265_adv_control_eng

01 0 k1 k2 s2 4s 4 s 0 4 1 s 1 0 0 2 0 s

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Unformatted text preview: e. hence 1 ˆ 4, 0 ˆ 4 (a) Direct comparison method: From equations (8.99) and (8.111) jsI À A ‡ BKj ˆ s2 ‡ 4s ‡ 4  s  0 (8:113)  ! !  01 0 ‰ k1 k2 Š ˆ s2 ‡ 4s ‡ 4 À ‡  s 0 À4 1  ! !  s À1 0 0 2    0 s ‡ 4 ‡ k k  ˆ s ‡ 4s ‡ 4 1 2   s  À1 2    k s ‡ 4 ‡ k  ˆ s ‡ 4s ‡ 4 0 ! 1 2 2 s ‡ (4 ‡ k2 )s ‡ k1 ˆ s2 ‡ 4s ‡ 4 (8:114) From equation (8.114) k1 ˆ 4 (4 ‡ k2 ) ˆ 4 i:e: k2 ˆ 0 (8:115) //SYS21/D:/B&H3B2/ACE/REVISES(08-08-01)/ACEC08.3D ± 253 ± [232±271/40] 9.8.2001 2:34PM State-space methods for control system design 253 (b) Controllable canonical form method: From equation (8.100) K ˆ [ 0 À a0 X 1 À a1 ]TÀ1 ˆ [4 À 0 X 4 À 4]TÀ1 0 ]TÀ1 ˆ [4 (8:116) now T ˆ MW where M ˆ [B X AB] 0 AB ˆ 0 ! ! ! 0 1 ˆ 1 À4 0 1 1 À4 1 À4 giving Mˆ ! (8:117) Note that the determinant of M is non-zero, hence the system is controllable. From equation (8.102) ! ! a1 41 Wˆ 1 ˆ 10 10 Hence 0 1 T ˆ MW ˆ 1 À4 ! 4 1 ! 1 1 ˆ 0 0 ! 0 ˆI...
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This note was uploaded on 01/18/2014 for the course MECH 108 taught by Professor Sali mon during the Winter '12 term at Bingham University.

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