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# Lect_35 - Nonlinear Systems and Control Lecture 35 Tracking...

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Unformatted text preview: Nonlinear Systems and Control Lecture # 35 Tracking Feedback Linearization & Sliding Mode Control – p. 1/1 1 SISO relative-degree ρ system: ˙ x = f ( x ) + g ( x ) u, y = h ( x ) f (0) = 0 , h (0) = 0 L g L i − 1 f h ( x ) = 0 , for 1 ≤ i ≤ ρ − 1 , L g L ρ − 1 f h ( x ) negationslash = 0 Normal form: ˙ η = f ( η, ξ ) ˙ ξ i = ξ i +1 , 1 ≤ i ≤ ρ − 1 ˙ ξ ρ = L ρ f h ( x ) + L g L ρ − 1 f h ( x ) u y = ξ 1 f (0 , 0) = 0 – p. 2/1 1 Reference signal r ( t ) r ( t ) and its derivatives up to r ( ρ ) ( t ) are bounded for all t ≥ and the ρ th derivative r ( ρ ) ( t ) is a piecewise continuous function of t ; the signals r ,. . . , r ( ρ ) are available on-line. Goal: lim t →∞ [ y ( t ) − r ( t )] = 0 R = r . . . r ( ρ − 1) , e = ξ 1 − r . . . ξ ρ − r ( ρ − 1) = ξ −R – p. 3/1 1 ˙ η = f ( η,e + R ) ˙ e = A c e + B c bracketleftBig L ρ f h ( x ) + L g L ρ − 1 f h ( x ) u −...
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