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Significance of 1/s

  1. Mar 4, 2008 #1

    Suppose we have a closed feedback system with loop gain = L(s) = G(s)H(s). The characteristic equation is

    [tex]1 + L(s) = 0[/tex]

    What is the significance of the transformation [itex]s \rightarrow 1/s[/itex] and what bearing does it have on root loci and Nyquist stability?

    I can see that the points [itex]s = \pm \infty[/itex] will be mapped to [itex]s = 0[/itex].

  2. jcsd
  3. Mar 15, 2008 #2
  4. Mar 15, 2008 #3
    I don't get why you transform s to 1/s. Can you elaborate more on the question? Do you mean the invertibility of the char. eq i.e. [itex](1+L(s))^{-1}[/itex] ?
    Last edited: Mar 15, 2008
  5. Mar 18, 2008 #4
    Well, the question really is: what happens to the Root Locus and the Nyquist Stability criterion when I replace s by 1/s? Are they valid? Also, what is the physical significance of such a transformation. Intuitively, I think that such a substitution allows us to map points at infinity to the origin (and conversely)...so, it allows us to get a better "idea" of the high frequency behavior. But I am not fully convinced.
  6. Mar 22, 2008 #5
    But we have already an understanding of the points at infinity, it is completely meaningful when we take [itex]s|_{j\omega}\to\infty[/itex].

    Besides that, though I am not sure, I don't think that it will map the high frequency region as such because you have to also modify the laplace or fourier transform accordingly.
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