265_adv_control_eng

117 m 1 1 4 1 1 1 4 0 1 from 8104 a a2 1 a 0

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Unformatted text preview: 1 (8:118) Thus proving that equation (8.108) is already in the controllable canonical form. Since TÀ1 is also I, substitute (8.118) into (8.116) K ˆ [4 0 ]I ˆ [ 4 0] (8:119) (c) Ackermann's formula: From (8.103) K ˆ [0 1 ]MÀ1 (A) (8:120) From (8.117) MÀ 1 ˆ 1 À4 À1 À1 ! À1 4 ˆ 0 1 From (8.104) (A) ˆ A2 ‡ 1 A ‡ 0 I 1 0 ! (8:121) //SYS21/D:/B&H3B2/ACE/REVISES(08-08-01)/ACEC08.3D ± 254 ± [232±271/40] 9.8.2001 2:34PM 254 Advanced Control Engineering inserting values 4 52 4 ˆ 4 ˆ 1 0 À4 0 À4 0 4 16 5 0 0 (A) ˆ 0 4 5 4 4 5 4 ‡ 1 0 ‡4 0 À4 0 4 5 0 À16 1 5 4 0 0 ‡ 5 4 (8:122) Insert equations (8.121) and (8.122) into (8.120) ! 41 4 K ˆ [0 1] 10 0 ! 16 4 ˆ [0 1] 40 K ˆ [4 4 0 0 ‡4 1 0] 0 4 ! (8:123) These results agree with the root locus diagram in Figure 5.9, where K ˆ 4 produces two real roots of s ˆ À2, s ˆ À2 (i.e. critical damping). 8.4.3 State observers In section 8.4.2 where state feedback design was discussed, it was assumed that all the state variables were available for the cont...
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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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