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Homework Help: Averaging, integral of special function

  1. Mar 13, 2010 #1
    1. The problem statement, all variables and given/known data

    Integrate the right hand side of the state equation to find the average system

    [tex]\dot{x_1} = x_2[/tex]
    [tex]\dot{x_2} = -x_1 + 1 -2u(0.5sat(x_2) + 0.5 - p(t))[/tex]

    2. Relevant equations

    u(s) = 0 for s<0, u(s) = 1 for s>=0
    p(t) is periodic with T = 1
    [tex]f_{avg} =\frac{1}{T}\int_0^Tf(x,t)[/tex]

    3. The attempt at a solution

    [tex]\dot{x_1} = x_2[/tex]
    [tex]\dot{x_2} = -x1 - sat(x_2)[/tex]
     
    Last edited: Mar 13, 2010
  2. jcsd
  3. Mar 13, 2010 #2
    Im almost 100% certain that this is suppose to end up as

    x1_dot = x2
    x2_dot = -x1 - sat(x2)

    but I can't make the argument..
     
  4. Mar 14, 2010 #3
    No one in here with a steady averaging-theory brain?
     
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