EEL5173 Fall 2009 Lecture _16

EEL5173 Fall 2009 Lecture _16 - v r 4. Observer (State...

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Unformatted text preview: v r 4. Observer (State Estimator) The state vector is internal, not accessible. The model of the system is known. dt v d r i. Open-loop Observer B C A u ( t ) D y ( t )? d Bu t x t t x t ) ( ) ( ) ( ) ( ) ( + = r r d Bu t v t t v t ) ( ) ( ) ( ) ( ) ( + = r r [ ] ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( z t v x t v t x t t v t x t z r r r r r r r r = = = = r Only if the system is internal stable, i.e. the poles are all in the open LHP. always? A Plant with an Open-loop Observer u ( t ) plant y(t) ii. Closed-loop Observer dt v d r v r B A u ( t ) plant y(t) dt v d r v r B A C ) ( t y D The Plant plus an Open-loop Observer with an output u ( t ) plant y(t) dt v d r v r B A C ) ( t y D + Q dt v d r v r B C A u ( t ) plant Q y(t) + ) ( t y D The Plant with a Closed-loop Observer [ ] ( ) x QC Bu v QC A Du v C Du x C Q Bu v A y y Q Bu v A dt v d Bu x A dt x d r r r r r r r r r + + = + + + + = + + = + = ) ( ) ( [ ] ( ) [ ] [ ] [ ] [ ]( ) [ ] z QC A v x QC A v QC A x QC A x QC Bu v QC A Bu x A dt v d dt x d dt z d r r r r r r r r r r r = = = + + + = = The speed at which...
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EEL5173 Fall 2009 Lecture _16 - v r 4. Observer (State...

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