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Use Routh's Criterion to determine the stability characteristics of the following systems. In each case determine the number of positive roots. i) s² + 4s + 1 = 0, ii) s³ + 4s2 + 5s + 6 = 0, iii) s³ + 3s² – 6s + 10 = 0, iv) s* + s + 2s² + 4s + 8 = 0

Use Routh's Criterion to determine the stability characteristics of the following systems. In each case determine the number of positive roots. i) s² + 4s + 1 = 0, ii) s³ + 4s2 + 5s + 6 = 0, iii) s³ + 3s² – 6s + 10 = 0, iv) s* + s + 2s² + 4s + 8 = 0

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Use Routh's Criterion to determine the stability characteristics of the following systems. In each case determine the number of positive roots. i) s² + 4s + 1 = 0, ii) s + 4s2 + 5s + 6 = 0, iii) s³ + 3s? - 6s + 10 = 0, iv) s* + s + 2s² + 4s + 8 = 0 Use Routh's Criterion to determine the range of values of K which give stability for the systems with closed loop characteristic equations: i) s* + 3s³ + s² + 2s + K = 0, ii) s* + s³ + 3s² + 2s + K = 0 Determine the closed loop transfer function of the system shown in Figure Q8. Investigate the stability of this system when: 1 g1(s) = s + 1 2 82(s) = s+ 2 1 h2(s) = s + 1 hj(s) = 0.5s R(s) C(s) 81(s) 82(s) hi(s) h2(s)
Transcribed Image Text:Use Routh's Criterion to determine the stability characteristics of the following systems. In each case determine the number of positive roots. i) s² + 4s + 1 = 0, ii) s + 4s2 + 5s + 6 = 0, iii) s³ + 3s? - 6s + 10 = 0, iv) s* + s + 2s² + 4s + 8 = 0 Use Routh's Criterion to determine the range of values of K which give stability for the systems with closed loop characteristic equations: i) s* + 3s³ + s² + 2s + K = 0, ii) s* + s³ + 3s² + 2s + K = 0 Determine the closed loop transfer function of the system shown in Figure Q8. Investigate the stability of this system when: 1 g1(s) = s + 1 2 82(s) = s+ 2 1 h2(s) = s + 1 hj(s) = 0.5s R(s) C(s) 81(s) 82(s) hi(s) h2(s)
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