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Linearization with a Constant Block in Matlab

  1. Sep 15, 2009 #1
    Hi All,

    1. The problem statement, all variables and given/known data
    I have modeled a simple spring mass system in Matlab and trying to use linmod to linearize the system.

    The system models a mass that hangs from ceiling with a spring and damper. So, the forces that act on the mass are gravity, spring force and damping force. I attached the Simulink model and a picture of the model to the question.

    Now, the problem is that, Matlab's linmod seems to completely ignore the gravity (constant block). I would like to know how should I change the model or simulation parameters to get correct results.

    2. Relevant equations

    state vector x is [h V]' (height and speed)
    output vector y is [h a] (height and acceleration)
    input vector is empty

    linmod('trim_linmod_test') gives following matrices:

    A:
    0.0000 1.0000
    -0.5000 -0.5000

    C:
    1.0000 0.0000
    -0.5000 -0.5000

    B,D empty because there are no inputs.

    Now,

    y= C*x, hence a = -0.5 * h - 0.5*V

    On the other hand, if we simply look at the model we can see that
    a = (-5*h - 5*V + 9.81) / (m) ( m = 0.1, the gain block )

    So, obviously, the constant block is ignored.

    3. The attempt at a solution
    I can see that the state space equation of the form y=C*x can't really represent the gravity term. C is a 2x2 matrix but acceleration equation needs 3 terms.

    I thought of making gravity an input. This way state space equation will be y = C*x + D*u and there are enough terms to represent acceleration. But this doesn't really look logical to me.


    Thanks in Advance
     

    Attached Files:

  2. jcsd
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