P9.21 Consider a unity feedback system with the loop transfer function K G(s)G(s) %3D s(s + 1)(s + 4)' (a) For K = 4. Determine the gain margin. (b) the value of K required to pro-vide a gain margin equal to 12 dB, and (c) the value of K to yield a steady-state error of 25% of the magni-tude A for the ramp input r(t) = At, t > 0. Can this gain be utilized and achieve acceptable performance?
P9.21 Consider a unity feedback system with the loop transfer function K G(s)G(s) %3D s(s + 1)(s + 4)' (a) For K = 4. Determine the gain margin. (b) the value of K required to pro-vide a gain margin equal to 12 dB, and (c) the value of K to yield a steady-state error of 25% of the magni-tude A for the ramp input r(t) = At, t > 0. Can this gain be utilized and achieve acceptable performance?
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![**Problem P9.21: Analysis of a Unity Feedback System**
Consider a unity feedback system with the loop transfer function given by:
\[
G_c(s)G(s) = \frac{K}{s(s + 1)(s + 4)}
\]
**Tasks:**
(a) For \( K = 4 \), determine the gain margin.
(b) Find the value of \( K \) required to provide a gain margin equal to 12 dB.
(c) Determine the value of \( K \) necessary to achieve a steady-state error of 25% of the magnitude \( A \) for the ramp input \( r(t) = At \), \( t > 0 \).
*Question: Can this gain be utilized and achieve acceptable performance?*
**Note:** Gain margin and steady-state error are critical in understanding the stability and accuracy of the system responses. Explore these calculations to ensure optimal system performance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb6e49c2-d01d-4438-a99a-92f670cec770%2F0149136c-8609-4266-a541-5812f927018c%2Fcncibo_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem P9.21: Analysis of a Unity Feedback System**
Consider a unity feedback system with the loop transfer function given by:
\[
G_c(s)G(s) = \frac{K}{s(s + 1)(s + 4)}
\]
**Tasks:**
(a) For \( K = 4 \), determine the gain margin.
(b) Find the value of \( K \) required to provide a gain margin equal to 12 dB.
(c) Determine the value of \( K \) necessary to achieve a steady-state error of 25% of the magnitude \( A \) for the ramp input \( r(t) = At \), \( t > 0 \).
*Question: Can this gain be utilized and achieve acceptable performance?*
**Note:** Gain margin and steady-state error are critical in understanding the stability and accuracy of the system responses. Explore these calculations to ensure optimal system performance.
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