Question

Question 2 (a) A unity feedback system has the following characteristic equation: $\Delta(s) = s^4 + 22s^3 + 10s^2 + 2s + K$ (i) List the characteristics of a stable system in terms of the output (in response to a bounded input) and also the location of the roots of the characteristic equation in the s-plane. [3 marks] (ii) Identify the range of K for the system to be stable using the Routh-Hurwitz criterion. [5 marks] (iii) If the value of K is chosen such that the system is marginally stable, determine the exact location of the roots on the imaginary axis in the s- plane. [2 marks] (b) A system with a forward transfer function $G(s) = \frac{K}{s^2 + 15s + 36}$ and negative unity feedback is to be designed to have critical damping. Find the value of K to meet the specification and determine the steady-state error, $e_{ss}$ for a unit step input. [3 marks] (c) A negative feedback system has a loop transfer function given by $G(s)H(s) = \frac{K(s^2 - 3s + 5)}{(s + 1)(s + 3)}$ Sketch the root locus of the system and hence determine the range of K for stability. [12 marks]

          Question 2
(a) A unity feedback system has the following characteristic equation:
$\Delta(s) = s^4 + 22s^3 + 10s^2 + 2s + K$
(i) List the characteristics of a stable system in terms of the output (in response to
a bounded input) and also the location of the roots of the characteristic equation
in the s-plane.
[3 marks]
(ii) Identify the range of K for the system to be stable using the Routh-Hurwitz
criterion.
[5 marks]
(iii) If the value of K is chosen such that the system is marginally stable, determine
the exact location of the roots on the imaginary axis in the s-
plane.
[2 marks]
(b) A system with a forward transfer function $G(s) = \frac{K}{s^2 + 15s + 36}$ and negative unity
feedback is to be designed to have critical damping. Find the value of K to meet the
specification and determine the steady-state error, $e_{ss}$ for a unit step
input.
[3 marks]
(c) A negative feedback system has a loop transfer function given by
$G(s)H(s) = \frac{K(s^2 - 3s + 5)}{(s + 1)(s + 3)}$
Sketch the root locus of the system and hence determine the range of K for stability.
[12 marks]

Question 2
(a) A unity feedback system has the following characteristic equation:
Δ(s) = s^4 + 22s^3 + 10s^2 + 2s + K
(i) List the characteristics of a stable system in terms of the output (in response to
a bounded input) and also the location of the roots of the characteristic equation
in the s-plane.
[3 marks]
(ii) Identify the range of K for the system to be stable using the Routh-Hurwitz
criterion.
[5 marks]
(iii) If the value of K is chosen such that the system is marginally stable, determine
the exact location of the roots on the imaginary axis in the s-
plane.
[2 marks]
(b) A system with a forward transfer function G(s) = (K)/(s^2 + 15s + 36) and negative unity
feedback is to be designed to have critical damping. Find the value of K to meet the
specification and determine the steady-state error, ess for a unit step
input.
[3 marks]
(c) A negative feedback system has a loop transfer function given by
G(s)H(s) = (K(s^2 - 3s + 5))/((s + 1)(s + 3))
Sketch the root locus of the system and hence determine the range of K for stability.
[12 marks]

Added by Kristy W.

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