Simulation of a non-parametric model

Hello,

as a result of a measurement I have the amplitude and the phase shift for a system for special frequencies.

Now I would like to build a simulation in Simulink with this point-wise transfer function (e.g. with a linear interpolation between the points).

What is the best way to do this?

My thoughts went in the direction of fitting a parametric transfer function to the nonparametric or Fourier transform of the input signal, but the latter variant seems to me to be difficult, at least for a priori unknown signal characteristics.

I would be very grateful for hints on more elegant solutions.

Answer 1

[Shreshth]

Hey SKRE,

Creating a simulation in Simulink using point-wise transfer function data can indeed be challenging but is certainly doable. Here are some steps and considerations that might help you achieve your goal.

• Prepare Data:Organize your frequencies, amplitudes, and phase shifts.
• Create Interpolation Functions in MATLAB:

amp_interp = @(f) interp1(freq, amplitude, f, 'linear');
phase_interp = @(f) interp1(freq, phase, f, 'linear');

• Implement MATLAB Function Block in Simulink: Add a MATLAB Function block with the following code

function y = pointwise_transfer_function(u, freq)
% Define interpolation functions
amp_interp = @(f) interp1(freq, amplitude, f, 'linear');
phase_interp = @(f) interp1(freq, phase, f, 'linear');

% Interpolate amplitude and phase
amplitude = amp_interp(freq);
phase_shift = phase_interp(freq);

% Apply transfer function
y = amplitude * u * exp(1i * phase_shift);
end

• Connect Blocks:Connect your input signal to the MATLAB Function block.
• Connect the output to a Scope for visualization.
• Test and Validate.

Hope it helps.