Question

7. Determine the stability of the closed-loop transfer function using Routh's Criterion. (Consider Unity feedback) (a) $s^5 + 6s^3 + 5s^2 + 8s + 20$ The auxiliary polynomial for row 4 is $Q(s) = 5s^2 + 20$, with $Q'(s) = 10$, so there are two roots on the $j\omega$-axis. The first column shows two sign changes so there are two roots on the right half-plane. The balance, one root must be in the left half-plane. (b) $T(s) = \frac{10}{s^5 + 2s^4 + 3s^3 + 6s^2 + 5s + 3}$ a positive choice for $\epsilon$. Thus, the system is unstable, with two poles in the right half-plane. (c) $T(s) = \frac{s+8}{s^5 - s^4 + 4s^3 - 4s^2 + 3s - 2}$ 3 rhp, 2 lhp

          7. Determine the stability of the closed-loop transfer function using Routh's Criterion. (Consider Unity
feedback)
(a) $s^5 + 6s^3 + 5s^2 + 8s + 20$
The auxiliary polynomial for row 4 is $Q(s) = 5s^2 + 20$, with $Q'(s) = 10$, so there are two roots on
the $j\omega$-axis. The first column shows two sign changes so there are two roots on the right half-plane.
The balance, one root must be in the left half-plane.
(b) $T(s) = \frac{10}{s^5 + 2s^4 + 3s^3 + 6s^2 + 5s + 3}$
a positive choice for $\epsilon$. Thus, the system is unstable, with two poles in the right
half-plane.
(c) $T(s) = \frac{s+8}{s^5 - s^4 + 4s^3 - 4s^2 + 3s - 2}$
3 rhp, 2 lhp

7. Determine the stability of the closed-loop transfer function using Routh's Criterion. (Consider Unity
feedback)
(a) s^5 + 6s^3 + 5s^2 + 8s + 20
The auxiliary polynomial for row 4 is Q(s) = 5s^2 + 20, with Q'(s) = 10, so there are two roots on
the jω-axis. The first column shows two sign changes so there are two roots on the right half-plane.
The balance, one root must be in the left half-plane.
(b) T(s) = (10)/(s^5 + 2s^4 + 3s^3 + 6s^2 + 5s + 3)
a positive choice for ϵ. Thus, the system is unstable, with two poles in the right
half-plane.
(c) T(s) = (s+8)/(s^5 - s^4 + 4s^3 - 4s^2 + 3s - 2)
3 rhp, 2 lhp

Added by Michael S.

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