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Homework Help: Determining the range of a controller for a stable system

  1. May 4, 2017 #1
    1. The problem statement, all variables and given/known data
    The controller K(s) = Kp, determine the range of Kp over which the closed loop system is stable.

    2. Relevant equations
    I found the transfer function of system = Y(s)/V(s)=Kp/(1.5s^2 + 2.5s - 1 + Kp)

    3. The attempt at a solution
    So i know (1.5s^2 + 2.5s - 1 + Kp) is the characteristic equation is been a while since ive done these i think i remember that all roots of the polynomial for a stable system must be negative real parts and i know its probably obvious but i just cant remember how to find the range of Kp. Thanks!
  2. jcsd
  3. May 4, 2017 #2


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    Science Advisor
    Gold Member
    2017 Award

    Solve for the roots of the denominator. It's only second order, so you can use a formula.
  4. May 5, 2017 #3
    yeah it's just the Kp being part of the denominator that's throwing me a bit, how do I include that in the quadratic formula
  5. May 5, 2017 #4


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    Staff: Mentor

    Um, by including it in the quadratic formula? Treat Kp as a constant and write out the formula. Then see how the value of Kp affects the roots. What range of values for Kp will satisfy your requirements? Be discriminating :smile:
  6. May 5, 2017 #5


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    As far as I can see IT IS included in the formula (see your own post).
  7. May 5, 2017 #6
    Yeah I got it now, cheers guys.
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