EEL5173 Fall 2009 Lecture _2

EEL5173 Fall 2009 Lecture _2 - II. State Equation...

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II. State Equation Representation and Solution For CT systems, For DT systems, () () t Bu t x A dt x d + = r r ? ? ? ( ) ( ) ( ) , k Bu k x A k x + = + r r 1 ? ? ?
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1. State-variable Analysis for CT systems Differential equation: Convolution: State equation: () ( )( ) ( ) () ( ) () () t u b u b u b u b t y a y a y a y n n n n n n n 0 1 1 1 1 0 1 1 1 1 + + + + = + + + + L L () ( ) ( ) ( ) ( ) () () 0 0 , 0 = = = = t for t h t u if d u t h d u t h t y t ττ τ () () t Bu t x A dt x d + =
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i. Realization (Simulation, Decomposition) - from the transfer function to the state equation a) State diagram 3 basic elements: summer, scalar multiplier, and integrator. 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 s a s a s b s b s b s b s U s Y t h L s H n n n n n n n + + + + + + + + = = = L L
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b) Controller Canonical Form = dt
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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 _2 - II. State Equation...

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