Numerical integration of the ERROR in a PI controller

good day all.i've just written a program in fortran77 for the model of a binary distillation column.i included a PI controller in my program.To obtain the integral term of the PI,I used the explicit euler to numerically integrate the error.i would love to compare my results using another method to numerically integrate the error.but i'm confused.the euler method was quite simple.i defined ERINT as the integral of the error (∫E).and since E(i.e the error) is the derivative of the integral i simply employed euler to solved the resulting ODE.That is,

ERINT(n+1)=ERINT(n) + TE(n) where T is the step size

please which other method simple can i use to obtain the integral term.can i also see simple chemical processes (in fortran77) where they are applied in a PI controller it obtain the integral term? please an answer would be greatly appreciated.many thanks
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There are many algorithms for numerical integration. But there is no justification for them in a PI controller. You are not integrating a specific differential equation. You are not predicting position by integrating velocity. All you want is some function that forces E(n) to zero in the steady state. It doesn't matter whether it is a pure or an accurate integration.



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The use of an integral in a PI feedback system is very forgiving of any errors in the integration (and of many other errors for that matter). The only real requirement is that the integral value will increase if there is a sustained error. In fact, the value of the integrator is usually multiplied by a constant before it is used. That is done to give the system the desired dynamic response.

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