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€7.27 Consider the unity feedback system in Figure E7.27. Sketch the root locus as 0 s p< ∞. €7.28. Consider the feedback system in Figure E7.28. Obtain the negative gain root locus as -0 < K< 0. For what values of Kis the system stable? Controller Process E(s) 10 R(s) K Y(s) s + 25 Sensor 1 FIGURE E7.25 Nonunity feedback system with parameter K. Controller Process E(s) s + 10 4 R(s) Y(s) s + p FIGURE E7.27 Unity feedback system with parameter p.

€7.27 Consider the unity feedback system in Figure E7.27. Sketch the root locus as 0 s p< ∞. €7.28. Consider the feedback system in Figure E7.28. Obtain the negative gain root locus as -0 < K< 0. For what values of Kis the system stable? Controller Process E(s) 10 R(s) K Y(s) s + 25 Sensor 1 FIGURE E7.25 Nonunity feedback system with parameter K. Controller Process E(s) s + 10 4 R(s) Y(s) s + p FIGURE E7.27 Unity feedback system with parameter p.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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### Educational Website Content #### Control Systems: Root Locus and Stability Analysis ##### Problem E7.27 **Task:** Consider the unity feedback system in Figure E7.27. Sketch the root locus as \( 0 \le p < \infty \). **Solution Outline:** To sketch the root locus, you will have to follow the standard procedure of root locus plotting which involves identifying open-loop poles and zeros, calculating angles of departure and arrival, and plotting the trajectory of the system poles as parameter \( p \) changes from 0 to \(\infty\). --- ##### Problem E7.28 **Task:** Consider the feedback system in Figure E7.28. Obtain the negative gain root locus as \(-\infty < K \le 0\). For what values of \( K \) is the system stable? **Solution Outline:** For this problem, it requires plotting the root locus for negative gains, i.e., as \( K \) varies from 0 to \(-\infty\). You need to determine the stability of the system by identifying where the real parts of the system poles are negative (this implies the system being stable). --- ### Figures Explained #### FIGURE E7.25 **Title:** Nonunity feedback system with parameter \( K \). **Description:** 1. **Components:** - **Controller:** \( K \) - **Process:** \( \frac{10}{s + 25} \) - **Sensor:** \( \frac{1}{s} \) 2. **System:** - The reference signal \( R(s) \) is input to a summing junction. - The error signal \( E_a(s) \) is generated by subtracting feedback from the actual output. - The controller \( K \) processes \( E_a(s) \). - The process block processes the output of the controller. - The sensor measures the process output which is then fed back to the summing junction. #### FIGURE E7.27 **Title:** Unity feedback system with parameter \( p \). **Description:** 1. **Components:** - **Controller:** \( \frac{s + 10}{s} \) - **Process:** \( \frac{4}{s + p} \) 2. **System:** - The reference signal \( R(s) \) is input to a summ
Transcribed Image Text:### Educational Website Content #### Control Systems: Root Locus and Stability Analysis ##### Problem E7.27 **Task:** Consider the unity feedback system in Figure E7.27. Sketch the root locus as \( 0 \le p < \infty \). **Solution Outline:** To sketch the root locus, you will have to follow the standard procedure of root locus plotting which involves identifying open-loop poles and zeros, calculating angles of departure and arrival, and plotting the trajectory of the system poles as parameter \( p \) changes from 0 to \(\infty\). --- ##### Problem E7.28 **Task:** Consider the feedback system in Figure E7.28. Obtain the negative gain root locus as \(-\infty < K \le 0\). For what values of \( K \) is the system stable? **Solution Outline:** For this problem, it requires plotting the root locus for negative gains, i.e., as \( K \) varies from 0 to \(-\infty\). You need to determine the stability of the system by identifying where the real parts of the system poles are negative (this implies the system being stable). --- ### Figures Explained #### FIGURE E7.25 **Title:** Nonunity feedback system with parameter \( K \). **Description:** 1. **Components:** - **Controller:** \( K \) - **Process:** \( \frac{10}{s + 25} \) - **Sensor:** \( \frac{1}{s} \) 2. **System:** - The reference signal \( R(s) \) is input to a summing junction. - The error signal \( E_a(s) \) is generated by subtracting feedback from the actual output. - The controller \( K \) processes \( E_a(s) \). - The process block processes the output of the controller. - The sensor measures the process output which is then fed back to the summing junction. #### FIGURE E7.27 **Title:** Unity feedback system with parameter \( p \). **Description:** 1. **Components:** - **Controller:** \( \frac{s + 10}{s} \) - **Process:** \( \frac{4}{s + p} \) 2. **System:** - The reference signal \( R(s) \) is input to a summ
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