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.please which other simple methods can i use to obtain the integral term.can i also see an example of a simple process/system (in fortran77) where they are applied in a PI controller to obtain the integral term?please an answer would be greatly appreciated.many thanks

 

Please show us what you have done to date.

Using an explicit integration technique generally involves obtaining at least some of the information from the differential equation being modelled. This hopefully reduces the number of integration steps needed to achieve the same quality of an answer. But it relies on the assumption that the differential equation, including the forcing functions, is adequately well known. In most physical processes, the error function is a bit too erratic for such an approach to work well (but there are exceptions, it mostly depends on the nature of the perturbing elements at play). At the risk of making too sweeping a generalization, I think most PI and PID controllers assume that the error function is a completely unknown function except at the points where it is sampled and then use a pretty brute force technique to integrate the error signal. If you sample fast enough, you can get away with this.

 

Many thanks for your prompt response.