# Lect_33 - Nonlinear Systems and Control Lecture # 33 Robust...

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Unformatted text preview: Nonlinear Systems and Control Lecture # 33 Robust Stabilization Sliding Mode Control p. 1/1 5 Regular Form: = f a ( , ) = f b ( , ) + g ( , ) u + ( t,,,u ) R n 1 , R, u R f a (0 , 0) = 0 , f b (0 , 0) = 0 , g ( , ) g &gt; Sliding Manifold: s = ( ) = 0 , (0) = 0 s ( t ) = f a ( , ( )) Design s.t. the origin of = f a ( , ( )) is asymp. stable p. 2/1 5 s = f b ( , ) f a ( , ) + g ( , ) u + ( t,,,u ) u = 1 g parenleftbigg f b f a parenrightbigg + v or u = v u = L parenleftbigg f b f a parenrightbigg + v, L = 1 g or L = 0 s = g ( , ) v + ( t,,,v ) = f b f a + gL parenleftbigg f b f a parenrightbigg vextendsingle vextendsingle vextendsingle vextendsingle ( t,,,v ) g ( , ) vextendsingle vextendsingle vextendsingle vextendsingle ( , ) + | v | p. 3/1 5 vextendsingle vextendsingle vextendsingle vextendsingle ( t,,,v ) g ( , ) vextendsingle vextendsingle vextendsingle vextendsingle ( , ) + | v | ( , ) , &lt; 1 ( Known ) s s = sgv + s sgv + | s | | | s s g [ sv + | s | ( + | v | )] v = ( , ) sgn( s ) ( , ) ( , ) 1 + , &gt; s s g [ | s | + | s | + | s | ] = g [ (1 ) | s | +...
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## This note was uploaded on 07/25/2008 for the course ME 859 taught by Professor Choi during the Spring '08 term at Michigan State University.

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Lect_33 - Nonlinear Systems and Control Lecture # 33 Robust...

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