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did up to he Using the standard rules, draw the root locus diagrams (for increasing K) for the following open-loop transfer functions. Also comment upon the stability of the sys- tem. K (a) G(s) = %3D s2(s + a) & did up to hew K (b) G(s) = %3D (s+1)(s+2)(s +3) K(1+ aTs) s2(1+ sT) (c) G(s) with T = 1, for %3D %3D 7. (i) a = 5, and (ii) a = 0.2.

did up to he Using the standard rules, draw the root locus diagrams (for increasing K) for the following open-loop transfer functions. Also comment upon the stability of the sys- tem. K (a) G(s) = %3D s2(s + a) & did up to hew K (b) G(s) = %3D (s+1)(s+2)(s +3) K(1+ aTs) s2(1+ sT) (c) G(s) with T = 1, for %3D %3D 7. (i) a = 5, and (ii) a = 0.2.

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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Do c i) and ii)
In simple cases the root locus diagram (the paths take by the closed-loop poles then a parameter, e.g., the gain, is changed) can be found exactly by algebra. In this way (i.e., not using the 'rules') draw the root locus, for K increasing from zero, for the following open-loop transfer functions: K (a) G(s) = K (c) G(s) s+1 %3D s2 (b) G(s) = K s(s+ 1) (d) G(s) (s+1)1 Check your answers using MATLAB. For example, the commands >> num=[1; >> den=[1 0 0]; >> sys=tf(num, den) >> rlocus (sys) will draw the root locus for (c). Using the standard rules, draw the approximate root-locus diagrams for the systems in question Q1. Using the standard rules, draw the root locus diagrams (for increasing K) for the following open-loop transfer functions. Also comment upon the stability of the sys- tem. K (a) G(s) = s2(s + a) < did up to here K (b) G(s) = (s +1)(s+ 2)(s + 3) K(1+ aTs) s2(1+ sT) (c) G(s) = with T = 1, for (i) a = 5, and (ii) a = 0.2. Check your answers using MATLAB. You may find the following useful: The polynomial 3? + 12r + 11 = 0 has the solutions r1 = -2.58 and x2 = -1.42.
Transcribed Image Text:In simple cases the root locus diagram (the paths take by the closed-loop poles then a parameter, e.g., the gain, is changed) can be found exactly by algebra. In this way (i.e., not using the 'rules') draw the root locus, for K increasing from zero, for the following open-loop transfer functions: K (a) G(s) = K (c) G(s) s+1 %3D s2 (b) G(s) = K s(s+ 1) (d) G(s) (s+1)1 Check your answers using MATLAB. For example, the commands >> num=[1; >> den=[1 0 0]; >> sys=tf(num, den) >> rlocus (sys) will draw the root locus for (c). Using the standard rules, draw the approximate root-locus diagrams for the systems in question Q1. Using the standard rules, draw the root locus diagrams (for increasing K) for the following open-loop transfer functions. Also comment upon the stability of the sys- tem. K (a) G(s) = s2(s + a) < did up to here K (b) G(s) = (s +1)(s+ 2)(s + 3) K(1+ aTs) s2(1+ sT) (c) G(s) = with T = 1, for (i) a = 5, and (ii) a = 0.2. Check your answers using MATLAB. You may find the following useful: The polynomial 3? + 12r + 11 = 0 has the solutions r1 = -2.58 and x2 = -1.42.
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