5- For the control system shown in Fig. 4, determine the steady state error for step input to 5, and for ramp with slope 10. (1,3,6] R(s) k s² + 5s +6 1 (s+1) C(s)
5- For the control system shown in Fig. 4, determine the steady state error for step input to 5, and for ramp with slope 10. (1,3,6] R(s) k s² + 5s +6 1 (s+1) C(s)
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter12: Power System Controls
Section: Chapter Questions
Problem 12.2P
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STEADY STATE ERROR (NEED A NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE)
![### Control System Steady State Error Analysis
**Problem Statement:**
For the control system shown in Figure 4, determine the steady-state error for a step input of 5 and for a ramp input with a slope of 10.
**System Description:**
The control system contains the following components:
1. A summing junction, taking \( R(s) \) as the input and producing the error signal.
2. A transfer function, \( \frac{k}{s^2 + 5s + 6} \), representing the system dynamics.
3. A feedback loop with a transfer function \( \frac{1}{s + 1} \).
**Figure 4:**
- **Input Signal \( R(s) \):** This is the initial input into the system.
- **Summing Junction:** This component adds the input signal \( R(s) \) and subtracts the feedback signal.
- **System Block:** Consists of the transfer function \( \frac{k}{s^2 + 5s + 6} \).
- **Output Signal \( C(s) \):** The output of the system before being fed back.
- **Feedback Loop:** The output passes through the transfer function \( \frac{1}{s + 1} \) and is fed back into the summing junction.
**Objective:**
- To calculate the steady-state error for a step input of magnitude 5.
- To calculate the steady-state error for a ramp input with a slope of 10.
---
To solve these problems, students will need to use concepts from control system theory such as steady-state error calculations, transfer function manipulation, and sensitivity functions. Detailed steps and assumptions must be provided to arrive at the solution for each type of input.
Reminder for Students:
- Review the final value theorem and apply it appropriately for both step and ramp inputs.
- Recall that steady-state error can be different for various types of inputs, depending on the type and order of the system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa22dd6ba-b194-4859-8383-05d4d2bb5a27%2F5e0f293b-4f99-43d4-99e7-b9d41094766d%2Fexu92xl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Control System Steady State Error Analysis
**Problem Statement:**
For the control system shown in Figure 4, determine the steady-state error for a step input of 5 and for a ramp input with a slope of 10.
**System Description:**
The control system contains the following components:
1. A summing junction, taking \( R(s) \) as the input and producing the error signal.
2. A transfer function, \( \frac{k}{s^2 + 5s + 6} \), representing the system dynamics.
3. A feedback loop with a transfer function \( \frac{1}{s + 1} \).
**Figure 4:**
- **Input Signal \( R(s) \):** This is the initial input into the system.
- **Summing Junction:** This component adds the input signal \( R(s) \) and subtracts the feedback signal.
- **System Block:** Consists of the transfer function \( \frac{k}{s^2 + 5s + 6} \).
- **Output Signal \( C(s) \):** The output of the system before being fed back.
- **Feedback Loop:** The output passes through the transfer function \( \frac{1}{s + 1} \) and is fed back into the summing junction.
**Objective:**
- To calculate the steady-state error for a step input of magnitude 5.
- To calculate the steady-state error for a ramp input with a slope of 10.
---
To solve these problems, students will need to use concepts from control system theory such as steady-state error calculations, transfer function manipulation, and sensitivity functions. Detailed steps and assumptions must be provided to arrive at the solution for each type of input.
Reminder for Students:
- Review the final value theorem and apply it appropriately for both step and ramp inputs.
- Recall that steady-state error can be different for various types of inputs, depending on the type and order of the system.
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