Consider the feedback system given the open loop transfer function below G(s)H(s) = K / ( S (s+3) (s+2)) a) Using the Routh-Hurwitz criterion, for which value of K, the poles of the closed-loop system take the pure imaginary value. b) What will be the maximum value of K for the system to be stable? c) Calculate the value of K, where the real value of the complex root of the system is Re{s}=-1.
Consider the feedback system given the open loop transfer function below
G(s)H(s) = K / ( S (s+3) (s+2))
a) Using the Routh-Hurwitz criterion, for which value of K, the poles of the closed-loop system take the pure imaginary value.
b) What will be the maximum value of K for the system to be stable?
c) Calculate the value of K, where the real value of the complex root of the system is Re{s}=-1.
Tip 1: Closed loop transfer function T(s) = G(s) / ( 1+ G(s)H(s)) .Routh HurwitzIn order to perform the criterion analysis, the denominator of the closed-loop function will be examined.
Tip 2: The real value of the system complex root Re{s}=-1 is expressed by the following formula
f^2(s) = p(s-1)
p(s) is the payoff of the closed-loop function.
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