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Consider a closed-loop control with the following loop transfer function: 1 L(s) = Ge(s)G(s) = s(4s + 1)(6s + 1) (a) State L(jw), and then determine the phase crossover frequency @₁, i.e., angular frequency at which the phase angle of L(jw) = -180°. Assume that w > 0. (b) Calculate the gain margin of the system, and comment on the system stability.

Consider a closed-loop control with the following loop transfer function: 1 L(s) = Ge(s)G(s) = s(4s + 1)(6s + 1) (a) State L(jw), and then determine the phase crossover frequency @₁, i.e., angular frequency at which the phase angle of L(jw) = -180°. Assume that w > 0. (b) Calculate the gain margin of the system, and comment on the system stability.

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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Question 6 Consider a closed-loop control with the following loop transfer function: 1 L(s) = Ge(s)G(s) = s(4s + 1)(6s + 1) (a) State L(jw), and then determine the phase crossover frequency @₁, i.e., angular frequency at which the phase angle of L(jw) = -180°. Assume that w > 0. (b) Calculate the gain margin of the system, and comment on the system stability. (c) Sketch the bode magnitude plot of L(jw) (i.e., |L(jw)|dB vs log w). Clearly indicate the corner frequencies, the asymptotic lines and their gradients, and the approximated curve. with the corresponding (d) If it is later found that system L(s) has a new transfer function of s(6s+1)' Bode plot shown in Fig. Q6. Comment, based on Bode analysis, the stability of the closed-loop system. Bode Diagram 40 20 0 Magnitude (dB) Phase (deg) -20 -40 -60 -90 -135 -180 10-² 10-1 Frequency (rad/s) Fig. Q6 10⁰ 10¹
Transcribed Image Text:Question 6 Consider a closed-loop control with the following loop transfer function: 1 L(s) = Ge(s)G(s) = s(4s + 1)(6s + 1) (a) State L(jw), and then determine the phase crossover frequency @₁, i.e., angular frequency at which the phase angle of L(jw) = -180°. Assume that w > 0. (b) Calculate the gain margin of the system, and comment on the system stability. (c) Sketch the bode magnitude plot of L(jw) (i.e., |L(jw)|dB vs log w). Clearly indicate the corner frequencies, the asymptotic lines and their gradients, and the approximated curve. with the corresponding (d) If it is later found that system L(s) has a new transfer function of s(6s+1)' Bode plot shown in Fig. Q6. Comment, based on Bode analysis, the stability of the closed-loop system. Bode Diagram 40 20 0 Magnitude (dB) Phase (deg) -20 -40 -60 -90 -135 -180 10-² 10-1 Frequency (rad/s) Fig. Q6 10⁰ 10¹
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