Section 4.5.1: Modelling a Simple Control System

This is essentially the same example used to illustrate the modelling language and the solution of DAEs.

dx/dt = (u-x) / T₁ dy/dt = (x-y) / T₂ u = mu (s - y)

The initial conditions are: x = 1 ; y = 0 at t=0 This represents a process consisting of two lags in series, with its out put y regulated at setpoint s with a proportional controller with gain mu.

You can copy the model here generate a spreadsheet from it.

Notice the form of the simple proportional controller equation. If we wanted to model a P+I controller this would require a further differential equation to model the integral action.

We can write the equations for a P+I controller with input measurement y and output u as follows:


e = s - y  ;         ! error

u = mu * (e + ei/ti) ! controller algebraic equation

.ei = e              ! o.d.e. for integral action

Here mu is the controller gain and ti is the integral action time.

The modified program is here. Save it and try it out.

Click here to go to the model generator.

Next - Section 4.5.2: Modelling a Vaporiser
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Last Modified 4/9/00