wave_energy.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( )
{
        // Parameters
        double h_hw = 10;    // water level
        double A_hw = 1.0;   // amplitude of the waves
        double T_hw = 5.0;   // duration of a wave
        double rho  = 1000;  // density of water
        double A    = 1.0;   // bottom area of the buoy
        double m    = 100;   // mass of the buoy
        double g    = 9.81;  // gravitational constant

        // Free varameter
        double a = 1.0;      // take to be constant here

        // Variables
        DifferentialState h; // Position of the buoy
        DifferentialState v; // Velocity of the buoy
        DifferentialState w; // Produced wave energy
        TIME t;

        // Differential equation
        DifferentialEquation f;

        // Height of the wave
        IntermediateState hw;
        hw = h_hw + A_hw*sin(2*M_PI*t/T_hw);
        f << dot(h) ==  v;
        f << dot(v) ==  rho*A*(hw-h)/m - g - a*v;
        f << dot(w) ==  a*v*v;

        // Define an initial value:
        // ------------------------
        DVector xStart( 3 );
        xStart(0) = h_hw - 2.0*A_hw;
        xStart(1) = 0.0;
        xStart(2) = 0.0;

        Grid timeHorizon( 0.0,25.0 );

    // DEFINE AN INTEGRATOR:
    // ---------------------

    IntegrationAlgorithm intAlg;

        intAlg.addStage( f, timeHorizon, INT_RK45 );

        intAlg.set( INTEGRATOR_PRINTLEVEL, MEDIUM );
        intAlg.set( PLOT_RESOLUTION, HIGH );
        intAlg.set( FREEZE_INTEGRATOR, NO );

        GnuplotWindow window;
        window.addSubplot( h );
        window.addSubplot( v );
        window.addSubplot( w );
        
        intAlg << window;

        // START THE INTEGRATION:
    // ----------------------

        intAlg.integrate( timeHorizon, xStart );

        return 0;
}