Lect_38 - Nonlinear Systems and Control Lecture 38...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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?...
View Full Document

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.

Page1 / 12

Lect_38 - Nonlinear Systems and Control Lecture 38...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online