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Unformatted text preview: Nonlinear Systems and Control Lecture # 40 Observers HighGain Observers Stabilization – p. 1/1 1 ˙ x = Ax + Bφ ( x,z,u ) ˙ z = ψ ( x,z,u ) y = Cx ζ = q ( x,z ) u ∈ R p , y ∈ R m , ζ ∈ R s , x ∈ R ρ , z ∈ R ℓ A,B,C are block diagonal matrices A i = 1 ··· ··· 1 ··· . . . . . . ··· ··· 1 ··· ··· ··· ρ i × ρ i , B i = . . . 1 ρ i × 1 – p. 2/1 1 C i = bracketleftBig 1 0 ··· ··· bracketrightBig 1 × ρ i , ρ = m summationdisplay i =1 ρ i Normal form Mechanical and electromechanical systems Example: Magnetic Suspension ˙ x 1 = x 2 ˙ x 2 = g − k m x 2 − L ax 2 3 2 m ( a + x 1 ) 2 ˙ x 3 = 1 L ( x 1 ) bracketleftbigg − Rx 3 + L ax 2 x 3 ( a + x 1 ) 2 + u bracketrightbigg – p. 3/1 1 Stabilizing (partial) state feedback controller: u = γ ( x,ζ ) ˙ ϑ = Γ( ϑ,x,ζ ) , u = γ ( ϑ,x,ζ ) Closedloop system under state feedback:...
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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.
 Spring '08
 CHOI

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