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Unformatted text preview: mated and subtracted from the actual output
vector y, the difference can be used, in a closed-loop sense, to modify the dynamics of
the observer so that the output error (y À ) is minimized. This arrangement, somey
times called a Luenberger observer (1964), is shown in Figure 8.9. //SYS21/D:/B&H3B2/ACE/REVISES(08-08-01)/ACEC08.3D ± 255 ± [232±271/40] 9.8.2001 2:34PM State-space methods for control system design 255 u
B x + ∫ x C y + System A B 1 +
+ ∫ 0 Observer A Fig. 8.8 A simple full-order state observer. Let the system in Figure 8.9 be defined by
x Ax Bu (8:125) y Cx (8:126)
Assume that the estimate x of the state vector is
x Ax Bu Ke (y À Cx) (8:127) where Ke is the observer gain matrix.
If equation (8.127) is subtracted from (8.125), and (x À x) is the error vector e, then
e (A À Ke C)e (8:128) and, from equation (8.127), the equation for the full-order state observer is
x (A À Ke C)x Bu Ke y (8:129) Thus from equation (8.128) the dynamic behaviour...
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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.
- Winter '12
- Sali mon