Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
For the system shown below, find the values of K₁ and K₂ to yield a peak time of 1 second and a settling time of 2 seconds for the closed-loop system's step response. R(s) K₁ 10 FER s(s+2) K₂ s C(s)

For the system shown below, find the values of K₁ and K₂ to yield a peak time of 1 second and a settling time of 2 seconds for the closed-loop system's step response. R(s) K₁ 10 FER s(s+2) K₂ s C(s)

Introductory Circuit Analysis (13th Edition)
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...
See similar textbooks
icon
Related questions
Question

Thanks

For the system shown below, find the values of \( K_1 \) and \( K_2 \) to yield a peak time of 1 second and a settling time of 2 seconds for the closed-loop system's step response. **Block Diagram Explained:** 1. **Input Signal (R(s)):** - This is the reference input to the system. 2. **Summing Junction:** - The first summing junction has two inputs: R(s) and the feedback signal from the output. The feedback signal is subtracted from R(s). 3. **Gain Block (K₁):** - The output of the summing junction is passed through a gain block with a gain of \( K_1 \). 4. **Second Summing Junction:** - The output from the gain \( K_1 \) is combined with the feedback signal that passes through another block. 5. **Transfer Function Block:** - Contains \( \frac{10}{s(s+2)} \), indicating the system's dynamics. 6. **Output Signal (C(s)):** - This is the output of the system, which is fed back into the system. 7. **Feedback Path and Gain Block (K₂s):** - The output \( C(s) \) is multiplied by \( K_2 \) and \( s \) as feedback, which is fed into the second summing junction. **Goal:** - Calculate the values of \( K_1 \) and \( K_2 \) such that: - The peak time (\( T_p \)) is 1 second. - The settling time (\( T_s \)) is 2 seconds. This is a classic control systems problem aimed at tuning a feedback control system to meet specific dynamic performance criteria.
Transcribed Image Text:For the system shown below, find the values of \( K_1 \) and \( K_2 \) to yield a peak time of 1 second and a settling time of 2 seconds for the closed-loop system's step response. **Block Diagram Explained:** 1. **Input Signal (R(s)):** - This is the reference input to the system. 2. **Summing Junction:** - The first summing junction has two inputs: R(s) and the feedback signal from the output. The feedback signal is subtracted from R(s). 3. **Gain Block (K₁):** - The output of the summing junction is passed through a gain block with a gain of \( K_1 \). 4. **Second Summing Junction:** - The output from the gain \( K_1 \) is combined with the feedback signal that passes through another block. 5. **Transfer Function Block:** - Contains \( \frac{10}{s(s+2)} \), indicating the system's dynamics. 6. **Output Signal (C(s)):** - This is the output of the system, which is fed back into the system. 7. **Feedback Path and Gain Block (K₂s):** - The output \( C(s) \) is multiplied by \( K_2 \) and \( s \) as feedback, which is fed into the second summing junction. **Goal:** - Calculate the values of \( K_1 \) and \( K_2 \) such that: - The peak time (\( T_p \)) is 1 second. - The settling time (\( T_s \)) is 2 seconds. This is a classic control systems problem aimed at tuning a feedback control system to meet specific dynamic performance criteria.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Root Locus
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)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS