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For a control system shown in Figure Q1(b), the input signal is r(t) = 5 + 10t. (i) Initially, the designer set the proportional gain K=200. Calculate the steady-state error for this setting. (ii) If the designer demanded that the steady-state error in (i) to be reduced by 5%, what would be the new value for K? (iii) Stick to the previous setting K=200, calculate the natural frequency and damping ratio of the closed-loop system C(s)/R(s). State whether the system behaves as overdamped, underdamped or un-damped. Hence, calculate the settling time, peak time and the percentage overshoot of the closed-loop system. Due to unit step r(t) = u(t – 1), sketch the time response for c(t) and label all its transient criterion. R(s) E(s) C(s) S+2 G(s) Figure O1(b)

For a control system shown in Figure Q1(b), the input signal is r(t) = 5 + 10t. (i) Initially, the designer set the proportional gain K=200. Calculate the steady-state error for this setting. (ii) If the designer demanded that the steady-state error in (i) to be reduced by 5%, what would be the new value for K? (iii) Stick to the previous setting K=200, calculate the natural frequency and damping ratio of the closed-loop system C(s)/R(s). State whether the system behaves as overdamped, underdamped or un-damped. Hence, calculate the settling time, peak time and the percentage overshoot of the closed-loop system. Due to unit step r(t) = u(t – 1), sketch the time response for c(t) and label all its transient criterion. R(s) E(s) C(s) S+2 G(s) Figure O1(b)

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
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(b) For a control system shown in Figure Q1(b), the input signal is r(t) = 5 + 10t. (i) Initially, the designer set the proportional gain K=200. Calculate the steady-state error for this setting. (ii) If the designer demanded that the steady-state error in (i) to be reduced by 5%, what would be the new value for K? (iii) Stick to the previous setting K=200, calculate the natural frequency and damping ratio of the closed-loop system C(s)/R(s). State whether the system behaves as overdamped, underdamped or un-damped. Hence, calculate the settling time, peak time and the percentage overshoot of the closed-loop system. Due to unit step r(t) = u(t – 1), sketch the time response for c(t) and label all its transient criterion. R(s) E(s) C(s) 1 K S+ 2 G(s) Figure Q1(b)
Transcribed Image Text:(b) For a control system shown in Figure Q1(b), the input signal is r(t) = 5 + 10t. (i) Initially, the designer set the proportional gain K=200. Calculate the steady-state error for this setting. (ii) If the designer demanded that the steady-state error in (i) to be reduced by 5%, what would be the new value for K? (iii) Stick to the previous setting K=200, calculate the natural frequency and damping ratio of the closed-loop system C(s)/R(s). State whether the system behaves as overdamped, underdamped or un-damped. Hence, calculate the settling time, peak time and the percentage overshoot of the closed-loop system. Due to unit step r(t) = u(t – 1), sketch the time response for c(t) and label all its transient criterion. R(s) E(s) C(s) 1 K S+ 2 G(s) Figure Q1(b)
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