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Averaging, integral of special function

  • Thread starter psl86
  • Start date
  • #1
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Homework Statement



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]

Homework 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]

The Attempt at a Solution



[tex]\dot{x_1} = x_2[/tex]
[tex]\dot{x_2} = -x1 - sat(x_2)[/tex]
 
Last edited:

Answers and Replies

  • #2
3
0
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..
 
  • #3
3
0
No one in here with a steady averaging-theory brain?
 

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