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

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HUANG ZI YOU 2022-1-5

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评论： Mathieu NOE 2022-1-7

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

I need to invers the transfer function.

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Mathieu NOE 2022-1-5

can you share the measurement ?

HUANG ZI YOU 2022-1-5

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

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HUANG ZI YOU 2022-1-5

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https://ww2.mathworks.cn/matlabcentral/answers/1622465-how-to-estimate-the-transfer-function-with-positive-zero-and-pole-use-system-identification-tool-box#answer_868455

OK~

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Mathieu NOE 2022-1-5

在 MATLAB Online 中打开

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 2022-1-7

OK~ I will try the PFCD method.

Thanks for answer my question.

Mathieu NOE 2022-1-7

My pleasure

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