Q.4 A control system has the block diagram configuration shown in Figure Q.4a. R(s) s+1 5 S+10 Figure Q.4a 7 C(s) (a) Determine the location of the closed-loop poles and plot on the s-plane. (b) The control system can be approximated as a second order system. Explain why this is so. (c) A unit step input is applied to the system. Determine the settling time T₁, peak time Tp. percent overshoot %OS and steady state error ess.

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Q.4 A control system has the block diagram configuration shown in Figure Q.4a.
R(s)
s+1
5
s + 10
Figure Q.4a
(a)
Determine the location of the closed-loop poles and plot on the s-plane.
R(S) +
(b) The control system can be approximated as a second order system. Explain why
this is so.
(c) A unit step input is applied to the system. Determine the settling time T., peak
time Tp. percent overshoot %OS and steady state error ess.
controller
K(s + 5)
(d) Sketch the expected output response from the information obtained in part (c).
Then discuss the stability of the system.
115
(e) If a controller is added to the system as shown in Figure Q.4b, determine the
range of K for the new system stability.
S+1
C(s)
Figure Q.4b
5
S+10
1
SIT
C(s)
Transcribed Image Text:Q.4 A control system has the block diagram configuration shown in Figure Q.4a. R(s) s+1 5 s + 10 Figure Q.4a (a) Determine the location of the closed-loop poles and plot on the s-plane. R(S) + (b) The control system can be approximated as a second order system. Explain why this is so. (c) A unit step input is applied to the system. Determine the settling time T., peak time Tp. percent overshoot %OS and steady state error ess. controller K(s + 5) (d) Sketch the expected output response from the information obtained in part (c). Then discuss the stability of the system. 115 (e) If a controller is added to the system as shown in Figure Q.4b, determine the range of K for the new system stability. S+1 C(s) Figure Q.4b 5 S+10 1 SIT C(s)
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