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State space representation

  1. Oct 30, 2014 #1
    JL*QL'' + BL*QL' + k(QL - Qm) = 0
    Jm*Qm'' + Bm*Qm' - k(QL - Qm) = u

    This is the equation set I have for a motor with a load.
    QL'' means second derivative and QL' means first derivative.

    I need to be able to obtain the state space representation of this model where X = [QL;QL';Qm;Qm'] (This is of course a column array)

    I tried my best but couldn't obtain it.
    Started off with QL' = [-JL*QL'' - k(QL - Qm)]/BL

    But when I try to represent this, I don't have the QL'' term in my state variable array X, so couldn't proceed further.

    How am I supposed to approach this problem ?
     
  2. jcsd
  3. Oct 30, 2014 #2

    donpacino

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    Gold Member

    as you are most likely aware, state space representation is usually of the form

    X'=A*X+B
    Y=C*X+D

    your first goal is to define your X array.
    then you need to define your A and B matrix.

    I would define each element of your X array.
    SO you already stated
    QL = X1
    QL' =X2
    Qm=X3
    Qm'=X4

    so right off the bat you know X1'=X2 and X3'=X4, that gives you half of your A matrix

    So you need to find your A matrix rows for X2' and X4'.

    So use equation one to solve for X2', then use equation 2 to solve for X4'. as you can see there is only one input which is in equation 2, so there will only be one nonzero element in the B matrix.
     
  4. Oct 30, 2014 #3
    Perfect !

    Thanks a lot
     
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