1. SEC PI Meeting 10/00 Fault-Adaptive Control Technology Gabor Karsai Gautam Biswas Sriram Narasimhan Tal Pasternak Gabor Peceli Gyula Simon Tamas Kovacshazy Feng Zhao ISIS, Vanderbilt University Technical University of Budapest, Hungary Xerox PARC

2. SEC PI Meeting 10/00 Objective Develop and demonstrate FACT tool suite Components: Modeling approach Hybrid Diagnosis and Mode Identification System Discrete Diagnosis and Mode Identification System Dynamic Control Synthesis System Transient Management System

3. SEC PI Meeting 10/00 Model-based Approach Modeling Environment Model Database Run-time Environment Hybrid/Discrete Diagnostics Controller selection Transient management Run-time platform (OCP) Design-time and run-time activities are separated Technology target: run-time SW

4. SEC PI Meeting 10/00 What to model?

5. SEC PI Meeting 10/00 Run-time System Architecture Reconfigurable Monitoring and Control System Hybrid Observer Hybrid Diagnostics Failure Propagation Diagnostics Active Model Controller Selector Monitor/ Controller Library Transient Manager Reconfiguration Controller Fault Detector Tools/components are model-based Embedded Models Embedded Models

6. SEC PI Meeting 10/00 Modeling language summary System [plant] models Physical components and assemblies Aspects:  Structure: hierarchy and interconnectivity  Bond graph: quantitative/discrete nominal behavior, discrepancies  Local failures: failure modes, discrepancies,alarms  Failure propagations: causal chain of events Failure models  Fine-grain: parametric failures in terms of bond-graph parameters  Large-grain: (discrete) failure modes and their functional effects (discrepancies) Multi-modal behavior  Switched junctions in the bond graph model  Discrete modes in failure propagation graphs Component types and system instances

7. SEC PI Meeting 10/00 Modeling language summary Functional models Modes contain Capabilities that reference Parameters in Components Controller models Hierarchical signal flow blocks TBD: Sensor/actuator interfaces Controller characterization  Conditions for using a controller architecture

8. SEC PI Meeting 10/00 Continuous behavior is interspersed with discontinuities Discontinuities attributed to  supervisory control and reconfiguration ( fast switching )  modeling abstractions ( parameter & time-scale ) Modeling language based on hybrid bond graphs (Jour. Franklin Inst. ‘97) Bond graphs for energy-based modeling of continuous behavior Switching junctions model controller and autonomous jumps systematic principles: piecewise linearization around operating points & derive transition conditions ( CDC’99, HS’00 ) Plant modeling: Nominal behavior Dynamic Physical Systems

9. SEC PI Meeting 10/00 Plant modeling: Nominal behavior Example Hybrid system: Three tank model of a Fuel System ON OFF 1,2,3,5,7,8: s off i s on i R23v h i = level of fluid in Tank i H i = height of connecting pipe V1V5 Tank 1Tank 2Tank 3 h1h1 h2h2 h3h3 H1H1 H2H2 H3H3 H4H4 V2V3V4V6 R1R2 Sf1 Sf2 R12v R12n R23n R23v h 3 <H 3 and h 4 <H 4 R12v C1C2 C3 R2R12nR23n 7 h 3  H 3 or h 4  H 4 ON OFF h 1  H 1 or h 2  H 2 ON OFF 4: h 1 <H 1 and h 2 <H 2 1313 1515 14 Sf1Sf2 0001 R1 21 22 20 12 8 6 4 3 21 1 1414 1212 1818 1616 1717 6: 5 9 10 11 13 15 16 17 18 23 24 6 controlled junctions (1,2,3,5,7,8) 2 autonomous junctions (4,6)

10. SEC PI Meeting 10/00 GME Model: Three Tank System

11. SEC PI Meeting 10/00 Application example: Fuel System Control for Fighter/Attack Aircraft Problems: Maintain fuel flow to the engines Maintain A/C center of gravity Affected by modes of operation: attack, cruise, take-off, and landing Compensate for component degradations and failures

12. SEC PI Meeting 10/00 Simplified Fuel System Schematics Pump Transfer Tank FM Pump Wing Tank Feed Tank Pump Load (Engine) Detailed Model of AC Pump One Side Only

13. SEC PI Meeting 10/00 Hybrid Bond Graph Model (Simplified Fuel System) Sf n TF 01 3 1 1 I m1 2 R R1 I m2 MGY a 4 5 6 7 8 Bond Graph Fragment: AC Pump Pump BG Fragment 0 1 I m p2 R R p3 CCWCCW Pump BG Fragment 10 I m p1 R R p1 C C TR R R p2 0 1 R R p4 R R p4 R R Load 1 I m p3 CCFCCF Pump BG Fragment 0 1 Controlled Junction Level Control Valve Fuel System BG: one side (valves – controlled junctions not shown)

14. SEC PI Meeting 10/00 Plant modeling: Nominal behavior Using the Hybrid Bond-Graph Hybrid Bond-graph Model Hybrid Bond-graph Model Hybrid Automata Generation Hybrid Automata Model Hybrid Observer Bz -1 C A xkxk X k+1 ykyk ukuk m3m3 m1m1 m2m2 Mode switching logic Continuous observer System Generation

15. SEC PI Meeting 10/00 Plant modeling: Nominal behavior Implementation of the hybrid observer Embedded Hybrid Bond-graph Model Embedded Hybrid Bond-graph Model Generate Current State-Space Model (A,B,C,D) Recalculate Extended Kalman Filter Extended Kalman Filter Extended Kalman Filter u k,y k XkXk Calculate: transition conditions, next states On-line Hybrid Observer Mode change Detector Not necessary to pre-calculate all the modes, only the immediate follow-up modes are needed. High-level Mode (Switch settings) Implement continuous + switching behavior

16. SEC PI Meeting 10/00 Plant modeling: Nominal behavior Hybrid Observer: Tracking tank levels through mode changes Mode 1: 0  t  10: Filling tanks v1, v3, & v4 open, v2, v5, & v6: closed Mode 2: 10  t  20: Draining tanks v2, v3, v4, & v6 open, v1, & v5: closed Mode 3: 20  t : Tank 3 isolated v3 open, all others: closed h1h1 h2h2 h3h3 : actual measurement : predicted measurement V1V5 Tank 1Tank 2Tank 3 h1h1 h2h2 h3h3 H1H1 H2H2 H3H3 H4H4 V2V3V4V6 R1R2 Sf1 Sf2 R12v R12n R23n R23v

17. SEC PI Meeting 10/00 f h’ u Observer and mode detector Plant y r ŷ Fault detection [Binary decision] mimi u = input vector, y = measured output vector, ŷ = predicted output using plant model, r = y – ŷ, residual vector, r= derived residuals m i = current mode, f h = fault hypotheses Hybrid models Diagnosis models hypothesis generation hypothesis refinement progressive monitoring Fault Isolation - Nominal Parameters Fault Parameters Symbol generation fhfh FDI for Continuous Dynamic Systems Hybrid Scheme Parameter Estimation

18. SEC PI Meeting 10/00 Diagnosis results Measured variables e10 and f3 under fault conditions Qualitative diagnosis results Step 0 Step 1Step 2 For more details: see (i) Mosterman and Biswas, IEEE SMC’99 & (ii) Manders, Narasimhan, Biswas, & Mosterman, Safeprocess 2000.

19. SEC PI Meeting 10/00 FDI for Continuous Dynamic Systems Quantitative Analysis: Fault Refinement,Degradations True Fault (C 1 ) Other hypothesis (R 12 ) fhfh fh’fh’ Multiple Fault Observers

20. SEC PI Meeting 10/00 Discrete Fault Models Timed Failure Propagation Graph Failure Mode Discrepancy D +Alarm Sensor Time Interval

21. SEC PI Meeting 10/00 Discrete Fault Models Graphical Representation in GME Propagation Attributes: Time delay Likelihood

22. SEC PI Meeting 10/00 Discrete Fault Models Research Issues: Managing complexity in models Locality: Some phenomenon are not local (e.g. fire in the engine) or are a composite of local phenomena To provide useful information the diagnosis must trace failures to individual components Failure Modes are attributes of components Hierarchy For scalability it is important that the model accommodates diagnosis with different resolution An FPG at one level will often incorporate Failure Modes of components at a lower level

23. SEC PI Meeting 10/00 Discrete Fault Models Research Issues: Semantics of models Failure Mode: A condition of a component, which manifests in abnormal behavior.  Structural defect: parameter deviation  Failure modeled as “input” Discrepancy: An abnormal change in system state  Transition into abnormal state  Normal state, but abnormal transition Fault Propagation: Ordering of events Where an event is a region in the extended system state space  Input x State x Next State

24. SEC PI Meeting 10/00 Discrete Fault Models Research Issues: Expressing Constraints and Interactions Incompatibility When symptoms (or causes) can not co-occur ( stuck_open  stuck_closed ) Additivity When the combination of effects produces an extra effect ( primary and backup fail ) Cancellation When effects negate, decrease, or mask each other

25. SEC PI Meeting 10/00 Discrete Fault Models Research Issues: TFPG, FSM and Diagnostics A model of a system as a timed (non- deterministic) Finite State Automata provides sufficient information to draw the full TFPG Diagnosis can be performed using a partial TFPG model of the system

26. SEC PI Meeting 10/00 Discrete Fault Models Research Issues: Implementing the Discrete Diagnostics Extended Relational Algebra Relational Algebra is used in databases to manipulate relations Extended Relational Algebra allows nested relations This allows to model logical constraints involving arbitrary logical expressions Role Discrete fault models as FSM-s The complex state transition function of FSM-s can be represented using the Extended Relational Algebra and OBDD-s as the physical data structure

27. SEC PI Meeting 10/00 Component Digraph A link represents the fact that the faulty operation of the source component results in the faulty operation of the destination component A Transition Event represents the cause and nature of the change: Failure Propagation Graph links each transition event to its immediate successor. Only failure trajectories are represented Discrete Fault Models Relating an FPG to FSM Flow Controller Flow Sensor PipeValve V FC FSP

28. SEC PI Meeting 10/00 Discrete Fault Models Relating an FPG to FSM: Example

29. SEC PI Meeting 10/00 Discrete Fault Models Relating an FPG to FSM: Composed FSM

30. SEC PI Meeting 10/00 Discrete Fault Models Relating an FPG to FSM: FPG

31. SEC PI Meeting 10/00 Discrete Fault Models Diagnosis using Extended Relational Models Contents of the hypothesis set: State (Which nodes are we “in”) Failure modes (Which got us “here”) All combinations Previously Hypothesized Set of Alarm Instances Ringing Alarms Next Hypothesized Set of Alarm Instances Previously Hypothesized Set of Failure Modes Any Set of Failure Modes Set of Failure Mode Instances

32. SEC PI Meeting 10/00 Discrete Fault Models Summary Extended Relational Models offer a general formalism to express causality relations between failures and their symptoms, as well as constraints, interactions and composition Extended Relational Models can also represent ordering of transition events in a dynamic system Failure Propagation Graphs have been disambiguated by redefining them with a precise mapping to the Extended Relational Model See MSc thesis of Tal Pasternak on ISIS website

33. SEC PI Meeting 10/00 Transient Management

34. SEC PI Meeting 10/00 Data processing for FD

35. SEC PI Meeting 10/00 Towards an OCP implementation: Model-based software generation Software models: Controllers Datatypes Architectures

36. SEC PI Meeting 10/00 Plans Vanderbilt/ISIS Improve modeling language Finish implementing Hybrid Diagnostics Develop controller selection component Fuel system example Integration with OCP Technical University of Budapest Transient management techniques Controller examples Xerox/PARC Data processing for fault detection