LSQCURVEFIT for transfer function frequency response magnitude and phase curve fitting

Hi all, can somebody please help me to find out transfer function time constants from LSQCURVEFIT function for identifying the transfer function through curvefitting the data available.

• Avaiable data frequency points (xdata)
• Magnitude and phase data(ydata)

tau1Omega to tau6Omega are time constants required to be find out.

current code is attached below, i'm encountering error

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Error using lsqcurvefit (line 251)

Function value and YDATA sizes are not equal.

Error in Untitled (line 32)

e = lsqcurvefit(ObjFun01,var01,xdata,ydata2,lb,ub);

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cnst11 = 0.002777;
lb = [0 0 0 0 0 0 0 0];
ub = [10 10 10 10 10 10 10 10];
var01 = [0 0 0 0 0 0 0 0];
xdata = load('xdata.txt');
ydata = load('ydata_in_magnitude_phase_form.txt');
ydata1 = ydata(1:1:end,:);
ydata1(:,1) = ydata(:,1) ;   %Load frequency
ydata1(:,2) = ydata(:,2) ;   %Load magnitude
ydata1(:,3) = ydata(:,3) ;   %Load frequency
ydata1(:,4) = ydata(:,4) ;   %Load phase
ydata1(:,5) = 1;             % weights
ydata2 = ydata1(:,2).*exp(1i.*ydata1(:,4)); %converting to complex number form

tau1Omga = var01(1,1) ; 
tau2Omga = var01(1,2) ;
tau3Omga = var01(1,3) ;
tau4Omga = var01(1,4) ;
tau5Omga = var01(1,5) ;
tau6Omga = var01(1,6) ;
tau7Omga = var01(1,7) ;
tau8Omga = var01(1,8) ;
ObjFun01 = @(x,xdata)cnst11*((1+ tau1Omga*1i*x).*(1+ tau2Omga*1i*x).*(1+ tau3Omga*1i*x))./ ( (1+ tau4Omga*1i*x).*(1+ tau5Omga*1i*x).*(1+ tau6Omga*1i*x) );
e = lsqcurvefit(ObjFun01,var01,xdata,ydata2,lb,ub);

any help in this regard would be greatly appreciated.

[KALYAN ACHARJYA]

Undefined function or variable 'cnst11'.?

[PRAKASH G]

Sir,

Its a constant.

[PRAKASH G]

Dear Kalyan,

I tried with modified code , here is the output

modified code as below but still unable get the correct solution.

% clc
cnst11 = 0.002777;
lb = [0 0 0 0 0 0 0 0];
ub = [10 10 10 10 10 10 10 10];
var01 = [0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1];

xdata = load('xdata.txt');
ydata = load('ydata_in_magnitude_phase_form.txt');

ydata1 = ydata(1:1:end,:);
ydata1(:,1) = ydata(:,1) ;   %Load frequency
ydata1(:,2) = ydata(:,2) ;   %Load magnitude
ydata1(:,3) = ydata(:,3) ;   %Load frequency
ydata1(:,4) = ydata(:,4) ;   %Load phase

ydata2 = ydata1(:,2).*exp(1i.*ydata1(:,4)); %converting to complex number form

curveest = @(var01,xdata)cnst11.*((1+ var01(1,1)*1i*xdata).*(1+ var01(1,2)*1i*xdata).*(1+ var01(1,3)*1i*xdata))./ ( (1+ var01(1,4)*1i*xdata).*(1+ var01(1,5)*1i*xdata).*(1+ var01(1,6)*1i*xdata) );

e = lsqcurvefit(curveest,var01,xdata,ydata2,lb,ub);

e(1)
e(2)
e(3)
e(4)
e(5)
e(6)

%plotting
figure()
loglog((xdata/(2*pi)),ydata1(:,2),'r--');
hold
curveest2 = cnst11.*((1+ e(1)*1i*xdata).*(1+ e(2)*1i*xdata).*(1+ e(3)*1i*xdata))./ ( (1+ e(4)*1i*xdata).*(1+ e(5)*1i*xdata).*(1+ e(6)*1i*xdata) );
y = abs(curveest2);
loglog((xdata/(2*pi)),y,'g-o');
hold off


figure()
semilogx((xdata/(2*pi)),ydata1(:,4),'r--');
hold
curveest2 = cnst11.*((1+ e(1)*1i*xdata).*(1+ e(2)*1i*xdata).*(1+ e(3)*1i*xdata))./ ( (1+ e(4)*1i*xdata).*(1+ e(5)*1i*xdata).*(1+ e(6)*1i*xdata) );
z = phase(curveest2);
semilogx((xdata/(2*pi)),z,'g-o');
hold off

Still not satisfied as its not providing the correct solution. You can see from the graphs

[Matt J]

Be mindful of the documentation page on Complex Numbers in Optimization Toolbox Solvers.

[PRAKASH G]

Dear Matt,

Thanks for your comments.

Actually i need real roots (time constants for the transfer function mentioned)

Moreover my code results are not mathing with the curve, when plotted.

Am i making anything wrong...?

[Matt J]

Your ydata and model function have complex numbers. Did you read the documentation link I gave you to see why that might be a problem?

[PRAKASH G]

Checked complex numbers, there is no issue.