Modeling for Designing. An essential Stage

Transcription

1 Modeling for Designing An essential Stage Geneviève Dauphin-Tanguy École Centrale de Lille genevieve.dauphin-tanguy@ec-lille.fr

2 Outline Introduction Bond Graph methodology Industrial applications 2 Conclusion

3 Designing new technological engineering systems : a complex task Difficulties linked to the system: Multiphysics, multienergy (mechanical, hydraulic, electrical, thermal ) Mixing power and information Constraints : Energy consumption, safety and reliability Teams with specialists of different physical domains «Mechatronic approach» «Integrated design» 3 Difficulties linked to the industrial context: Economical constraints: Costs for research, production Industrial strategy : To be the first To guarantee the «just necessary» quality asked for by the market Study on virtual prototypes first

4 Integrated design Modeling Model building Analysis Model simplification Control Analysis for control Actuator choice Control designing Supervision Simulation 4 Fault Detection and Isolation Physical system/ real world Virtual Prototype Virtual world G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

5 Objective : choice of a model usable during all the steps of this design procedure - a knowledge model * with real physical insight * for all the domains of physics * for dynamic study and analysis * for energetic approach 5 - a representation model for controller designing. the bond graph tool is well adapted for that purpose G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

6 ) Functional Analysis : Decomposition in sub-systems exchanging power Word bond graph Bond Graph Modeling Procedure 2) Phenomena Analysis : Identification of physical components and phenomena transforming the supplied power into stored or dissipated energy Detailed bond graph 3) Causal Analysis : Visualisation of cause-to-effect relations and analysis of causality 6 Causal bond graph 4) Structural Analysis : Causal paths, causal loops Model reduction, Designing of actuator and sensor architecture 5) Writing of associated mathematical models : Differential equations, state equation, transfer function G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

7 ) Functional Analysis DC Motor Orifice Word bond graph Shaft e Pinion Piston Cylinder f Power = e. f Rack 7 u i DC Motor T ω Shaft T 2 ω 2 Pinion + Rack F V Piston P qv Cylinder + Orifice P env qvo Electrical +Mechanical rotation Mechanical rotation Mechanical rotation+ Translation G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25 Mechanical translation+ Pneumatic Pneumatic

8 Generalized Variables Power Variables Energy Variables Domain Effort Flow Momentum Displacement e f p ( t) = e( τ ) dτ q ( t) = f ( τ ) dτ Mechanical Translation Rotation force torque velocity ang. velocity momentum ang. moment. displacement angle Electrical voltage current flux linkage charge 8 Hydraulic pressure volume flow rate Chemical chemical potential molar flow rate pressure momentum volume mole number Thermodynamic temperature entropy flow entropy G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

9 2) Phenomena Analysis Basic Elements Sources Se, Sf 3 passive elements (receive power) R : energy dissipation C, I : energy storage Energy Storage I, C Junction Structure (O,,, GY) Energy Dissipation R 2 active elements (supply power) Se, Sf : effort source, flow source 4 junction elements (power conservative),,, GY 9 2 sensors supposed ideal De, Df Detectors De, Df G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

10 Example : DC motor I A I F U F Heat dissipation T ω U A ( R a, La ) R : R a R : b U,τ ( J, b) Se : U A U A I A U Ra U La I : I A T ω T b I A L a e I A MGY r = k I ( F ) Coupling between domains T J I : ω T e ω ω J load Electrical domain T e = k ( I F ) I A ( I ) ω = k F Mechanical domain Energy storage (magnetic, kinetic Change of physical domain

11 Orifice DC Motor shaft Pinion Piston Cylinder Hypothesis : Jpinion neglected Rack Jpinion I : L a I : J mot I : J pinion I : m crem C : C cyl R : R orif Se : ua i r GY : k ω T T 2 ω 2 T 2 r p F m Vm F A p P P q vo Se :- P env R : R a R : b mot C :/ k sh DC Motor Shaft Pinion+Rack Piston Cylinder+orifice G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

12 2) Causal Analysis Causality Convention The causal stroke is placed CLOSE to (FAR from) the element for which the EFFORT (FLOW) is known A e f B P = e. f A B A B 2 e f A B A B f e Rules for assigning causality to elements Integral causality in storage elements I and C should be preferred G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

13 Jpinion u i I : L A I : GY J mot T Ω T 2 Ω 2 I:Jpin r p F m I : m crem Vm F V A p P C : C cyl P R : R orif q vo Penv 3 R : R A R : b mot C :/ k sh No causal singularity If the pinion inertia taken into account Derivative Causality! G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

14 Orifice DC Motor shaft Pinion Piston Cylinder Rack u i DC Motor T ω shaft T 2 ω 2 Pinion + rack F V Piston P qv Cylinder + Orifice P env q v 4 u T DC Motor i ω Model libraries: Sub-models with a defined energetic environment a coherent choice of coupling variables a systematic determination of I/O variables G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

15 Singularities in causality assignment - Non determinist causality (possibility of choice on R -elements) - Derivative causality on a I- or C-element! Implicit Equations or x = ax + by + i i j cz k 5 x = i f i ( xi, y j, zk ) detected before writing equations What to do? Treate them by hand? Use an adequate software? Solve the problem physically by going back to the BG model and modify some hypothesis? G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

16 4) Structural Analysis Se: ua u i I : L A I : GY J mot I : m crem : r p A p C : C cyl R : R orif 6 R : R A R : B mot C :/ k sh Df: qv Input/Output causal path G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

17 4) Structural Analysis I : L A I : J mot I : m crem C : C cyl R : R orif Se: ua u i GY : r p A p 7 R : R A R : B mot C :/ k sh Df: qv Causal loops between R, I, C elements Gains give an approximation of time constants and natural periods R L A A s τ elect B J mot mot s τ mec m k sh crank 2 s 2 ω n T n 2π = ω n

18 4) Structural Analysis Structural Controllability Structural Observability Structural Invertibility Structural I/O decouplability Structural monitoriability Important for *building the actuator and sensor architecture *designing control laws * designing FDI and FTC systems 8 Only using graphical procedures on the BG: causal paths, causal loops and causality assignment G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

19 Simulation BG dedicated software (2Sim, CAMPG+Matlab, Symbols, MTT, Dymola Bond Graph library for Modelica.)! No need to write global mathematical models Only the relations for elements Classical simulation software (Matlab/Simulink, Modelica, Scicos ) 9 Transformation of the BG into block-diagram Mathematical models derived from the BG Transfer function State equation Differential equations G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

20 Industrial applications 3 industrial studies where modeling was an essential stage and BG methodology a true advantage RAT for Airbus A38 High speed train 2 EHA for Airbus A32 G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

21 Application : RAT on Airbus 38 (/6) Crash of the US Airways Airbus A32 on January 5 th, 29 on Hudson River, New York (bird strike resulted in an immediate and complete loss of thrust from both engines). European Aeronautic Defence and Space company 2 Airbus planes are equipped with a ram air turbine (RAT), a type of wind turbine that can be deployed into the airstream to provide backup hydraulic pressure and electrical power at certain speeds G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

22 Application : RAT on Airbus 38 (2/6) 22 G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

23 Application : RAT on Airbus 38 (3/6) 23 G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

24 Application : Ram Air Turbine on Airbus 38 (4/6) Problem: Sizing of Ram Air Turbine on Airbus A38, the biggest of Airbus planes with the greatest number of electrical devices (Fly by wire) 24 G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

25 Application : Ram Air Turbine on Airbus 38 (5/6) Methology used : BG modeling of all the devices using electrical power Calculation of the instantaneous power and global energy consumed by the electrical devices Sizing of the RAT 25 G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

26 Application : Ram Air Turbine on Airbus 38 (6/6) Great advantages in using BG tool for modeling Decomposition in sub-systems exchanging power Energy consumption estimation directly from the BG model 26 G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

27 Application 2 : High Speed Train (TGV) (/8) 27 G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

28 Application 2 : High Speed Train (TGV) (2/8) 28 catenary : system of overhead wires used to supply electricity to the locomotive equipped with a pantograph pantograph G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

29 Application 2 : High Speed Train (TGV) (3/8) Problem : the break down of the catenary Railway traction device Power Supply Filter DC/AC Inverter Induction Motor Mechanical Transmission catenary PWM Control BB36 G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

30 Application 2 : High Speed Train (TGV) (4/8) BG of Railway traction device Filter Rf Se Lf Cf Electrical part Inverter M M M Va Vb Vc Direct field oriented control Induction motor Bogie C:/K5 I3 Wheel C:/ Kess I9 3 Rs M M M LF Rs M M M LF I4 C:/K4 : -/R3 :R4 C:/ Kjac R: Cjac Ieq :/ Rwheel LM RR MGY φ r α φ r β LM RR MGY I6 (Ω) C:/ Kacc R: Cacc I5 :-/R4 :R5 Se:- Fres Rail Mechanical transmission line G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

31 Application 2 : High Speed Train (TGV) (5/8) Mechanical transmission line model. C:/Kacc I:I6 R:Cacc C:/K4 I:I4 Cem R5 -/R4 R4 th order I:I5 3 I:Ieq I:I9 I:I3 Se : - Fres /Rroue -/R3 C:/Kess R:Cjac C:/K5 C:/Kjac G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

32 Cem I:I6 C:/Kacc R:Cacc R5 C:/K4 -/R4 I:I4 R4 Application 2 : High Speed Train (TGV) (6/8) I:I5 I:Ieq I:I9 I:I3 Se : - Fres /Rroue -/R3 C:/Kess R:Cjac C:/K5 C:/Kacc C:/Kjac 32 R:Cacc C:/K4 I:I4 I:I6 R:Cjac C:/Kjac R5 -/R4 R4 Se Cem : Cem Tem R5/R3 I:I5 I:I9 I:I3 Se : - Fres /Rwheel -/R3 C:/Kess I:Ieq R:Cjac C:/K5 Fig.. SPM : fast model. Fig. 2. SPM : slow model. G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

33 Application 2 : High Speed Train (TGV) (7/8) I:I6 R:Cjac C:/Kjac BG model of the electrical part R5/R3 Se : - Fres /Rwheel I:Ieq Slow BG model of the mechanical part. 33 Resonance Mode of the train at 8.6 Hz due to the coupling between the I:L of the filter and the C of the mechanical part = resonance frequency of the catenary!! Solution: modify the value of the filter inductance L G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

34 Application 2 : High Speed Train (TGV) (8/8) No means to do in an other way than using BG models Unique way to determine the causal links between components, 34 estimate the resonance frequencies and identify the corresponding elements G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

35 Application 3 : EHA for Airbus A32 (/8) Flight control surfaces 35 G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

36 Application 3: EHA for Airbus A32 (2/8) Problem : Sizing of EHA components Hydraulic jack DC/AC network Power electronic converter β Electrical motor Hydraulic Pump Flight control surface Control I Control Ω Control β Example «fiction» : APU with Fuel Cell 6 different physical domains Hydraulic Chemical Electrical Mechanical Hydraulic Mechanical Thermal G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

37 Direct Model Hydraulic jack Application 3 : EHA for Airbus A32 (3/8) DC net chopper DC motor Pump Control surface Position reference Current control Speed control K Position control + - Duty cycle U bus I bus Df : i U M I GY I R I T m Ω m Df : Ω m R R R P Q R C R R C F V I Df : Ω G R T ch Ω G rot speed Se DC Motor Pump R C Jack Control surface G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

38 Application 3 : EHA for Airbus A32 (6/8) Sizing of actuators Actuator? e A System to control e= Load f A y Desired output De : y Determine the requirements for the actuator in terms of the power variables e A and f A and the prescribed output specifications flow f max ef=p max Admissible operating domain of a chosen actuator 38 -e max e max effort The chosen actuator is sized, oversized or inadequate? Operating curve (e A (t), f A (t)) -f max Inverse model G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

39 Application 3 : EHA for Airbus A32 (5/8) inputs Direct Model outputs Model inversion using bicausality (invertibility condition to be verified) Applications: outputs Inverse Model inputs 39 - Designing of control laws (open loop closed loop) references - Actuator sizing Inverse Model Control law Real System Variables to be controlled G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

40 Application 3 : EHA for Airbus A32 (4/8) «Classical» Causality B B e data for B f data for B f B = Ψ B ( e B ) B e B = Ψ ( f B ) 4 Bicausality B e data for B (e.g. imposed) f data for B (e.g. measured) Possible to estimate Ψ B G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

41 Application 4 : EHA for Airbus A32 (7/8) Inverse model Electrical constraints Flight Cycles Absorbed power Duty cycle Aerodyn torque 4 U bus I bus M Load current U I DC Motor T m Ω m Pump Q P Jack F V Control surface T ch Ω G SeSf Control Surface Rotation speed G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

42 Application 3 : EHA for Airbus A32 (8/8) No means to determine inverse dynamic models without using BG tool Bicausality : specific to BG tool Graphical analysis of the model structural invertibility property 42 Systematic determination of the inverse mathematical model G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

43 Bond Graph Modeling for «Integrated Design», «System Approach», «Mechatronic Approach» + Virtual test benchs Graphical representation of power exchanges Generic approach for all physical domains (analogy) 43 Easy to implement bottom-up or top-down modeling procedures Causality for analysis G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25

44 Thank you for your attention Any question? G. Dauphin-Tanguy - SIM@SL - ENS Cachan - 5//25