b) In another unity feedback system, the root locus is depicted in Figure Q.1 (b). If the system is operated at a damping ratio of 0.5, identify the following: (i) (ii) (iii) The dominant closed-loop poles for this case. The operational gain, K at the dominant closed-loop poles. For a step input response, determine the (approximated) settling time, T, and the peak time, Tp. (iv) Determine the range of K for stability

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solve q.1.b

Question 1
A unity feedback system as shown in Figure Q.1(a) has a forward transfer function:
R(s)
(i)
(ii)
G(s):
K
s²2-10s +24
s² +8s + 30
G(s)
C(s)
Figure Q.1(a)
Sketch the root locus of the closed loop system
Determine the range of gain K if the system operates in the
underdamped region
b) In another unity feedback system, the root locus is depicted in Figure Q.1(b).
If the system is operated at a damping ratio of 0.5, identify the following:
(i) The dominant closed-loop poles for this case.
(ii)
The operational gain, K at the dominant closed-loop poles.
(iii)
WI
For a step input response, determine the (approximated) settling time,
T, and the peak time, Tp.
(iv) Determine the range of K for stability
Transcribed Image Text:Question 1 A unity feedback system as shown in Figure Q.1(a) has a forward transfer function: R(s) (i) (ii) G(s): K s²2-10s +24 s² +8s + 30 G(s) C(s) Figure Q.1(a) Sketch the root locus of the closed loop system Determine the range of gain K if the system operates in the underdamped region b) In another unity feedback system, the root locus is depicted in Figure Q.1(b). If the system is operated at a damping ratio of 0.5, identify the following: (i) The dominant closed-loop poles for this case. (ii) The operational gain, K at the dominant closed-loop poles. (iii) WI For a step input response, determine the (approximated) settling time, T, and the peak time, Tp. (iv) Determine the range of K for stability
Imaginary
1012
Root Locus
-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
Real
Figure Q.1(b)
Transcribed Image Text:Imaginary 1012 Root Locus -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 Real Figure Q.1(b)
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