3d 261 23227140 982001 234pm state space methods for

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Unformatted text preview: the difference between the actual and observed state variables is ” e(t) ˆ x(t) À x(t) then ” x(t) ˆ x(t) À e(t) (8:153) Combining equations (8.151), (8.152) and (8.153) gives the closed-loop equations • x ˆ Ax À BK(x À e) ˆ (A À BK)x ‡ BKe (8:154) The observer error equation from equation (8.128) is • e ˆ (A À Ke C)e Combining equations (8.154) and (8.155) gives ! !! • x x A À BK BK ˆ • e 0 A À Be C e (8:155) (8:156) Equation (8.156) describes the closed-loop dynamics of the observed state feedback control system and the characteristic equation is therefore jsIA ‡ BKjjsI À A ‡ Ke Cj ˆ 0 (8:157) //SYS21/D:/B&H3B2/ACE/REVISES(08-08-01)/ACEC08.3D ± 261 ± [232±271/40] 9.8.2001 2:34PM State-space methods for control system design 261 System r=0 + u y x = Ax+ Bu y = Cx – + Ke – +1 + B + ∫ y 0 C Full-Order Observer A K 0 Fig. 8.10 Closed-loop control system with full-order observer state feedback. Equation (8.157) shows that the desired closed-loop poles for the control system are not chang...
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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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