3. Sketch the root locus for the unity feedback system shown in Figure P8.3 for the following transfer functions: [Section: 8.4] K(s+2)(s+6) s2 + 8s + 25 а. G(s) - K(s² + 4) (s2 + 1) K(s? + 1) b. G(s) = с. G(s): K d. G(s) = (s+1)°(s+4)

3. Sketch the root locus for the unity feedback system shown in Figure P8.3 for the following transfer functions: [Section: 8.4] K(s+2)(s+6) s2 + 8s + 25 а. G(s) - K(s² + 4) (s2 + 1) K(s? + 1) b. G(s) = с. G(s): K d. G(s) = (s+1)°(s+4)

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

3. Sketch the root locus for the unity feedback system
shown in Figure P8.3 for the following transfer
functions: [Section: 8.4]
K(s+2)(s+6)
s2 + 8s + 25
а. G(s)
K(s² + 4)
(s² + 1)
K(s² + 1)
b. G(s)
c. G(s) =
K
d. G(s) =
(s+1)°(s+4)

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s+10 A unity feedback system has G(s) = K s4+20s³+132s²+128s-960 a. Build the R-H table. b. Find the range of K for a stable system. C. On what frequency (in rad/s) does the system oscillate when it is marginally stable?
16. Sketch the root locus for a unity-feedback system where Then find the following: [Section: 8.5] G (s) = K (8-2) (8-3) s(s+ 2) (8+3) a. The breakaway and break-in points b. The crossing of the jo-axis c. The range of K for closed-loop stability d. The value of K that will result in a stable system with complex conjugate poles and damping factor of 0.5
Ex. 453. G(s)=k(s+96)/(s(s+88)) is the FTF of a unity-feedback closed-loop system. Sketch the root locus with respect to k. Determine the number of asymptotes (N), number of root loci (M), the breakaway point (s=B) and the entry point (s=E). Answers: N,M,B, and E. ans:4
ASAP
P9.23 A closed-loop system has a loop transfer function K G,(8)G(s) = s(s + 5)(s + 10)" (a) Determine the gain K so that the phase nmargin is 60°. (b) For the gain K selected in part (a), determine the gain margin of the system.
3. In this problem, use the two closed loop systems given in the figure to answer the questions below. 4 R(s) K₁ 0.0099 In thin K₂ Y(s) R(s) K₁ 4 S(s) = 0.09 K₂ 0.09 (a) Show that these two systems have the same transfer function for K₁ = K₂ = 100 (b) Using the definition of sensitivity, S(s), for each system calculate the sensitivity to the parameter K₁ with K₁ and K₂ as variables. Recall: Y(s) OG G OG Gal (c) Substitute K₁ = K₂ = 100 into each S(s) and compare the sensitivities to parameter K₁.
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