delays: https://www.mathworks.com/matlabcentral/answers/246815
Also, check the documentation on how this Pade approximation works: http://www.mathworks.com/help/symbolic/pade.html

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