USING_NAMESPACE_ACADO
int main( )
{
// Define a Right-Hand-Side:
// -------------------------
DifferentialState phi; // the angle phi
DifferentialState dphi; // the first derivative of phi w.r.t time
Control F; // a force acting on the pendulum
Parameter l; // the length of the pendulum
const double m = 1.0; // the mass of the pendulum
const double g = 9.81; // the gravitational constant
const double alpha = 2.0; // friction constant
IntermediateState z;
DifferentialEquation f;
z = sin(phi);
f << dot(phi ) == dphi;
f << dot(dphi) == -(m*g/l)*z - alpha*dphi + F/(m*l);
// DEFINE INITIAL VALUES:
// ----------------------
DVector xStart( 2 );
xStart(0) = 1.0;
xStart(1) = 0.0;
DVector xa;
DVector u( 1 );
u(0) = 0.0;
DVector p( 1 );
p(0) = 1.0;
double tStart = 0.0;
double tEnd = 2.0;
Grid timeHorizon( tStart,tEnd );
// DEFINE AN INTEGRATOR:
// ---------------------
IntegrationAlgorithm intAlg;
intAlg.addStage( f, timeHorizon, INT_RK45 );
//intAlg.set( INTEGRATOR_TYPE, INT_RK45 );
intAlg.set( INTEGRATOR_PRINTLEVEL, HIGH );
intAlg.set( INTEGRATOR_TOLERANCE, 1.0e-6 );
// START THE INTEGRATION:
// ----------------------
intAlg.integrate( timeHorizon, xStart,xa,p,u );
// GET THE RESULTS
// ---------------
VariablesGrid differentialStates;
intAlg.getX( differentialStates );
cout << "x = " << endl << differentialStates << endl;
return 0;
}
/* >>> start tutorial code >>> */
int main( ){
USING_NAMESPACE_ACADO
// Define a Right-Hand-Side:
// -------------------------
DifferentialState x;
DifferentialEquation f;
TIME t;
f << dot(x) == -x + sin(0.01*t);
// Define an initial value:
// ------------------------
Vector xStart( 1 );
xStart(0) = 1.0;
double tStart = 0.0;
double tEnd = 1000.0;
Grid timeHorizon( tStart,tEnd,2 );
Grid timeGrid( tStart,tEnd,20 );
// Define an integration algorithm:
// --------------------------------
IntegrationAlgorithm intAlg;
intAlg.addStage( f, timeHorizon );
intAlg.set( INTEGRATOR_TYPE, INT_BDF );
intAlg.set( INTEGRATOR_PRINTLEVEL, MEDIUM );
intAlg.set( INTEGRATOR_TOLERANCE, 1.0e-3 );
intAlg.set( PRINT_INTEGRATOR_PROFILE, YES );
intAlg.set( PLOT_RESOLUTION, HIGH );
GnuplotWindow window;
window.addSubplot( x,"x" );
intAlg << window;
// START THE INTEGRATION
// ----------------------
intAlg.integrate( timeHorizon, xStart );
// GET THE RESULTS
// ---------------
VariablesGrid differentialStates;
intAlg.getX( differentialStates );
differentialStates.print( "x" );
Vector xEnd;
intAlg.getX( xEnd );
xEnd.print( "xEnd" );
return 0;
}