lec17 - Outline Motivation Generating Input-Output Relation...

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1 Outline ± Motivation stems ± Generating Input-Output Relation ± Normal Forms ± Tracking Control ± Examples ME6402, Nonlinear Control Sys Motivation ± Conditions for input-State feedback are rather stringent ± In many applications only a certain output is to be controlled ± Output feedback linearization achieves output tracking or regulation only ± It requires less stringent conditions than input-state linearization.
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2 Problem Statement ± Given the nonlinear system stems ) ( ) ( ) ( x h y u x g x f x = + = & ± Find u that achieves regulation and/or tracking of the output y using state feedback. Some issues to be discussed ME6402, Nonlinear Control Sys ± How to generate input-output relation ± Internal or zero dynamics ± Controller design based on input-output linearization Generating Input-Output Relation h dh ± Main idea : take derivatives of the output y=h(x) until the input appears explicitly on the RHS Using tha h L dt ug f + = = x x & the RHS. Using that ± We have ± If L g h(x) 0 on a neighborhood Ω ⊂ R n then the input transformation h uL h L dt dh y g f + = = & ( ) v x x + = ) ( ) ( h L h L u f g ± Yields the LTI system where v is the new input. v y = &
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3 Relative Degree If L g h(x)=0 on a finite region Ω ⊂ R n then the process continues until for some integer r L g L f r-1 h(x) 0: stems + = = + = = + = = h L uL h L dt h dL y h L uL h L dt h dL y h uL h L dt dh y r f g r f r f r f g f f g f 2 1 2 ) 1 ( 2 M & & & 0 0 0 ME6402, Nonlinear Control Sys + = = h L uL h L dt h dL y r f g r f r f r 1 1 ) ( 0 Such an 1 r n is called the relative degree . Input Transformation for Relative degree r Assuming L g L f r-1 h(x) 0 on a finite region Ω ⊂ R n then the input transformation ( ) v x x + = ) ( ) ( 1 1 h L h L L u r r g f f Yields the LTI system . The new input v as before can be set to v y r = ) ( Applied to h L uL h L y r f g r f r 1 ) ( + = d r n r d y y e e e e y v = β β
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This note was uploaded on 09/22/2011 for the course ME 6402 taught by Professor Staff during the Spring '08 term at Georgia Institute of Technology.

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lec17 - Outline Motivation Generating Input-Output Relation...

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