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Consider the following feedback control system. The plant transfer function is: as+b P(s) Consider a controller C(s) = cs+d The desired closed-loop poles are at p1 = %3D s2+3s+1 -30, p2,3 = -3±j4. (a) What is the expression of the actual closed-loop characteristic equation obtained based on P(s) and C(s)? (b) What is the expression of the desired closed-loop characteristic equation obtained based on the desired closed-loop pole locations P1 and p2,3? (c) What are the values of a, b, c, and d such that the closed-loop poles are at the desired locations? R(s) C(s) P(s) Y(s) Controller Plant

Consider the following feedback control system. The plant transfer function is: as+b P(s) Consider a controller C(s) = cs+d The desired closed-loop poles are at p1 = %3D s2+3s+1 -30, p2,3 = -3±j4. (a) What is the expression of the actual closed-loop characteristic equation obtained based on P(s) and C(s)? (b) What is the expression of the desired closed-loop characteristic equation obtained based on the desired closed-loop pole locations P1 and p2,3? (c) What are the values of a, b, c, and d such that the closed-loop poles are at the desired locations? R(s) C(s) P(s) Y(s) Controller Plant

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 feedback control system. The plant transfer function is: 1 as+b P(s) = Consider a controller C(s) The desired closed-loop poles are at p1 = s2+3s+1 cs+d -30, P2.3 = -3±j4. (a) What is the expression of the actual closed-loop characteristic equation obtained based on P(s) and C(s)? (b) What is the expression of the desired closed-loop characteristic equation obtained based on the desired closed-loop pole locations pį and p2,3? (c) What are the values of a, b, c, and d such that the closed-loop poles are at the desired locations? R(s) C(s) P(s) Y(s) Controller Plant
Transcribed Image Text:Consider the following feedback control system. The plant transfer function is: 1 as+b P(s) = Consider a controller C(s) The desired closed-loop poles are at p1 = s2+3s+1 cs+d -30, P2.3 = -3±j4. (a) What is the expression of the actual closed-loop characteristic equation obtained based on P(s) and C(s)? (b) What is the expression of the desired closed-loop characteristic equation obtained based on the desired closed-loop pole locations pį and p2,3? (c) What are the values of a, b, c, and d such that the closed-loop poles are at the desired locations? R(s) C(s) P(s) Y(s) Controller Plant
acccading to given. pole location.. ch (8 +30) ( 8+3 +j4) (8+3-) 9). A: (8+30j (8+3) ² + 4 27 =0 (8+ 30) 82+9+ 68+16.)=0 (8+36) [82+ c8+25]=0 83+68? +958+308? +1&8+ 750 = o. 83 +3682+ 2058 + 750 =o b) poles are given as P1=-30 P2,3=-3 + j4 characteristic equation will be (s + 30) (s + (3 – 4j)) (s + (3 + 4j))=0 (s + 30) (s + 6s + 16)=0 53 + 36s2 + 196s + 480=0
Transcribed Image Text:acccading to given. pole location.. ch (8 +30) ( 8+3 +j4) (8+3-) 9). A: (8+30j (8+3) ² + 4 27 =0 (8+ 30) 82+9+ 68+16.)=0 (8+36) [82+ c8+25]=0 83+68? +958+308? +1&8+ 750 = o. 83 +3682+ 2058 + 750 =o b) poles are given as P1=-30 P2,3=-3 + j4 characteristic equation will be (s + 30) (s + (3 – 4j)) (s + (3 + 4j))=0 (s + 30) (s + 6s + 16)=0 53 + 36s2 + 196s + 480=0
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