What is the zero of this TF

Discussion in 'Math' started by fadelo, Nov 3, 2012.

  1. fadelo

    Thread Starter New Member

    Apr 12, 2011
    22
    0
    Hello
    I'm confused when working with transfere function in order to know poles and zeroz the for functions having (K) = gain in the numerator for examble

    g(s)H(s)=k/s(s+4)(s+2)

    here the poles are s=-4 and s=-2 ok what is the zero??
    what about this examble also:

    ks/(s+6)(s+2)

    regards
     
  2. panic mode

    Senior Member

    Oct 10, 2011
    1,318
    304
    your transfer function can be represented as
    k*(A1*A2*A3*....) / (B1*B2*B3*...)
    where A are zeroes and B are poles.

    it should be obvious that whan any of A is zero, transfer function is zero.
    when any of B is zero we get division by zero which is a pole.

    each of A and B terms has general form
    Ai=s+ci
    or
    Bj=s+cj

    in case of

    H(s)=ks/ (s+6)(s+2)

    there is only one zero: A1=s
    but there are two poles
    B1=s+6 and B2=s+2)
    since we are intersted in cases where A and B are zero, solutions are
    A1: s=0
    B1: s=-6
    B2: s=-2

    when you plot Bode diagram, you will use those values of s as corner frequencies.

    in case of H(s)=k/s(s+4)(s+2)
    there is no zeroes because numerator does not have any s-terms
    we only have three poles:
    B1=s
    B2=s+6
    B3=s+2

    they are zero values when s=0, s=-2 ans s=-6
     
  3. fadelo

    Thread Starter New Member

    Apr 12, 2011
    22
    0
    Thnx a milion sir now I could proceed my solutions in root locis and bode plot

    regards
     
  4. mathteacher019

    New Member

    Nov 12, 2012
    2
    0
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