crane_mpc3_stepped.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>


int main( ){

    USING_NAMESPACE_ACADO;

    // VARIABLES:
    // ------------------------
    DifferentialState        x;   // Position of the trolley
    DifferentialState        v;   // Velocity of the trolley
    DifferentialState      phi;   // excitation angle
    DifferentialState     dphi;   // rotational velocity

        Control                                 ax;   // trolley accelaration
        Disturbance                      W;   // disturbance

    double L = 1.0 ;              // length
        double m = 1.0 ;              // mass
        double g = 9.81;              // gravitational constant
        double b = 0.2 ;              // friction coefficient


    // DIFFERENTIAL EQUATION:
    // ------------------------
    DifferentialEquation     f, fSim;   // The model equations

    f << dot(x) ==  v;
    f << dot(v) ==  ax;
    f << dot(phi ) == dphi;
    f << dot(dphi) == -g/L*sin(phi) -ax/L*cos(phi) - b/(m*L*L)*dphi;

        L = 1.2;                                                        // introduce model plant mismatch
        
        fSim << dot(x) ==  v;
        fSim << dot(v) ==  ax + W;
        fSim << dot(phi ) == dphi;
        fSim << dot(dphi) == -g/L*sin(phi) -ax/L*cos(phi) - b/(m*L*L)*dphi;
        

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

    h << x;
    h << v;
    h << phi;
    h << dphi;

    DMatrix Q(4,4); // LSQ coefficient matrix
    Q.setIdentity();

    DVector r(4); // Reference


    // DEFINE AN OPTIMAL CONTROL PROBLEM:
    // ----------------------------------
    const double t_start = 0.0;
    const double t_end   = 5.0;

    OCP ocp( t_start, t_end, 25 );

    ocp.minimizeLSQ( Q, h, r );
    ocp.subjectTo( f );
    ocp.subjectTo( -5.0 <= ax <= 5.0 );


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

        Process process( dynamicSystem,INT_RK45 );

        VariablesGrid disturbance; disturbance.read( "dist.txt" );
        if (process.setProcessDisturbance( disturbance ) != SUCCESSFUL_RETURN)
                exit( EXIT_FAILURE );

    // SETTING UP THE MPC CONTROLLER:
    // ------------------------------
    double samplingTime = 0.1;
        RealTimeAlgorithm alg( ocp, samplingTime );
//      alg.set( USE_REALTIME_ITERATIONS,NO );
//      alg.set( MAX_NUM_ITERATIONS,20 );

        StaticReferenceTrajectory zeroReference;

        Controller controller( alg, zeroReference );
        
        DVector x0(4);
        x0.setZero();
        x0(3) = 1.0;

        double startTime =  0.0;
        double endTime   = 20.0;


        DVector uCon;
        VariablesGrid ySim;
        
        if (controller.init( startTime,x0 ) != SUCCESSFUL_RETURN)
                exit( EXIT_FAILURE );
        controller.getU( uCon );
        
        if (process.init( startTime,x0,uCon ) != SUCCESSFUL_RETURN)
                exit( EXIT_FAILURE );
        process.getY( ySim );


        //      hand-coding call to 
        //      sim.run( )

        int nSteps = 0;
        double currentTime = startTime;

        while ( currentTime <= endTime )
        {
                printf( "\n*** Simulation Loop No. %d (starting at time %.3f) ***\n",nSteps,currentTime );
        
                if (controller.step( currentTime,ySim.getLastVector() ) != SUCCESSFUL_RETURN)
                        exit( EXIT_FAILURE );
                controller.getU( uCon );
                
                if (process.step( currentTime,currentTime+samplingTime,uCon ) != SUCCESSFUL_RETURN)
                        exit( EXIT_FAILURE );
                process.getY( ySim );
                
                ++nSteps;
                currentTime = (double)nSteps * samplingTime;
        }

    return EXIT_SUCCESS;
}

/* <<< end tutorial code <<< */