//
// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) ????-2008 - INRIA
//
// This file is distributed under the same license as the Scilab package.
//



function [xdot]=ivpd(t,x)
    //ydot=ivpd(t,y) non linear equations of the pendulum
    // y=[x;d(x)/dt,teta,d(teta)/dt].
    // mb, mc, l must be predefined
    //!
    g=9.81;
    u=0
    qm=mb/(mb+mc)
    cx3=cos(x(3))
    sx3=sin(x(3))
    d=4/3-qm*cx3*cx3
    xd4=(-sx3*cx3*qm*x(4)**2+2/(mb*l)*(sx3*mb*g-qm*cx3*u))/d
    //
    xdot=[x(2);
    (u+mb*(l/2)*(sx3*x(4)**2-cx3*xd4))/(mb+mc);
    x(4);
    xd4]
endfunction


function [y,xdot]=pendu(x,u)
    //[y,xdot]=pendu(x,u) input (u) - output (y) function of the pendulum
    //!
    g=9.81;
    qm=mb/(mb+mc)
    cx3=cos(x(3))
    sx3=sin(x(3))
    d=4/3-qm*cx3*cx3
    xd4=(-sx3*cx3*qm*x(4)**2+2/(mb*l)*(sx3*mb*g-qm*cx3*u))/d
    //
    xdot=[x(2);
    (u+mb*(l/2)*(sx3*x(4)**2-cx3*xd4))/(mb+mc);
    x(4);
    xd4]
    //
    y=[x(1);
    x(3)]
endfunction


function [xdot]=regu(t,x)
    //xdot=regu(t,x) simulation of the compound system
    // pendulum - observer - compensator
    //!
    xp=x(1:4);xo=x(5:8);
    u =-kr*xo   //control
    [y,xpd]=pendu(xp,u)
    xod=(f-k*h)*xo+k*y+g*u
    xdot=[xpd;xod]
endfunction