# Lect_38 - Nonlinear Systems and Control Lecture 38...

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Unformatted text preview: Nonlinear Systems and Control Lecture # 38 Observers Exact Observers – p. 1/1 2 Observer with Linear Error Dynamics Observer Form: ˙ x = Ax + γ ( y,u ) , y = Cx where ( A,C ) is observable, x ∈ R n , u ∈ R m , y ∈ R p From Lecture # 24: An n-dimensional SO system ˙ x = f ( x ) + g ( x ) u, y = h ( x ) is transformable into the observer form if and only if φ = bracketleftBig h, L f h, ··· L n- 1 f h bracketrightBig T , rank bracketleftbigg ∂φ ∂x ( x ) bracketrightbigg = n b = bracketleftBig , ··· , 1 bracketrightBig T , ∂φ ∂x τ = b – p. 2/1 2 [ ad i f τ,ad j f τ ] = 0 , ≤ i,j ≤ n- 1 [ g,ad j f τ ] = 0 , ≤ j ≤ n- 2 Change of variables: τ i = (- 1) i- 1 ad i- 1 f τ, 1 ≤ i ≤ n ∂T ∂x bracketleftBig τ 1 , τ 2 , ··· τ n bracketrightBig = I z = T ( x ) – p. 3/1 2 ˙ x = Ax + γ ( y,u ) , y = Cx ˙ ˆ x = A ˆ x + γ ( y,u ) + H ( y- C ˆ x ) ˜ x = x- ˆ x ˙ ˜ x = ( A- HC )˜ x Design H such that ( A- HC ) is Hurwitz What about feedback control?What about feedback control?...
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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_38 - Nonlinear Systems and Control Lecture 38...

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