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    Stability of systems

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    1. A single-loop negative feedback system has a loop transfer function.

    GH(s) = K(s+2)^2 / s(s^2+1)(s+8)

    Determine the range of the gain K for which the system is stable.

    Choose either
    a. 23 < K < 367
    b. K > 14
    c. 0 < K < 5

    2. A system has a characteristic equation q(s) = s^4 +9s^3 +45s^2 +87s +50 +0. Determine whether the system is stable using the Routh-Hurwitz criterion and also determine the roots of the characteristic equation.

    Choose either
    a. unstable and s1,2 = -3 ±j4. s3 = -2, s4 = -1
    b. stable and s1,2 = -3 ± j4. s3 = -2, s4 = -1
    c. marginally stable and s1,2 = -3 ± j4. s3 = -.2, s4 = -1

    3. A system has a characteristic equation s3 + 9s2 + 26s + 24 = 0. Using the Routh-Hurwitz criterion, determine if the system is stable.

    Choose either
    a. Stable
    b. Unstable

    © BrainMass Inc. brainmass.com October 9, 2019, 8:16 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/stability-systems-145128

    Solution Preview

    1. A single-loop negative feedback system has a loop transfer function.

    GH(s) = K(s+2)^2 / s(s^2+1)(s+8)

    Determine the range of the gain K for which the system is stable.

    Choose either
    a. 23 < K < 367
    b. K > 14
    c. 0 < K < 5

    Solution
    The characteristic equation of the system is

    1
    8 0
    0
    0

    The system is stable if all of the signs of the first column are ...

    Solution Summary

    This is a set of questions regarding control systems, the Routh-Hurwitz criterion, and stability.

    $2.19