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Digital modelling of Inverted Pendulum on a cart

  1. May 2, 2012 #1
    I am pursuing bachelor in engineering.i have a case study involving the stabilization of an inverted pendulum about it's unstable equilibrium point.

    My problem is that I have to digitalize my system before i can implement it.
    Can anyone tell me how to digitalize the system.
     
  2. jcsd
  3. May 2, 2012 #2
    my system model is of the form y = f(x) + g(x) * u.
    the system is an underactuated 4th order system with the states as the cart position(x1) and velocity(x3) and the pendulum position(x2) and velocity(x4).
    the control law 'u' consist of 3 parts.the first part contains log term and signum term,the second contains signum,log and exponential terms and the 3rd is a linear controller.

    for specific expressions.
    Len=.4;
    V = 2;
    ksu = 1.63;
    kcw = 2.3;
    kvw = 5;
    kem = 6;
    n = 1.05;
    E = .5*((M + m)*x3^2 + 2*m*l*cos(x2)*x3*x4 + m*l^2*x4^2) + m*g*l*(cos(x2) - 1);
    E0 = 0;
    ucw = kcw*sign(x1)*log(1-abs(x1)/Len);
    uvw = kvw*sign(x3)*log(1 - abs(x3)/V);
    uem = kem*(exp(abs(E - n*E0)) - 1)*sign(E - E0)*sign(x4*cos(x2));

    u1 = -ksu*sign(x4*cos(x(2))) + ucw
    u2 = ucw + uvw + uem
    u3 = k*x
     
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