add the magnitude ratio and the phase angles data points on bode diagram

I plotted a bode diagram and wanted to add some magnitude ratio and phase angle to it , however it seems I can not get it right so please help with that .

w=[0.2 0.3 0.4 0.5 0.6 0.7 ];% frequency

mag=[61.1250012 55.9468284 53.92586737 52.3231432 51.3640345 50.0399108];% Magnitude Ratio

ph=[83.964 355.2663 156.7372 1166.141 1434.389 1432.116]; % phase angle (degree)

nz=0; np=1; %

zfr= mag.*exp(1j*ph);

data=frd(zfr,w);

Gc=tfest(data,np,nz);

Gc

Answer 1

[Star Strider]

I am not certain what you want for the result.

The fit is not the best, however the compare function will plot the data and the estimated transfer function together in one plot —

w=[0.2 0.3 0.4 0.5 0.6 0.7 ];% frequency 
mag=[61.1250012 55.9468284 53.92586737 52.3231432 51.3640345 50.0399108];% Magnitude Ratio
ph=[83.964 355.2663 156.7372 1166.141 1434.389 1432.116]; % phase angle (degree) 
nz=0; np=1; % 
zfr= mag.*exp(1j*ph);
data=frd(zfr,w);    
Gc=tfest(data,np,nz);
Gc 

Gc =
    -6.131
  ----------
  s + 0.2454
 
Continuous-time identified transfer function.

Parameterization:
   Number of poles: 1   Number of zeros: 0
   Number of free coefficients: 2
   Use "tfdata", "getpvec", "getcov" for parameters and their uncertainties.

Status:                                                 
Estimated using TFEST on frequency response data "data".
Fit to estimation data: 1.695%                          
FPE: 5525, MSE: 2762                                    
 

figure
compare(data, Gc)
grid

.

[Hassen Mohamed Yousif Abdelatif]

@Star Strider I wanted to be in a bode diagram , somthing similar to this. I know my data is not the best .

[Star Strider]

The best I can suggest is something like this —

w=[0.2 0.3 0.4 0.5 0.6 0.7 ];% frequency 
mag=[61.1250012 55.9468284 53.92586737 52.3231432 51.3640345 50.0399108];% Magnitude Ratio
ph=[83.964 355.2663 156.7372 1166.141 1434.389 1432.116]; % phase angle (degree) 

figure
subplot(2,1,1)
semilogx(w, mag)
ylabel('Magnitude')
subplot(2,1,2)
semilogx(w, ph)
xlabel('Frequency (rad/s)')
ylabel('Phase (deg)')

.

[Hassen Mohamed Yousif Abdelatif]

would this considere as a bode diagram ?

[Star Strider]

I would consider it to be, given the data. Ideally, a Bode plot would start at D-C (0 Hz or 0 rad/s) and extend to the Nyquist frequency (Hz) or π rad/s.

It would be easier to work with if I knew what process produced the data, and what the magnitude units are (absolute or decibel).

[Hassen Mohamed Yousif Abdelatif]

the phase angle is in degree and the magnitude ratio in db

[Star Strider]

That helps. In that instance, your original code is in error. The phase angle needs to be in radians, and the magnitude in absolute units. (I was aware of the phase angle units, however my previous experiments with this did not show a significant improvement by converting them to radians earlier. Converting both improves things.)

Try this version —

w=[0.2 0.3 0.4 0.5 0.6 0.7 ];% frequency 
mag=[61.1250012 55.9468284 53.92586737 52.3231432 51.3640345 50.0399108];% Magnitude Ratio
ph=[83.964 355.2663 156.7372 1166.141 1434.389 1432.116]; % phase angle (degree) 
nz=2; np=4; % 
zfr= db2mag(mag).*exp(1j*deg2rad(ph));
data=frd(zfr,w);    
Gc=tfest(data,np,nz);

Warning: Noise variance and Final Prediction Error (FPE) could not be calculated because the number of free parameters and states is larger than the number of data samples.

Gc 

Gc =
             -64.97 s^2 + 5.293 s - 8.163
  ---------------------------------------------------
  s^4 + 0.3109 s^3 + 0.2232 s^2 + 0.0364 s + 0.007788
 
Continuous-time identified transfer function.

Parameterization:
   Number of poles: 4   Number of zeros: 2
   Number of free coefficients: 7
   Use "tfdata", "getpvec", "getcov" for parameters and their uncertainties.

Status:                                                 
Estimated using TFEST on frequency response data "data".
Fit to estimation data: 68.68%                          
MSE: 2.855e+04                                          
 

figure
compare(data, Gc)
grid

This is a significant improvement in the estimation, however more data will be required for an acceptable fit. Experiment with increasing the numbers of poles and zeros with added data.

.

[Hassen Mohamed Yousif Abdelatif]

@Star Strider this one is so much better. However, I'm required to keep np=1 and nz=0 , so do not know how i will get higher accuracy .

[Star Strider]

Thank you!

I did not realise that constraining the numbers of poles and zeros was a requirement. In that event, the only way to get more accuracy is to gather more data.

If that is also not an option, then this is the best you can do —

w=[0.2 0.3 0.4 0.5 0.6 0.7 ];% frequency 
mag=[61.1250012 55.9468284 53.92586737 52.3231432 51.3640345 50.0399108];% Magnitude Ratio
ph=[83.964 355.2663 156.7372 1166.141 1434.389 1432.116]; % phase angle (degree) 
nz=0; np=1; % 
zfr= db2mag(mag).*exp(1j*deg2rad(ph));
data=frd(zfr,w);    
Gc=tfest(data,np,nz);
Gc 

Gc =
    -137.4
  -----------
  s - 0.05004
 
Continuous-time identified transfer function.

Parameterization:
   Number of poles: 1   Number of zeros: 0
   Number of free coefficients: 2
   Use "tfdata", "getpvec", "getcov" for parameters and their uncertainties.

Status:                                                 
Estimated using TFEST on frequency response data "data".
Fit to estimation data: 9.975%                          
FPE: 4.719e+05, MSE: 2.359e+05                          
 

figure
compare(data, Gc)
grid

At the very least, now the ‘mag’ and ‘ph’ units are compatible with the frd requirements. That may be the best that can be done with these data.

.