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C(s) Problem 3. For each of the second order transfer function given below, where G (s) = R(s) (a)Find the locations of the poles, natural frequency and damping ratio values. (h) Dotor formo ..undemRed

C(s) Problem 3. For each of the second order transfer function given below, where G (s) = R(s) (a)Find the locations of the poles, natural frequency and damping ratio values. (h) Dotor formo ..undemRed

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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Electrical Engineering course.

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EE350 ( System Dynamics and control )

C(s) Problem 3. For each of the second order transfer function given below, where G (s) = R(s) (a)Find the locations of the poles, natural frequency and damping ratio values. (b) Determine the forms (undamped, etc.) and write the general expressions of the unit step responses. (c) Find the steady-state, Css, and peak values, Cmax, of the responses (depending on the forms of the responses, you may use the formulas at the bottom of the page). (d) Revise each transfer function to produce unit step responses approximately two times slower in terms of the settling time while maintaining the same forms and steady-state values. (e) Plot each response pairs (the original and its slower version) on the same plane as seen in the example below. 12 29 522 (i) Gı(s) = (ii) G2(s) = (iii) G3(s) = (s+2)(s+8) s2+6s+58 s3+24s2+166s+1044 54 24(s+20) (1v) Ga(s) = (V) Gs(s) = s2+12s+36 (s+4)2(s+24) PS. Check if the 2nd order approximations of the 3ra order systems are valid to use the formulas given. Please fill in the table below with your results you found with your computations. (a) (b) (c) (d) Poles, General Expression Cmax Proposed Tr. Fn. Form Css Zeros (i) (ii) (ii) (iv) (v)
Transcribed Image Text:C(s) Problem 3. For each of the second order transfer function given below, where G (s) = R(s) (a)Find the locations of the poles, natural frequency and damping ratio values. (b) Determine the forms (undamped, etc.) and write the general expressions of the unit step responses. (c) Find the steady-state, Css, and peak values, Cmax, of the responses (depending on the forms of the responses, you may use the formulas at the bottom of the page). (d) Revise each transfer function to produce unit step responses approximately two times slower in terms of the settling time while maintaining the same forms and steady-state values. (e) Plot each response pairs (the original and its slower version) on the same plane as seen in the example below. 12 29 522 (i) Gı(s) = (ii) G2(s) = (iii) G3(s) = (s+2)(s+8) s2+6s+58 s3+24s2+166s+1044 54 24(s+20) (1v) Ga(s) = (V) Gs(s) = s2+12s+36 (s+4)2(s+24) PS. Check if the 2nd order approximations of the 3ra order systems are valid to use the formulas given. Please fill in the table below with your results you found with your computations. (a) (b) (c) (d) Poles, General Expression Cmax Proposed Tr. Fn. Form Css Zeros (i) (ii) (ii) (iv) (v)
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