Bond Graph for Modelling, Analysis, Control Design, Fault Diagnosis

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1 Bond Graph for Modelling, Analysis, Control Design, Fault Diagnosis Geneviève Dauphin-Tanguy Christophe Sueur Laboratoire d Automatique et d Informatique Industrielle de Lille

2 Bond Graph Research Group Laboratoire d Automatique et d Informatique Industrielle de Lille Ecole Centrale de Lille 6 academics (2 Profs, 2 associate profs, 2 assistant profs) 0 PhD students Application areas : power systems (electrical machines, photovoltaic systems, fuel cells), thermofluid process, car industry

3 Studies performed in collaboration with Peugeot -Citroën Mechatronic design of an automatic gear box Clutch management and drive comfort Mechatronic design of an active hydraulic suspension Thermal comfort regulation in a car interior Modelling and simulation of a fuel cell system Analysis of structural properties of bond graph models Robustness of control laws for systems with parametric uncertainties.. Rosario - 22//02 LAIL - Ecole Centrale de Lille 3

4 Why a bond graph approach? Multidisciplinary systems need for a communication language between people from different physical domains Need for models with physical insight (virtual testing facility) Unified modelling methodology for knowledge storage in model libraries Integrated («mechatronic») design of controlled systems Rosario - 22//02 LAIL - Ecole Centrale de Lille 4

5 Mechatronic design Objectives Identification Analysis Validation Simulation Modelling Control Simplification Actuators Sensors Maintaining Faulty mode Diagnosis Fault Detection and Isolation Rosario - 22//02 LAIL - Ecole Centrale de Lille 5

6 - Mechatronic design of an automatic gear box computer engine torque converter automatic gear box vehicle Complete driveline Differential, Transmission shaft Wheels, Vehicle mass, air resistance, road friction Rosario - 22//02 LAIL - Ecole Centrale de Lille 6

7 - Mechatronic design of an automatic gear box Problem statement Design control laws for the driving of an automatic gear box by a computer with the following objectives: Complete satisfaction of the customer corresponding to a variation of the engine torque as continue as possible (no jerk in acceleration during a shift) Respect of technological constraints (actuator response duration, minimization of the energy dissipated in the clutchs) When to shift? How to shift? Rosario - 22//02 LAIL - Ecole Centrale de Lille 7

8 - Mechatronic design of an automatic gear box Automatic gear box : physical scheme Arrangement of 2 epicyclic gear trains which allows 3 ratios plus one reverse ω Planet Different ratios : one element blocked or 2 elements maintained at the same speed ωplanet carrier ω ω ωring ω R PC = P ωpc m Clutches between 2 rotating elements Brakes between one element and the housing block Rosario - 22//02 LAIL - Ecole Centrale de Lille 8

9 - Mechatronic design of an automatic gear box Bond graph model of the automatic gear box brake :housing :housing :PC2 Free wheel clutch 2 :P brake 2 :m2 :Jinp :-m2 :input :-m :m :load Clutch :R :PC_R2 :friction Rosario - 22//02 LAIL - Ecole Centrale de Lille 9

10 - Mechatronic design of an automatic gear box Bond graph model of a clutch or a brake :friction_coeff :pressure torque pressure slip Coulomb friction depending on the pressure applied on the clutch disks, defining the «limited torque» If clutch torque < limited torque clutch closed, all the torque transmitted If clutch torque = limited torque clutch opened, slipping velocity Rosario - 22//02 LAIL - Ecole Centrale de Lille 0

11 - Mechatronic design of an automatic gear box Decision block Contains the schift schedule (diagram throttle position vs vehicle speed) which permits to know «when to shift» Different programs: economical, sport, snow When a shift is decided, the different pressures in the clutches are controlled pressure time «How to shift» : - action on only 2 clutches or 2 brakes at the same time, - control of the pressure to have a smooth shift and no jerk in acceleration Rosario - 22//02 LAIL - Ecole Centrale de Lille

12 - Mechatronic design of an automatic gear box Bond graph model of the vehicle : AGB output torque left_shaft :Jshaft_l :Cshaft_l :Jwheel_l :Cwheel_l left_wheel :Mveh vehicle :rwh_ :diff :slope :Idiff :rwh_2 :air_friction differential right_shaft :Jshaft_r :Cshaft_r :Jwheel_r :Cwheel_r right_wheel Rosario - 22//02 LAIL - Ecole Centrale de Lille 2

13 2- Clutch management and drive comfort Ojectives: Reduce the well-known fore and aft oscillation of a vehicle occuring when a sudden torque variation takes place in the transmission (throttle step sollicitation) Satisfy comfort and driving pleasure Means: Define an hydraulic-electronic-mechanical actuator transforming the numerical output into pressure on the plates of the clutch Design control laws for this electrohydraulic servovalve Rosario - 22//02 LAIL - Ecole Centrale de Lille 3

14 3 - Thermal comfort regulation in a car interior Usual climate control Try to reach and maintain the passenger compartment temperature to a specified target temperature. The regulator acts on the mixing flap to increase or decrease the blown air temperature. Usually, a proportional strategy is used to control the mixing flap T a,target + - ε Prop. T b,target Mixing Flap T b CAB T a Rosario - 22//02 LAIL - Ecole Centrale de Lille 4

15 3 - Thermal comfort regulation in a car interior Usual climate control! Usually the air temperature in the compartment does not reach the target temperature Tcons Thab( C) 0 5 Thab( C) Tcons Text = -0 C temps(s) heating Text = 25 C temps(s) cooling) Rosario - 22//02 LAIL - Ecole Centrale de Lille 5

16 3 - Thermal comfort regulation in a car interior Comfort strategy comfort : much more than only thermal comfort. Our five senses, our cerebral state, our thermal state have an influence on our comfort estimating. thermal sensations rather than thermal comfort - a very subjective notion. in PSA Peugeot-Citroën, quantitative scale to evaluate a thermal sensation : an integer between (very cold) and 9 (very hot) sensation. Objectives: define a regulation strategy for a climate controller for car interior, taking into account the car passenger's thermal sensations. Rosario - 22//02 LAIL - Ecole Centrale de Lille 6

17 3 - Thermal comfort regulation in a car interior Block representation of the model driving conditions climatic conditions ACTUATORS recycling flap mixing flap blower tension compressor on/off spreading air flaps thermal car interior model air temperature walls temperature air speed physiological model clothes activity thermal feelings interior geometry materials properties REGULATOR SENSORS e Rosario - 22//02 LAIL - Ecole Centrale de Lille 7

18 3 - Thermal comfort regulation in a car interior Physiological model human body divided into seven parts called segments: the head, the trunk, the left arm, the right arm, the hands, the legs and the feet. head and hands segments are bare. bare segment center muscle fat skin center muscle fat skin air clothes dressed segment Rosario - 22//02 LAIL - Ecole Centrale de Lille 8

19 3 - Thermal comfort regulation in a car interior Physiological model respiration convection convection BLOOD convection convection conduction conduction conduction CENTER MUSCLE FAT SKIN shivers Activity evaporation Sun radiation convection walls radiation AMBIENT AIR R O MEDIUM AIR METABOLISM Rosario - 22//02 LAIL - Ecole Centrale de Lille 9

20 3 - Thermal comfort regulation in a car interior Physiological model R To the blood C:C(m) Bc Bc(c) Bc (f) C: Cblood 0 Tblood Bc(s) Bc (m) Sf Qb (m) Td (c) 0 T(m) Sf :Qsh (m) Sf:Qa (m) R Td (m) to the fat For each segment Blood layer Muscle layer Rosario - 22//02 LAIL - Ecole Centrale de Lille 20

21 3 - Thermal comfort regulation in a car interior Physiological mathematical model x state vector (order = 57) : temperature, water mass, sudation production and water partial pressure of the layers. u input vector (size = 4) : air temperature and air speed of the ambient air close to the 7 segments. d disturbance vector (size = 35) : ambient air humidity, sun and wall radiation on clothes and skin layers. y output vector (size = 7) : thermal feelings of the 7 segments. x = y = f ( x, u, d) g( x, u, d) Rosario - 22//02 LAIL - Ecole Centrale de Lille 2

22 3 - Thermal comfort regulation in a car interior Linearized physiological mathematical model A nominal functioning point defined as a comfortable situation for the human (air temperature=299k, air speed=0.5m/s and humidity=50%). Two linear models containing saturations, because heat transfers are different whether the body is warm or cold. x = ( ba + baw y = C x + D u m < K x < M c ) x + B u + E d + F b = if the body is cold, and 0 if not. F vector that results from constant thresholds due to saturations. K matrix selecting the x components concerning the saturations. Rosario - 22//02 LAIL - Ecole Centrale de Lille 22

23 3 - Thermal comfort regulation in a car interior Physiological model : simplifications 34.6 comparison of linear and non-linear 4.8 comparison of order 57 and order 9 linear models order 9 model non linear model 4.75 tru 34 nk ski 33.8 n te 33.6 mp er atu 33.4 linear model air temperature=22 C air humidity=50% trunk sensation order 57 model 33.2 air speed=0.m/s time (s ) time(s) Trunk skin temperature Trunk sensations Rosario - 22//02 LAIL - Ecole Centrale de Lille 23

24 3 - Thermal comfort regulation in a car interior Proposed comfort strategy Control strategy based on the thermal feelings : Determine the air temperature close to the head driver to ensure him a comfortable thermal feeling (level 5 in PSA scale) Take into account the wall temperatures and the air flows in the compartment. Compute the best air temperature target for the driver to be comfortable by using the inverted human model In case of chilly driver, a target sensation superior to 5 can be asked for Rosario - 22//02 LAIL - Ecole Centrale de Lille 24

25 3 - Thermal comfort regulation in a car interior Proposed comfort strategy T a Thermal feelings target Inverted human T a,target + - ε Regulator T b,target Mixing Flap Tb Cab Human Thermal feelings Wall temp. model Air temp. model T air,model T wall Predictive control (GPC) Rosario - 22//02 LAIL - Ecole Centrale de Lille 25

26 3 - Thermal comfort regulation in a car interior Comfort strategy - Air temperature model linear convex formulation: T α α a = ( + )( λatout + ( λa T + τ s + τ s ) 2 b T a air temperature, T out outside air temperature, T b blown air temperature, convex parameter depending essentially of the blown air flow and the vehicle speed. There are two dynamic modes : a fast mode caused by the mass transfer and a slow mode caused by the thermal transfers with the outside. Rosario - 22//02 LAIL - Ecole Centrale de Lille 26

27 3 - Thermal comfort regulation in a car interior Comfort strategy - Wall temperature model first order model: T w = ( )( λwtout + ( λw) Ta ) + τ s w T w the surface temperature, T a the air compartment temperature close to the surface. Experiments in a wind tunnel to identify the parameters of each air temperature model and wall temperature model : several wind-tunnel air flows (for the air flow due to the vehicle speed), several outside temperatures, several blown air temperatures and flows Rosario - 22//02 LAIL - Ecole Centrale de Lille 27

28 3 - Thermal comfort regulation in a car interior Comfort strategy 6 HEATING 9 COOLING thermal feeling 4 2 thermal feeling Ta( C) time(s) time(s) Ta( C) time(s) time(s) Rosario - 22//02 LAIL - Ecole Centrale de Lille 28

29 4 Modelling of a fuel cell system engine reforming H 2 Compressor i U P max? fuel ( natural gaz, methanol) air Humidifier Compressor H 2 humid air Fuel Cell recovering recycling Rosario - 22//02 LAIL - Ecole Centrale de Lille 29

30 4 Modelling of a fuel cell Fuel cell : principle anode electrolyte 2 O cathode H 2 O 2 H O H 2O + e 2 2 O2 + 2 e O e load Rosario - 22//02 LAIL - Ecole Centrale de Lille 30

4 Modelling of a fuel cell Fuel cell : tubular design mesh α mesh 2 ½ anode interconnect interconnect fuel,i α 2 Anode canal fuel,o gaz,diffa Anode diffusion zone H 2 Ov producted cathode Reaction

31 4 Modelling of a fuel cell Fuel cell : tubular design mesh α mesh 2 ½ anode interconnect interconnect fuel,i α 2 Anode canal fuel,o gaz,diffa Anode diffusion zone H 2 Ov producted cathode Reaction zone anode active layer Q air electrolyte anode electrolyte post combustion interconnect Cathode active layer air,diffc Cathode diffusion layer Fuel flow (hydrogen) air,e α 2 Cathode canal ½ cathode i nterconnect air,s Rosario - 22//02 LAIL - Ecole Centrale de Lille 3 α environment

32 4 Modelling of a fuel cell Variables Fluid Pressure: P Temperature: T Mass or molar flow rate: Enthalpy flow H = m. c. p T m or n Chemical reaction Molar flow rate: n Chemical potential : µ Electrical Current: Voltage: i U Rosario - 22//02 LAIL - Ecole Centrale de Lille 32

33 FC Word BG load U i n O 2,cons Electro-chemical reaction Q ohm, e n H 2,cons n H 2 Ov,prod m air, e T air, e MSf MSf Se H T environt m H air,e air,e T gf T wf cathode + Cathode canal + interconnect Q ohm, c Q ohm, elc electrolyte Q ohm, a Q ohm, ela anode + anode canal + interconnect m gaz,e H T gf T wf gaz,e MSf MSf Se H T environt m air, s Pext MSe T ext MSe T air, s m gaz, s T gaz, s Pext MSe T ext MSe Pext T ext Pext T ext Rosario - 22//02 LAIL - Ecole Centrale de Lille 33

34 E le c tr o l y te Q ohm, ela Anode active layer nh 2,diffa nh 2 Ov,diffa n H 2Ov,prod. diffa n Ar,diffa Q diffa H gaz, diffa anode diffusion zone nh 2,diffa nh 2 Ov,diffa n H 2Ov,prod. diffa n Ar,diffa Q diffa H gaz, diffa Anode canal Q pba Anode intercon nect m gaz,e H T gf T wf gaz,e Q ohm, a nh 2,cons nh 2 Ov,prod m gaz,s P ext T ext T gaz, s Electrochemical réaction U i no 2,cons FC Anode Word BG Rosario - 22//02 LAIL - Ecole Centrale de Lille 34

35 P cnlaj m gaz, sj x, M i, cnlaj i * n P H 2 Ov, cnlaj H 2Ov, cnlaj n H 2, sj n H 2Ov, sj n Ar, sj 0 * P Ar,cnlaj 0 C cnlaj * P H 2, cnlaj n Ar, cnlaj 0 n H 2, cnlaj T cnlaj H gaz, cnlaj n H 2, ej n Ar, ej n H 2Ov, ej x, M i, ej i m gaz, ej n = 2 Fuel supply m gaz, ej H, ej mgaz, ej. xh, ej. M H 2 2 T cnlaj H gaz, sj 0 H gaz, ej n H 2Ov, proddiffaj. n H 2Ov, diffaj n Ar, difafj n H 2, diffaj Q diffaj H gaz, diffaj Q dpbaj anode J-th diffusion zone jth anode interconnect Anode canal BG Rosario - 22//02 LAIL - Ecole Centrale de Lille 35

36 E l e c t r o c h e m i c h a l r e a c t i o n n H 2, n H2Ov, consj prodj 0 Q ohm, aj µ Ar, caaj n Ar,caaj µ H 2Ov, CC caaj caaj 0 nh 2 Ov,caaj nh 2,caaj Q ohm, elaj electrolyte 0 µ H 2,caaj H caaj T caaj 0 nh 2 µ H 2,caaj nh 2 µ µ Ov,diffaj H 2Ov, Q diffaj,diffaj n H2 Ov,prod. diffaj n Ar,diffaj T caaj T caaj H 2Ov, caaj caaj µ Ar,caaj H gaz, diffaj R R diffaj * P H2, cnlaj n H 2,diffa * P n H 2 Ov, cnlaj H 2 Ov,diffaj * P H 2Ov, cnlaj n H2 Ov,prod. diffaj * P Ar T cnlaj, cnlaj R pdcj diffaj * P Ar,cnlaj 0 n Ar,cnlaj P ext P cnla * P H 2Ov,cnlaj ou ( j + ) CC cnlaj 0 nh 2 m Ov,cnlaj ou gaz,s m gazj * P H2,cnlaj nh 2,cnlaj 0 x i,cnlaj, M i H gaz, nh 2,ej nh 2 Ov,ej H gaz, n Ar,ej s x i,e ou x i,cnla m gaz, e n Ar,diffaj n Ar,sj n H 2 Ov,sj n H 2,sj Q 0 H gaz ou, e H gaz ( j ) H gaz, diffaj m gaz,s if last mesh P cnlaj T cnlaj cnlaj R H ou thermj m gaz s m, ou gazj T ext T cnla environment or mesh (j+) ou ( j + ) gazj ( j ) T gaz,s if last mesh ou Q dpbaj m gaz, ( j ) Rosario - 22//02 LAIL - Ecole Centrale de Lille 36

37 cathode active layer no 2,cons Q ohm, c RS R c ì O2, cac ì H2, caa TF / υo 2 TF nef ÄG v TF / υ H 2 TF υ H 2 Ov nh 2,cons electrolyte load U i Q ohm, el RS R el E η ohm i RS R c i ηpol i η diff R pol R diff ì H 2Ov, caa nh 2 Ov,prod anode active layer T caa Q ohm, a Electrochemical reaction Rosario - 22//02 LAIL - Ecole Centrale de Lille 37

38 x, M i, cnlaj i * n P H 2 Ov, cnlaj H 2Ov, cnlaj C cnlaj * P H 2, cnlaj n H 2, cnlaj H gaz, cnlaj x, M i, ej i P cnlaj m gaz, sj n H 2, sj n H 2Ov, sj n Ar, sj 0 * P Ar,cnlaj 0 n Ar, cnlaj 0 n H 2, ej n Ar, ej n H 2Ov, ej m gaz, ej T cnlaj T cnlaj H gaz, sj 0 H gaz, ej n H 2Ov, proddiffaj. n H 2Ov, diffaj n Ar, difafj n H 2, diffaj Q diffaj H gaz, diffaj Q dpbaj anode Diffusion zone j interconnect anode j BG to Simulink Rosario - 22//02 LAIL - Ecole Centrale de Lille 38

39 4 Modelling of a fuel cell Results Complete dynamic model of the fuel cell system (no similar result in the literature, only static models) Simulation results validated by comparison with experimental data Work with PSA is running for: Control designing : how to maximize the power delivered by the fuel cell system Fault diagnosis Rosario - 22//02 LAIL - Ecole Centrale de Lille 39

40 5 - Structural properties of bond graph models A z B LSS m w G (m, J) theta bs RSS b s 2 m w2 x C w b w C w2 b w2 Vr V r 2 Bicycle heave and pitch physical model Rosario - 22//02 LAIL - Ecole Centrale de Lille 40

41 5 - Structural properties of bond graph models I : m Se : F mt C : LSS 0 0 C : RSS TF TF 0 0 R : bs I : m w I : J I : m w2 R : b s 2 C : C w C : C w2 R : b w 0 0 R : b w2 Sf : Vr Sf : V r 2 Bicycle heave and pitch BG model Rosario - 22//02 LAIL - Ecole Centrale de Lille 4

42 5 - Structural properties of bond graph models Passive model State equation x = Ax + Ed p x = q d = I C d d 2 = inertia impulses spring displacements d = F masstransfer d 2 = V V road road 2 Rosario - 22//02 LAIL - Ecole Centrale de Lille 42

43 5 - Structural properties of bond graph models Passive model State equation x = Ax + Ed order n of a model : number of I and C elements in integral causality when a preferred integral causality is assigned to the bond graph model BG-rank q of the state space matrix A : number of I and C elements in derivative causality when a preferred derivative causality is assigned to the bond graph model. number of structurally null modes of A-matrix : number of I and C elements which have to stay in integral causality when a preferred derivative causality is assigned to the bond graph model Rosario - 22//02 LAIL - Ecole Centrale de Lille 43

44 5 - Structural properties of bond graph models Passive model State equation x = Ax + Ed minimum number of actuators for the model to be controllable : If BG-rank A = n, the model is controllable with a single actuator If BG-rank A = n-k, for the model to be controllable, k well-located actuators are needed minimum number of sensors for the model to be observable : idem Rosario - 22//02 LAIL - Ecole Centrale de Lille 44

45 5 - Structural properties of bond graph models Design of the measurement and control architecture for the active system definition of the control objectives what variables to be controlled? for what performances (dynamical or frequential criteria)? with what strategy (pole placement, disturbance rejection, )? what type of control law? state feedback? Is the state measurable? output feedback? Rosario - 22//02 LAIL - Ecole Centrale de Lille 45

46 5 - Structural properties of bond graph models Design of the measurement and control architecture for the active system Choice here State feedback for pole placement and rejection of the disturbance corresponding to the mass transfer due to driver actions (braking or accelerating) on the 2 velocity variables (heave and pitch)! the 2 variables (absolute velocities) to be controlled are not measurable an observer is needed! We want to perform input/output decoupling 2 control inputs are needed Rosario - 22//02 LAIL - Ecole Centrale de Lille 46

47 Rosario - 22//02 LAIL - Ecole Centrale de Lille Structural properties of bond graph models Design of the measurement and control architecture for the active system 2 outputs to be controlled : not measurable (Df*) measurement vector (Df) 2 control inputs (MSe) disturbance vector measurable to be rejected (Se) non- measurable (Sf) = = J V m y y y ω 2 = = 2 2 rel rel V V z z z = = 2 2 F act act F u u u = masstransfer F d = 2 2 road V road V d

48 5 - Structural properties of bond graph models Design of the measurement and control architecture for the active system Df* : V m I : m Se : F mt Df : V s MSe: F a C : LSS TF TF Df* : J R : bs I : m w I : J I : m w2 R : b s 2 ω 0 C : RSS Df : V s 2 MSe : F a2 C : C w C : C w2 0 0 R : b w Sf : Vr Sf : V r 2 R : b w2 Rosario - 22//02 LAIL - Ecole Centrale de Lille 48

49 Conclusion * bond graph : language quite «strange» which needs a learning time * Could appear difficult to implement, but what is difficult is PHYSICS * more and more introduced in the industrial world in France (better than in the academic world!) Rosario - 22//02 LAIL - Ecole Centrale de Lille 49

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