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Homework Help: Low-Order Approximation of System

  1. Mar 1, 2015 #1
    1. The problem statement, all variables and given/known data
    I have a pretty simple question. I was going over an older exam when I encountered something that did not quite make sense to me.

    If [tex]\frac{(2s+5)(-s+0.5)}{(s+3)(s^2+0.1s+0.01)}[/tex],

    find a low order approximation for the system.

    I understand that the pole at s=-3 can be neglected, and that we can drop the terms containing the zeros. I also know that we need to consider the DC gain of these portions when dropping those terms for low-order approximation. What I do not understand, is how the DC gain from (2s+5) term is 5/2, rather than merely 5. Wouldn't you simply plug in a zero for s?
  2. jcsd
  3. Mar 2, 2015 #2


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    My approach is as follows:
    Divide numerator and denominator by "2". Thus, in the numerator we have (s+2.5). Now - as a first approximation, the zero at "-2.5" and the pole at "-3" cancel each other.
    This leads to a "low-order approximation" of the given function. Why do you think, that you can "neglect" the pole at "-3" ?
  4. Mar 2, 2015 #3
    The behaviour of the system will primarily be governed by the poles that are close the s-axis (relative to the pole at s=-3). The solution reduces the equation to 5/(12(s^2+0.1s+0.01)), but I was certain that it should be 5/(6(s^2+0.1s+0.01)).

    EDIT* I plotted it in MATLAB and determined that their solution is wrong. Thanks!
    Last edited: Mar 2, 2015
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