Introduction to physical systems, their modeling and simulation: A Bond Graph Approach

Transcription

1 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Introduction to physical systms, thir modling and simulation: A Bond Graph Approach Anand Vaz Prossor Dpartmnt o Mchanical Enginring Dr. B. R. Ambdkar National Institut o Tchnology Jalandhar Punjab 440, India Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06

2 Physical Systms Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India What do w undrstand by physical systms? What is a systm? ntity sparabl rom th rst o th univrs by mans o a physical or concptual boundary Composd o intracting parts Physical systms ar thos in which Enrgy or Powr is transactd btwn thir componnts Powr can hav divrs orms Mchanical, Elctrical, Elctronic, Thrmal, Chmical, Fluid, What about caus and ct? Input and output? Causality is an important aspct o Physical systms It is th caus and ct rlationship btwn componnts o th physical systm Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06

3 Physical Systms Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Why ar modls ndd? To study and undrstand th bhaviour or rspons o a systm whn it is subjct to various conditions. To prorm xprimnts or simulations and mak masurmnts. For dsign and tsting Control o physical systms is an important objctiv in Enginring Systmatic drivation o systm quations and Computr coding or simulation Modling o Physical systms is an ssntial prrquisit or studying rspons Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 3

4 Computr Aidd Dsign Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Digital Computr: What ar its major capabilitis and aturs? Programmabl Rapid xcution o rptitiv tasks Intrac with priphrals and machins Aordabl CAD Commrcially availabl sotwar: AutoDsk, I-DEAS, CATIA, Drawings and matrial spciications Planning o procsss Estimation Intgration with Manuacturing Automatd Invntory monitoring and control Costing Markting Entrpris managmnt Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 4

5 Stat dtrmind systms Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Stat variabls Minimum numbr o variabls rquird to dscrib th bhaviour o a systm compltly Systm quations Ordinary dirntial quations rats o chang o stats Algbraic quations constraints outputs Linar systms Wll dvlopd thory Nonlinar systms Rsort to simulation Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 5

6 Uss o dynamic modls Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Analysis Givn input utur history and initial conditions, dtrmining th outputs Idntiication Givn input history and output history, dtrmining th systm Synthsis Givn input utur history and som dsird output history, dtrmining th systm so that th input to it will produc th dsird output Control Givn th systm, dtrmining th inputs to it that will produc dsird output Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 6

7 Dynamics and CAD Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Analysis o Dynamics is mor important than Statics which may b mislading Picturs and graphs ar asir to undrstand than quations Can mathmatical aturs o dynamics b rprsntd pictorially? Can this modling mthodology b applid to any nrgy domain? Can systm quations b drivd asily rom this pictorial modl? How to simulat this modl o a dynamic systm in an asy mannr? Can simulation cod b drivd automatically? Can a pictorial modl or insight into analysis or dsign and control? Bond Graph is a uniid approach to th modling o Physical systm dynamics Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 7

8 Exampl o an lctro-mchanical systm Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India V(t) i a R a L a S :V(t) J d R b V(t) R: R a E b (t) m.. GY τ () t i i a a ω t R: R b p w Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 I: L a τ () t = µ i () t i a () b a E () t = µω() t ω ω() t I: J d 8

9 Bond graphs: A bri introduction Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Hnry Payntr (MIT, 959): Th invntor o Bond graphs. Pictorial grammar or Physical Systm Dynamics Powr bond Powr transaction as a product o ort and low variabls Elmnts Junctions, lmnts and connctions Caus and ct Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 9

10 Bond graph modlling o physical systm Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India dynamics Bond graph modling Why? Graphical rprsntation o th dynamics o th systm Ors insight into physics o th systm Applid uniormly to multi-nrgy domains Intraction o powr btwn th lmnts o th systm Rprsntation o Caus-ct rlationships Algorithmic drivation o Systm quations in I-ordr stat spac orm Suitabl or numrical Intgration..g. Rung-Kutta, Basis or modrn control thory Coding or simulation Modiy th BG, appnd or dlt part o it asily Hlps in dvloping stratgis or control and diagnosis,.g. th impdanc control stratgy (Nvill Hogan) Ovrwhlming or ghost control stratgy (Mukhrj, ) Structural control proprtis (Gnviv Dauphin-Tanguy, Christoph Suur,...) Fault idntiication and diagnosis (Gnviv Dauphin-Tanguy, Bouamama, Samantaray, Mukhrj, ) Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 0

11 Sotwar Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India CAMP-G 0-SIM SYMBOLS Shakti/Vista AMESim MATLAB/SCILAB basd coding Easy to program All control with th modlr Easy to modiy, appnd, tc. Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06

12 Powr transaction through a bond Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India ort = (t) low = (t) Variabls o powr: (t), (t) Powr = (t) (t) V I F v P Q T s τ ω Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06

13 Elmnts Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Sourcs Elmnts Junctions Transormr Gyrator Sourc o ort Sourc o low Inrtia I Stinss C Dissipation R 0 S S junction junction Transormr TF Gyrator GY Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 3

14 Causality Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India caus ct rlationship btwn lmnts/subsystms A ort = (t) low = (t) Input - Output rlationship B Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 4

15 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Eort rciving nd A Flow rciving nd B Causal strok Eort rciving nd A Flow rciving nd B Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 5

16 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India F(t) K m R v = x S : F(t) F v Exampl: A simpl mchanical systm 4 p R v I: m vt () v = m K q v v 3 R: R p p C: K - q Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 6

17 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India V(t) i i Exampl: A simpl lctrical systm L C R S : V(t) I: L it () R: R It is th sam Bond graph!!! Bond graph can modl in multi-nrgy domains can t it??? V i 4 p R i i i 3 = p p L q C i C: C q Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 7

18 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India F(t) K M R v = x v 0 = x 0 S : v 0 (t) 4 Exampl: A simpl mchanical systm q v t 0 F 0 () C: K - 0 v 7 5 R: R 8 6 I: M v () t p F(t) v 0 v v 3 S : F(t) Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 8

19 Causality o Sourcs & Junctions Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Sourc o ort Output = ct S S Sourc o low Input = caus Input = caus Output = ct = = Junctions Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 9

20 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Input = caus t () Causality o I lmnt = p = Ψ( p) Output = ct p I:M p () t = Ψ ( p) = = pd τ = ( τ) dτ M M M ct = unction t t i t t i ( caus) dτ ; t t i d(ct) dt Natural or Intgral causality or I lmnt = Mass M v unction(caus) Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 0

21 I lmnt in Drivativ Causality Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Output = ct p t () = p I:M = Ψ( p) Input = caus dp d ( () ( )) d t = p = = Ψ = ( M ) dt dt dt ct d dt Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 = ( unction (caus)) Ect dos not dpnd on past caus? Not natural causality or I lmnt

22 Causality o C lmnt Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Output = ct = Φ( q) Input = caus Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 = q q C:K () t =Φ ( q) = K q = K qd τ = K ( τ) dτ t ct = unction ( caus) dτ ti d(ct) = unction(caus) dt t t Natural or Intgral causality or C lmnt i t t i Spring K v A A dq A dt = = v B B q v v B

23 C lmnt in Drivativ Causality Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Input = caus = Φ( q) Output = ct Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 = q q C:K dq d d t = q = = Φ = K dt dt dt ( ) ( ( )) ( ) ct = d dt ( unction (caus)) Ect dos not dpnd on past caus? Not natural causality or C lmnt Spring K v A A dq A dt = = v B B q v v B 3

24 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Input = caus Output = ct Output = ct Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 Causality o R lmnt = Φ() = Φ( ) Input = caus R R ( ) Rsistanc R V A V B A B VA VB = i = = = Φ() R R = ( V V ) = Ri = R =Φ( ) A B 4

25 Transormr Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Powr consrving transormr = µ ω, τ µ = = µ TF = µ ( µ ) = ( µ ) = Ex. Gars in msh N ω τ = N N = N ω, τ ω τ N N Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 5

26 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India F(t) F(t) V(t) A.. TF Hydraulic Cylindr P V(t) A P Q Q Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 6

27 Causality or th Transormr Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 = µ µ TF = µ = µ µ TF = µ 7

28 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India = µ µ GY Powr consrving gyrator Gyrator = = µ ( µ ) = ( µ ) = µ = X V Ex. Mchanical gyrator F V F F F = µ V = µ V Z Y Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 8

29 Causality or th Gyrator Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India = µ µ GY = µ = µ µ GY = µ Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 9

30 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India x F ( t) : SE ( ) F t l l m m I : m I : m rigid, masslss l l T F x x Drivativ causality! x Dirntial Causality What dos causality tll us? x F ( t) : SE F ( t ) m l Intrprtation o th modiid systm I : m l l l T F I : m x x m 0 x C : K st Salvaging causality by BG surgry Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 30

31 Exampl o an lctro-mchanical systm Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India V(t) i a J d R a R b R: R a τ () t = µ ia () t 3 L a m V(t) E b (t).. 5 τ () t S :V(t) i i a GY a i a ω() t 6 7 E () t = µω() t b R: R b 4 8 ω p w ω() t p I: J d p Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 I: L a q 8 C: 3

32 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Vt () K R it () Elctromchanical Actuator Ft () = µ it () Had mass = M vt () = x Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 3

33 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Disk Magnt Prim ary turns Spindl motor Magntic lux Shortd turns VOICE COIL MOTOR a + - R a i a - b L a + L as R s i s L s a ( t) : SE R : R a I : L a Voic coil motor L as : I F ( t) = ki ia( t) k i F ( t) GY i a b 0 k b GY ( t) K v( t) b = b i s R : R s v ( t) I : L s I : M T Dirntial Causality R : B T Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 33

34 A simpl Machin Tool Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India θ R V ( t ): SE I : L a i θ LS G µ Y I : J R R : R a x Gar rduction N T F m TP Rotor inrtia Lad scrw Tool post inrtia θ R Dirntial Causality I : L LS θ LS P π T F I : m TP x R : R slid Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 34

35 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India r θ m A K B θ J R S ( θ ) x B = r dx B = r d θ dt θ dt = r x B θ θ A Cam - Followr (Spring Loadd) x A 0 x B A Simpliication C : K R : R s Exampl: Cam ollowr mchanism S 0 F R s : R 0 0 θ t S F ( ) x A x B r TF : θ θ THE BONDGRAPH C : K I : m I : J S 0 F θ t S F ( ) x A 0 r TF : ϑ θ I : J THE SIMPLIFIED BONDGRAPH I : m C : K R : R s Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 35

36 v B v A v E M B M A M E K AB K AE B A Engin F RB R AB F RA R AE F RE C: K AB - R: R AB C: K AE - R: R AE I: M B B V A I: M A A V E I: M E V B 0F AB V A 0F AE V B V A V A V E V E V E F E R B R A R E 36

37 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India S : F(t) F(t) K F v m 4 Driving Systm Equations p R v R I: m vt () v = x v = m K q v C: K - R: R p Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 v 3 p Q.. What do th lmnts giv to th systm? (Outputs o lmnts.) 4 = Ft ( ); p = = kq; 3 3 m = R, = R, p = R ; m Q.. What dos th systm giv to lmnts with intgral causality? (Inputs to lmnts with intgral causality.) q ; = p = q 4 3 p = = ; m p = F t kq R m = ( ) Thy can b arrangd in a matrix orm R k p F m p ( t) = q + 0 q 0 m Th I-ordr stat-spac orm! ; 37

38 Equivalnc with th classical quation? Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Applying Nwton s II law ( ) mq F t R q k q =, m q + R q + k q = F( t) F(t) m Rq kq v = q Fr body diagram Thy ar quivalnt!!! From Bond graphs q p m = = =, R p = F( t) p kq m mq = F( t) R ( mq ) kq m Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 38

39 Skat board systm F(t) M v = x q C: K - R: R K R v 0 = x 0 5 p 0 v I: M S : v 0 (t) v 0 () t 0F KR 7 v () t F(t) v 0 v v 3 S : F(t) 39

40 I. What do th lmnts giv to th systm? 3 = Ft () = v t p = M 4 0 () = Kq = = 6 7 = 6 8 = 5 7 = 8 4 R 5 5 p M F(t) K = R M S : v 0 (t) v0 () t Procdur or driving Systm Equations R 4 v = x v 0 = x 0 q v t 0 F 0 () C: K v 7 R: R 8 6 II. What dos th systm giv to lmnts with intgral causality? 7 = + 5 = 6 7 = 3 6 = p 7 = q I: M v () t p F(t) v 0 v v = = Ft () Kq p M = 3 v0 () t S : F(t) p R M v0 () t 40

41 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Simulation rom Bond graphs dx() t xt ( ) = = ( x, u, t) ; xt ( dt i ) dx = (,, ) x u t dt Using sparation o variabls, dx = ( x, u, τ) dτ x () t t dx = ( x, u, τ) dτ x ( t ) t i i t i t x ( t) x ( t ) ( x, u, τ) dτ = i t i t x ( t) = x ( t ) + ( x, u, τ) dτ i = x 0 x () t x (t i ) t i t x (t) t Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 4

42 Simulating Bond Graph modls Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India & Mor xampls Anand Vaz Prossor Dpartmnt o Mchanical Enginring Dr. B. R. Ambdkar National Institut o Tchnology Jalandhar Punjab 440, India Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 4

43 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India F(t) K m R v = x S : F(t) F v Exampl: A simpl mchanical systm 4 p R v I: m vt () v = m K q v v 3 R: R p p C: K - q Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 43

44 Exampl: Th Van dr Pol Oscillator Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India F(t) K m R v = x systm S : F(t) F v 4 p R ( q ) v I: m vt () v = m K q v v 3 R: R p p C: K - q Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 44

45 This imag cannot currntly b displayd. Exampl o an lctro-mchanical systm Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India V(t) i a J d R a R b τ () t = µ ia () t 3 L a m V(t) E b (t).. 5 τ () t S :V(t) i i a GY a i a ω() t R: R a R: R b E () t = µω() t b 4 ω ω() t p I: J d p Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 I: L a q 8 C: 45

46 v B v A v E M B M A M E K AB K AE B A Engin F RB R AB F RA R AE F RE C: K AB - R: R AB C: K AE - R: R AE I: M B B V A I: M A A V E I: M E V B 0F AB V A 0F AE V B V A V A V E V E V E F E R B R A R E 46

47 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Bond Graph or th Fluid systm F (t) R V (t) V (t) F M Cross-sctional A ara A.. TF P C:? V 0 P Q M Comprssibl luid F x x P Q Cross-sctional A ara /A.. TF R V F (t) V (t) I: M Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 I: M 47

48 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India F(t) F(t) V(t) A.. TF Hydraulic Cylindr P V(t) A P Q Q Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 48

49 .. with riction and lakag Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India F(t) V(t) F(t) R riction Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 R riction P V(t) A A.. P V TF 0 P V(t) Q R lakag P Q 49

50 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India F(t) R riction V(t) P A F(t) V(t) t () = p M piston Q..adding piston inrtia R riction R lakag A.. P V TF 0 V(t) P I: M piston P Q Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 50

51 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India P A Q P A Q x v(t) p P I: Q A l ρ l A Q P B Q Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 Fluid inrtia P B Q d dt x v = lim t 0 t x Q = lim A= v A t 0 t Applying Nwton s II Law, x lim ρ Al = ( PA PB) A t 0 t d [ ] d ρ p l = Q P P dt dt = A P A B 5

52 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India τ (t) ω(t).. µ P TF Q BG or Pump Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 Pump or motor τ (t), ω(t) P B P A Q Pump P B P A Q Q τ (t) ω(t) µ.. P TF Q BG or Motor P B P A Q 5

53 Fluid systm Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India F M Cross-sctional A ara x x M Comprssibl luid F Cross-sctional A ara Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 53

54 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Bond Graph or th Fluid systm F (t) R V (t) V (t) F M Cross-sctional A ara A.. TF P C:? V 0 P Q M Comprssibl luid F x x P Q Cross-sctional A ara /A.. TF R V F (t) V (t) I: M Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 I: M 54

55 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Hydraulic Cylindr drivn Tool post Ara = A B Ara = A A F R P A Q A P B Q B M T F R s vt () t Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 55

56 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India τ (t) ω(t) P D C Hydraulic Cylindr drivn Tool post A PRV E Q E (t) Ara = A A P A (t) Q A (t) P B (t) Q B (t) Ara = A B M T F S Vt () = x Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 56

57 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India τ (t) ω(t) µ TF DP C Q BG or Mchanical-Fluid systm P C P D Q C S :P D 0P C, AE, Q E 0P D /A A TF R:R PRV I: M T V R:R S TF: A B Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 57

58 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India τ (t) ω(t) P D C PRV E Q E (t) A τ (t) ω(t) BG or Mchanical-Fluid systm Ara = A A µ TF DP C Q P C P D Q C P A (t) Q A (t) P B (t) Q B (t) 0P C, AE, Q E 0P D Ara = A B /A A TF R:R PRV M T F S I: M T V R:R S Vt () = x TF: A B Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 S :P D 58

59 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Thumb link (passiv) String P X L String basd actuation P θ L m (opning) m (closing) Y R Y 0 A θ R L R X 0 X A R Activ ingr link String Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 59

60 Bond graph or th systm with Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India C : I : J P Dirntial causality 5 θ L 4 dirntial causality -r L TF r L TF 3 s L 0 F Ectiv during closing s L 0 F 0 s R Ectiv during opning s R 9 6 r R TF -r R TF C : I : J θ A R 3 S :τ R Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 60

61 Bond graph or th string basd prosthsis Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Ectiv during closing Ectiv during opning Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 6

62 Dvlopmnts in Bond graph thory Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Structural controllability and obsrvability Bicausality Dirntial bond graphs Multibond graphs Fault diagnosis Control stratgis Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 6

63 Dvlopmnts at NITJ Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Multibond graph modling o Rigid body mchanics Mchanisms and machins Robotic systms, Crankshat-conncting-rod-piston-cylindr, Univrsal joint, Quick rturn mchanism, Pantograph, Powr hacksaw, Epicyclic gar trains, Dirntial gar mchanism, Sot contact dynamics Rigid objcts intracting with sot matrial Biomchanics Dvlopmnt o hand prosthtic systms Extnsor mchanism o th hand, th Winslow tndon ntwork, Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 63

64 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Dvlopmnts at NITJ Control systms Coding in MATLAB Larning and taching Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 64

65 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Ruus Oldnburgr Award Conrral at th Dynamic Systms and Control Lunchon, Thursday, Dcmbr 6, 979, during th Wintr Annual Mting in Nw York, N. Y. Prsntation by Donald N. Zwip, ASME Prsidnt, , PROFESSOR HENRY M. PAYNTER, Prossor o Mchanical Enginring, Massachustts Institut o Tchnology, Cambridg, Massachustts Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 65

66 Hnry Payntr: Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Th invntor o Bond Graphs 959 At th birth o Bond Graphs 997 Upon his lction to th NAE Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 66

67 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 67

68 Summary Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Modling o Physical Systm Dynamics Bond graphs Causality Drivation o systm quations Simulation using Bond graphs Exampls Rsourcs: Books Karnopp, Margolis and Rosnbrg Amalndu Mukhrj, Ranjit Karmakar and Arun Samantaray Jan Thoma F T Brown Wolgang Borutzky Journals ASME JDSM&C, IEEE SMC Journal o th Franklin Institut - Elsvir Simpra Elsvir Simulation - SCS Othr Lctur nots: P. J. Gawthrop and G. P. Bvan, "Bond-graph modling," in IEEE Control Systms, vol. 7, no., pp. 4-45, April 007. doi: 0.09/MCS Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 68

69 Josph Anand Vaz, Dpartmnt o Mchanical Enginring, Dr B R Ambdkar NIT, Jalandhar 440, India Thank you! Qustions? anandvaz@i.org, or anandvaz@nitj.ac.in Lcturs on Bond Graph Modling o Mchatronic Systms, July Dcmbr 06 69