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Test Stability using Routh Stability Method

  1. Jul 17, 2011 #1
    1. The problem statement, all variables and given/known data

    For a control system that has G(s)H(s) = [itex]\frac{1}{s^{2}*(s+\alpha)}[/itex]

    2. Relevant equations

    1 + G(s)H(s) = 0

    3. The attempt at a solution

    Exam question i messed up . I really need to know the answer.
  2. jcsd
  3. Jul 18, 2011 #2


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    i + G(s)H(s) = 0 means:
    [tex]s^3+\alpha s^2 + 1 = 0[/tex]
    Since the polynomial is incomplete (there is no term in [tex]s^1[/tex]) there is at least one root in the RHP and the system is unstable. No need to use Routh algorithm.
  4. Jul 19, 2011 #3
    I forgot one more thing. It also says find the value of [itex]\alpha[/itex] for which the system can be classified in the critically stable state.
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