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Consider the system shown below. We want to sketch the root locus of this system as the parameter a varies from zero to infinity. R(s) s+α s+8 10 s(s+1) C(s) (a) Convert the characteristic equation into a proper form, (b) Find the asymptotes and show them in the s-plane, (c) Determine the breakaway or re-entry points, if any, (d) Determine the range of a for which the system is stable. Also, determine the points where root-locus branches cross the jw-axis, and (e) Sketch the root locus.

Consider the system shown below. We want to sketch the root locus of this system as the parameter a varies from zero to infinity. R(s) s+α s+8 10 s(s+1) C(s) (a) Convert the characteristic equation into a proper form, (b) Find the asymptotes and show them in the s-plane, (c) Determine the breakaway or re-entry points, if any, (d) Determine the range of a for which the system is stable. Also, determine the points where root-locus branches cross the jw-axis, and (e) Sketch the root locus.

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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Consider the system shown below. We want to sketch the root locus of this system as the parameter a varies from zero to infinity. R(s) s+α s+8 10 s(s+1) C(s) (a) Convert the characteristic equation into a proper form, (b) Find the asymptotes and show them in the s-plane, (c) Determine the breakaway or re-entry points, if any, (d) Determine the range of a for which the system is stable. Also, determine the points where root-locus branches cross the jw-axis, and (e) Sketch the root locus.
Transcribed Image Text:Consider the system shown below. We want to sketch the root locus of this system as the parameter a varies from zero to infinity. R(s) s+α s+8 10 s(s+1) C(s) (a) Convert the characteristic equation into a proper form, (b) Find the asymptotes and show them in the s-plane, (c) Determine the breakaway or re-entry points, if any, (d) Determine the range of a for which the system is stable. Also, determine the points where root-locus branches cross the jw-axis, and (e) Sketch the root locus.
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