A unity feedback system is shown in Figure Q1. R(s) C(s) K G() Figure Q1 Given that K(s -4s +8) G(s) = (s+ 4)(s +10) From the given open-loop transfer function, G(s) detemnine the following: O The imaginary crossing of the root locus of the closed-loop transfer function. Hence the gain at that crossing. (i) The arrival angle of the root locus of the closed-loop transfer funetion. (ii) The breakaway point of the root locus of the closed-loop transfer function is given as s=-6.05. Hence, determine the gain at that point.

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A unity feedback system is shown in Figure Q1.
R(s)
C(s)
K
G(S)
Figure Q1
Given that
K(s-4s +8)
G(s) =
(s+4)(s +10)
%3D
From the given open-loop transfer function, G(s) detemine the following:
) The imaginary erossing of the root locus of the closed-loop transfer function.
Hence the gain at that crossing.
(i) The arrival angle of the root locus of the closed-loop transfer function.
(iii) The breakaway point of the root locus of the closed-loop transfer function is given as
s=-6.05. Hence, determine the gain at that point.
(iv) Using the information gathered from (i) until (ii), sketch the root locus of the closed-
loop transfer fiunction.
(v) Hence determine the range of gain K for the underdamped stable system and the
critically damped system.
Transcribed Image Text:A unity feedback system is shown in Figure Q1. R(s) C(s) K G(S) Figure Q1 Given that K(s-4s +8) G(s) = (s+4)(s +10) %3D From the given open-loop transfer function, G(s) detemine the following: ) The imaginary erossing of the root locus of the closed-loop transfer function. Hence the gain at that crossing. (i) The arrival angle of the root locus of the closed-loop transfer function. (iii) The breakaway point of the root locus of the closed-loop transfer function is given as s=-6.05. Hence, determine the gain at that point. (iv) Using the information gathered from (i) until (ii), sketch the root locus of the closed- loop transfer fiunction. (v) Hence determine the range of gain K for the underdamped stable system and the critically damped system.
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