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Let G[s] = (s+2) s(s+10) (s²+10s+24) locus breakaway from the real axis? (a) An interval does not exist (b) -2 < s <0 (c) −4 < s < -2 (d) -6 < s <-4 (e) -10 < s <-6 and Ge[s] = K. In what interval(s) does the root

Let G[s] = (s+2) s(s+10) (s²+10s+24) locus breakaway from the real axis? (a) An interval does not exist (b) -2 < s <0 (c) −4 < s < -2 (d) -6 < s <-4 (e) -10 < s <-6 and Ge[s] = K. In what interval(s) does the root

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 \( G[s] = \frac{(s+2)}{s(s+10)(s^2+10s+24)} \) and \( G_c[s] = K \). In what interval(s) does the root locus break away from the real axis? (a) An interval does not exist (b) \(-2 < s < 0\) (c) \(-4 < s < -2\) (d) \(-6 < s < -4\) (e) \(-10 < s < -6\)
Transcribed Image Text:Let \( G[s] = \frac{(s+2)}{s(s+10)(s^2+10s+24)} \) and \( G_c[s] = K \). In what interval(s) does the root locus break away from the real axis? (a) An interval does not exist (b) \(-2 < s < 0\) (c) \(-4 < s < -2\) (d) \(-6 < s < -4\) (e) \(-10 < s < -6\)
**Block Diagram Description:** The diagram provided is a control system represented in block diagram form and involves the following components: 1. **Input Signal \( R[\omega] \):** - This is the reference input signal entering the system. 2. **Summation Junction (\(\Sigma\)):** - This junction sums the input signal \( R[\omega] \) and the feedback signal, subtracting the feedback from the reference. The output of this summation is denoted as \( E[\omega] \), which represents the error signal. 3. **Controller Block \( G_C[\omega] \):** - The error signal \( E[\omega] \) is fed into the controller block. The controller processes this signal to generate a control action to reduce the error. 4. **System Block \( G[\omega] \):** - The output from the controller \( G_C[\omega] \) is then passed through the main system block \( G[\omega] \), which represents the dynamics of the system being controlled. 5. **Output Signal \( Y[\omega] \):** - The final output of the system is \( Y[\omega] \). 6. **Feedback Loop:** - The output signal \( Y[\omega] \) is fed back to the summation junction, completing the feedback loop. This loop allows the system to dynamically adjust based on the difference between the reference input and the actual output. This diagram describes a typical closed-loop control system used in numerous engineering applications to maintain desired output closer to the reference input by minimizing the error signal \( E[\omega] \).
Transcribed Image Text:**Block Diagram Description:** The diagram provided is a control system represented in block diagram form and involves the following components: 1. **Input Signal \( R[\omega] \):** - This is the reference input signal entering the system. 2. **Summation Junction (\(\Sigma\)):** - This junction sums the input signal \( R[\omega] \) and the feedback signal, subtracting the feedback from the reference. The output of this summation is denoted as \( E[\omega] \), which represents the error signal. 3. **Controller Block \( G_C[\omega] \):** - The error signal \( E[\omega] \) is fed into the controller block. The controller processes this signal to generate a control action to reduce the error. 4. **System Block \( G[\omega] \):** - The output from the controller \( G_C[\omega] \) is then passed through the main system block \( G[\omega] \), which represents the dynamics of the system being controlled. 5. **Output Signal \( Y[\omega] \):** - The final output of the system is \( Y[\omega] \). 6. **Feedback Loop:** - The output signal \( Y[\omega] \) is fed back to the summation junction, completing the feedback loop. This loop allows the system to dynamically adjust based on the difference between the reference input and the actual output. This diagram describes a typical closed-loop control system used in numerous engineering applications to maintain desired output closer to the reference input by minimizing the error signal \( E[\omega] \).
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