Numerical integration of the ERROR in a PI controller

In summary, the conversation discusses the use of a PI controller in a program written in Fortran77 for a binary distillation column model. The explicit Euler method is used to numerically integrate the error, but the speaker is also interested in exploring other methods for this purpose. However, the use of an integral in a PI controller is forgiving of errors, so the specific method used may not be as important as the desired dynamic response.
  • #1
pid3control
4
0
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
 
Last edited by a moderator:
Technology news on Phys.org
  • #2
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.
https://en.wikipedia.org/wiki/Numerical_integration
 
  • #3
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.
 

1. What is numerical integration in the context of a PI controller?

Numerical integration is a method used to calculate the accumulated error in a PI controller. It involves discretizing the integral term and using numerical methods, such as the trapezoidal rule or Simpson's rule, to approximate the integral.

2. Why is numerical integration necessary for a PI controller?

Numerical integration is necessary because the integral term in a PI controller represents the accumulated error over time. Without numerical integration, it would be difficult to accurately calculate this error, which is crucial for the controller's performance.

3. How does numerical integration affect the performance of a PI controller?

Numerical integration can greatly improve the performance of a PI controller by accurately calculating and adjusting for the accumulated error. It helps the controller to respond more quickly and accurately to changes in the system.

4. Are there different methods for numerical integration in a PI controller?

Yes, there are various numerical methods that can be used for integration in a PI controller. Some common methods include the trapezoidal rule, Simpson's rule, and Euler's method. The choice of method depends on the specific system and desired level of accuracy.

5. How can numerical integration be implemented in a PI controller?

Numerical integration can be implemented in a PI controller by discretizing the integral term and using a numerical method to approximate the integral. This can be done using software or programmable logic controllers (PLCs), which allow for easy implementation and adjustment of the integration method.

Similar threads

  • Programming and Computer Science
Replies
5
Views
2K
Replies
3
Views
336
  • Programming and Computer Science
Replies
15
Views
2K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
13
Views
2K
  • Quantum Physics
Replies
1
Views
538
  • Calculus and Beyond Homework Help
Replies
4
Views
651
  • Programming and Computer Science
Replies
1
Views
613
  • Programming and Computer Science
Replies
1
Views
3K
  • Programming and Computer Science
Replies
19
Views
2K
Replies
2
Views
412
Back
Top