design a feedback control system which results in a closed system that reaches a commaned Өc with a transient response for the given DC motor that will be given below Damping ratio is 0.6 natural frequency is 10 rad/sec
design a feedback control system which results in a closed system that reaches a commaned Өc with a transient response for the given DC motor that will be given below Damping ratio is 0.6 natural frequency is 10 rad/sec
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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design a feedback control system which results in a closed system that reaches a commaned Өc with a transient response for the given DC motor that will be given below
Damping ratio is 0.6
natural frequency is 10 rad/sec
![The equation depicted in the image is a transfer function, which is a mathematical representation used in control systems to model the relationship between the input and output of a system in the Laplace domain.
The transfer function given is:
\[
\frac{\Theta(s)}{V_{in}(s)} = \frac{200}{5(s + 16)}
\]
### Components of the Equation:
- \(\Theta(s)\): Represents the output of the system in the Laplace domain.
- \(V_{in}(s)\): Represents the input to the system in the Laplace domain.
- \(\frac{200}{5(s + 16)}\): This is the system's transfer function, which defines how the input \(V_{in}(s)\) is transformed into the output \(\Theta(s)\).
### Explanation:
- **Transfer Function**: The form \( \frac{200}{5(s + 16)} \) suggests a first-order system where the output is affected by a pole at \( s = -16 \). The constant \(200\) is the gain, and when divided by the factor of \(5\), it scales the response of the system.
- **System Behavior**: This transfer function can be used to analyze the time response of the system, stability, and frequency response characteristics in various control system applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbb5604a-0a4b-46ed-92e3-55159cd22786%2F07373ad3-c424-4d84-8673-b959b7ed2a49%2Fq1pi0ol_processed.png&w=3840&q=75)
Transcribed Image Text:The equation depicted in the image is a transfer function, which is a mathematical representation used in control systems to model the relationship between the input and output of a system in the Laplace domain.
The transfer function given is:
\[
\frac{\Theta(s)}{V_{in}(s)} = \frac{200}{5(s + 16)}
\]
### Components of the Equation:
- \(\Theta(s)\): Represents the output of the system in the Laplace domain.
- \(V_{in}(s)\): Represents the input to the system in the Laplace domain.
- \(\frac{200}{5(s + 16)}\): This is the system's transfer function, which defines how the input \(V_{in}(s)\) is transformed into the output \(\Theta(s)\).
### Explanation:
- **Transfer Function**: The form \( \frac{200}{5(s + 16)} \) suggests a first-order system where the output is affected by a pole at \( s = -16 \). The constant \(200\) is the gain, and when divided by the factor of \(5\), it scales the response of the system.
- **System Behavior**: This transfer function can be used to analyze the time response of the system, stability, and frequency response characteristics in various control system applications.
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