interfaces/matlab/examples/integrator/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) 2008-2009 by Boris Houska and Hans Joachim Ferreau, K.U.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
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 */



void pendulum( DifferentialEquation *f ){


    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  ;    // frictional constant


    IntermediateState z;

    z = sin(phi);

    *f << dot(phi) == dphi;
    *f << dot(dphi) == -(m*g/l)*z - alpha*dphi + F/(m*l);
}