examples/integration_algorithm/pendulum.cpp

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/*
 *    This file is part of ACADO Toolkit.
 *
 *    ACADO Toolkit -- A Toolkit for Automatic Control and Dynamic Optimization.
 *    Copyright (C) 2008-2014 by Boris Houska, Hans Joachim Ferreau,
 *    Milan Vukov, Rien Quirynen, KU Leuven.
 *    Developed within the Optimization in Engineering Center (OPTEC)
 *    under supervision of Moritz Diehl. All rights reserved.
 *
 *    ACADO Toolkit is free software; you can redistribute it and/or
 *    modify it under the terms of the GNU Lesser General Public
 *    License as published by the Free Software Foundation; either
 *    version 3 of the License, or (at your option) any later version.
 *
 *    ACADO Toolkit is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 *    Lesser General Public License for more details.
 *
 *    You should have received a copy of the GNU Lesser General Public
 *    License along with ACADO Toolkit; if not, write to the Free Software
 *    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 *
 */



#include <acado_optimal_control.hpp>
#include <acado_gnuplot.hpp>

using namespace std;

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;
}