smooth operator in functions

[jesse-gohl]

I'm curious about using the smooth operator in functions. My first thought about this was that it wouldn't be safe to use, at least for generic functions, since I couldn't guarantee the smoothness of inputs that might be passed. I suppose the same argument could be made for a real input to a model though too. Maybe the point is that the continuity assertion is on the expression, not the variables in the expression?

Anyway, this seemed like the appropriate forum for this discussion. Here is a simple example (notice smooth is used in the regStep function):

    Real u;
    Real y;
    parameter Real y1 = 2;
    parameter Real y2 = 1;
    parameter Real small = 2;
    Real x;
    Real z;
equation 
    u = if time <= 5 then time - 6 else time - 4;
    y = .Modelica.Fluid.Utilities.regStep(u, y1, y2, small);
    x = y;
    z = der(x);

[HansOlsson]

I don't see any difference between smooth in functions and smooth in models, as smooth in functions sort of require that the function is inlined (as this function normally is).

As you noted, smooth only states that the expression itself is smooth - so whether u is discontinuous (yes, there's a discontinuity at 5 seconds) has the same effect regardless of whether it is called inside regStep or it would have been manually inlined as:

y = smooth(1, if u >  small then y1 else 
                 if u < small then y2 else 
                 if small > 0 then (u/small)*((u/small)^2 - 3)*(y2-y1)/4 + (y1+y2)/2 else (y1+y2)/2);