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Control system with equation C = A*x + B*dx/dt

  1. May 13, 2012 #1
    1. The problem statement, all variables and given/known data
    This question came up in a computer science / robotics exam and I still don't know the solution for it. I figured out that it's classical mechanics related, so I thought this might be the best place to ask it.


    2. Relevant equations
    C = A*x + B*dx/dt


    3. The attempt at a solution
    I've figured out that the steady state doesn't change, as it happens when dx/dt is 0, thus B is not affecting the solution.

    And this is how far I understand it. Can you explain to me, what kind of movement is this, what is the real-life meaning of the steady state and half-life for this movement and that how to calculate the change in the half-life?
     
  2. jcsd
  3. May 13, 2012 #2

    tiny-tim

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    hi zsero! :smile:

    write it Bdx/dt = C - Ax, then solve it by "separating the variables" :wink:
     
  4. May 13, 2012 #3
    OK, I arrive at the following equation:

    -B/A*ln(x) = c*t + k1

    My problem here is that I don't understand the meaning of the equations and that what is asked by half-life and steady state.

    How can I get the half-time from this equation?
     
  5. May 13, 2012 #4

    tiny-tim

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    ok, now multiply by -1/B and then e-to-the on both sides …

    x = xoe-ACt/B (where xo = e-kA/B)

    does that look familiar? :wink:
     
  6. May 13, 2012 #5
    Thanks for the help! Actually, I'm not a Physics student, so I don't really know, but I'd guess it's the exponential delay. So if B doubles then the constant becomes half, thus the half-life becomes double. Is this correct?
     
  7. May 13, 2012 #6

    tiny-tim

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    good guess! :smile:

    but you really should make yourself familiar with half-life (and exponential decay generally) …

    look it up in wikipedia or the pf library :wink:
     
  8. May 13, 2012 #7
    Thanks for the help!
     
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