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Converting a simple mass-spring system to state-space model, how?

  1. Oct 6, 2009 #1
    1. The problem statement, all variables and given/known data

    Hi guys/girls

    Professor gave this very simple homework where I need to convert the system below to a state-space model. Mass_spring.png
    The system itself is represented by the equation
    Code (Text):
    m*x" + k*x = f(t)
    Where m = 5 and k = 1. Note that, " (doublequote) is a second-order derivative.
    Unfortunately I don't have the background to solve it because I slacked too much :redface:

    2. Relevant equations
    State-space model that we use is below:
    ddfd74546a0e35f9ec054af2ecd3f2fa.png
    d0ac09f5cde2ce822ecc3e369692d04b.png

    Any help&explanation would be appreciated, thank you.

    EDIT: Ok, I've just read the rules and apparently I'm not allowed to as for solutions without an attempt to solve it. Since I can't even attempt, may I ask a good place/source to start?
     
    Last edited by a moderator: Apr 18, 2017
  2. jcsd
  3. Oct 6, 2009 #2
    attempt:

    Code (Text):

    5y" + 0y' + y = u
     
    since my diff. eq. is second order, I should have 2 state variables:
    Code (Text):

    x1 = y
    x2 = y'
     
    so the state space model's matrixes become
    Code (Text):

    A = [ 0 1 ]   B = [ 0 ]
        [ 1 0 ]       [ 1 ]

    C = [ 1 0 ]   D = [ 0 ]
     
    does it look ok?
     
  4. Apr 9, 2011 #3
    Dude,

    A = [0 1]
    [(-k/m 0]

    -k/m = -1/5 lol!
     
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