For the system given below determine: b. C. Find the mathematical expression of E(s) as a function of R(s) Calculate the Steady-state positional error using the Final Value Theorem (Hint: lim f(t) = lim SF (s)) [-00 $40 What is the "Type" of this system? R(s) + E(s) G(s) C(s) T= S 5+10 1 + $
For the system given below determine: b. C. Find the mathematical expression of E(s) as a function of R(s) Calculate the Steady-state positional error using the Final Value Theorem (Hint: lim f(t) = lim SF (s)) [-00 $40 What is the "Type" of this system? R(s) + E(s) G(s) C(s) T= S 5+10 1 + $
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
Related questions
Question
This is a part of a review I'm studying, NOT a graded assignment, please do not reject. Thank you!
Am I doing this problem right? I would like someone to verify I'm doing this correctly, thank you!
![### Analysis of a Control System
#### Problem Statement
For the given system, determine the following:
a. Find the mathematical expression of \(E(s)\) as a function of \(R(s)\).
b. Calculate the steady-state positional error using the Final Value Theorem (Hint: \(\lim_{t \to \infty} f(t) = \lim_{s \to 0} sF(s)\)).
c. Determine the “Type” of this system.
#### System Diagram
- **Components**: The system involves \(R(s)\), \(E(s)\), a feedback loop with a transfer function \(G(s)\), and output \(C(s)\).
- **Block Diagram**: \(G(s) = \frac{5}{s+10}\).
- **Transfer Function**:
- Total Transfer Function \(T = \frac{\frac{5}{s+10}}{1 + \frac{5}{s+10}} = \frac{5}{s+15} = \frac{C}{R}\).
- Relationship derived: \(\frac{W}{R} = \frac{1}{s+15}\).
#### Solutions
a. **Expression for \(E(s)\)**:
\[
E(s) = R(s) \cdot \left( \frac{5}{s+15} \right)
\]
This equation highlights the dependence of the error function \(E(s)\) on the reference input \(R(s)\).
b. **Steady-State Positional Error**:
- Apply the Final Value Theorem: \(\lim_{t \to \infty} f(t) = \lim_{s \to 0} sF(s)\).
- Calculate \(K_p\):
\[
K_p = \lim_{s \to 0} G(s) = \lim_{s \to 0} \frac{5}{s+10} = \frac{1}{2}
\]
- Steady-state error \(e_{ss}\):
\[
e_{ss} = \frac{A}{1 + K_p} = \frac{E}{1 + \lim_{s \to 0} 5 \left(\frac{5}{s}\right)}
\]
\[
e_{ss} = \frac{0.3}{1.5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecd9d238-92a1-4a47-af9e-c758e887edd1%2Fb8280392-a27b-47c3-9dad-0b558f096f47%2Fe5gijeh_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of a Control System
#### Problem Statement
For the given system, determine the following:
a. Find the mathematical expression of \(E(s)\) as a function of \(R(s)\).
b. Calculate the steady-state positional error using the Final Value Theorem (Hint: \(\lim_{t \to \infty} f(t) = \lim_{s \to 0} sF(s)\)).
c. Determine the “Type” of this system.
#### System Diagram
- **Components**: The system involves \(R(s)\), \(E(s)\), a feedback loop with a transfer function \(G(s)\), and output \(C(s)\).
- **Block Diagram**: \(G(s) = \frac{5}{s+10}\).
- **Transfer Function**:
- Total Transfer Function \(T = \frac{\frac{5}{s+10}}{1 + \frac{5}{s+10}} = \frac{5}{s+15} = \frac{C}{R}\).
- Relationship derived: \(\frac{W}{R} = \frac{1}{s+15}\).
#### Solutions
a. **Expression for \(E(s)\)**:
\[
E(s) = R(s) \cdot \left( \frac{5}{s+15} \right)
\]
This equation highlights the dependence of the error function \(E(s)\) on the reference input \(R(s)\).
b. **Steady-State Positional Error**:
- Apply the Final Value Theorem: \(\lim_{t \to \infty} f(t) = \lim_{s \to 0} sF(s)\).
- Calculate \(K_p\):
\[
K_p = \lim_{s \to 0} G(s) = \lim_{s \to 0} \frac{5}{s+10} = \frac{1}{2}
\]
- Steady-state error \(e_{ss}\):
\[
e_{ss} = \frac{A}{1 + K_p} = \frac{E}{1 + \lim_{s \to 0} 5 \left(\frac{5}{s}\right)}
\]
\[
e_{ss} = \frac{0.3}{1.5
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 5 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,