# Algebraic state in algebraic loop

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Meddour Aissam riad 2020 年 7 月 15 日

Hi there, i hope you're doing fine!
i simplified my problem in order to get a fast answer.
My complicated simulink model dosen't work fo the same problem as this simplified example ( because of the derivative bloc).
is there ani tricks to make it work and to make the derivative block ignore the fact that it don't have the first point of the first itteration.
Thanks a lot for your help
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Walter Roberson 2020 年 7 月 16 日
I do not understand the question.
"is there ani tricks to make it work and to make the derivative block ignore the fact that it don't have the first point of the first itteration."
No, that model has an algebraic loop. It expresses
sin(t) / diff(f(t),t) == diff(f(t),t)
which is
sin(t) == diff(f(t),t)^2
which has solutions
C1 - 2*ellipticE(t/2 - pi/4, 2)
C2 + 2*ellipticE(t/2 - pi/4, 2)
At t = 0 that gives you
C1 + 2*ellipticE(pi/4, 2)
C2 - 2*ellipticE(pi/4, 2)
however, no initial conditions were specified for your model.
If you say that the initial conditions are 0 then f(t) is
- 2*ellipticE(pi/4, 2) - 2*ellipticE(t/2 - pi/4, 2)
2*ellipticE(pi/4, 2) + 2*ellipticE(t/2 - pi/4, 2)
... at least it has a solution in theory. But the solution goes imaginary after t = pi.

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### 回答 (1 件)

maiaL 2020 年 7 月 16 日
You could try adding a Delay block before the input to the derivative block.
I don't know if the signal in your actual model is also sinewave-like, but the derivative will be zero on every half-period, so that's another problem on top of the algebraic loop.

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