How to derive the space state form of this system?

  1. Hi all,

    I need to derive the space state form of this simple system:

    http://imageshack.us/photo/my-images/856/system.png/

    The two springs end are moving.

    I derived the equation fo motion:

    m*ddxm+kl*(xm-xl)+ku*(xm-xu)+cl*(dxm-dxl)+cu*(dxmdxu)

    where ddxm is the mass acceleration
    dxm is the mass speed
    xm is the mass position
    xl is the lower spring end position
    dxl is the lower spring end velocity
    xu is the lower spring end position
    dxu is the lower spring end velocity

    My system has two inputs and one output and my problem is to understand how to manage them.

    so I changed the variables in this way:
    y1=xm
    y2=dxm

    and I derived the following equation:

    dy2=-y1*(kl/m+ku/m)-y2*(cl/m+cu/m)+kl/m*xl+ku/m*xu+cl/m*xl+cu/m*xu.

    And this should be the A matrix:

    A=[0 1 ;
    -kl/m-ku/m -cl/m-cu/m]



    How should I define the input matrix since I have speed and velocity in the input and they are related each other? Hopefully to have properly explained my doubt, if not don't hesitate to ask me please
     
    Last edited: Sep 6, 2011
  2. jcsd
  3. none can help me?
     
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