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8. Consider the unity feedback system of Figure 4, where G(s) is the plant and K is a proportional(or series gain) compensator. Let R K Figure 4. G(s): = G(s) 1 (s + 2)² (s + 3) -Y (a) In the s-plane, sketch the locus of roots of the closed loop system of Figure 4 as K varies from 0 to ∞. (b) Determine the range of K for which the steady state error to a unit step is less than or equal to 0.2. (c) At what value of K does the closed loop system have poles on the jo-axis? Having found this, determine the range of K for which the gain margin is greater than or equal to 3 (a gain of 3 corresponds to 9.5dB).

8. Consider the unity feedback system of Figure 4, where G(s) is the plant and K is a proportional(or series gain) compensator. Let R K Figure 4. G(s): = G(s) 1 (s + 2)² (s + 3) -Y (a) In the s-plane, sketch the locus of roots of the closed loop system of Figure 4 as K varies from 0 to ∞. (b) Determine the range of K for which the steady state error to a unit step is less than or equal to 0.2. (c) At what value of K does the closed loop system have poles on the jo-axis? Having found this, determine the range of K for which the gain margin is greater than or equal to 3 (a gain of 3 corresponds to 9.5dB).

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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8. Consider the unity feedback system of Figure 4, where G(s) is the plant and K is a proportional(or series gain) compensator. Let R K Figure 4. G(s): = G(s) 1 (s + 2)²(s + 3) -Y (a) In the s-plane, sketch the locus of roots of the closed loop system of Figure 4 as K varies from 0 to 0. (b) Determine the range of K for which the steady state error to a unit step is less than or equal to 0.2. (c) At what value of K does the closed loop system have poles on the jo-axis? Having found this, determine the range of K for which the gain margin is greater than or equal to 3 (a gain of 3 corresponds to 9.5dB). (d) Thus, is it possible to achieve both the steady state error and requirement and gain margin requirement with the proportional gain K?
Transcribed Image Text:8. Consider the unity feedback system of Figure 4, where G(s) is the plant and K is a proportional(or series gain) compensator. Let R K Figure 4. G(s): = G(s) 1 (s + 2)²(s + 3) -Y (a) In the s-plane, sketch the locus of roots of the closed loop system of Figure 4 as K varies from 0 to 0. (b) Determine the range of K for which the steady state error to a unit step is less than or equal to 0.2. (c) At what value of K does the closed loop system have poles on the jo-axis? Having found this, determine the range of K for which the gain margin is greater than or equal to 3 (a gain of 3 corresponds to 9.5dB). (d) Thus, is it possible to achieve both the steady state error and requirement and gain margin requirement with the proportional gain K?
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