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2. A system has an open-loop transfer function given by s2 + 6s + 18 G(s) 82 along with a negative feedback gain H(s) = K. %3D (a) How many branches does the root locus of the feedback system consist of? Where does each branch end to as K + oo? (b) For any K > 0, which category does this closed-loop system belong to: over-, critical-, or under-damping? (c) Convert it to a state-space oquation in controllable canonical form in terms of K; (d) For K > 0, does the point s = -0.5 belong to the root loci of the closed-loop system? Why?

2. A system has an open-loop transfer function given by s2 + 6s + 18 G(s) 82 along with a negative feedback gain H(s) = K. %3D (a) How many branches does the root locus of the feedback system consist of? Where does each branch end to as K + oo? (b) For any K > 0, which category does this closed-loop system belong to: over-, critical-, or under-damping? (c) Convert it to a state-space oquation in controllable canonical form in terms of K; (d) For K > 0, does the point s = -0.5 belong to the root loci of the closed-loop system? Why?

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
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2. A system has an open-loop transfer function given by s2 + 6s + 18 G(s) 82 along with a negative feedback gain H(s) = K. %3D (a) How many branches does the root locus of the feedback system consist of? Where does each branch end to as K + oo? (b) For any K > 0, which category does this closed-loop system belong to: over-, critical-, or under-damping? (c) Convert it to a state-space oquation in controllable canonical form in terms of K; (d) For K > 0, does the point s = -0.5 belong to the root loci of the closed-loop system? Why?
Transcribed Image Text:2. A system has an open-loop transfer function given by s2 + 6s + 18 G(s) 82 along with a negative feedback gain H(s) = K. %3D (a) How many branches does the root locus of the feedback system consist of? Where does each branch end to as K + oo? (b) For any K > 0, which category does this closed-loop system belong to: over-, critical-, or under-damping? (c) Convert it to a state-space oquation in controllable canonical form in terms of K; (d) For K > 0, does the point s = -0.5 belong to the root loci of the closed-loop system? Why?
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