Use Transfer Function to Predict input for desired output

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Discussion Overview

The discussion revolves around the use of transfer functions in the Laplace domain to determine the input required to achieve a desired output time signal. Participants explore both numerical and analytical methods, particularly in the context of MATLAB simulations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about methods to determine the necessary input for a desired output time signal using a given transfer function.
  • Another participant suggests that if the transfer function is a ratio of polynomials, the inverse can be used to find the required input by applying the inverse transformation to the desired output.
  • A participant questions the feasibility of determining the input for arbitrary desired outputs that are not easily described in the Laplace domain, proposing the use of FFT techniques as a potential approach.
  • There is mention of the limitations of using FFT/IFFT for predicting inputs, particularly regarding the accuracy in accounting for settling times of modes in the transfer function.
  • Another participant suggests applying MATLAB's lsim function with the inverse transfer function to obtain a solution, though they note that the uniqueness of the result is uncertain.
  • Concerns are raised about the applicability of MATLAB's transfer function methods, particularly when dealing with transfer functions that have more poles than zeros.

Areas of Agreement / Disagreement

Participants express differing views on the methods available for determining the necessary input for arbitrary outputs, with no consensus reached on a definitive approach. Some propose using inverse transfer functions, while others highlight limitations and uncertainties in the methods discussed.

Contextual Notes

Participants note that the methods discussed may not be universally applicable, particularly regarding the uniqueness of solutions and the limitations of MATLAB functions in certain scenarios.

swraman
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Hello,

I have a laplace domain system transfer function.

I know I can use (say Matlab's lsim()) to simulate the output for any arbitrary input.

Is there any way (numerically in Matlab or analytically) to determine the input necessary for a desired output time signal?
 
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If the transfer function is in the form of a ratio of polynomials, P1/P2, then the inverse of the polynomial, P2/P1, is the inverse transformation. The desired output operated on by P2/P1 would give the answer.
 
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Is there any way to then determine the input necessary for an arbitrary desired output, if the output is not some function easily described in the laplace domain?

ie. when our desired output is some arbitrary time waveform, can we use the inverse transfer function P2/P1 to determine the arbitrary input needed to generate that desired waveform as the output?

For example, if we capture an impulse (force) and a reaction vinration, we could take FFT(response)/FFT(impulse) and the resulting frequency response function can be used to predict the input necessary for a desired output by:

input_required = IFFT(FFT([response)/FFT(impulse)]*FFT(desired_output))

this is not completely accurate though because it doesn't properly take into account the setting time of each of the modes in our transfer function (it is, after all, a only a frequency response function). But the simple trick that allows us to do this is the FFT/IFFT, which converts between time and frequency domain. There is no such tool (as I know of) for the laplace domain, that would allow us to convolve the outout with P2/P1 transfer function.
 
swraman said:
Is there any way to then determine the input necessary for an arbitrary desired output, if the output is not some function easily described in the laplace domain?

ie. when our desired output is some arbitrary time waveform, can we use the inverse transfer function P2/P1 to determine the arbitrary input needed to generate that desired waveform as the output?
I would try applying Matlab lsim to the desired output using P2/P1. Of course it is not clear that the result is unique, but it should give you one solution. Other than that, I think you are on your own.
 
That is what I was thinking, but lsim (and many of matlabs transfer function methods) only works for transfer functions with more poles than zeros.
 

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