Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
Four systems are represented by the transfer functions given below. A. GA(S) = C. Gc(s) = 20 2s + 1 B. GB(s)=2+40s +400 24000 3s2+36s + 1200 D. GD(s) = 8000 48000 3s2 + 12s + 4800 Your tasks: A. Find the time constant of GA. B. Find the natural frequency, wn, and damping ratio, C, of the 2nd order transfer functions: GB, GC, GD C. Match the Transfer Functions given in the problem statement with their respective step responses. Be aware of the axis limits for the step functions, as they are unique. • For each of the four systems, format your answers in the following form: Gx-step-y Provide justification (no more than a sentence) to explain your choice (for each system). Amplitude Amplitude 20 15 5 0 30 20 10 0 0 Step Response 1 0.2 Time (seconds) Step Response 3 0.4 0.2 0.4 0.6 0.8 Time (seconds) Amplitude Amplitude 20 0 20 15 0 0 0 Step Response 2 1 2 Time (seconds) Step Response 4 5 10 Time (seconds) 15 3

Four systems are represented by the transfer functions given below. A. GA(S) = C. Gc(s) = 20 2s + 1 B. GB(s)=2+40s +400 24000 3s2+36s + 1200 D. GD(s) = 8000 48000 3s2 + 12s + 4800 Your tasks: A. Find the time constant of GA. B. Find the natural frequency, wn, and damping ratio, C, of the 2nd order transfer functions: GB, GC, GD C. Match the Transfer Functions given in the problem statement with their respective step responses. Be aware of the axis limits for the step functions, as they are unique. • For each of the four systems, format your answers in the following form: Gx-step-y Provide justification (no more than a sentence) to explain your choice (for each system). Amplitude Amplitude 20 15 5 0 30 20 10 0 0 Step Response 1 0.2 Time (seconds) Step Response 3 0.4 0.2 0.4 0.6 0.8 Time (seconds) Amplitude Amplitude 20 0 20 15 0 0 0 Step Response 2 1 2 Time (seconds) Step Response 4 5 10 Time (seconds) 15 3

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
### Transfer Function Analysis **Four systems are represented by the transfer functions given below:** - **A.** \( G_A(s) = \frac{20}{2s + 1} \) - **B.** \( G_B(s) = \frac{8000}{s^2 + 40s + 400} \) - **C.** \( G_C(s) = \frac{24000}{3s^2 + 36s + 1200} \) - **D.** \( G_D(s) = \frac{48000}{3s^2 + 12s + 4800} \) --- ### Your Tasks: **A.** Find the time constant of \( G_A \). **B.** Find the natural frequency, \( \omega_n \), and damping ratio, \( \zeta \), of the second-order transfer functions: \( G_B, G_C, G_D \). **C.** Match the transfer functions with their respective step responses. Be aware of the axis limits for the step functions, as they are unique. - Format answers in the form: \( G_X - \text{step-y} \). - Provide justification (no more than a sentence) for each choice. --- ### Step Responses: **Step Response 1:** - **Graph Description:** A gradual curve starting at 0 and settling around 17. It approaches the final value over time with no oscillations. - **Axes:** - X-axis: Time (seconds) from 0 to 0.5 - Y-axis: Amplitude from 0 to 20 **Step Response 2:** - **Graph Description:** An oscillatory response that eventually settles. Initial amplitude is about 20, showing decay over time. - **Axes:** - X-axis: Time (seconds) from 0 to 3 - Y-axis: Amplitude from 0 to 20 **Step Response 3:** - **Graph Description:** Shows quick oscillations, stabilizing around a constant amplitude after a short time. - **Axes:** - X-axis: Time (seconds) from 0 to 1 - Y-axis: Amplitude from 0 to 10 **Step Response 4:** - **Graph Description:** A slow curve increasing from 0 to about 20, approaching final value with no overs
Transcribed Image Text:### Transfer Function Analysis **Four systems are represented by the transfer functions given below:** - **A.** \( G_A(s) = \frac{20}{2s + 1} \) - **B.** \( G_B(s) = \frac{8000}{s^2 + 40s + 400} \) - **C.** \( G_C(s) = \frac{24000}{3s^2 + 36s + 1200} \) - **D.** \( G_D(s) = \frac{48000}{3s^2 + 12s + 4800} \) --- ### Your Tasks: **A.** Find the time constant of \( G_A \). **B.** Find the natural frequency, \( \omega_n \), and damping ratio, \( \zeta \), of the second-order transfer functions: \( G_B, G_C, G_D \). **C.** Match the transfer functions with their respective step responses. Be aware of the axis limits for the step functions, as they are unique. - Format answers in the form: \( G_X - \text{step-y} \). - Provide justification (no more than a sentence) for each choice. --- ### Step Responses: **Step Response 1:** - **Graph Description:** A gradual curve starting at 0 and settling around 17. It approaches the final value over time with no oscillations. - **Axes:** - X-axis: Time (seconds) from 0 to 0.5 - Y-axis: Amplitude from 0 to 20 **Step Response 2:** - **Graph Description:** An oscillatory response that eventually settles. Initial amplitude is about 20, showing decay over time. - **Axes:** - X-axis: Time (seconds) from 0 to 3 - Y-axis: Amplitude from 0 to 20 **Step Response 3:** - **Graph Description:** Shows quick oscillations, stabilizing around a constant amplitude after a short time. - **Axes:** - X-axis: Time (seconds) from 0 to 1 - Y-axis: Amplitude from 0 to 10 **Step Response 4:** - **Graph Description:** A slow curve increasing from 0 to about 20, approaching final value with no overs
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Routh Hurwitz Criteria
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