265_adv_control_eng

00 10 01 1 100 0 0 0 1 100 8149 1 0 0 1 77

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Unformatted text preview: om equation (8.135) Nˆ 1 0 ! 0 , 1 Thus 31 WN ˆ 10 T ! and Qˆ 1 0 À1 À1 NT ˆ 1 0 1 0 ! 1 0 (8:144) 0 1 ! ! 0 3 ˆ 1 1 ! À1 0 ˆ 3 1 1 À3 (8:145) 1 0 ! ! Since Q Tˆ I then A is not in the observable canonical form. From equation (8.143) ! ! ! 98 7 01 Ke ˆ ˆ 7 77 1 À3 (c) Ackermann's Formula: From (8.134) C Ke ˆ (A) CA ! À1 0 1 ! (8:146) (8:147) (8:148) //SYS21/D:/B&H3B2/ACE/REVISES(08-08-01)/ACEC08.3D ± 260 ± [232±271/40] 9.8.2001 2:34PM 260 Advanced Control Engineering Using the definition of (A) in equation (8.104) Ke ˆ (A2 ‡ 1 A ‡ 0 I) Ke ˆ ˆ ˆ 8.4.4 À2 À3 ! 6 7 ! 98 7 1 14 98 14 ‡ 0 10 À20 À30 !! 00 ! ‡ 10 01 !À1 100 0 0 0 1 !! 100 ! (8:149) 1 0 0 ! 1 77 0 1 1 !! ! 7 0 7 ˆ 77 1 77 0 ! 1 (8:150) Effect of a full-order state observer on a closed-loop system Figure 8.10 shows a closed-loop system that includes a full-order state observer. In Figure 8.10 the system equations are • x ˆ Ax ‡ Bu y ˆ Cx (8:151) The control is implemented using observed state variables ” u ˆ ÀKx (8:152) If...
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