Make the transfer function from magnitude and phase data

Following are the practical magnitude and phase data, now i want to make the transfer function of any order whose magnitude and phase response should approx. match with this data. I tried many time using system identification but end up with unstable transfer function , please help .

Magnitude_dB = [0,0.0294382792088619,0.0621252890325977,-0.0317757995233922,-0.529502211330154,-1.50167657755005,-2.43642719895843,-3.24485628416788,-3.98529452106657,-4.56346322230199,-5.13670696756743,-5.41005379073451,-5.76590849844941,-6.36303108991967,-6.42397690778927,-6.56136765621800,-7.00077651119822,-7.37130232917411,-7.72121762130983,-9.01958493128253];

Phase_deg = [-1.86617534558493,-4.59853973674537,-7.62466018649141,-14.3210302476963,-20.3444251905058,-36.3420780563449,-50.8612623082813,-52.7685476392275,-62.4730146334328,-74.8270616852208,-74.2327606392636,-79.9698622712670,-86.1645419213363,-92.5982487919277,-92.8045908328856,-103.595378289453,-107.504690696956,-118.822856754981,-126.986214461683,-130.614971839560];

Frequency_Hz = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20];

[Paul]

Hi Anil,

Can you post the code that you tried?

Answer 1

[Sandeep Mishra]

Hi Anil,

I observe that you have data which includes magnitude , phase , and frequency values, and you want to create a transfer function which resembles this data.

You can refer to a related MATLAB Answers post here: https://www.mathworks.com/matlabcentral/answers/290404-how-can-i-find-the-transfer-function-having-magnitude-phase-and-frequency-w-and-its-bode-diagram#answer_225775

Based on this approach, you can determine the numerator polynomial ‘b’ and denominator polynomial ‘a’ by adjusting their respective orders to achieve the optimal result.

Once you have the polynomials, you can generate the transfer function using the ‘tf’ command in MATLAB as shown below:

sys = tf(b, a); 

To validate the transfer function, you can compute its frequency response using the ‘bode’ function as demonstrated:

w = Frequency_Hz * 2 * pi 
[mag, phase, wout] = bode(sys, w); 

For more information, refer to the following MathWorks Documentation:

1. ‘tf’ (Transfer function model) function: https://www.mathworks.com/help/releases/R2024a/control/ref/tf.html
2. ‘bode’ (Bode frequency response of dynamic system) function: https://www.mathworks.com/help/releases/R2024a/ident/ref/dynamicsystem.bode.html

I hope this helps you.