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)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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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 \( R \).
Expert Solution

Step 1
Given the block diagram:
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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