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R(s) C(s) G(s) H(s) A. Find the equivalent transfer function of the negative feedback system if G(s) = K s(s+2)2 and H(s) = 1 B. Find a value of gain, K, that will yield closed-loop, overdamped, second-order poles. C. Find a value of gain, K, that will yield closed-loop, underdamped, second-order poles. D. Find the value of gain, K, that will make the system critically damped. E. Find the value of gain, K, that will make the system marginally stable. Also, find the frequency of oscillation at that value of K that makes the system marginally stable. F. Plot on one graph the pole locations for each case and write the corresponding value of gain, K, at each pole.

R(s) C(s) G(s) H(s) A. Find the equivalent transfer function of the negative feedback system if G(s) = K s(s+2)2 and H(s) = 1 B. Find a value of gain, K, that will yield closed-loop, overdamped, second-order poles. C. Find a value of gain, K, that will yield closed-loop, underdamped, second-order poles. D. Find the value of gain, K, that will make the system critically damped. E. Find the value of gain, K, that will make the system marginally stable. Also, find the frequency of oscillation at that value of K that makes the system marginally stable. F. Plot on one graph the pole locations for each case and write the corresponding value of gain, K, at each pole.

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...
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Please only do part E and F. 

Please show your work and be as detailed as possible. Please explain the relationship between K the gain and stability of the system. Also, show how to plot the poles and why they are on either the real or imaginary axis. What is it about the example that indicated that?

thank you

R(s) C(s) G(s) H(s) A. Find the equivalent transfer function of the negative feedback system if G(s) = K s(s+2)2 and H(s) = 1 B. Find a value of gain, K, that will yield closed-loop, overdamped, second-order poles. C. Find a value of gain, K, that will yield closed-loop, underdamped, second-order poles. D. Find the value of gain, K, that will make the system critically damped. E. Find the value of gain, K, that will make the system marginally stable. Also, find the frequency of oscillation at that value of K that makes the system marginally stable. F. Plot on one graph the pole locations for each case and write the corresponding value of gain, K, at each pole.
Transcribed Image Text:R(s) C(s) G(s) H(s) A. Find the equivalent transfer function of the negative feedback system if G(s) = K s(s+2)2 and H(s) = 1 B. Find a value of gain, K, that will yield closed-loop, overdamped, second-order poles. C. Find a value of gain, K, that will yield closed-loop, underdamped, second-order poles. D. Find the value of gain, K, that will make the system critically damped. E. Find the value of gain, K, that will make the system marginally stable. Also, find the frequency of oscillation at that value of K that makes the system marginally stable. F. Plot on one graph the pole locations for each case and write the corresponding value of gain, K, at each pole.
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