한양대 에리카 제어 중간 족보.pdf

Solutions of Midterm Exam
Subject : Control System Engineering 1, Lecturer : Prof. Youngjin Choi, Date : Apr. 22, 2013 (Contact e-mail :xxxx@xxxxang.ac.kr)

Problem 1 (20pt) Draw both polar plot and bode plot of the following transfer function: G(s) = 1 s(s + 1) (1)

Solution of Problem 1 (20pt) 1. (5pt) Consider G(jω) = 1 jω(jω + 1) (2)

2. (5pt) The magnitude and phase are obtained for ω ≥ 0 as follow: |G(jω)| = 1 ω 1 + ω2 √ → |G(jω)|dB = 20 log10 ω 20 log10 1 + ω2 (3) (4)

∠G(jω) = 90 tan1 ω 3. (5pt) first at ω = 0 |G(jω)| = ∞ ∠G(jω) = 90 second at ω = 0.1 |G(jω)| 1 = 10 0.1 → |G(jω)|dB 20[dB] → |G(jω)|dB = ∞

(5) (6)

(7) (8)

∠G(jω) 90 third at ω = 1 1 |G(jω)| = √ 2 ∠G(jω) = 135 third at ω = 10 |G(jω)| 1 √ = 0.01 10 100 → |G(jω)|dB = 20 log10 40[dB] → |G(jω)|dB = 20 log10 √ 2 = 3[dB] 0[dB]

(9) (10)

(11) (12)

∠G(jω) 180 4. (5pt)

Problem 2 (10pt) Solve the following differential equation by means of the…