MAE142_Solution4

# MAE142_Solution4 - MAE 142 Homework Set#4(Winter 2011...

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Unformatted text preview: MAE 142 Homework Set #4 (Winter 2011) Problem 1 (10 pts) Find the eigenvectors and eigenvalues for the following linear AUV model. Characterize the dominate motion axis (longitudinal, lateral, or directional) for each eigenvalue/eigenvector pair. AUV state vector: u(ft/s), v(ft/s), w(ft/s), p(r/s), q(r/s), r(r/s), phi(r), theta(r), psi(r) A = [ column 1 to 4- 0.5502641 - 0.0003671 2.2699114 0. 0.0143200 - 1.7182979 0. - 0.0277492 - 0.0476610 - 0.0000002 - 1.6831678 0. 7.208165 1.3656433 0. 0. - 0.3988524 - 0.0000055 5.3581857 0. - 0.0048184 - 5.3127938 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. column 5 to 9 0.0749600 0. 0. 0.0006866 0. 0. - 0.3912209 - 0.0154463 0.0051024 0. 0.3894952 0. 0. - 0.0048737 0. 0. - 0.8810150 - 7.7750883 - 0.0040552 0. - 1.1337988 0. 0. - 0.1398404 0. 0. - 1.1339163 0.0051974 - 0.1466307 0. 0. - 0.0185026 0. 0. 0. 1. 0. 0. 0. 0. 0. 1.0001712 0. 0. 0. ] Problem 2 (10 pts) Find the value of Kq so that a business jet can meet the following short period requirements. biz jet: [ ˙ w ˙ q ] = [ − 0.61 170.0 − 0.01 − 1.12 ][ w q ] [ 8.47 − 2.03 ] e (V = 170 ft/s) control law: e = K q q ec specification: sp 1.8rad/sec sp 0.8 Problem 3 (10 pts) Find a model-following control law so that the F-16 aircraft meets the suggested Dutch Roll mode handling qualities criteria. [ ˙ v ˙ r ] = [ − 0.22 − 747.5 0.016 − 0.31 ][ v r ] [ 8.47 23.1 − 2.03 − 3.36 ] [ a r ] (V = 750 ft/s) dr 1.0 rad/sec dr 0.2 dr dr 0.35rad/sec Problem 4 (10 pts) A linear model for the roll mode of the F-16 aircraft is given below. Compare the roll rate time response with and without the following aileron actuator model. Use an aileron doublet input, with 2 degree amplitude and duration of two seconds for each step. F-16 roll mode: ˙ p =− 2.35 p − 41.86 a (p in rad/s, delta_a in rad) aileron actuator: ˙ a =− 10.0 a 10.0 ac (delta_a, delta_ac in rad) MAE 142 Homework #4 SOLUTIONS λ 1 Eigenvector Amplitudes λ 2 λ 3 λ 4 λ 5 λ 6 λ 7 λ 8 u v w p q r phi theta psi λ 9 (a) 1....
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MAE142_Solution4 - MAE 142 Homework Set#4(Winter 2011...

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