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Find the value of K for the system given below that will place the closed-loop poles as shown.

Find the value of K for the system given below that will place the closed-loop poles as shown.

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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**Description:** The image presents a control system with the task of finding the value of K that will position the closed-loop poles as depicted. **System Components:** - **R(s):** Input signal. - **Block 1:** Transfer function \( s^2 \). - **Summation Point 1:** Subtracts feedback from the output of the \( s^2 \) block. - **Block 2:** Transfer function \( \frac{K}{s^2} \) leading to output \( C(s) \). - **Block 3:** Transfer function \( \frac{2}{s} \) providing feedback to the summation point. - **Block 4:** Transfer function \( \frac{1}{s+1} \) also providing feedback to the summation point. - **Summation Point 2:** Adds the outputs of the feedback transfer functions before returning to the input summation point. **Pole-Zero Plot:** - **Axes:** - Horizontal axis (\( \sigma \)): Represents the real part of the poles. - Vertical axis (\( j\omega \)): Represents the imaginary part of the poles. - Two poles (marked with 'X') are situated symmetrically across the real and imaginary axes, indicating desired closed-loop pole positions. **Objective:** Identify the value of \( K \) that will adjust the system such that the closed-loop poles align with the given points on the pole-zero plot.
Transcribed Image Text:**Description:** The image presents a control system with the task of finding the value of K that will position the closed-loop poles as depicted. **System Components:** - **R(s):** Input signal. - **Block 1:** Transfer function \( s^2 \). - **Summation Point 1:** Subtracts feedback from the output of the \( s^2 \) block. - **Block 2:** Transfer function \( \frac{K}{s^2} \) leading to output \( C(s) \). - **Block 3:** Transfer function \( \frac{2}{s} \) providing feedback to the summation point. - **Block 4:** Transfer function \( \frac{1}{s+1} \) also providing feedback to the summation point. - **Summation Point 2:** Adds the outputs of the feedback transfer functions before returning to the input summation point. **Pole-Zero Plot:** - **Axes:** - Horizontal axis (\( \sigma \)): Represents the real part of the poles. - Vertical axis (\( j\omega \)): Represents the imaginary part of the poles. - Two poles (marked with 'X') are situated symmetrically across the real and imaginary axes, indicating desired closed-loop pole positions. **Objective:** Identify the value of \( K \) that will adjust the system such that the closed-loop poles align with the given points on the pole-zero plot.
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