Given the following feedback control system, a. Find the system type b. Find the static constants (Kp, Kv, and Ka) c. Find the value of K that will yield a steady-state error = 0.35
Given the following feedback control system, a. Find the system type b. Find the static constants (Kp, Kv, and Ka) c. Find the value of K that will yield a steady-state error = 0.35
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![### Feedback Control System Analysis
Given the following feedback control system, analyze and determine:
a. The system type.
b. The static constants \( K_p \), \( K_v \), and \( K_a \).
c. The value of \( K \) that will yield a steady-state error of 0.35.
#### System Diagram
The system diagram is represented as follows:
1. **Input (R(s))**: The reference input signal to the system.
2. **Summing Junction**: The reference signal \( R(s) \) is subtracted from the feedback signal to produce the error signal.
3. **Gain Block (K)**: Multiplies the error signal by a gain constant \( K \).
4. **First Transfer Function Block**:
\[
\frac{s + 6}{s^2 +10s + 21}
\]
5. **Second Transfer Function Block**:
\[
\frac{s + 2}{s(s + 1)}
\]
6. **Output (C(s))**: The output response of the system.
7. **Feedback Loop**: The output \( C(s) \) is fed back to the summing junction to form a closed-loop system.
#### Steps to Follow
1. **Determine System Type**:
- The system type is determined by the number of integrations (poles at the origin) in the open-loop transfer function.
2. **Find Static Constants**:
- \( K_p \): Position error constant.
- \( K_v \): Velocity error constant.
- \( K_a \): Acceleration error constant.
3. **Calculate the Value of \( K \) for Desired Steady-State Error**:
- Use the given steady-state error requirement and the form of the system to solve for the gain \( K \).
This analysis is crucial for understanding the behavior of the feedback control system, and its ability to meet desired performance specifications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe36fb7f7-6381-4add-b52b-9085dfd27844%2F04bac544-33cf-4bfa-b736-52dfe239c8bc%2Fpvgb8ru_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Feedback Control System Analysis
Given the following feedback control system, analyze and determine:
a. The system type.
b. The static constants \( K_p \), \( K_v \), and \( K_a \).
c. The value of \( K \) that will yield a steady-state error of 0.35.
#### System Diagram
The system diagram is represented as follows:
1. **Input (R(s))**: The reference input signal to the system.
2. **Summing Junction**: The reference signal \( R(s) \) is subtracted from the feedback signal to produce the error signal.
3. **Gain Block (K)**: Multiplies the error signal by a gain constant \( K \).
4. **First Transfer Function Block**:
\[
\frac{s + 6}{s^2 +10s + 21}
\]
5. **Second Transfer Function Block**:
\[
\frac{s + 2}{s(s + 1)}
\]
6. **Output (C(s))**: The output response of the system.
7. **Feedback Loop**: The output \( C(s) \) is fed back to the summing junction to form a closed-loop system.
#### Steps to Follow
1. **Determine System Type**:
- The system type is determined by the number of integrations (poles at the origin) in the open-loop transfer function.
2. **Find Static Constants**:
- \( K_p \): Position error constant.
- \( K_v \): Velocity error constant.
- \( K_a \): Acceleration error constant.
3. **Calculate the Value of \( K \) for Desired Steady-State Error**:
- Use the given steady-state error requirement and the form of the system to solve for the gain \( K \).
This analysis is crucial for understanding the behavior of the feedback control system, and its ability to meet desired performance specifications.
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