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Control Theory

  1. Feb 1, 2012 #1
    Good day to you people,

    I have just started learning control theory at Uni, as part of my course, and I have to admit it is quite difficult to grasp.

    I am starting from the basics, and I am having difficulty understanding what 's' is supposed to represent as regards the Laplace transform.

    for example:

    L{f(t)} = F(s)

    Now to me these variables represent the following:

    L - as in Laplace transform of a
    f - function of
    t - time

    is equal to

    F - Laplace function of
    s - ??

    I am slightly confusing it with Dynamics and Statics I think, where 's' refers to displacement. And so I am naming that as something I am aware of.
    My guessing is that the 's' is referring to the s-plane as a complex plane, but still that is a difficult concept to grasp.
    Can anyone give me some sort of analogy or point me at a resource that might be able to help a student understand this concept and it's relationship to the poles of a system.

    Sorry for giving such a vague post, but I don't know how to narrow this down any more at the moment.

    Kind regards

    Rob
     
  2. jcsd
  3. Feb 1, 2012 #2
    S is the complex frequency.

    The imaginary part is the usual frequency. In fact, you often see S=jw when there is no real part. w=2pi * frequency (Hz)

    The real part represents an imaginary frequency which is also called exponential damping.

    f(t) = e^(-St).

    If S is pure imaginary you have time harmonic signals (sinusoids). If its only real you have exponentially decaying (or growing) signals. If S is complex then you have a ringing bell- an exponentially decaying sinusoid.

    It's a very general way to exite a linear system, a little more general than Fourier analysis where S is pure imaginary.
     
  4. Feb 2, 2012 #3
    Brilliant, after an evening of studying the intuition of complex numbers, this now makes a little bit of sense to me.

    Thank you very much antiphon.

    I a may be back for a little more, but this is good for me to be going on with.

    Kind regards

    Rob K
     
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