Date: Mar 3, 2013 10:58 PM
Author: Albert Retey
Subject: Re: Strange behavior of System Modeler
Hi,

>

> I have just started studying WSM and the Modelica language by

> implementing the simple pendulum model (class) es. described on p.33 of

> Peter Fritzson's book Introduction to "Modeling and Simulation of

> Technical and Physical Systems with Modelica". The code (pendulum

> equation written as a DAE) is:

> model DAEExample "DAEExample"

> constant Real PI=3.14159265358979;

> parameter Real m=1,g=9.81,l=0.5;

> output Real F;

> output Real x(start=0.5),y(start=0);

> output Real vx,vy;

> equation

> m*der(vx)=-x/l*F;

> m*der(vy)=-y/l*F - m*g;

> der(x)=vx;

> der(y)=vy;

> x^2 + y^2=l^2;

> end DAEExample;

>

> I run the example in WSM and I get totally meaningless results. The

> solver is the default one (DASSL) which, I think, is the right one

> for handling DAEs.

>

> Any ideas?

If your meaningless results look similar to the ones I get it might be a deficiency of the WSM solver. The way it is written the problem is quite "unfriendly" for a numeric DAE solver and needs some more involved tricks to be solved, see e.g.:

<https://www.modelica.org/events/workshop2000/proceedings/old/Mattsson.pdf>

where the tricks that Dymola uses to get this solved are described. It came as a pleasant surprise to me that Mathematicas NDSolve (with the IndexReduction option) solves this correctly, so it might be a problem that WRI actually knows how to solve and you probably want to report this.

A workaround is of course to use a formulation that is more "friendly" to the solver, e.g. by reformulating in terms of polar coordinates (but I think Peter Fritzson might well use it in this form to demonstrate something...).

hth,

albert

(* Mathematica code for the above: *)

m=1;g=9.81;l=0.5;

res=NDSolve[{

m*vx'[t]==-x[t]/l*f[t],

m*vy'[t]==-y[t]/l*f[t]-m*g,

x'[t]==vx[t],

y'[t]==vy[t],

x[t]^2+y[t]^2==l^2,

x[0]==0.5,

vx[0]==0,

y[0]==0,

vy[0]==0

},{x,vx,y,vy,f},{t,0,5},

Method->{"IndexReduction"->Automatic}

]

xsol=x/.res[[1]]

ysol=y/.res[[1]]

Plot[{xsol[t],ysol[t]},{t,0,5}]