Question

Q.5 (a) Using the Routh-Hurwitz crition, determine if the following systems are stable or unstable, and how many roots lie in the left-hand plane of the s-plane diagram. $\frac{s^3 + 2s^2 + 6}{s^5 + 6s^3 + 5s^2 + 8s + 20}$ (i) $T(s) = $ $\frac{1}{2s^2 + 5s^3 + s^2 + 2s + 1}$ (ii) $T(s) = $ (10 marks) (b) For the negative closed loop feedback system with an open loop gain G(s) and a feedback gain H(s) = 1, where $G(s) = K \frac{(s - a)}{s(s + b)}$ determine the range of values for the gain K when (i) a < 0 and b < 0, and (ii) a > 0 and b > 0. (10 marks)

          Q.5 (a) Using the Routh-Hurwitz crition, determine if the following systems are stable or
unstable, and how many roots lie in the left-hand plane of the s-plane diagram.
$\frac{s^3 + 2s^2 + 6}{s^5 + 6s^3 + 5s^2 + 8s + 20}$
(i)
$T(s) = $
$\frac{1}{2s^2 + 5s^3 + s^2 + 2s + 1}$
(ii)
$T(s) = $
(10 marks)
(b) For the negative closed loop feedback system with an open loop gain G(s) and a
feedback gain H(s) = 1, where
$G(s) = K \frac{(s - a)}{s(s + b)}$
determine the range of values for the gain K when (i) a < 0 and b < 0, and (ii)
a > 0 and b > 0.
(10 marks)

Q.5 (a) Using the Routh-Hurwitz crition, determine if the following systems are stable or
unstable, and how many roots lie in the left-hand plane of the s-plane diagram.
(s^3 + 2s^2 + 6)/(s^5 + 6s^3 + 5s^2 + 8s + 20)
(i)
T(s) =
(1)/(2s^2 + 5s^3 + s^2 + 2s + 1)
(ii)
T(s) =
(10 marks)
(b) For the negative closed loop feedback system with an open loop gain G(s) and a
feedback gain H(s) = 1, where
G(s) = K ((s - a))/(s(s + b))
determine the range of values for the gain K when (i) a < 0 and b < 0, and (ii)
a > 0 and b > 0.
(10 marks)

Added by Jose Francisco G.

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