265_adv_control_eng

# 5 solution from equation 889 the observability matrix

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Unformatted text preview: P where (A) is defined in equation (8.104). Example 8.12 (See also Appendix 1, examp812.m) A system is described by ! ! ! !  x1 0 1 x1 0   u  À2 À3 x2 1 x2 ! x1 y  [1 0] x2 (8:134) //SYS21/D:/B&H3B2/ACE/REVISES(08-08-01)/ACEC08.3D ± 258 ± [232±271/40] 9.8.2001 2:34PM 258 Advanced Control Engineering Design a full-order observer that has an undamped natural frequency of 10 rad/s and a damping ratio of 0.5. Solution From equation (8.89), the observability matrix is h i 1 N  CT X AT CT  0 0 1 ! (8:135) N is of rank 2 and therefore non-singular, hence the system is completely observable and the calculation of an appropriate observer gain matrix Ke realizable. Open-loop eigenvalues: j s I À A j  s 2  3s  2  s 2  a1 s  a0 (8:136) Hence a0  2, a1  3 And the open-loop eigenvalues are s 2  3s  2  0 (s  1)(s  2)  0 s  À1, s  À2 (8:137) Desired closed-loop eigenvalues: s2  2!n s  !2  0 n s2  10s  100  s2  1 s  0  0 (8:138) Hence 0...
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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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