ME360Homework09Answers

ME360Homework09Answers - Homework #9 (Chapter 6) Answers ME...

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Homework #9 (Chapter 6) Answers ME 3600 Control Systems 1. E 6.1: 1 st column: 1, 3 K , 2 36 5 3 KK K ⎛⎞ + ⎜⎟ ⎝⎠ , 5; 0.633 K > for the system to be stable. 2. E 6.4: C.E.: () 0 2 3 2 3 = + + + K s K s s . Stable for 5 1 0 . K < < . 3. E 6.6: C.E.: ( ) 0 18 27 10 2 3 = + + + + K s s s a) K = 252 b) poles: 10 , 5.196 i ± 4. P 6.1(e): 1 st column: 1, 1, 1, 2 -K , K . System is stable for 2 0 < < K . 5. P 6.1(g): 1 st column: 1, 1, 1, K , -K , K . Unstable for all values of K . 6. P 6.3: a) C.E.: ( ) 0 400 800 1604 1008 205 2 3 4 = + + + + + K s s s s , 56 17 . K max = . b) Let 8 8 . K = , then the poles are: 200 , 326 4 , 209 2 3374 0 ± . j . . . (The complex poles are dominant.) c) For 8 8 . K = ( ) ( ) 9935 4 6748 0 0684 4 ) 9935 4 6748 0 ( 326 4 200 200 6 17 2 2 . s . s . . s . s . s s s . s T + + + + + + + = So, the damping ratio 15 0 . ζ , and the % OS % 62 . 7. P 6.9: a) C.E.: ( ) 0 10 000 40 4400 140 2 3 = + + + + K , s s s , so system is stable for 600 57 4000 , K < < . b) Using concept of dominant poles, and
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