How to estimate the transfer function with positive zero and pole use System identification tool box

How to estimate the transfer function with negative zero and pole use System identification tool box.

I need to invers the transfer function.

[Mathieu NOE]

hello

could you please clarify from which data (time or frequency domain) you want a TFE

if you could share the data + the code you have done so far it's even better

[HUANG ZI YOU]

I had already get the transfer function from Displacement command to Displacement meter data.

The transfer function is like this (-0.309s+58.2)/(s+60.21), but this is not the minimum-phase system, I want to get the

invers transfer function, so the zeros and pole should be negative.

thanks for answer my question~

[Mathieu NOE]

can you share the measurement ?

[HUANG ZI YOU]

sorry~ I make the type fail, both pole and zero are negative

Answer 1

[HUANG ZI YOU]

OK~

[Mathieu NOE]

what is the sampling rate ?

[Mathieu NOE]

FYI

i assumed here a sampling rate FS = 1000 Hz

notice that the usefull info is in the lower frequency range (above 30 Hz the coherence drops significantly)

this must be quite in line with your actual sampling rate as I got more or less the same model

(-0.3511s + 54)/(s+56)

now the fact that this is a non minimum phase process hinders the possibility to make a direct pole zero compensation (a brute force approach IMHO), but still you have the possibility to create a better system with a lead compensator witthin a closed loop

also see this PFCD method in ref :

Analytical Statistical Study of Linear Parallel Feedforward Compensators for Nonminimum-Phase Systems | DSCC | ASME Digital Collection

below my code if it helps you

clc;clearvars
load('input.mat'); % input : Exd_Com
load('output.mat'); % output : Exd
Fs = 1000; % sampling rate

fmin_visu = 0.1;
% fmax_visu = round(100*Fs/256);
fmax_visu = 30;


% to be compared to the FRF computed by Welch's periodogram (tfe.m)
nfft = 512*8;
window = hanning(nfft);
noverlap = 0.75*nfft;
[Txy,Freq] = tfe(Exd_Com,Exd,nfft,Fs,window,noverlap) ;
[Cxy,Freq] = cohere(Exd_Com,Exd,nfft,Fs,window,noverlap) ;
ind = find(Freq>fmin_visu & Freq<fmax_visu);


%% Id with invfreqs (IIR)
nb = 1; % nb of zeroes
na = 1; % nb of poles
iter = 1000;
[bb,aa] = invfreqs(Txy(ind),2*pi*Freq(ind),nb,na,[],iter); % stable approximation to system
[g,p] = bode(bb,aa,2*pi*Freq(ind));
p = p-360;

figure(1)
set(gcf,'name','Identified Model','numbertitle','off')
subplot(3,1,1),semilogx(Freq(ind),20*log10(abs(Txy(ind))),Freq(ind),20*log10(g));
title('Secondary path FRF');
ylabel('dB');
legend('data','model');
subplot(3,1,2),semilogx(Freq(ind),180/pi*(angle(Txy(ind))),Freq(ind),p);
ylabel('Phase (°)');
legend('data','model');
subplot(3,1,3),semilogx(Freq(ind),Cxy(ind));
xlabel('Frequency (Hz)');
ylabel('Coherence');

[HUANG ZI YOU]

OK~ I will try the PFCD method.

Thanks for answer my question.

[Mathieu NOE]

My pleasure