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Consider the following closed-loop system including plant G(s) = 4 s²+38+4 and PD controller. What are the requirements on Kd and Kp to achieve the desired closed loop transient specifications to a step reference input? Assume for this problem that you can ignore the effect of the closed-loop zero on the step response. R(s) Kas+Kp Closed-loop step response specifications: • no specification on rise time • settling time t, = 1.53 seconds .no specification on percent overshoot O K₂=5, no requirement on Kd O K₂=5, Kd=1 O Ka-3, no requirement on Kp O K₂=3, Kd=4 G(s) Y(s)

Consider the following closed-loop system including plant G(s) = 4 s²+38+4 and PD controller. What are the requirements on Kd and Kp to achieve the desired closed loop transient specifications to a step reference input? Assume for this problem that you can ignore the effect of the closed-loop zero on the step response. R(s) Kas+Kp Closed-loop step response specifications: • no specification on rise time • settling time t, = 1.53 seconds .no specification on percent overshoot O K₂=5, no requirement on Kd O K₂=5, Kd=1 O Ka-3, no requirement on Kp O K₂=3, Kd=4 G(s) Y(s)

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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Consider the following closed-loop system including plant: \[ G(s) = \frac{4}{s^2 + 3s + 4} \] and PD controller. What are the requirements on \( K_d \) and \( K_p \) to achieve the desired closed-loop transient specifications to a step reference input? Assume for this problem that you can ignore the effect of the closed-loop zero on the step response. ### Diagram Explanation: The diagram illustrates a feedback control system where: - \( R(s) \) is the reference input. - The controller is defined by \( K_d s + K_p \). - \( G(s) \) is the plant, with transfer function \( \frac{4}{s^2 + 3s + 4} \). - \( Y(s) \) is the output. ### Closed-loop step response specifications: - No specification on rise time. - Settling time \( t_s = 1.53 \) seconds. - No specification on percent overshoot. ### Options for \( K_p \) and \( K_d \): - \( K_p = 5 \), no requirement on \( K_d \) - \( K_p = 5 \), \( K_d = 1 \) - \( K_d = 3 \), no requirement on \( K_p \) - \( K_p = 3 \), \( K_d = 4 \)
Transcribed Image Text:Consider the following closed-loop system including plant: \[ G(s) = \frac{4}{s^2 + 3s + 4} \] and PD controller. What are the requirements on \( K_d \) and \( K_p \) to achieve the desired closed-loop transient specifications to a step reference input? Assume for this problem that you can ignore the effect of the closed-loop zero on the step response. ### Diagram Explanation: The diagram illustrates a feedback control system where: - \( R(s) \) is the reference input. - The controller is defined by \( K_d s + K_p \). - \( G(s) \) is the plant, with transfer function \( \frac{4}{s^2 + 3s + 4} \). - \( Y(s) \) is the output. ### Closed-loop step response specifications: - No specification on rise time. - Settling time \( t_s = 1.53 \) seconds. - No specification on percent overshoot. ### Options for \( K_p \) and \( K_d \): - \( K_p = 5 \), no requirement on \( K_d \) - \( K_p = 5 \), \( K_d = 1 \) - \( K_d = 3 \), no requirement on \( K_p \) - \( K_p = 3 \), \( K_d = 4 \)
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