How to measure the steady state amplitude of a control system output

Dear Matlab Answers,

Hello. I have included below an image concerning my problem

Here I have a sinusoidal weaveform that has an initial transient then settles to a steady state amplitude. It looks odd ebcause the plot is so dense, but the data is all sinsoidal with a transient offset. The data is represented as an array of time points and an array of ampltiude points. (tout and Y). How can I write an algorithm to detect when the transient is complete and return the final steady state amplitude? Technically, this is not only a MATLAB question, but a solution written in MATLAB code is preffered.

[Pat Gipper]

Is this the response of your model to a sinusoidal input?

[Michael Sohnen]

yeah

[Paul]

Does this question only concern LTI systems with a single sinusoidal input?

If so, do you know a priori the frequency of the input or is that something that the algorithm has to determine?

[Pat Gipper]

The frequency of the injected signal is under control of the app. If that is not the case then you would need to use some form of a spectrum analyzer.

[Michael Sohnen]

@Paul Dear Paul, thank you for your comment. Thank you to other commenters as well. I need to be able to analyuze the data WITHOUT ACCESS TO THE INPUT SIGNAL, and WITHOUT ACCESS TO THE SIMULINK MODEL. I need to find a statistical approach. I am basically looking for an algorithm that can seperate the transient from the steady state component in ANY signal, knowing that the steady state is some sinusoid of a singe frequency.

I basically want to high pass filter my signal, then measure the amplitude using (max(data)-min(data))/2. How can I do a high pass filter on a signal in MATLAB given only data?

Answer 1

[Michael Sohnen]

I figured it out. If you have some idea of what frequencies will be present in the signal, just use the highpass command. In my problem, I know the exact sampling rate, so it works. I highpass the data with a lower cutoff of 1 hertz and then measure the amplitude using max and min.

Thanks all.

Best,

Mike

[Paul]

Glad you found a solution that works. But I want to point ot that your solution is making some assumptions about the problem that may or may not be warranted based on your comment above. Offhand, these assumptions are:

The system is LTI.

The inputs is a single sine wave.

The output is, in fact, in steady state at the end of the simulation.

The input sine wave frequency is greater than 1 Hz by some amount.

The sample frquency of the output is hgih enough relative to the frequency of the output.

[Michael Sohnen]

Hi. The system is far from LTI. Most of my assumptions are from empirical data from my simulation. Sorry I phrased the question as such a puzzle but I wanted to boil it down to the most pressing parts. Anyway, if you want to collaborate on my project, I am trying to publish it. I'm looking for a volunteer to help develop my experiment. We could co-author. If ur interested email me [e-mail]

[Paul]

If your system is "far from LTI" then there is no guarantee, in general, that the steady state output is a single sinusoid. So you have to have some idea about what's going on inside the system and what the output should be.

Good luck. Go Panthers!

[Michael Sohnen]

Good luck to you too!

Answer 2

[Pat Gipper]

Try using this app. It injects a sine wave and measures the gain and phase after a number of cycles that you specify.

https://www.mathworks.com/matlabcentral/fileexchange/85448-frequency-response-analyzer

[Michael Sohnen]

I was looking for something that worked exclusively on the output data, in the time domain.