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5.) Sketch the positive root locus for the system shown below. Determine the required value of K so that the control system has critically damped poles. Find the pole locations using this value of K. Estimate the rise time and the steady-state error with a unit-step reference input using this value of K. + s + 4 K s2 + 3s + 2

5.) Sketch the positive root locus for the system shown below. Determine the required value of K so that the control system has critically damped poles. Find the pole locations using this value of K. Estimate the rise time and the steady-state error with a unit-step reference input using this value of K. + s + 4 K s2 + 3s + 2

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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### Transcription: **Problem 5:** Sketch the positive root locus for the system shown below. Determine the required value of \( K \) so that the control system has critically damped poles. Find the pole locations using this value of \( K \). Estimate the rise time and the steady-state error with a unit-step reference input using this value of \( K \). ~~Use Matlab to plot the unit-step response using this value of \( K \).~~ #### System Diagram: The system block diagram consists of the following components: 1. **Summation Block (\(\Sigma\)):** - Inputs: \( R \) (Reference) as the positive input and feedback as the negative input. 2. **Gain Block:** - Denoted by \( K \). 3. **Transfer Function Block:** - Transfer Function: \( \frac{s + 4}{s^2 + 3s + 2} \). - Output: \( Y \). The system is a closed-loop feedback control system, where the output \( Y \) is fed back into the summation block to compare against the reference input \( R \).
Transcribed Image Text:### Transcription: **Problem 5:** Sketch the positive root locus for the system shown below. Determine the required value of \( K \) so that the control system has critically damped poles. Find the pole locations using this value of \( K \). Estimate the rise time and the steady-state error with a unit-step reference input using this value of \( K \). ~~Use Matlab to plot the unit-step response using this value of \( K \).~~ #### System Diagram: The system block diagram consists of the following components: 1. **Summation Block (\(\Sigma\)):** - Inputs: \( R \) (Reference) as the positive input and feedback as the negative input. 2. **Gain Block:** - Denoted by \( K \). 3. **Transfer Function Block:** - Transfer Function: \( \frac{s + 4}{s^2 + 3s + 2} \). - Output: \( Y \). The system is a closed-loop feedback control system, where the output \( Y \) is fed back into the summation block to compare against the reference input \( R \).
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Step 1

Given the block diagram:

Electrical Engineering homework question answer, step 1, image 1

We need to sketch the root locus for the system.

We need to determine the required value of K so that the control system has critically damped poles, we need to find the pole locations using this value of K.

We need to estimate the rise time and the steady-state error with a unit reference input using this value of K.

 

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