Figure I shows a general feedback control system with forward-path transfer functions Gds) (controller) and Gr(s) (plant) and feedback transfer functions H(s). Given the following transfer functions, determine the closed-loop transfer function T(s) = Y(sYR(s a. G.(s) = Kp G„(s) = s+2 H(s) = 2 1 H(s) = 1 d. G.(s) = Kp f. G.(s) = Kp G,(s) = G,(s) = 3, 55 s2+ 6s + 8 10 H(s) s+10

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Figure I shows a general feedback control system with forward-path transfer funetions
Gds) (controller) and Gr(s) (plant) and feedback transfer functions H(s). Given the
following transfer functions, determine the closed-loop transfer function T(s)= Y(sYR(s).
a. G.(s) = Kp
d. G.(s) = Kp
6.
G„(s) =
S+2
H(s) = 2
H(s) = 1
H(s) =
Gp(s) =
s2+ 6s + 8
10
f. G,(s) = Kp
Gp (s) =
Kps+Kj
G,(s) =
s2+5s
S+10
g G (s) =
H(s) = 1
(s+1)(s+3)
H()
Figure 1. A general feedback control system
Transcribed Image Text:Figure I shows a general feedback control system with forward-path transfer funetions Gds) (controller) and Gr(s) (plant) and feedback transfer functions H(s). Given the following transfer functions, determine the closed-loop transfer function T(s)= Y(sYR(s). a. G.(s) = Kp d. G.(s) = Kp 6. G„(s) = S+2 H(s) = 2 H(s) = 1 H(s) = Gp(s) = s2+ 6s + 8 10 f. G,(s) = Kp Gp (s) = Kps+Kj G,(s) = s2+5s S+10 g G (s) = H(s) = 1 (s+1)(s+3) H() Figure 1. A general feedback control system
Figure 2 shows a general closed-loop control system. The plant transfer function is
1.
Gp(s) =
s + 6s + 12
Reference
Input,
Proportional
gain
Plant
Figure 2. A general closed-loop system
a. Determine whether the closed-loop system is stable for control gain K,-2.
b. Compute the controller gain K, so that step response shows 25 % overshoot.
c. Estimate the settling time for a step reference input if the control gain is K,-0.5.
Transcribed Image Text:Figure 2 shows a general closed-loop control system. The plant transfer function is 1. Gp(s) = s + 6s + 12 Reference Input, Proportional gain Plant Figure 2. A general closed-loop system a. Determine whether the closed-loop system is stable for control gain K,-2. b. Compute the controller gain K, so that step response shows 25 % overshoot. c. Estimate the settling time for a step reference input if the control gain is K,-0.5.
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