simple_mpc.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_toolkit.hpp>
#include <acado_gnuplot.hpp>

using namespace std;

USING_NAMESPACE_ACADO

int main( )
{
    // INTRODUCE THE VARIABLES:
    // -------------------------
        DifferentialState xB;
        DifferentialState xW;
        DifferentialState vB;
        DifferentialState vW;

        Control R;
        Control F;

        double mB = 350.0;
        double mW = 50.0;
        double kS = 20000.0;
        double kT = 200000.0;


    // DEFINE A DIFFERENTIAL EQUATION:
    // -------------------------------
    DifferentialEquation f;

        f << dot(xB) == vB;
        f << dot(xW) == vW;
        f << dot(vB) == ( -kS*xB + kS*xW + F ) / mB;
        f << dot(vW) == (  kS*xB - (kT+kS)*xW + kT*R - F ) / mW;


    // DEFINE LEAST SQUARE FUNCTION:
    // -----------------------------
    Function h;

    h << xB;
    h << xW;
        h << vB;
    h << vW;

    DMatrix Q(4,4);
    Q.setIdentity();
        Q(0,0) = 10.0;
        Q(1,1) = 10.0;

    DVector r(4);
    r.setAll( 0.0 );


    // DEFINE AN OPTIMAL CONTROL PROBLEM:
    // ----------------------------------
    const double t_start = 0.0;
    const double t_end   = 1.0;

    OCP ocp( t_start, t_end, 20 );

    ocp.minimizeLSQ( Q, h, r );

        ocp.subjectTo( f );

        ocp.subjectTo( -500.0 <= F <= 500.0 );
        ocp.subjectTo( R == 0.0 );



    // SETTING UP THE (SIMULATED) PROCESS:
    // -----------------------------------
        OutputFcn identity;
        DynamicSystem dynamicSystem( f,identity );

        Process process( dynamicSystem,INT_RK45 );

    // SETTING UP THE MPC CONTROLLER:
    // ------------------------------
        RealTimeAlgorithm alg( ocp,0.05 );
        alg.set( MAX_NUM_ITERATIONS, 2 );
        
        StaticReferenceTrajectory zeroReference;

        Controller controller( alg,zeroReference );


    // SETTING UP THE SIMULATION ENVIRONMENT,  RUN THE EXAMPLE...
    // ----------------------------------------------------------
        SimulationEnvironment sim( 0.0,3.0,process,controller );

        DVector x0(4);
        x0(0) = 0.01;
        x0(1) = 0.0;
        x0(2) = 0.0;
        x0(3) = 0.0;

        if (sim.init( x0 ) != SUCCESSFUL_RETURN)
                exit( EXIT_FAILURE );
        if (sim.run( ) != SUCCESSFUL_RETURN)
                exit( EXIT_FAILURE );

    // ...AND PLOT THE RESULTS
    // ----------------------------------------------------------
        VariablesGrid sampledProcessOutput;
        sim.getSampledProcessOutput( sampledProcessOutput );

        VariablesGrid feedbackControl;
        sim.getFeedbackControl( feedbackControl );

        GnuplotWindow window;
        window.addSubplot( sampledProcessOutput(0), "Body Position [m]" );
        window.addSubplot( sampledProcessOutput(1), "Wheel Position [m]" );
        window.addSubplot( sampledProcessOutput(2), "Body Velocity [m/s]" );
        window.addSubplot( sampledProcessOutput(3), "Wheel Velocity [m/s]" );
        window.addSubplot( feedbackControl(1),      "Damping Force [N]" );
        window.addSubplot( feedbackControl(0),      "Road Excitation [m]" );
        window.plot( );

    return EXIT_SUCCESS;
}