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MAE142_Lecture19

# MAE142_Lecture19 - Modal Analysis Transfer Function...

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Modal Analysis Transfer Function Matrices Eigenvalues and Stability Eigenvectors and Modes F16 Modes MAE 142 NASA Image

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2 MAE 142 Linear State Space Models The linear state space model represents a collection of differential equations. ˙ x t = [ f x ] r x t  [ f u ] r u t ˙ x = A x B u ˙ x t = f [ x t ] y t = h [ x t ] 0 = f [ x r ] State Equations Output Function Equilibrium Linearize Nonlinear Model Linear Model (Small Deviations) y r = h [ x r ] y t = [ h x ] r x t y = C x
3 MAE 142 Transfer Function Matrices Transfer functions are found be converting time-domain equations into the Laplace domain (and assume zero initial conditions). L [ d dt x t ] = s X s − x 0 ˙ x = A x B u s X s = A X s  B U s Y s = C X s Y s = C [ sI A ] 1 B U s y = C x L [ x t ] = X s [ sI A ] X s = B U s Y s = C X s A matrix of transfer functions!

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MAE142_Lecture19 - Modal Analysis Transfer Function...

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