ME360Homework07Answers

ME360Homework07Answers - Homework #7 Answers (4/1) ME 3600...

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Homework #7 Answers (4/1) ME 3600 Control Systems 1. E 4.2: a) 2 1 1 1 2 K K S T K + = b) 2 12 () 1 o d VK s TK K = + c) 1 K as large as possible 2. E 4.4: K s s s s s P E d 10 ) 1 ( ) 1 ( ) ( + + τ + τ = a) Step input: 0 ss e = , b) Ramp input: for 1 0 . e ss (mm), choose 100 K . 3. E 4.6: 2 5( 2) 5( 2) ( 0.7)( 14.3) 15 10 ss Ts ++ =≅ . Using Matlab, the system is noted have first order (over-damped) response with a 2% settling time of approximately 5 sec. 4. E 4.7: a) ) ( ) ( 2 1 1 K K K s KK s T + + = b) ) ( 2 1 1 K K K s s S T K + + = and ) ( 2 1 2 1 K K K s K K s S T K + + + = c) d EK s K K K = , so that 0 1 lim ss s d es K KK ⎛⎞ =⋅ = / ⎜⎟ + / ⎝⎠ . d) = t K e t c 1 2 1 ) ( 2 1 , so choose largest possible K 1 for the fastest response. 5. P 4.3: a) open loop: 1 = T K S , and closed loop: th 1 1 KK s s S T K + + τ + τ = . b) open loop: 1 1 + τ = s s T T e , and closed loop: th 1 1 KK s s T T e + + τ = . c) open loop: th 1 KK e ss = , and closed loop: th 1 1 KK e ss + = . 6. P 4.6: a) e e e T
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This note was uploaded on 02/02/2010 for the course ME 3600 taught by Professor Kamman during the Fall '09 term at Western Michigan.

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