Using the Traditional Approach

Below, we show how to model a tank system using the traditional approach. A tank system with a tank, a source for liquid, and a controller.

1 FlatTank Model

The FlatTank model is a "flat" model of the tank system with no internal hierarchical "system structure" visible, i.e., just a collection of variables and equations that model the system dynamics. The internal system structure consisting of components, interfaces, couplings between the components, etc. is not reflected by this model.

model FlatTank // Tank related variables and parameters parameter Real flowLevel(unit = "m3/s") = 0.02; parameter Real area(unit = "m2") = 1; parameter Real flowGain(unit = "m2/s") = 0.05; Real h(start = 0, fixed=true,unit = "m") "Tank level"; Real qInflow(unit = "m3/s") "Flow through input valve"; Real qOutflow(unit = "m3/s") "Flow through output valve"; // Controller related variables and parameters parameter Real K = 2 "Gain"; parameter Real T(unit = "s") = 10 "Time constant"; parameter Real minV = 0, maxV = 10; // Limits for flow output Real ref = 0.25 "Reference level for control"; Real error "Deviation from reference level"; Real outCtr "Control signal without limiter"; Real x(fixed=true) "State variable for controller"; equation assert(minV>=0, "minV must be greater or equal to zero"); der(h) = (qInflow - qOutflow)/area; // Mass balance equation qInflow = if time > 150 then 3*flowLevel else flowLevel; qOutflow = limitValue(minV, maxV, -flowGain*outCtr); error = ref - h; der(x) = error/T; outCtr = K*(error + x); end FlatTank;

2 The limitValue Function

A limiter function is needed in the model to reflect minimum and maximum flows through the output valve:

function limitValue input Real pMin; input Real pMax; input Real p; output Real pLim; algorithm pLim := if p>pMax then pMax else if p<pMin then pMin else p; end limitValue;

3 Examples of Calling limitValue

Three calls. a) 6 is between 4 and 10; b) 3 is less than 4 which is returned; c) 12 is greater than 10 which is returned.

limitValue(4, 10, 6)
limitValue(4, 10, 3)
limitValue(1, 10, 12)

4 Take a Look at the Flattened FlatTank Class

instantiateModel(FlatTank)

5 Simulation of FlatTank

simulate( FlatTank, stopTime=250 )
plot( h )

Diagram 1: Simulation of the FlatTank model with plot of the tank level.