Perfeer **Plot a Root Locus for the System**Given the transfer function:\[ G(s)H(s) = \frac{k}{s(s + 5)(s + 10)}\]**Explanation:**In control systems engineering, the root locus plot is an essential technique for analyzing the stability of a system as a parameter (typically gain, \( k \)) is varied. The provided transfer function suggests a system with poles at \( s = 0 \), \( s = -5 \), and \( s = -10 \).To plot the root locus:1. Identify and plot the poles on the complex plane.2. Determine the segments on the real axis where the root locus exists.3. Determine the asymptotes as \( k \) approaches infinity.4. Calculate the angle of departure and arrival (if applicable).5. Plot the root locus branches as \( k \) varies from 0 to ∞.**Note:** The exact numerical plotting will require computational tools or further manual calculations using control system techniques.

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Answered: * Plot Root Locus for the system (5+2)…

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Electrical Engineering

* Plot Root Locus for the system (5+2) (5+2) te G(s)H(s) = S(S+5)(S+10)

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Question

Perfeer

**Plot a Root Locus for the System**

Given the transfer function:

\[
G(s)H(s) = \frac{k}{s(s + 5)(s + 10)}
\]

**Explanation:**

In control systems engineering, the root locus plot is an essential technique for analyzing the stability of a system as a parameter (typically gain, \( k \)) is varied. The provided transfer function suggests a system with poles at \( s = 0 \), \( s = -5 \), and \( s = -10 \).

To plot the root locus:
1. Identify and plot the poles on the complex plane.
2. Determine the segments on the real axis where the root locus exists.
3. Determine the asymptotes as \( k \) approaches infinity.
4. Calculate the angle of departure and arrival (if applicable).
5. Plot the root locus branches as \( k \) varies from 0 to ∞.

**Note:** The exact numerical plotting will require computational tools or further manual calculations using control system techniques.

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