Lect_39 - Nonlinear Systems and Control Lecture 38 Observers High-Gain Observers Motivating Example – p 1/1 4 ˙ x 1 = x 2 ˙ x 2 = φ x,u y = x

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Unformatted text preview: Nonlinear Systems and Control Lecture # 38 Observers High-Gain Observers Motivating Example – p. 1/1 4 ˙ x 1 = x 2 , ˙ x 2 = φ ( x,u ) , y = x 1 Let u = γ ( x ) stabilize the origin of ˙ x 1 = x 2 , ˙ x 2 = φ ( x,γ ( x )) Observer: ˙ ˆ x 1 = ˆ x 2 + h 1 ( y − ˆ x 1 ) , ˙ ˆ x 2 = φ (ˆ x,u ) + h 2 ( y − ˆ x 1 ) φ ( x,u ) is a nominal model φ ( x, u ) ˜ x 1 = x 1 − ˆ x 1 , ˜ x 2 = x 2 − ˆ x 2 ˙ ˜ x 1 = − h 1 ˜ x 1 + ˜ x 2 , ˙ ˜ x 2 = − h 2 ˜ x 1 + δ ( x, ˜ x ) δ ( x, ˜ x ) = φ ( x,γ (ˆ x )) − φ (ˆ x,γ (ˆ x )) – p. 2/1 4 Design H = bracketleftBigg h 1 h 2 bracketrightBigg such that A o = bracketleftBigg − h 1 1 − h 2 bracketrightBigg is Hurwitz Transfer function from δ to ˜ x : G o ( s ) = 1 s 2 + h 1 s + h 2 bracketleftBigg 1 s + h 1 bracketrightBigg Design H to make sup ω ∈ R bardbl G o ( jω ) bardbl as small as possible h 1 = α 1 ε , h 2 = α 2 ε 2 , ε > G o ( s ) = ε ( εs ) 2 + α 1 εs + α 2 bracketleftBigg ε εs + α 1 bracketrightBigg – p. 3/1 4 G...
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This note was uploaded on 09/29/2009 for the course ME 859 taught by Professor Choi during the Spring '08 term at Michigan State University.

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Lect_39 - Nonlinear Systems and Control Lecture 38 Observers High-Gain Observers Motivating Example – p 1/1 4 ˙ x 1 = x 2 ˙ x 2 = φ x,u y = x

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