Modelling and Simulation of Marine Craft DYNAMICS

Transcription

1 Modellig ad Simulatio of Maie Caft DYNAMICS Edi Omedi Seio Reseah Fellow Moile & Maie Rootis Reseah Cete Uiesity of Limeik

2 Outlie Uiesity of Limeik Moile & Maie Rootis Reseah Cete Dyamis Rigid-Body Euatios of Motio Euatios of Motio aout CG Euatios of Motio aout CO 6 DoF Euatios of Motio (ROV) Restoig Foes ad Momets Oea Cuet Foes ad Momets Wae Foes ad Momets Populsio System Popelle Thust ad Toue Modellig Full thuste model Simulatio Diagams Noliea 6DoF ROV model (Eule Agles) Noliea 6DoF ROV model (Quateios)

3 GNC Sigal Flow Uiesity of Limeik Moile & Maie Rootis Reseah Cete Waypoits Weathe outig pogam Weathe data Waes, wid ad oea uets Tajetoy Geeato Motio Cotol System Fusio Cotol Maie Caft INS (GNSS + AHRS) Alloatio OA Sesos (Rada, Cameas, et.) GNC Sigal Flow Ostale Aoidae Module Osee Guidae System Cotol System Estimated positios ad eloities Naigatio System

4 ሶ Dyamis Rigid-Body Euatios of Motio Euatios of Motio aout CG ሶ mi I g CG M RB gτ w Τ + ms w Τ 3 3 CG C RB Uiesity of Limeik 3 3 S I g w Τ gτ w Τ Moile & Maie Rootis Reseah Cete = f g m g Desiale to deie Euatios of Motio aout CO (to take adatage of geometi popeties of aft) Coodiate Tasfomatio: gτ w Τ = H g Τ w Τ H g = I 3 3 S T g 3 3 I 3 3 Ԧ CO Ԧ g CG Ԧ g

5 ሶ ሶ ሶ ሶ Dyamis Rigid-Body Euatios of Motio Euatios of Motio aout CO Uiesity of Limeik Moile & Maie Rootis Reseah Cete M CG RB H g Τ w Τ + C CG RB H g Τ w Τ = f g m g H T g M CG RB H g CO M RB Τ w Τ νሶ CO RB + H T g C CG RB H g CO C RB Τ w Τ CO ν RB = H T g f g m g = f m CO τ RB Rigid-Body System Ietia Matix M CO RB = mi 3 3 ms g CO = M T ms RB > g I Uiue epesetatio! Ietia Matix (Paallel-Axes Theoem) I = I g ms 2 g I g = = I I x I xy I xz I yx I x I yz T > I zx I zy I x g

6 ሶ ሶ H T g M CG RB H g C CO RB = Dyamis Rigid-Body Euatios of Motio Rigid-Body Coiolis ad Cetipetal Matix Multiple epesetatios! C CO RB = CO M RB ms Τ ms Τ Τ w Τ νሶ CO RB 3 3 ms S w Τ H T g C CG RB H g CO C RB g + ms g S w Τ Τ w Τ CO ν RB ms Τ ms S Τ Uiesity of Limeik = H T g ms S w Τ g ms Τ ms w Τ S I w Τ g S I w Τ f g S g Moile & Maie Rootis Reseah Cete m g = f m CO τ RB CO = C T RB > CO = C T RB > C CO RB = ms w Τ ms g S w Τ ms w Τ S I w Τ S g Geealized eto of Exteal foes ad momets τ CO RB = f m

7 Moile & Maie Rootis Reseah Cete Uiesity of Limeik Dyamis Rigid-Body Euatios of Motio 6 DoF Rigid-Body Simulatio Model Attitude epesetatio: Eule Agles p w u w θ p η Y P R z y x θ p η Gai Itegato θ p η w ሶ p Τ ሶ θ = R θ T θ θ Τ w Τ ሶ η = J Θ η ν w M RB ሶ ν + C RB = τ RB ሶ ν = M RB 1 τ RB C RB Gai C RB KINEMATICS DYNAMICS + τ RB M RB 1 Gai Itegato

8 Moile & Maie Rootis Reseah Cete Uiesity of Limeik Dyamis Rigid-Body Euatios of Motio 6 DoF Rigid-Body Simulatio Model Attitude epesetatio: Quateios p w u w Gai Itegato w w M RB ሶ ν + C RB = τ RB ሶ ν = M RB 1 τ RB C RB Gai C RB KINEMATICS DYNAMICS + τ RB M RB 1 Gai Itegato p η z y x p η ሶ p Τ ሶ = R T Τ w Τ ሶ η = J η ν p η

9 Dyamis 6 DoF Euatios of Motio (ROV) Uiesity of Limeik Moile & Maie Rootis Reseah Cete 6 DoF Euatios of Motio iludig Oea Cuets (ROV) M RB ν ሶ + C RB + g η + M A νሶ + C A + D = τ wae + τ populsio igid-ody ad hydostati tems hydodyami tems Restoig Foes ad Momets W = mg B = ρg g η = f g + f g f g + f f g = W f = B Eule Agles Quateios f g = R θ 1 f g f = R θ 1 f f g = R 1 f g f = R 1 f CB CG f f g z Buoyay foe Weight foe

10 Dyamis 6 DoF Euatios of Motio (ROV) Uiesity of Limeik Moile & Maie Rootis Reseah Cete 6 DoF Euatios of Motio iludig Oea Cuets (ROV) M RB ν ሶ + C RB + g η + M A νሶ + C A + D = τ wae + τ populsio igid-ody ad hydostati tems Oea Cuet Veloity Veto (Iotatioal Fluid) 3 1, R 1 θ R θ hydodyami tems Relatie Veloity Veto = = Τ w Τ 3 1 = Τ w Τ Assumptio: M RB + M A M νሶ ν ሶ + C RB + C A + D + g η = τ wae + τ populsio C

11 Moile & Maie Rootis Reseah Cete Uiesity of Limeik Dyamis 6 DoF Euatios of Motio (ROV) 6 DoF Euatios of Motio iludig Oea Cuets (ROV) Hydodyami System Ietia (Added-Mass) Matix Hydodyami Coiolis-Cetipetal (Added-Mass) Matix M RB + M A ሶ ν + C RB + C A + D + g η = τ wae + τ populsio M C M A = M A T p w u N M K Z Y X M A M A = M 11 M 12 M 21 M 22 C A = 3 3 S M M 12 2 S M M 12 2 S M M 22 2 C A = C A T Hydodyami Dampig Matix p p p w w w u u u N N M M p K K w Z Z Y Y u X X D

12 Dyamis 6 DoF Euatios of Motio (ROV) Uiesity of Limeik Moile & Maie Rootis Reseah Cete 6 DoF Euatios of Motio iludig Oea Cuets (ROV) M RB + M A ν ሶ + C RB + C A + D + g η = τ wae + τ populsio M C Wae Speta

13 Dyamis 6 DoF Euatios of Motio (ROV) Uiesity of Limeik Moile & Maie Rootis Reseah Cete Modellig of Oea Waes Refeee: T. Peez. Ship Motio Cotol Couse Keepig ad Roll Stailisatio usig Ruddes ad Fis. Spige, 25.

14 Dyamis 6 DoF Euatios of Motio (ROV) Uiesity of Limeik Moile & Maie Rootis Reseah Cete Modellig of Oea Waes

15 Waes i shot-ested seas Dyamis 6 DoF Euatios of Motio (ROV) Waes i log-ested seas Uiesity of Limeik Moile & Maie Rootis Reseah Cete Wae spetum (mea dietio 45 ) Wae spetum (dietio 45 ) Refeee: O. Smogeli. Maie Systems Simulato (MSS), Nowegia Uiesity of Siee ad Tehology, Todheim, 26. Eleatio of the sufae (2 ompoets) Eleatio of the sufae (2 ompoets) Potetial (z = m) Pessue (z = m) Potetial (z = m) Pessue (z = m) N E

16 Kiematis Tasfomatios BODY-NED Quateios Uiesity of Limeik Moile & Maie Rootis Reseah Cete Foe RAO: Wae Amplitude Wae-Idued Foe Sea State H s, T z Wae Spetum S ω Wae Amplitude A k 1 st ode Foe RAO 1 st ode Wae Idued Foe τ wae1 2 d ode Foe RAO 2 d ode Wae Dift Foe τ wae2

17 Dyamis Populsio System Uiesity of Limeik Moile & Maie Rootis Reseah Cete 6 DoF Euatios of Motio iludig Oea Cuets (ROV) M RB + M A ν ሶ + C RB + C A + D + g η = τ wae + τ populsio M C Populsio System

18 Dyamis Populsio System Thuste Modellig Popelle Thust: Uiesity of Limeik Moile & Maie Rootis Reseah Cete Popelle Toue: Popelle Effiiey: Adae Ratio: Liea appoximatio: Biliea Thuste Model: Refeee: Fosse, T.I. ad Sagatu, S.I. Adaptie Cotol of Noliea Udewate Rooti Systems. Poeedigs of the IEEE Iteatioal Cofeee o Rootis ad Automatio, Saameto, CA, 1991, pp Affie Thuste Model:

19 Dyamis Populsio System Biliea Thuste Model Uiesity of Limeik Moile & Maie Rootis Reseah Cete

20 Dyamis Populsio System Affie Thuste Model Uiesity of Limeik Moile & Maie Rootis Reseah Cete

21 Dyamis Populsio System Affie Thuste Model Uiesity of Limeik Moile & Maie Rootis Reseah Cete

22 Dyamis Populsio System Affie Thuste Model Uiesity of Limeik Moile & Maie Rootis Reseah Cete

23 Dyamis Populsio System Full Thuste Model Uiesity of Limeik Moile & Maie Rootis Reseah Cete

24 Dyamis Simulatio Diagams Noliea 6DoF ROV model (Eule Agles) Uiesity of Limeik Moile & Maie Rootis Reseah Cete ν ሶ = M RB + M 1 A τ wae + τ populsio C RB + C A D g η τ pop + g DYNAMICS + τ wae Gai M RB + M A 1 Gai Gai C RB + C A D Itegato + w 3 KINEMATICS η η θ η 1 Gai R η Itegato 1 θ R θ p

25 Dyamis Simulatio Diagams Noliea 6DoF ROV model (Quateios) Uiesity of Limeik Moile & Maie Rootis Reseah Cete ν ሶ = M RB + M 1 A τ wae + τ populsio C RB + C A D g η τ pop + DYNAMICS + τ wae Gai M RB + M A 1 Gai Gai C RB + C A D Itegato + w KINEMATICS η η η 3 1 Gai R η Itegato 1 R p g

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