# How to find time constants from given 2+ order transfer function?

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shrivardhan suryawanshi on 16 Oct 2016
Edited: Gerard Nagle on 29 Apr 2023
I have a transfer function let us take for e.g k/(100*s^2+20*s+1).In this TF I want to access the denominator as k/(10*s+1)(10*s+1) in such a way that algorithm will return tau1=10,tau2=10.How to get it?

David Wilson on 26 Aug 2020
If you just want to display the transfer function in time-constant form, you can do the following:
s = tf('s');
k = 45; % anyhting
G = k/(100*s^2+20*s+1) % expanded polynomial form
[z,p,k] = zpkdata(G)
G1 = zpk(z,p,k,'DisplayFormat','timeconstant')
damp(G)
[w, zeta, p] = damp(G)
tau = 1./w
I',m assuming you have a stable TF. Check with isstable.
Gerard Nagle on 29 Apr 2023
Edited: Gerard Nagle on 29 Apr 2023
Was trying for hours to get a nice format and do this using my own code. Should have read the documentation closer. Thanks for the answer

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