Consider a feedback-based causal LTI system with input x(t) shown in Figure 6.41, where G(s) is the transfer function of a "loop filter" and 1/s is an integrator. The idea is to use the error e(t) to drive these, so as to make y(t) track x(t). Y(s) X(s) E(s) (a) Find the transfer functions H(s) = X (8) and He(s) = X(3) (b) Now set G(s) = 10. This is termed “proportional feedback,” where the feedback is propor- tional to the error. (i) Find y(t) and e(t) for x(t) = sin 10t. = (ii) How do your answers change (provide a qualitative discussion) for x(t) = sint and x(t) = sin 100t? (iii) For x(t) = u(t) (unit step), find and sketch y(t) and e(t), and specify their asymptotic values as t∞. (iv) For x(t) = tu(t) (ramp starting at time zero), find the asymptotic value of the error e(t) as t→ ∞. Hint: You can simply use the final value theorem in (iii). 2 (c) Redo (b)(iv) for G(s) = 10+ ("proportional plus integral" feedback). S

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...
icon
Related questions
Question

i only want part b and c please. i want a step by step solution and explanation 

Consider a feedback-based causal LTI system with input x(t) shown in Figure
6.41, where G(s) is the transfer function of a "loop filter" and 1/s is an integrator. The idea is
to use the error e(t) to drive these, so as to make y(t) track x(t).
(a) Find the transfer functions H(s) =
Y(s)
X(s)
and He(s) =
=
E(s)
X(s)*
(b) Now set G(s) = 10. This is termed “proportional feedback," where the feedback is propor-
tional to the error.
(i) Find y(t) and e(t) for x(t)
sin 10t.
(ii) How do your answers change (provide a qualitative discussion) for x(t)
sin 100t?
=
sint and x(t)
(iii) For x(t) = u(t) (unit step), find and sketch y(t) and e(t), and specify their asymptotic values
as t∞.
(iv) For x(t) = tu(t) (ramp starting at time zero), find the asymptotic value of the error e(t) as
t → ∞.
Hint: You can simply use the final value theorem in (iii).
(c) Redo (b)(iv) for G(s) = 10+ 2/3 ("proportional plus integral" feedback).
Transcribed Image Text:Consider a feedback-based causal LTI system with input x(t) shown in Figure 6.41, where G(s) is the transfer function of a "loop filter" and 1/s is an integrator. The idea is to use the error e(t) to drive these, so as to make y(t) track x(t). (a) Find the transfer functions H(s) = Y(s) X(s) and He(s) = = E(s) X(s)* (b) Now set G(s) = 10. This is termed “proportional feedback," where the feedback is propor- tional to the error. (i) Find y(t) and e(t) for x(t) sin 10t. (ii) How do your answers change (provide a qualitative discussion) for x(t) sin 100t? = sint and x(t) (iii) For x(t) = u(t) (unit step), find and sketch y(t) and e(t), and specify their asymptotic values as t∞. (iv) For x(t) = tu(t) (ramp starting at time zero), find the asymptotic value of the error e(t) as t → ∞. Hint: You can simply use the final value theorem in (iii). (c) Redo (b)(iv) for G(s) = 10+ 2/3 ("proportional plus integral" feedback).
x(t) —
e(t)
G(s)
y(t)
1/s
Transcribed Image Text:x(t) — e(t) G(s) y(t) 1/s
Expert Solution
steps

Step by step

Solved in 8 steps with 50 images

Blurred answer
Knowledge Booster
Mason’s Rule & Block Diagram Reduction
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.
Similar questions
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,