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Find the steady-state error es, due to a unit step input 1 (t) in terms of K

Find the steady-state error es, due to a unit step input 1 (t) in terms of K

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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Please explain Part C in detail. i dont understand how to get to that solution 

Problem 1: For a second order system with no zeros, the table shows some values of Percent Overshoot PO corresponding to the Damping Ratio : Let P(s) = = a) 3/4 2/3 3/5 1/2 2/5 P0|25| PO 2.84% 6.02% 9.5% 16.3% 25.38 % 1 (s + 5)² b) 16.3 %. You will design a constants controller C(s) = K Find the closed-loop transfer function. Then find the range of K such that the closed-loop system is BIBO stable PC 1+ PC BIBO stable for -25 < K < ∞ i.e., K>-25 Hyr = € > 0.5 = Find the range of K so that the percent overshoot PO of the step response is not more than α ¤gs = lim s Her 8+0 = = 1/3 1/4 1/8 14.44% 32.93% 44.43% 67.31% K s² + 10s +25+ K Range within the stability region: -25 < K≤ 75 = 5 √25+ K Find the steady-state error es due to a unit step input 1 (t) in terms of K 1 1 S 1+ KP(0) 1+ K≤ 75 1 K 25 25 25+ K d) What is the smallest steady-state error €ss due to a unit step input while the percent overshoot PO of the step response is not more than 16.3 %? For small ess need K large. Maximum K = 75 for PO ≤ 16.3%
Transcribed Image Text:Problem 1: For a second order system with no zeros, the table shows some values of Percent Overshoot PO corresponding to the Damping Ratio : Let P(s) = = a) 3/4 2/3 3/5 1/2 2/5 P0|25| PO 2.84% 6.02% 9.5% 16.3% 25.38 % 1 (s + 5)² b) 16.3 %. You will design a constants controller C(s) = K Find the closed-loop transfer function. Then find the range of K such that the closed-loop system is BIBO stable PC 1+ PC BIBO stable for -25 < K < ∞ i.e., K>-25 Hyr = € > 0.5 = Find the range of K so that the percent overshoot PO of the step response is not more than α ¤gs = lim s Her 8+0 = = 1/3 1/4 1/8 14.44% 32.93% 44.43% 67.31% K s² + 10s +25+ K Range within the stability region: -25 < K≤ 75 = 5 √25+ K Find the steady-state error es due to a unit step input 1 (t) in terms of K 1 1 S 1+ KP(0) 1+ K≤ 75 1 K 25 25 25+ K d) What is the smallest steady-state error €ss due to a unit step input while the percent overshoot PO of the step response is not more than 16.3 %? For small ess need K large. Maximum K = 75 for PO ≤ 16.3%
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