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Problem #2 Sketch the root locus for the following system. R(s) K(s² + 1) s² C(s)

Problem #2 Sketch the root locus for the following system. R(s) K(s² + 1) s² C(s)

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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**Problem #2** Sketch the root locus for the following system. **Block Diagram Explanation:** The system depicted is a feedback control system which includes a summation block and a transfer function block. - **Summation Block:** - Inputs: \( R(s) \) and the feedback signal (negative feedback). - Output: The difference (error signal) between \( R(s) \) and the feedback. - **Transfer Function Block:** - Forward Path Transfer Function: \(\frac{K(s^2 + 1)}{s^2}\) - This represents a second-order system with a gain \( K \), a zero at \( s = -1 \), and poles at the origin \( s = 0 \). - **Feedback Path:** - Negative feedback loop from the output \( C(s) \) back to the summation block. **Objective:** - Sketching the root locus requires determining how the poles of the system transfer function change with varying gain \( K \). For educational purposes, a root locus plot would show the path of the closed-loop poles on the complex plane as the gain \( K \) varies from 0 to infinity.
Transcribed Image Text:**Problem #2** Sketch the root locus for the following system. **Block Diagram Explanation:** The system depicted is a feedback control system which includes a summation block and a transfer function block. - **Summation Block:** - Inputs: \( R(s) \) and the feedback signal (negative feedback). - Output: The difference (error signal) between \( R(s) \) and the feedback. - **Transfer Function Block:** - Forward Path Transfer Function: \(\frac{K(s^2 + 1)}{s^2}\) - This represents a second-order system with a gain \( K \), a zero at \( s = -1 \), and poles at the origin \( s = 0 \). - **Feedback Path:** - Negative feedback loop from the output \( C(s) \) back to the summation block. **Objective:** - Sketching the root locus requires determining how the poles of the system transfer function change with varying gain \( K \). For educational purposes, a root locus plot would show the path of the closed-loop poles on the complex plane as the gain \( K \) varies from 0 to infinity.
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Step 1: what is given and what to do:

Given:

a control system,

Electrical Engineering homework question answer, step 1, image 1

To do:

we need to sketch the root locus. 


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