tfest function does not recognize nearby poles and zeros in a 2dof system
I am using tfestimate and tfest to experimentally derive the frequency response function of a 2 dof system with 1 input and 2 output.
The problem is that tfest seems to cancel or does not recognize a complex pole pair (resonance) near a complex zero pair (antiresonance) around 6 Hz in the tf from input 1 to output 1 and consequently simplifies the frequency response of the system (see image, correct plot in blue vs simplified plot in red):
I tried different types of windowing in tfestimate but the only one that allows me to obtain the correct frequency response after tfest is rectwin without overlap: this works only with mathematical model I/O data, the blue plot shown above, but with the real model data the problem persists. Other windows like hann (which would be more suitable) also leads to a pole-zero simplification after tfest, with mathematical model I/O data too.
Increasing the number of zeros-poles from 2-4 to 6-8 tfest gives me the correct transfer functions, but I absolutely need the model with 2 zeros and 4 poles for a correct dynamic of the system to control by using the identification of its FRF.
To load I/O data see attachment .mat file
The code is the following:
% Upload I/O data
load ‘test_identificazione_chirp_tauGain_0,1.mat’
% Data from real model
th1abs = theta1_rad_MEAS.signals.values;
th2rel = theta2_rad_MEAS.signals.values;
th2abs = th1abs+th2rel;
tauIn = tauInput.signals.values;
nfs = 4096*4; % Number of samples for FFT
Fs = 1000; % Sampling frequency
% Transfer functions estimate from input 1 (tauIn) to outputs 1 and 2 (th1abs and th2abs)
[H_11, f_H_11] = tfestimate(squeeze(tauIn), squeeze(th1abs), rectwin(floor(size(squeeze(tauIn), 1))), 0, nfs*4, Fs);
[H_21, f_H_21] = tfestimate(squeeze(tauIn), squeeze(th2abs), rectwin(floor(size(squeeze(tauIn), 1))), 0, nfs*4, Fs);
% Try also hann window with overlap to get a better curve: hann(floor(size(squeeze(tauIn), 1) / 15)), 3000
% Estimated tf smoothing, by movmean with [x,x] values
H_11 = movmean(H_11,[2,2]);
H_21 = movmean(H_21,[2,2]);
% Estimated tf plot
figure(1)
subplot(1,2,1);
semilogx(f_H_11, mag2db(abs(H_11)), ‘b’, ‘LineWidth’, 0.7);
hold on;
subplot(1,2,2);
semilogx(f_H_21, mag2db(abs(H_21)), ‘b’, ‘LineWidth’, 0.7);
hold on;
% Frequency range to keep only relevant part of tf by tfestimate
fmin = 0.1; % min freq (Hz)
fmax = 15; % max freq (Hz)
idx_11 = (f_H_11 >= fmin) & (f_H_11 <= fmax); % frequency index in the selected range
idx_21 = (f_H_21 >= fmin) & (f_H_21 <= fmax); % frequency index in the selected range
H_11_filtered = H_11(idx_11);
f_11_filtered = f_H_11(idx_11); % corresponding frequencies
H_21_filtered = H_21(idx_21);
f_21_filtered = f_H_21(idx_21); % corresponding frequencies
% rad/s conversion to use in `idfrd`
f_11_rad = f_11_filtered * 2 * pi;
f_21_rad = f_21_filtered * 2 * pi;
% Filtered tf plot
subplot(1,2,1);
semilogx(f_11_filtered, mag2db(abs(H_11_filtered)), ‘r’, ‘LineWidth’, 0.7);
subplot(1,2,2);
semilogx(f_21_filtered, mag2db(abs(H_21_filtered)), ‘r’, ‘LineWidth’, 0.7);
% Creating an identified model based on frequency data
H_11_idfrd = idfrd(H_11_filtered, f_11_rad, ‘Ts’, 0); % continuous time
H_21_idfrd = idfrd(H_21_filtered, f_21_rad, ‘Ts’, 0); % continuous time
% tf estimation in "tf" variable type
np = 4; % system pole number
nz = 2; % system zero number
sys_est_11 = tfest(H_11_idfrd, np, nz);
sys_est_21 = tfest(H_21_idfrd, np, nz);
sys_est = [sys_est_11; sys_est_21]; % [2×1] dimension
% Estimated FRF plot
figure(2)
P = bodeoptions;
P.FreqUnits = ‘Hz’; % Frequency axys in Hz
bodeplot(sys_est, P);
grid on;
hold on;
% Print estimated tf in the Command Window
sys_est
Any help? Thank you in advance!I am using tfestimate and tfest to experimentally derive the frequency response function of a 2 dof system with 1 input and 2 output.
The problem is that tfest seems to cancel or does not recognize a complex pole pair (resonance) near a complex zero pair (antiresonance) around 6 Hz in the tf from input 1 to output 1 and consequently simplifies the frequency response of the system (see image, correct plot in blue vs simplified plot in red):
I tried different types of windowing in tfestimate but the only one that allows me to obtain the correct frequency response after tfest is rectwin without overlap: this works only with mathematical model I/O data, the blue plot shown above, but with the real model data the problem persists. Other windows like hann (which would be more suitable) also leads to a pole-zero simplification after tfest, with mathematical model I/O data too.
Increasing the number of zeros-poles from 2-4 to 6-8 tfest gives me the correct transfer functions, but I absolutely need the model with 2 zeros and 4 poles for a correct dynamic of the system to control by using the identification of its FRF.
To load I/O data see attachment .mat file
The code is the following:
% Upload I/O data
load ‘test_identificazione_chirp_tauGain_0,1.mat’
% Data from real model
th1abs = theta1_rad_MEAS.signals.values;
th2rel = theta2_rad_MEAS.signals.values;
th2abs = th1abs+th2rel;
tauIn = tauInput.signals.values;
nfs = 4096*4; % Number of samples for FFT
Fs = 1000; % Sampling frequency
% Transfer functions estimate from input 1 (tauIn) to outputs 1 and 2 (th1abs and th2abs)
[H_11, f_H_11] = tfestimate(squeeze(tauIn), squeeze(th1abs), rectwin(floor(size(squeeze(tauIn), 1))), 0, nfs*4, Fs);
[H_21, f_H_21] = tfestimate(squeeze(tauIn), squeeze(th2abs), rectwin(floor(size(squeeze(tauIn), 1))), 0, nfs*4, Fs);
% Try also hann window with overlap to get a better curve: hann(floor(size(squeeze(tauIn), 1) / 15)), 3000
% Estimated tf smoothing, by movmean with [x,x] values
H_11 = movmean(H_11,[2,2]);
H_21 = movmean(H_21,[2,2]);
% Estimated tf plot
figure(1)
subplot(1,2,1);
semilogx(f_H_11, mag2db(abs(H_11)), ‘b’, ‘LineWidth’, 0.7);
hold on;
subplot(1,2,2);
semilogx(f_H_21, mag2db(abs(H_21)), ‘b’, ‘LineWidth’, 0.7);
hold on;
% Frequency range to keep only relevant part of tf by tfestimate
fmin = 0.1; % min freq (Hz)
fmax = 15; % max freq (Hz)
idx_11 = (f_H_11 >= fmin) & (f_H_11 <= fmax); % frequency index in the selected range
idx_21 = (f_H_21 >= fmin) & (f_H_21 <= fmax); % frequency index in the selected range
H_11_filtered = H_11(idx_11);
f_11_filtered = f_H_11(idx_11); % corresponding frequencies
H_21_filtered = H_21(idx_21);
f_21_filtered = f_H_21(idx_21); % corresponding frequencies
% rad/s conversion to use in `idfrd`
f_11_rad = f_11_filtered * 2 * pi;
f_21_rad = f_21_filtered * 2 * pi;
% Filtered tf plot
subplot(1,2,1);
semilogx(f_11_filtered, mag2db(abs(H_11_filtered)), ‘r’, ‘LineWidth’, 0.7);
subplot(1,2,2);
semilogx(f_21_filtered, mag2db(abs(H_21_filtered)), ‘r’, ‘LineWidth’, 0.7);
% Creating an identified model based on frequency data
H_11_idfrd = idfrd(H_11_filtered, f_11_rad, ‘Ts’, 0); % continuous time
H_21_idfrd = idfrd(H_21_filtered, f_21_rad, ‘Ts’, 0); % continuous time
% tf estimation in "tf" variable type
np = 4; % system pole number
nz = 2; % system zero number
sys_est_11 = tfest(H_11_idfrd, np, nz);
sys_est_21 = tfest(H_21_idfrd, np, nz);
sys_est = [sys_est_11; sys_est_21]; % [2×1] dimension
% Estimated FRF plot
figure(2)
P = bodeoptions;
P.FreqUnits = ‘Hz’; % Frequency axys in Hz
bodeplot(sys_est, P);
grid on;
hold on;
% Print estimated tf in the Command Window
sys_est
Any help? Thank you in advance! I am using tfestimate and tfest to experimentally derive the frequency response function of a 2 dof system with 1 input and 2 output.
The problem is that tfest seems to cancel or does not recognize a complex pole pair (resonance) near a complex zero pair (antiresonance) around 6 Hz in the tf from input 1 to output 1 and consequently simplifies the frequency response of the system (see image, correct plot in blue vs simplified plot in red):
I tried different types of windowing in tfestimate but the only one that allows me to obtain the correct frequency response after tfest is rectwin without overlap: this works only with mathematical model I/O data, the blue plot shown above, but with the real model data the problem persists. Other windows like hann (which would be more suitable) also leads to a pole-zero simplification after tfest, with mathematical model I/O data too.
Increasing the number of zeros-poles from 2-4 to 6-8 tfest gives me the correct transfer functions, but I absolutely need the model with 2 zeros and 4 poles for a correct dynamic of the system to control by using the identification of its FRF.
To load I/O data see attachment .mat file
The code is the following:
% Upload I/O data
load ‘test_identificazione_chirp_tauGain_0,1.mat’
% Data from real model
th1abs = theta1_rad_MEAS.signals.values;
th2rel = theta2_rad_MEAS.signals.values;
th2abs = th1abs+th2rel;
tauIn = tauInput.signals.values;
nfs = 4096*4; % Number of samples for FFT
Fs = 1000; % Sampling frequency
% Transfer functions estimate from input 1 (tauIn) to outputs 1 and 2 (th1abs and th2abs)
[H_11, f_H_11] = tfestimate(squeeze(tauIn), squeeze(th1abs), rectwin(floor(size(squeeze(tauIn), 1))), 0, nfs*4, Fs);
[H_21, f_H_21] = tfestimate(squeeze(tauIn), squeeze(th2abs), rectwin(floor(size(squeeze(tauIn), 1))), 0, nfs*4, Fs);
% Try also hann window with overlap to get a better curve: hann(floor(size(squeeze(tauIn), 1) / 15)), 3000
% Estimated tf smoothing, by movmean with [x,x] values
H_11 = movmean(H_11,[2,2]);
H_21 = movmean(H_21,[2,2]);
% Estimated tf plot
figure(1)
subplot(1,2,1);
semilogx(f_H_11, mag2db(abs(H_11)), ‘b’, ‘LineWidth’, 0.7);
hold on;
subplot(1,2,2);
semilogx(f_H_21, mag2db(abs(H_21)), ‘b’, ‘LineWidth’, 0.7);
hold on;
% Frequency range to keep only relevant part of tf by tfestimate
fmin = 0.1; % min freq (Hz)
fmax = 15; % max freq (Hz)
idx_11 = (f_H_11 >= fmin) & (f_H_11 <= fmax); % frequency index in the selected range
idx_21 = (f_H_21 >= fmin) & (f_H_21 <= fmax); % frequency index in the selected range
H_11_filtered = H_11(idx_11);
f_11_filtered = f_H_11(idx_11); % corresponding frequencies
H_21_filtered = H_21(idx_21);
f_21_filtered = f_H_21(idx_21); % corresponding frequencies
% rad/s conversion to use in `idfrd`
f_11_rad = f_11_filtered * 2 * pi;
f_21_rad = f_21_filtered * 2 * pi;
% Filtered tf plot
subplot(1,2,1);
semilogx(f_11_filtered, mag2db(abs(H_11_filtered)), ‘r’, ‘LineWidth’, 0.7);
subplot(1,2,2);
semilogx(f_21_filtered, mag2db(abs(H_21_filtered)), ‘r’, ‘LineWidth’, 0.7);
% Creating an identified model based on frequency data
H_11_idfrd = idfrd(H_11_filtered, f_11_rad, ‘Ts’, 0); % continuous time
H_21_idfrd = idfrd(H_21_filtered, f_21_rad, ‘Ts’, 0); % continuous time
% tf estimation in "tf" variable type
np = 4; % system pole number
nz = 2; % system zero number
sys_est_11 = tfest(H_11_idfrd, np, nz);
sys_est_21 = tfest(H_21_idfrd, np, nz);
sys_est = [sys_est_11; sys_est_21]; % [2×1] dimension
% Estimated FRF plot
figure(2)
P = bodeoptions;
P.FreqUnits = ‘Hz’; % Frequency axys in Hz
bodeplot(sys_est, P);
grid on;
hold on;
% Print estimated tf in the Command Window
sys_est
Any help? Thank you in advance! tfest, system identification, frequency response MATLAB Answers — New Questions
