HW05_solutions

# HW05_solutions - Winter 2008 EECS 460 HW #5 Solutions 1....

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Winter 2008 EECS 460 HW #5 Solutions 1. (Problem 7-19) Closed-Loop Transfer Function: Characteristic Equation: () 2 25 ( ) 5 500 25 t Ys K Rs s K s K = ++ + ( ) 2 5 5000 25 0 t sK s K + = ζ ζω ω == + = 0 6 2 5 500 1 .. 2 nt n K From Eq. (7-118), settling time t s nn ≅= = 33 06 01 .2 .2 . . sec. Thus, n 3 006 53 33 .2 . . rad / sec ## KK t = = 15 500 0118 25 113 76 2 .2 ωω ## System Transfer Function: Y s s s = 2844 64 2844 2

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Winter 2008 2. (Problem 7-29) (a) Forward-Path Transfer function: Characteristic Equation: Gs H s Es N ss s N () ( ) ( ) ( ) == ++ + 10 11 0 1 s s N 2 0 + + = N=1: Characteristic Equation: s s 2 10 + + = ζ ω = = 05 1 . n rad/sec. Maximum overshoot = e = πζ 1 2 0163 . (16.3%) Peak time t n max = = π ωζ 1 3628 2 . sec. N=10: Characteristic Equation: 2 10 0 0158 += = = . 10 n = rad/sec. Maximum overshoot e 1 2 0 605 . (60.5%) Peak time t n max = = 1 1006 2 . sec. (b) Unit-Step Response: N = 1 Second-order System Third-order System Maximum overshoot 0.163 0.206 Peak time 3.628 sec. 3.628 sec.
Winter 2008 Unit-Step Response: N = 10 Second-order System Third-order System Maximum overshoot 0.605 0.926 Peak time 1.006 sec 1.14 sec 3. (Problem 6-2) (a) s s s 32 25 10 450 0 ++ + = Roots: + 25 31 01537 4.214, 01537 4.214 .,.

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## This note was uploaded on 04/13/2010 for the course CS 235 taught by Professor Sabnis during the Spring '10 term at Punjab Engineering College.

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HW05_solutions - Winter 2008 EECS 460 HW #5 Solutions 1....

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