EEL5173 Fall 2009 Lecture _6_1

# EEL5173 Fall 2009 Lecture _6_1 - iv. Realization...

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iv. Realization (Simulation, Decomposition) - from the transfer function to the state equation (1) State diagram: 3 basic elements: summer, scalar multiplier, and delay element. u 1 u 2 u 3 y = u 1 -u 2 + u 3 + + - Summer: Scalar multiplier : y = a u u a {} 0 1 1 1 0 1 1 1 ) ( ) ( ) ( ) ( a z a z a z a b z b z b z b z U z Y k h Z z H n n n n n n n n + + + + + + + + = = = L L

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) 1 ( ) ( = k u k y Delay Element: u ( k ) D U(z) z z U z Y ) ( ) ( = z 1 u ( k ) =y ( k+ 1)
(2) Controller Canonical Form 0 , ) ( ) ( ) ( ) ( ) ( 4 0 1 2 2 3 3 4 4 0 1 2 2 3 3 4 4 × + + + + + + + + = = a z W z W a z a z a z a z a b z b z b z b z b z U z Y z H Let n = 4 and assume that ) ( ) ( ) ( 0 1 2 2 3 3 4 4 z W b z b z b z b z b z Y + + + + = ) ( ) ( ) ( 0 1 2 2 3 3 4 4 z W a z a z a z a z a z U + + + + = Furthermore, assume that We have () W a zW a W z a W z a U a W z W a zW a W z a W z a U W z a 0 1 2 2 3 3 4 4 0 1 2 2 3 3 4 4 1 = =

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z -1 z 4 W z 3 W z 2 W zW W U -a 3 -a 2 -a 1 -a 0 z -1 z -1 z -1 1/a 4
z -1 z 4 W z 3 W z 2 W zW W U -a 3 -a 2 -a 1 -a 0 z -1 z -1 z -1 1/a 4 b 0 b 1 b 2 b 3 b 4 Y ) ( ) ( ) ( 0 1 2 2 3 3 4 4 z W b z b z b z b z b z Y + + + + =

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-1 z 4 W z 3 W z 2 W zW W U -a 3 -a 2 -a 1 -a 0 z -1 z -1 z -1 1/a
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## This note was uploaded on 07/15/2011 for the course EEL 5173 taught by Professor Tung during the Fall '09 term at FSU.

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EEL5173 Fall 2009 Lecture _6_1 - iv. Realization...

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