Hello, guys,
I performed a simulation with modeled system, and I put the input signal as an sine wave, with frequency varies from [1:1:1500] Hz.
(In detail, I performed simulation with sine input of fixed frequency for 2 seconds, and repeat this for every 1500 cases.)
As a result of simulation, I got 1500 pairs of input & output data.
I know how to get T.F. from impulse response but I don't know how to do it with sinusoidal waves..
Can anyone explain the process to get T.F for my case?
Thanks.
Use Fourier series to estimate the imajenry and real parts and then calculate the magnitude ratio and phase angle and from these parametrs find the approximate transfer function.
Dear Jong-Min Yoon,
Also you can use Sinusoidal steady-state and frequency response by Bode Plot.
Here is links and attached file in subject.
-System Identification Using Frequency Response Methods
https://www.facstaff.bucknell.edu/mastascu/.../Ident/Ident2.html
-Lecture 10 Sinusoidal steady-state and frequency response
https://stanford.edu/~boyd/ee102/freq.pdf
Best regards
If you want to do it numerically, use subspace identification (google Michel Verhaegen's work as a start). It is implemented in the SLICOT System Identification Toolbox. A new approach is the Loewner framework, check out the work by Athanassios C. Antoulas (Rice University, ECE). The above mentioned methods are numerically unstable, and will not give reasonable results if the McMillan degree of the system is large (say >10).
Dear Jong-Min Yoon,
I agree with my colleagues M.M.Lafifi and Peter Benner. It's a very classical problem and you can make a research on keywords "automatics, signal processing, linear estimation, linear dynamics systems". There is also the matlab toolbox as mentionned by P. Brenner
I would suggest you understand what Bode plot of a system (transfer function) means.
Hi,
Now you have the input and output data in sine wave form.
Obtain the FFT of input data and the output data.
Divide the FFT (Output) with the FFT(input)
let's say it's now FFT(Op)/FFT(ip) = x. Then by making use of the Real and Imag function find Real(x) and Imag(x). Then plot them as x axis as real and y as imaginary.
Now, you have the nyquist plot of the system from where you can easily find the poles and zeros and finally your transfer function.
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