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Unformatted text preview: Nonlinear Systems and Control Lecture # 37 Observers Linearization and Extended Kalman Filter (EKF) p. 1/1 2 Linear Observer via Linearization x = f ( x,u ) , y = h ( x ) 0 = f ( x ss ,u ss ) , y ss = h ( x ss ) Linearize about the equilibrium point: x = Ax + Bu , y = Cx x = x x ss , u = u u ss , y = y y ss What are A , B , C ? x = A x + Bu + H ( y C x ) , x = x ss + x ( A HC ) is Hurwitz It will work locally for sufficiently small bardbl x (0) bardbl , bardbl x (0) bardbl , and bardbl u ( t ) bardbl p. 2/1 2 Feedback Control: x = A x + Bu + H ( y C x ) u = K x , u = u ss K x Verify that the closedloop system has an equilibrium point at x = x ss , x = 0 and linearization at the equilibrium point yields bracketleftBigg x x bracketrightBigg = bracketleftBigg ( A BK ) BK ( A HC ) bracketrightBigg bracketleftBigg x x bracketrightBigg Which theorem would justify this controller locally?...
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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.
 Spring '08
 CHOI

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