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(S-1) (s+1)(s+2) Let G[s] = = the closed-loop system. (a) No such range for K exists. (b) 0 0) that stabilizes

(S-1) (s+1)(s+2) Let G[s] = = the closed-loop system. (a) No such range for K exists. (b) 0 0) that stabilizes

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Let \( G[s] = \frac{(s-1)}{(s+1)(s+2)} \) and \( G_c[s] = K \). Find a range of \( K \) (\( K > 0 \)) that stabilizes the closed-loop system. (a) No such range for \( K \) exists. (b) \( 0 < K < 2 \) (c) \( 2 < K < 4 \) (d) \( 4 < K \) This problem presents a transfer function \( G[s] \) and a controller gain \( G_c[s] \) that is a constant \( K \). The task is to identify a range for the parameter \( K \) that ensures the stability of the system when it forms a closed-loop. The choices explore different intervals of \( K \) to determine which, if any, will stabilize the system.
Transcribed Image Text:Let \( G[s] = \frac{(s-1)}{(s+1)(s+2)} \) and \( G_c[s] = K \). Find a range of \( K \) (\( K > 0 \)) that stabilizes the closed-loop system. (a) No such range for \( K \) exists. (b) \( 0 < K < 2 \) (c) \( 2 < K < 4 \) (d) \( 4 < K \) This problem presents a transfer function \( G[s] \) and a controller gain \( G_c[s] \) that is a constant \( K \). The task is to identify a range for the parameter \( K \) that ensures the stability of the system when it forms a closed-loop. The choices explore different intervals of \( K \) to determine which, if any, will stabilize the system.
The image presents a block diagram as follows: - The diagram begins with an input labeled \( R[a] \). - This input enters a summing junction (represented by a circle with a sigma, \( \Sigma \), inside). - At the summing junction, \( R[a] \) is combined with a feedback signal from the output. This feedback signal is subtracted at the junction. - The output of the summing junction is labeled \( E[a] \). - \( E[a] \) then enters a block labeled \( G_C[a] \), which represents a system or process. - The output of \( G_C[a] \) is then fed into another block labeled \( G[a] \). - The final output from \( G[a] \) is labeled \( Y[a] \). - \( Y[a] \) is also fed back into the summing junction to form a feedback loop. This block diagram represents a feedback control system where the output is fed back and subtracted from the input to regulate the process described by blocks \( G_C[a] \) and \( G[a] \).
Transcribed Image Text:The image presents a block diagram as follows: - The diagram begins with an input labeled \( R[a] \). - This input enters a summing junction (represented by a circle with a sigma, \( \Sigma \), inside). - At the summing junction, \( R[a] \) is combined with a feedback signal from the output. This feedback signal is subtracted at the junction. - The output of the summing junction is labeled \( E[a] \). - \( E[a] \) then enters a block labeled \( G_C[a] \), which represents a system or process. - The output of \( G_C[a] \) is then fed into another block labeled \( G[a] \). - The final output from \( G[a] \) is labeled \( Y[a] \). - \( Y[a] \) is also fed back into the summing junction to form a feedback loop. This block diagram represents a feedback control system where the output is fed back and subtracted from the input to regulate the process described by blocks \( G_C[a] \) and \( G[a] \).
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