2. Consider the following system. 1+ K 1 s(s² + 4s +13) = 0 (a) Draw the root locus. (b) Use Routh's criterion to find the range of the gain K for which the closed-loop system is stable. (c) The range of K for which the system is stable can also be obtained by finding a point of the root locus that crosses the Imaginary axis. When you have an Im-axis crossing, the point is given by s = jw. Find the values of and K at that crossing point. (Hint: The point s = ja must satisfy the closed-loop characteristic equation above since it's on the root locus.) (d) Confirm your calculations with a Matlab root locus plot.

2. Consider the following system. 1+ K 1 s(s² + 4s +13) = 0 (a) Draw the root locus. (b) Use Routh's criterion to find the range of the gain K for which the closed-loop system is stable. (c) The range of K for which the system is stable can also be obtained by finding a point of the root locus that crosses the Imaginary axis. When you have an Im-axis crossing, the point is given by s = jw. Find the values of and K at that crossing point. (Hint: The point s = ja must satisfy the closed-loop characteristic equation above since it's on the root locus.) (d) Confirm your calculations with a Matlab root locus plot.

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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Question

2. Consider the following system.
1+K
1
s(s² + 4s +13)
= 0
(a) Draw the root locus.
(b) Use Routh's criterion to find the range of the gain K for which the closed-loop system is stable.
(c) The range of K for which the system is stable can also be obtained by finding a point of the root locus
that crosses the Imaginary axis. When you have an Im-axis crossing, the point is given by s = jw. Find
the values of wand K at that crossing point. (Hint: The point s = ja must satisfy the closed-loop
characteristic equation above since it's on the root locus.)
(d) Confirm your calculations with a Matlab root locus plot.

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Step 1: State the given data

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Step 2: a) Finding the centroid and angle of asymptotes

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Step 3: Finding the root locus branches

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Step 4: Finding the imaginary axis crossing points

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Step 5: Finding the angle of departure at complex poles

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Step 6: Drawing the root locus

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Step 7: b) Finding the range of 'K' for closed loop system stability using Routh's criterion

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Step 8: c) Finding the range of 'K' for closed loop system stability using root locus

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