265_adv_control_eng

3d 259 23227140 982001 234pm state space methods for

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Unformatted text preview: ˆ 100, 1 ˆ 10 and the desired closed-loop eigenvalues are the roots of equation (8.138) 1 ˆ À5 ‡ j8:66, 2 ˆ À5 À j8:66 (8:139) (a) Direct comparison method: From equation (8.130) jsI À A ‡ Ke Cj ˆ s2 ‡ 1 ‡ 0 4 s   0 0 s 5    À ‡ [ 1 0 ] ˆ s2 ‡ 10s ‡ 100  À2 À3 ke2 4 5 54  s À1 ke1 0    ‡  ˆ s2 ‡ 10s ‡ 100   2 s‡3 ke2 0     s ‡ ke1 À1     ˆ s2 ‡ 10s ‡ 100   2 ‡ ke2 s ‡ 3  4 0 1 5 4 ke1 5 s2 ‡ (3 ‡ ke1 )s ‡ (3ke1 ‡ 2 ‡ ke2 ) ˆ s2 ‡ 10s ‡ 100 (8:140) //SYS21/D:/B&H3B2/ACE/REVISES(08-08-01)/ACEC08.3D ± 259 ± [232±271/40] 9.8.2001 2:34PM State-space methods for control system design 259 From equation (8.140) (3 ‡ ke1 ) ˆ 10, ke1 ˆ 7 (8:141) (3ke1 ‡ 2 ‡ ke2 ) ˆ 100 ke2 ˆ 100 À 2 À 21 ˆ 77 (8:142) (b) Observable canonical form method: From equation (8.132) 4 5 0 À a0 Ke ˆ Q 1 À a1 4 5 100 À 2 ˆQ 10 À 3 45 98 ˆQ 7 (8:143) From equation (8.133) Q ˆ (WNT )À1 and from equation (8.102) ! 1 3 ˆ 0 1 a Wˆ 1 1 Since fr...
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