Marine Vehicle Dynamics and Control

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Presentation transcript:

Marine Vehicle Dynamics and Control Marine vessel motion is more complicated than spacecraft motion due to the dependence of forces and moments on attitude and velocity Marine vessel motion is in some ways more complicated than aircraft motion Typical first investigations of ship dynamics and control focuses on the horizontal motion of symmetric (left-to-right) ships (surge, sway, and yaw)

Reference Frames for Ship D&C t i a l F m , . T y p c s u ° E h b o g d f 3 - x w v ¯ k ' B A 2 1 ( Ã ) µ Á : R =

Reference Frames for Ship D&C (2) l u s t r a i o n ( f m T . F - e ' G d c C O V h ) w p b x y , g

Motion Equations for a Rigid Ship b : _ v = ¡ ! £ + 1 m f ° u i d t h r s ¤ R a g I µ S ( ) w e [ ] T N o n x p , M c & l ; q A - y z 6

Motion Equations for a Rigid Ship y p c l w h M _ º + C ( ) D g ´ = ¿ [ v T ! ] , µ d ¯ x b j . I F G O V W - 1 9 4 S H 2 3

Modeling Fluid Forces A s u m p t i o n : F r c e a d g b y l f 1 . R - w h v x q ¡ M _ º C ( ) P D W ´ O ® , k 2 K 3 E 4 /

Horizontal Motion T h e s t a v c o r i x = ! µ [ u w p q y z Á Ã ] F , d ; g f : ( ¡ X _ ) + Y G U N I .

Horizontal Motion (2) L i n e a r z d q u t o s f h l m : ( ¡ X ) = + _ ) = + Y v x G U N I C y g c p w Ã T - · ¸ M A 1 B

Horizontal Motion (3) T h e c o u p l d s w a y - t m i · ¡ Y x N I ¸ _ v x G r N I z ¸ = U + f M A 1 B S b n ¯ : C ( ) > g ° k ; ,

Stability Analysis via Routh-Hurwitz p o s e w k n A i t r m f y a ; . , = ( I x ¤ ¢ ) H c d b l g ? R h - z D v : ¸ + ¡ 1 2 6 4 3 7 5

Stability Analysis via Routh-Hurwitz (2) e H u r w i t z m a x s = 2 6 4 n ¡ 1 3 ¢ . 7 5 D ¯ p c l o f b y d · ¸

Stability Analysis via Routh-Hurwitz (3) e c s a r y n d u ± i t o f h m p b l _ x = A ¢ > 8 1 ; S , ( ¸ ) T ¯ g w z - v I :

Stability Analysis via Routh-Hurwitz (4) f a r e l i g n v u c o s t h m y x , p ( ) = . ¢ ¡ 1 T b d ¯ w :

Stability Analysis via Routh-Hurwitz (5) p o s e A = · 1 2 ¸ . T h n t c a r i l y - m ( ) ¡ + f H ¢ > < d 3 w x D 4 v

Stability Analysis via Routh-Hurwitz (6) p o s e A = · ¡ 1 2 4 ¸ . T h n t c d i a r ¢ > ) < X ( + E x : v f y m l b ¯ w