MAE142_Lecture18

MAE142_Lecture18 - Linearization Reference and Small...

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Linearization Reference and Small Deviations Computational Method Linear Model Format SAMPEX Example MAE 142 NASA Image
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2 MAE 142 Small Deviations Suppose a reference trajectory has been determined for the vehicle (perhaps as a result of state-space simulation techniques). ˙ x r t = f [ x r t ] x t = x r t  x t Define the total system state vector as the sum of the reference trajectory and a vector of small deviations. ˙ x t = ˙ x r t  ˙ x t x t x r t
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3 MAE 142 Taylor Series (Again) The differential equations for the state vector of small deviations is found by a Taylor Series from the original equations of motion. ˙ x t = ˙ x r t  ˙ x t ˙ x t = f [ x t ] ˙ x r t  ˙ x t = f [ x r t  x t ] x t = x r t  x t ˙ x r t  ˙ x t = f [ x r t ] [ f x ] r x t ⋯ ˙ x r t = f [ x r t ]  ˙ x t ≈ [ f x ] r x t Trajectory of Small Deviations Reference Trajectory Taylor Series
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4 MAE 142
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MAE142_Lecture18 - Linearization Reference and Small...

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