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Problem 10. For the negative feedback systems having the following open-loop transfer functions, K(s + 1) S3 + 4s2 + 6s +4 KG(s)H(s) = K s(s+ 2)(s+5)(s+8)' KG(s)H(s) = sketch the root-loci of the systems for K = 1 by means of the computations requested below. (a) When sketching the root locus, if necessary, make use of the asymptotes finding and that are the intersecting point and angles with the real axis respectively with the following formula

Problem 10. For the negative feedback systems having the following open-loop transfer functions, K(s + 1) S3 + 4s2 + 6s +4 KG(s)H(s) = K s(s+ 2)(s+5)(s+8)' KG(s)H(s) = sketch the root-loci of the systems for K = 1 by means of the computations requested below. (a) When sketching the root locus, if necessary, make use of the asymptotes finding and that are the intersecting point and angles with the real axis respectively with the following formula

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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Problem 10. For the negative feedback systems having the following open-loop transfer functions, K(s + 1) S3+ 4s² + 6s + 4 KG(s)H(s) = K s(s+ 2)(s+5) (s + 8) KG(s)H(s) = sketch the root-loci of the systems for K = 1 by means of the computations requested below. (a) When sketching the root locus, if necessary, make use of the asymptotes finding and that are the intersecting point and angles with the real axis, respectively with the following formula, E finite poles- finite zeros %a = #finite poles-#finite pzeros and a = (2k+1)π #finite poles-#finite pzeros' where k = 0, +1, +2,... (b) If the root locus intersects the jo-axis, find the values of poles at the crossing points, the value of gain K at the crossings points and write the range of gain K making the system stable. (c) Find angles of departure and/or arrival if there are complex poles and/or complex zeros, (d) Plot the root-locus of the system for the positive values of gain in MATLAB to confirm your results. (e) Plot the unit step responses of the P-controlled system for the gain values of K = 124 and 324 on the same plane for the first 15 seconds. ( (f) Then plot the unit step response of the PD-controlled system for the gain value of K = 20. Determine the percent overshoot, peak time, settling time, maximum and final values of the response from the plot.
Transcribed Image Text:Problem 10. For the negative feedback systems having the following open-loop transfer functions, K(s + 1) S3+ 4s² + 6s + 4 KG(s)H(s) = K s(s+ 2)(s+5) (s + 8) KG(s)H(s) = sketch the root-loci of the systems for K = 1 by means of the computations requested below. (a) When sketching the root locus, if necessary, make use of the asymptotes finding and that are the intersecting point and angles with the real axis, respectively with the following formula, E finite poles- finite zeros %a = #finite poles-#finite pzeros and a = (2k+1)π #finite poles-#finite pzeros' where k = 0, +1, +2,... (b) If the root locus intersects the jo-axis, find the values of poles at the crossing points, the value of gain K at the crossings points and write the range of gain K making the system stable. (c) Find angles of departure and/or arrival if there are complex poles and/or complex zeros, (d) Plot the root-locus of the system for the positive values of gain in MATLAB to confirm your results. (e) Plot the unit step responses of the P-controlled system for the gain values of K = 124 and 324 on the same plane for the first 15 seconds. ( (f) Then plot the unit step response of the PD-controlled system for the gain value of K = 20. Determine the percent overshoot, peak time, settling time, maximum and final values of the response from the plot.
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