7. Consider the closed-loop system in Figure. Suppose that all gains are positive, that is, K1 : 0, K2 > 0, K3 > 0, K4 > 0, and K5 > 0. (a) Determine the closed-loop transfer function T(s) = Y(s)/R(s). (b) Obtain the conditions on selecting the gains K1, K2, K3, K4, and Ks, so that the closed-loop system is guaranteed to be stable.

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Author:Robert L. Boylestad
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7. Consider the closed-loop system in Figure. Suppose that all gains are positive, that is, K1 >
0, K2 > 0, K3 > 0, K4 > 0, and Kş > 0.
(a) Determine the closed-loop transfer function T(s) = Y(s)/R(s).
(b) Obtain the conditions on selecting the gains K1, K2, K3, K4, and Ks, so that the closed-loop
system is guaranteed to be stable.
(c) Using the results of part (b), select values of the five gains so that the closed-loop system is
stable, and plot the unit step response.
10
R(s)
K2
Y(s)
2s -4
s- 10
K3
K5
Transcribed Image Text:7. Consider the closed-loop system in Figure. Suppose that all gains are positive, that is, K1 > 0, K2 > 0, K3 > 0, K4 > 0, and Kş > 0. (a) Determine the closed-loop transfer function T(s) = Y(s)/R(s). (b) Obtain the conditions on selecting the gains K1, K2, K3, K4, and Ks, so that the closed-loop system is guaranteed to be stable. (c) Using the results of part (b), select values of the five gains so that the closed-loop system is stable, and plot the unit step response. 10 R(s) K2 Y(s) 2s -4 s- 10 K3 K5
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