I am performing a simulation of a system that involves a lot of random variables. The response of this system varies each time I run the simulation. It is always non-asymptotically stable though, as it eventually fluctuates around the equilibrium point with a variant magnitude (of the fluctuation) each time.
The attached figure illustrates how two different runs of the same simulation can look like.
I would like to have an automated function that calculates the fluctuation magnitude and the settling time each run, from the time response.
Could you be more specific? If I had those two curves in an Excel spreadsheet, I could easily calculate the asymptotic value and how many seconds it takes to get that number to a specified confidence interval (typically 95%) using the standard error of estimate and Student's-T.
Dear Dr. Dudley J Benton ,
Thank you very much for your answer.
If the system was asymptotically stable, it wouldn't have been a problem as you mentioned, but unfortunately it's not. The error signal rather fluctuates around "zero" with an amplitude (A) that differs each time I run the simulation.
I would like to -first of all- determine this amplitude (A) and then calculate the time it takes the error signal to get bounded by [-A, A].
I can simply do it with my eyes, but I want to teach the computer how to do it because it's going to be involved in a Monte Calro simulation.
I don't know if I got your point. Maybe you don't need a complex algorithm for your case. For example:
function [Ast,Tst]=func(T,Err)
%%
%The inputs T and Err are two vectors.
Ts=10;%Assume it is stable after T=Ts and Ts is much greater than Tst(the settling time).
Ts_index=sum(TAst);
Tst=T(Tst_index);
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