MATLAB: Frequency response!!

MATLABmatlab functionSystem Identification Toolbox

Dear All,

I am a bit puzzled with obtaining the frequency response of my system! I am applying a voltage V(t) at a certain frequency f, and I have computed the resulting current as I(t). I want to get the frequency response from these two sine waves! lets say the real and imaginary part of the impedance.

Could you show me a simple procedure to get it!! should I use "system identification toolbox"? or are there any alternative ways!

Thanks in advance

Best Answer

Please see tfestimate (Signal Processing Toolbox), spa, spafdr, etfe (System Identification Toolbox) for functions that calculate the frequency response from time domain signals in a non-parametric (empirical) fashion.

Perhaps a more reliable way is to compute a dynamic linear model from the data and then obtain the frequency response by calling BODE or FREQRESP on it. For example:

z = iddata(I, V, Ts); % Ts is sample time

model = n4sid(z, 1:10); % state-space model or order between 1 and 10

H = freqresp(model, linspace(0, pi/Ts, 100)); % the frequency response

This requires System Identification Toolbox.

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MATLAB: What is the difference between FRD and IDFRD

Both FRD and IDFRD are used to store Freqyency Response Data, that is, the complex frequency response vector (Mag.*exp(i*Phase)) measured over a given frequency grid. FRD belongs to Control System Toolbox. It has properties like ResponseData, and Frequency to store information on the frequency response.

IDFRD belongs to System Identification Toolbox. It extends FRD of Control System Toolbox to store additional information that is relevant for identification such as response covariance and spectrum information.

Either FRD or IDFRD can be used data source for identification of parametric models (transfer functions, state-space etc). For example, sys = tfest(FRD, n) creates an n-pole transfer function that fitsthe frequency response in FRD over its frequency range.

IDFRD can be an output of a non-paramteric estimation too. For example, the command SPA performs spectral analysis on a given time-domain data (that is, input and output signals) and returns the results as an IDFRD object. It contains the estimated frequency response in the property ResponseData, its covariance in the property CovarianceData, the estimated noise spectrum in the property SpectrumData, and its covariance in the property NoiseCovariance. You can "convert" this IDFRD into parametric form using commands such as TFEST, SSEST, PROCEST.

FRDs are non-parametric representation of linear dynamics. There is no underlying differential equation or difference equations stored in them. That is why they cannot be used directly in Simulink.

MATLAB: Use of modalfrf for operating measurements

This is essentially a system identification problem. You have non-parametric (tfestimate, spa, spafdr, etfe) techniques and parametric techniques (ssest, tfest). MODALFRF implements both approaches. When the 'Estimator' is H1 or H2, it is doing something similar to tfestimate and producing a non-parametric estimate of frequency response using correlation analysis (e.g., H = Syy/Sxy, where Syy is output spectrum = fft(Ryy), where Ryy is auto-correlation sequence, etc). When you use 'Estimator'/'subspace', it implements a parametric subspace identification (n4sid) algorithm to first estimate a state-space model and then compute its frequency response using FREQRESP.

If input signal is periodic, you will get much better speed by using a non-parametric technique. But the results are going to be sensitive to choice of technique (H1 or H2), frame-size, window shape and amount of overlapping. Parametric methods are much slower but less sensitive to tuning parameters (such as model order) and are more reliable IMO. You also get the additional insights into system dynamics in terms of poles/zeros, damping, I/O delays and feedthrough.

If you have system identification toolbox, I would recommend the following:

If data is transient (that is, the input is a step or impulse, or a pulse) and is not very long:

    data = iddata(outputsignal, inputsignal, sampletime); %sampletime = 1/Fs
    model = tfest(data, np); % np: number of poles

    w = linspace(0,pi/sampletime,100); % an example frequency grid (you can pick something different)
    G = freqresp(model,w); % or, simply do "bode(model)"

If data has periodic inputs:

    data = iddata(outputsignal, inputsignal, sampletime)
    data2 = fft(data) % data in frequency domain
    model = tfest(data2, np); % np: number of poles
    w = linspace(0,pi/sampletime,100);
    G = freqresp(model,w); % or, simply do "bode(model)"

If you have MIMO data, you could replace TFEST with SSEST (state-space estimator) and follow the steps similar to the above.

Best Answer

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