Use engineering paper to sketch the root locus plot for the characteristic equation s3 + 16s? + 63s + 1 = 0 and ensure that the following points are addressed: 1. Write the characteristic equation in the standard form 1+ KP(s) = 0. 2. Determine the poles and zeros and identify poles and zeros on the plot with x's and o's respectively. Use the same scale for both axes and label them properly. 3. Sketch the root locus on the real axis. 4. Solve the characteristic equation for K. 5. Determine any breakaway or breakin points and identify them on the plot. Show your work. 6. Determine the value(s) of K at any breakaway or breakin points. 7. Determine the angles and intersectian points for asymptotes and identify them on the plot. Show your work. 8. Determine any crossover points. Show your work. 9. Determine the value(s) of K at any crossover points.
Use engineering paper to sketch the root locus plot for the characteristic equation s3 + 16s? + 63s + 1 = 0 and ensure that the following points are addressed: 1. Write the characteristic equation in the standard form 1+ KP(s) = 0. 2. Determine the poles and zeros and identify poles and zeros on the plot with x's and o's respectively. Use the same scale for both axes and label them properly. 3. Sketch the root locus on the real axis. 4. Solve the characteristic equation for K. 5. Determine any breakaway or breakin points and identify them on the plot. Show your work. 6. Determine the value(s) of K at any breakaway or breakin points. 7. Determine the angles and intersectian points for asymptotes and identify them on the plot. Show your work. 8. Determine any crossover points. Show your work. 9. Determine the value(s) of K at any crossover points.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Use engineering paper to sketch the root locus plot for the characteristic equation
s3 + 16s2 + 63s +1 = 0 and ensure that the following points are addressed:
1. Write the characteristic equation in the standard form 1+ KP(s) = 0.
2. Determine the poles and zeros and identify poles and zeros on the plot with
x's and o's respectively. Use the same scale for both axes and label them
properly.
3. Sketch the root locus on the real axis.
4. Solve the characteristic equation for K.
5. Determine any breakaway or breakin points and identify them on the plot.
Show your work.
6. Determine the value(s) of K at any breakaway or breakin points.
7. Determine the angles and intersectian points for asymptotes and identify
them on the plot. Show your work.
8. Determine any crossover points. Show your work.
9. Determine the value(s) of K at any crossover points.
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