# Finding transfer function from bode plot

I try to estimate a system transfer function by hand calculation from a bode plot data but I could not succeed yet and I need someone help.

it will be appreciated if anyone explains or refer me to a source where I can learn to estimate the TF with Matlab tools/codes (I couldn't do it with system identification toolbox)

frequencies (rad/s): 0.5 ; 1 ; 2 ; 3 ; 4 ; 5 ; 7.5; 10 ; 15 ; 30 ; 50

magnitudes (dB) : 12 ; 6 ; 0 ; -3 ; -14 ; -20 ; -26 ; -30 ; -30 ; -34 ; -40

phase (degree) :-37 ; -54; -109 ; -112 ; -103; -106; -107; -86 ; -86 ; -86 ; -86

• Did you try plotting the values on a semilog plot (frequencies on the log axis)? And look for the -3dB points and the phase angles at those points? Sep 18 '19 at 3:32
• Yes I did and I try to estimate it as a normal minimum phase system by hand calculation but the magnitute slopes and phase are not correlated (+-20dB//+-90 deg). it seems like system has transport delay or a non-minimum phase system which has pole or zero on the right hand side. Therefore, I thought I need algorithm or a toolbox to exactly estimate it.
– lsn
Sep 18 '19 at 18:19
• Is this approximated first order bode? Can you solve it by hand? Sep 18 '19 at 23:36