Lect_40 - Nonlinear Systems and Control Lecture # 40...

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Unformatted text preview: Nonlinear Systems and Control Lecture # 40 Observers High-Gain Observers Stabilization p. 1/1 1 x = Ax + B ( x,z,u ) z = ( x,z,u ) y = Cx = q ( x,z ) u R p , y R m , R s , x R , z R A,B,C are block diagonal matrices A i = 1 1 . . . . . . 1 i i , B i = . . . 1 i 1 p. 2/1 1 C i = bracketleftBig 1 0 bracketrightBig 1 i , = m summationdisplay i =1 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 = ( x, ) = ( ,x, ) , u = ( ,x, ) Closed-loop system under state feedback:...
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Lect_40 - Nonlinear Systems and Control Lecture # 40...

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