Dynamic Supervision in Mechatronic Systems Using Bond Graph Approach.

1. Dynamic Supervision in Mechatronic Systems Using Bond Graph Approach. D. Benazzouz, Y. Touati & B. Ouled Bouamama Solid Mechanics & Systems Laboratory (LMSS) University M’Hamed Bougara Boumerdes, Algeria * Ecole Polytechnique Universitaire de Lille-France dbenazzouz@umbb.dz

2. Presentation • Introduction • Structurelle Analysis • FDI Methods • Various Residu Generation Approaches • Study case • Modelisation & Simulation • Resultats et Comments • Conclusion

3. Introduction Safety in critical or dangerous systems, such as the chemical factories, the nuclear centers, the thermal power stations or the air planes, any component failure can be extremely dangerous. As the case Tchernobyl (Skikda-Algeria), any partial failures or component failures or process malfunctions can be a desaster and increase operating factory expenses. There are many cause of these failures(operation – component or humain..)

4. Faulty Types Sensor Faulty: Variation between the real and the measured value. • Actuator Faulty: Incoherency between command & output (pump delivers an incohérent flow with respect to its hydraulic characteristic). Controler Faulty: Caracterised by the difference between the real ouput controler value and its measure. Physical Process Faulty: Faulty due to structure modifications or model parameters.

5. Supervision Supervion: supervise the state of process in optimal functionning and gives assistance to operator in case of emergency to increase the realiability. Supervion role : Fault Detection and Isolation (FDI) Fault Tolerence Control (FTC)

6. FDI Methods with model 1-Identification: I/O of the system used to estimate various parameter values of the analytical model 2- Observer: Estimate directly output system then compare it to measured output of sensors. 3- Analytical or Information redondancy: Rewriting state equations and measure (only known var. are considered)

7. Various System Representations Biparti Graph Representation Ex: Electrical Engineering

8. Using Matrix form which represents the set of var. Z and the set of constrains C: Tij =1 if Zj Є Cj Otherwise Tij=0

9. Structurel Analysis Determines system property starting from existing constrains. This will help the designer to be able with respect to the functionning conditions to supervise and detect any faulty. To perform the structurel analysis on biparti graph, we use DM-decomposition DM-Decomposition Dulmage & Mendelsohn (1958) denoted DM-decomposition is the starting structurel analysis point. We can obtain it by appling using graph theory principal.

10. Interchange colonn to raw of the incidence matrix to obtain the low triangular matrix. S+: sub-system (observable & supervisable) S°: sub-system (observable not supervisable) S-: sub-system (not observable & not supervisable).

11. Case of Simple system: graph biparti concept is easy But, for Complex system: it usefull to apply Bond Graph analysis which is powerfull in multi-energy processes BG : oriented graph, showes dynamic var. (effort-flow) energy transfer between systems Se: effort source (voltage) & Sf: flux source (current), 3 passif elements (I, C & R), 2 junctions (0 et 1) & 2 transductors (TF (transformer) &GY (motor)) Sensors (De, Df)

12. Structural Analysis on Bond Graph The SCAP (Sequential causality application procedure) is as follows: 1 – Affect necessary causality to sources 2 – Put I & C in integral causality in preferential 3 – Affect the causality to R elements with respect to restriction junctions. 4 – In case of junction conflit, find I & C element causing conflit & put them in derivative causality. Restart 3.

13. Observability from BG (2 canditions) 1- All the elements of storage must have a causal path towards at last 1 detector (reachability condition). 2- All the elements of storage can be put in preferential derivative causality (with detector causality inversion).

14. Surveillability Condition All BG models have a correct causality, with causality inversion of storage and detector elements are over-determined systems. In case of system causality conflit, we have a sub-determined system. Suveillability canditions: 1. Sub-system is observable. 2. A default j should be in the sub-system to be observable Conflit

15. The observators The methode by observator is based on residus analysis. (Residu or fault indicator expresses incoherency between avalable information & theoratical information given by the model.

16. Fundamental Eq. of the observor All linear systems are represented as follows: Observor Eq. Are:

17. We can simplify the previous Eq. as follows:

18. Generation of the RRAs When unknown variables are all coupled, in case sup-system, the constrains which are not coupled are called RRAs We can generate RRAs by using bi-party graph & coupled notation on the incidence matrix. This couple is then a causality which allow the construction the incidence matrix & calculate unknown variables from system constrains.

19. ARRs Generation An ARR is a constraint calculated from sub-system sup-determined & observable & expressed in terms of known process variables. It has the following symbolic form:

20. ARRs Generation by BG ARRs generation by BG methodology is based on same principal as biparti graph, namely unknown variables elimination in the sub-system, sup-determined & observable. On BG model, the known variables K are those of detectors & sources and the unknown variables X are those of power links in C, I & R elements. The unknown variables elimination is systematic in BG model because of causal properties.

21. ARRs Generations by Bond Graph For ARRs generations, the supervised process BG model should be in preferential derived causality. Note that the integral causality is recommanded for simulation to avoid differential data processing illness. However, the derived causality is suited for RRAs to avoid the influence due to initiale values.

22. ARRs Generation by BG Algorithm Systematical ARRs generation algorithm from BG model is as follows: 1- Put the BG model in preferential derived causality (by inversing the detectors causality if possible). 2- Write the equations of the obtained model: Behavior, junctions, measure, sources & command. 3- For each junction equation 0 & 1 containing at least one detector, eliminate the unknown variables by following the causal path of BG. 4- An ARR is obtained starting from each regulator by comparing the measured output with the predicted value given in its command algorithm

23. Application

24. Application BG Model in derived causality:

25. Application Equations of the system are obtained from the BG model: Where Q1, Q2 reprent Volumes in tank 1 & 2, R1 & R2 are discharge inverse capacity through the 2 elctromagnetic valves:

26. Simulation Evolution of V1 & V2 as function on time (without default)

27. ARRs Generation Using ARRs generation rules starting from BG

28. From the 6 ARRs, we can deduce the default signature matrix to determine the isolability & the detectability of default

29. Simulation 2-ARRs Let’s take examples to the behavior of RRAs in case of faulty 1- Residus response to leakage default on tank "C1" ARR1 ARR2 ARR3

30. Simulation 2-ARRs 2- Residus response to leakage default on tank ’C2’ r1 r2 r3

31. Simulation 2-ARRs 3- Stopped (bouchage) default in tube between the 2 tanks r1 r2 r3

32. Conclusion The advantages of this approach (structural) comparade to appraoch based on observer are: Simplicity of comprehentions of ARRs since they correspond to relations & variables which are fixed by the BG model, of the physical process, these relations are deduced directly from graphical representation, they can be generated in symbolic form & thus adapted to a data processing implementation. The goal of BG representation is to use only one modeling tool, generation of ARRs, structural analysis & surveillability & sensors placement.