EEL5173 Fall 2009 Lecture _3

EEL5173 Fall 2009 Lecture _3 - 1. State-variable Analysis...

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Unformatted text preview: 1. State-variable Analysis for CT systems i. Realization (Simulation, Decomposition) 1 1 1 1 1 1 1 1 1 1 1 1 ) ( ) ( ) ( a s a s a s s s b a s a s a s b s b s b s b s D s N s H n n n n n n n n n n n n n + + + + + + + + = + + + + + + + + = = L L L L Assume that b n is zero for the time being. b) Controller Canonical Form a) State diagram c) Observer Canonical Form Let n = 4 then we have Hence, 1 2 2 3 3 4 1 2 2 3 3 ) ( ) ( a s a s a s a s s s s s U s Y o + + + + + + + = ) ( ) ( ) ( ) ( 1 2 2 3 3 1 2 2 3 3 4 s U s s s s Y a s a s a s a s o + + + = + + + + o o o o o Y a sY a Y s a Y s a U sU U s U s Y s 1 2 2 3 3 1 2 2 3 3 4 + + + = ( ) [ ] { } ] [ 1 1 1 1 2 2 1 3 3 1 4 3 1 2 2 1 3 4 3 1 2 2 1 3 o o o o o o o o o Y a U s Y a U s Y a U s Y a U s Y s a Y s a Y s a Y s a U s U s U s U s Y + + + = + + + = Y o s-1-a 3-a 2-a 1-a 1 2 3 s-1 s-1 s-1 U Figure. Observer Canonical Form with b n being zero. Y...
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EEL5173 Fall 2009 Lecture _3 - 1. State-variable Analysis...

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