4. For the system in figure (a) as shownR(s) +K(s + 1)(s + 2)(s + 3)(s + 4)(a)R(s) +K(s + a)Cls)(s + 1)(s + 2)(s + 3)(x + 4)(b)sketch the root locus and do the following.a. Find the asymptotes.b. Find the breakaway points.c. Find the range of K for stability.d. Find the value of K to yield a 0.7 damping ratio for the dominant second-order pair.e. To improve stability, we desire the root locus to cross the jw-axis at j5.5. To accomplish this, the open-loop transfer funcion is cascadedwith a zero, as shown in figure (b). Find the value of a and sketch the new root locus.f. Repeat part (c) for the new root locus.g. Compare the results of part (c) and part (f). What improvement in transient response do you notice?

Answered: Image /qna-images/answer/e3c9fd5b-a99f-4811-be19-0a38f2e0de5a.jpg

4. For the system in figure (a) as shown RS) K Cs) (s+ 1Xs +2)(s + 3(s+ 4) (a) Rs) K(s + a) Cs) s+ 1Xs + 2(s+3)s+ 4) (b) sketch the root locus and do the following. a. Find the asymptotes. b. Find the breakaway points. c. Find the range of K for stability.

4. For the system in figure (a) as shown RS) K Cs) (s+ 1Xs +2)(s + 3(s+ 4) (a) Rs) K(s + a) Cs) s+ 1Xs + 2(s+3)s+ 4) (b) sketch the root locus and do the following. a. Find the asymptotes. b. Find the breakaway points. c. Find the range of K for stability.

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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Concept explainers

Sinusoids And Phasors

Sinusoids are defined as the mathematical waveforms that are used to describe the nature of periodic oscillations.

Circuit Theory

Electric circuits are a network that comprises of a closed-loop, which helps in providing a return path for the current through a switch. When the switch is activated, the load operates, and the current accepts a path to finish the circuit at a low potential level from the opposing high potential level. Electric circuits theory is a linear analysis that helps in establishing a linear relation of voltage and current for R (resistance), L (inductance), and C (capacitance).

Question

4. For the system in figure (a) as shown
R(s) +
K
(s + 1)(s + 2)(s + 3)(s + 4)
(a)
R(s) +
K(s + a)
Cls)
(s + 1)(s + 2)(s + 3)(x + 4)
(b)
sketch the root locus and do the following.
a. Find the asymptotes.
b. Find the breakaway points.
c. Find the range of K for stability.
d. Find the value of K to yield a 0.7 damping ratio for the dominant second-order pair.
e. To improve stability, we desire the root locus to cross the jw-axis at j5.5. To accomplish this, the open-loop transfer funcion is cascaded
with a zero, as shown in figure (b). Find the value of a and sketch the new root locus.
f. Repeat part (c) for the new root locus.
g. Compare the results of part (c) and part (f). What improvement in transient response do you notice?

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