Obatin s domain and transfer function from the data

8 vues (au cours des 30 derniers jours)
Venkatkumar M
Venkatkumar M le 9 Déc 2021
Commenté : Star Strider le 13 Déc 2021
I have two set of graph data
Frequency / phase , angle data - Freq_phase_angle.txt
Frequency / real , imaginary data - Freq_complex.txt
Could any one please help with procedure to obatin S-domain/ Transfer function from data(.txt) using system idenrtification tool in MATLAB?
To obtain this circuit. using cauer/foster method

Réponse acceptée

Star Strider
Star Strider le 9 Déc 2021
Start with the idfrd function and go from there. The documentation explains everything.
Actually though, to analyse the circuit using the Foster-Cauer approach, plot the imaginary part of the complex frequency vector and go from there —
T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/828710/Freq_complex.txt', 'VariableNamingRule','preserve')
T1 = 5479×2 table
Freq. V(i_s) ______ _______________________________________________ 100 {'5.25923694595431e-001,6.34606935959376e+000'} 100.23 {'5.26471741717689e-001,6.36067773821260e+000'} 100.46 {'5.27022310375074e-001,6.37531964864880e+000'} 100.69 {'5.27575412141180e-001,6.38999516719951e+000'} 100.93 {'5.28131058638060e-001,6.40470437033997e+000'} 101.16 {'5.28689261538566e-001,6.41944733471207e+000'} 101.39 {'5.29250032542678e-001,6.43422413714084e+000'} 101.62 {'5.29813383450318e-001,6.44903485459486e+000'} 101.86 {'5.30379326076855e-001,6.46387956423504e+000'} 102.09 {'5.30947872306298e-001,6.47875834338622e+000'} 102.33 {'5.31519034080622e-001,6.49367126954284e+000'} 102.57 {'5.32092823401404e-001,6.50861842036846e+000'} 102.8 {'5.32669252306374e-001,6.52359987370368e+000'} 103.04 {'5.33248332892240e-001,6.53861570756800e+000'} 103.28 {'5.33830077315765e-001,6.55366600013723e+000'} 103.51 {'5.34414497792562e-001,6.56875082976168e+000'}
T1{:,2} = cellfun(@(x)sscanf(x, '%f, %f'), T1{:,2}, 'Unif',0);
RI = cell2mat(table2cell(T1(:,2)).').';
RI = complex(RI(:,1),RI(:,2));
T2 = [T1(:,1) table(RI)];
T2.Properties.VariableNames = {'Freq','V(i_s)'}
T2 = 5479×2 table
Freq V(i_s) ______ _______________ 100 0.52592+6.3461i 100.23 0.52647+6.3607i 100.46 0.52702+6.3753i 100.69 0.52758+6.39i 100.93 0.52813+6.4047i 101.16 0.52869+6.4194i 101.39 0.52925+6.4342i 101.62 0.52981+6.449i 101.86 0.53038+6.4639i 102.09 0.53095+6.4788i 102.33 0.53152+6.4937i 102.57 0.53209+6.5086i 102.8 0.53267+6.5236i 103.04 0.53325+6.5386i 103.28 0.53383+6.5537i 103.51 0.53441+6.5688i
figure
semilogx(T2{:,1}, imag(T2{:,2}))
grid
There is one obvious pole, however there may be two others with real values far from the imaginary axis. There is a zero at the origin, and likely one at infinity.
.
  2 commentaires
Venkatkumar M
Venkatkumar M le 13 Déc 2021
@Star Strider Could you please let me know how to use vetcors in system identification tool to find the poles and zeros?
Star Strider
Star Strider le 13 Déc 2021
Using Cauer-Foster is not difficult, however I choose not to do it for you, since the assignment wants you to do it.
I will instead demonstrate how to identify it using the System Identification Toolbox —
T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/828710/Freq_complex.txt', 'VariableNamingRule','preserve')
T1 = 5479×2 table
Freq. V(i_s) ______ _______________________________________________ 100 {'5.25923694595431e-001,6.34606935959376e+000'} 100.23 {'5.26471741717689e-001,6.36067773821260e+000'} 100.46 {'5.27022310375074e-001,6.37531964864880e+000'} 100.69 {'5.27575412141180e-001,6.38999516719951e+000'} 100.93 {'5.28131058638060e-001,6.40470437033997e+000'} 101.16 {'5.28689261538566e-001,6.41944733471207e+000'} 101.39 {'5.29250032542678e-001,6.43422413714084e+000'} 101.62 {'5.29813383450318e-001,6.44903485459486e+000'} 101.86 {'5.30379326076855e-001,6.46387956423504e+000'} 102.09 {'5.30947872306298e-001,6.47875834338622e+000'} 102.33 {'5.31519034080622e-001,6.49367126954284e+000'} 102.57 {'5.32092823401404e-001,6.50861842036846e+000'} 102.8 {'5.32669252306374e-001,6.52359987370368e+000'} 103.04 {'5.33248332892240e-001,6.53861570756800e+000'} 103.28 {'5.33830077315765e-001,6.55366600013723e+000'} 103.51 {'5.34414497792562e-001,6.56875082976168e+000'}
T1{:,2} = cellfun(@(x)sscanf(x, '%f, %f'), T1{:,2}, 'Unif',0);
RI = cell2mat(table2cell(T1(:,2)).').';
RI = complex(RI(:,1),RI(:,2));
T2 = [T1(:,1) table(RI)];
T2.Properties.VariableNames = {'Freq','V(i_s)'}
T2 = 5479×2 table
Freq V(i_s) ______ _______________ 100 0.52592+6.3461i 100.23 0.52647+6.3607i 100.46 0.52702+6.3753i 100.69 0.52758+6.39i 100.93 0.52813+6.4047i 101.16 0.52869+6.4194i 101.39 0.52925+6.4342i 101.62 0.52981+6.449i 101.86 0.53038+6.4639i 102.09 0.53095+6.4788i 102.33 0.53152+6.4937i 102.57 0.53209+6.5086i 102.8 0.53267+6.5236i 103.04 0.53325+6.5386i 103.28 0.53383+6.5537i 103.51 0.53441+6.5688i
figure
semilogx(T2{:,1}, imag(T2{:,2}))
grid
frd = idfrd(T2{:,2}, T2{:,1}, 1/(2*T2{end,1}))
frd = IDFRD model. Contains Frequency Response Data for 1 output(s) and 1 input(s). Response data is available at 5479 frequency points, ranging from 100 rad/s to 3e+07 rad/s. Sample time: 1.6667e-08 seconds Status: Created by direct construction or transformation. Not estimated.
sys_tf = tfest(frd, 4, 4) % Poles: 4, Zeros: 4
sys_tf = 24.81 s^4 + 5.406e08 s^3 + 6.957e13 s^2 + 5.884e17 s + 2.879e19 --------------------------------------------------------------- s^4 + 1.295e05 s^3 + 4.636e10 s^2 + 2.381e15 s + 1.011e19 Continuous-time identified transfer function. Parameterization: Number of poles: 4 Number of zeros: 4 Number of free coefficients: 9 Use "tfdata", "getpvec", "getcov" for parameters and their uncertainties. Status: Estimated using TFEST on frequency response data "frd". Fit to estimation data: 98.7% FPE: 459.9, MSE: 458.4
poles = pole(sys_tf)
poles =
1.0e+05 * -0.3661 + 2.0164i -0.3661 - 2.0164i -0.5160 + 0.0000i -0.0467 + 0.0000i
zeros = zero(sys_tf)
zeros = 4×1
1.0e+07 * -2.1663 -0.0120 -0.0009 -0.0000
figure
pzmap(sys_tf)
figure
pzmap(sys_tf)
axis([-100000 1000 -500 500]) % Detail Near Origin
sys_ss = ss(sys_tf)
sys_ss = A = x1 x2 x3 x4 x1 -1.295e+05 -1.769e+05 -6.929e+04 -1.796e+04 x2 2.621e+05 0 0 0 x3 0 1.311e+05 0 0 x4 0 0 1.638e+04 0 B = u1 x1 3.277e+04 x2 0 x3 0 x4 0 C = x1 x2 x3 x4 y1 1.64e+04 7965 470.1 -12.04 D = u1 y1 24.81 Continuous-time state-space model.
figure
compare(frd,sys_ss)
grid
There is a constant phase difference from the original spectrum of about 360° (by observation, not calculation), and the approsimation appears to be good. I cannot determine where the output is taken from that network (assuming it is a two-port), so I assume it is simply a one-port with 4 obvious poles and 4 obvious zeros. The Cauer-Foster synthesis requires the transfer function, and this identification provides it.
Since that is the point of the assignment, I leave that to you. It would be easier to do it symbolically using polynomial division, the other option being to use the deconv function to get a numeric polynomial continued-fraction decomposition of the transfer function.
.

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