Van der Pol Oscillator (JModelica)

This page contains the source code to solve the Van der Pol Oscillator problem with JModelica. The automatic differentiation tool CasADI and the solver IPOPT were used to solve the problem.

Model file (VDP_Opt.mop)

//-------------------------------------------------------------------------
//Van der Pol Oscillator with direct collocation using JModelica
//(c) Madeleine Schroter
//--------------------------------------------------------------------------
 
optimization VDP_Opt(objectiveIntegrand = y^2+x^2+u^2, startTime = 0, finalTime = 20)
 
//The states
Real x(start=1, fixed=true); //position coordinate
Real y(start=0, fixed=true); 
 
 
//The control signal
input Real u; //damping of the oscillation
 
equation
der(y) = (1-x^2) * y - x +u;
der(x) = y;
 
constraint
u<=0.75;
 
end VDP_Opt;

Run file

#Import the function for transfering a model to CasADiInterface
from pyjmi import transfer_optimization_problem
 
op=transfer_optimization_problem("VDP_Opt", "VDP_Opt.mop")
 
res=op.optimize()