hw6sol

# hw6sol - ME 475 Out 2/17 due 2/24 PROBLEM 1 HOMEWORK#6...

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ME 475 Out: 2/17; due: 2/24 HOMEWORK #6 SOLUTION Spring 2011 PROBLEM 1 : FPE, Prob. 5.5(e) and (f), pp. 280. Make sure you compute departure and/or arrival angles. (e) N p – N z = 3 – 2 = 1 φ asy = 180 ° Departure angle : 90 ° + 90 ° φ 90 ° 90 ° = 180 ° φ = 180 ° Arrival angle : θ + 90 ° 270 ° 90 ° 90 ° = 180 ° θ = 180 ° MATLAB Statement : num=[1 0 1] den=conv([1 0],[1 0 4]) rlocus(num,den)

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(f) N p – N z = 3 – 2 = 1 φ asy = 180 ° Departure angle : 270 ° + 90 ° φ 90 ° 90 ° = 180 ° φ = 360 ° = 0 ° Arrival angle : θ + 90 ° 90 ° 90 ° 90 ° = 180 ° θ = 0 ° MATLAB Statement : num=[1 0 4] den=conv([1 0],[1 0 1]) rlocus(num,den)
PROBLEM 2 : Given : Specs .: (i) (ii) Find : (a) open-loop stability (b) stability for G c (s) = K (c) stability for PD and PI (d) appropriate controller to meet specs. (e) simulate step response; 2 nd order dominant? Solution : a) Open-loop system is unstable because it has a pole at s = +0.1. b) Sketch root locus for proportional control: angles of asymptotes: ± 90 ° breakaway

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c) PD controller : let α = 2 G c (s) = K(s + 2), 1 asymptote at 180
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hw6sol - ME 475 Out 2/17 due 2/24 PROBLEM 1 HOMEWORK#6...

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