Fault-Adaptive Control Technology

1. 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. Objective • Develop and demonstrate FACT tool suite • Components: • Hybrid Diagnosis and Mode Identification System • Discrete Diagnosis and Mode Identification System • Dynamic Control Synthesis System • Transient Management System

3. What to model?

4. System Architecture Tools/components are model-based

5. Continuous behavior is mixed with discontinuities Discontinuities attributed to modeling abstractions (parameter & time-scale) supervisory control and reconfiguration (fast switching) Implement discontinuities as transitions in continuous behavior systematic principles: piecewise linearization around operating points & derive transition conditions (CDC’99, HS’00) compositional modeling: using switched bond graphs Summary: continuous + discrete behavior => hybrid modeling Plant modeling: Nominal behaviorDynamic Physical Systems

6. Plant modeling: Nominal behavior • Switched bond-graphs • Bond-graph: energy-based model of continuous plant behavior in terms of effort & flow variables (effort x flow = power), • Switched bond-graph: introduce switchable (on/off) junctions for hybrid modeling components (R,I,C), transformers and gyrators, junctions, effort and flow sources.

7. Plant modeling: Nominal behaviorSwitched Bond-Graph Implementation Switched Bond-graph Model Hybrid Observer Continuous observer A uk yk System Generation B z-1 C Hybrid Automata Generation Xk+1 xk m1 m2 Hybrid Automata Model m3 Mode switching logic

8. f g y+ y a j ha i x+ g x+ fa  . x i u Plant modeling: Nominal behaviorHybrid System Model: State-space + switching sx ss Continuous model: 9 tuple: H=<I, S, f, C, U, f,,h, g, g > Discrete Model • I: modes S:events Interactions (State mapping) (Event generation) x g :y(y+)  S Multiple mode transitions may occur at same time point t0 results in and which causes further transitions.

9. Plant modeling: Nominal behaviorNon-autonomous mode switching • Operation mode changes • High-level user mode switching • Low-level component/subsystem switching • Mapping of high-level control commands into low-level switching actions

10. Plant modeling: Nominal behaviorImplementation of the observer switching On-line Hybrid Observer Embedded Switched Bond-graph Model Not necessary to pre-calculate all the modes, only the immediate follow-up modes are needed. Generate Current State-Space Model (A,B,C,D) High-level Mode (Switch settings) Mode change Detector Calculate: transition conditions, next states Recalculate Kalman Filter uk,yk Xk Kalman Filter

11. V1 Tank 1 Tank 2 Tank 3 V5 Sf2 Sf1 h1 h2 h3 R23n H4 H3 R12n H1 H2 V2 V3 V4 V6 R1 R2 R23v R12v 15 1,2,3,5,7,8: ON soni soffi OFF Plant modeling: Nominal behaviorExample Hybrid system: Three tank model of a Fuel System hi = level of fluid in Tank i Hi = height of connecting pipe R12v R23v 4: ON 14 7 h1 <H1 and h2<H2 h1H1 or h2H2 C3 C1 C2 13 20 5 12 13 17 1 2 6 21 9 24 Sf1 Sf2 OFF 11 0 0 1 0 18 10 18 8 15 3 22 14 12 16 17 4 11 16 23 6: R1 R12n R23n R2 ON h3 <H3 and h4<H4 h3H3 or h4H4 6 controlled junctions (1,2,3,5,7,8) 2 autonomous junctions (4,6) OFF

12. V1 Tank 1 Tank 2 Tank 3 V5 Sf2 Sf1 h1 h2 h3 R23n H4 H3 R12n H1 H2 V2 V3 V4 V6 R1 R2 R23v R12v Plant modeling: Nominal behaviorHybrid Observer: Tracking tank levels through mode changes h1 Mode 1: 0  t  10: Filling tanks v1, v3, & v4 open, v2, v5, & v6: closed h2 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 : actual measurement : predicted measurement h3

13. Plant modeling: Faulty behaviorFault categories • Sensor/actuator/parameter faults • Quantitative description • Component failure modes • Qualitative description • Hard/soft failures • Precursors and degradations • Failure propagations • Analytic redundancy (quantitative) • Causal propagation (qualitative) • Cascade effects (discrete event) • Secondary failure modes (discrete) • Functional impact (discrete)

14. FDI for Continuous Dynamic SystemsHybrid Scheme u y Plant - Nominal Parameters Observer and mode detector ŷ Hybrid models Fault Parameters mi progressive monitoring hypothesis refinement hypothesis generation Symbol generation Fault detection [Binary decision] r fh fh’ Parameter Estimation Diagnosis models Fault Isolation u = input vector, y = measured output vector, ŷ = predicted output using plant model, r = y – ŷ, residual vector, r= derived residualsmi= current mode, fh = fault hypotheses

15. ymeas r Residual Generator yest FDI for Continuous Dynamic SystemsFault detection:Faults with quantifiable effects System Generation State-Space Models (A,B,C,D) Quantitative Fault-effect Model (R1,R2) Residual Generator Design

16. fh r rs Detect discrepancy Generate faults Predict behavior fh, p e6- =>R -leak , I+rad-out , R-hy-blk fh progressive monitoring Magnitude: low, high Slope:below, above normal discontinuous change R -leak --> e6 = < -,+,- > FDI for Continuous Dynamic Systems Qualitative FDI Fault Isolation Algorithm 1. Generate Fault Hypotheses: Backward Propagation on Temporal Causal Graph 2. Predict Behavior for each hypothesized fault: Generate Signatures by Forward Propagation 3. Fault Refinement and Isolation: Progressive Monitoring

17. FDI for Continuous Dynamic Systems Quantitative Analysis: Fault Refinement,Degradations fh’ fh True Fault (C1) Other hypothesis (R12) Multiple Fault Observers

18. Hybrid DiagnosisIssues • Fault Hypothesis generation back propagates to past modes • Fault behavior prediction has to propagate forward across mode transitions • Mode identification and fault isolation go hand in hand -- need multiple fault observers tracking behavior till true fault is isolated. • Computationally intensive problem

19. F3 C1 DY6 FM1 DY7 DY12 DY4 FM2 DY5 DY8 DY11 DY3 C2 F2 DY2 FM3 DY9 DY10 FM4 DY1 F1 Failure Mode Discrepancy “Alarmed” Discrepancy Plant modeling: Faulty behaviorFaults with discrete effects • Qualitative fault description, propagations

20. Plant modeling: Faulty behaviorDegradations and precursors leading to discrete faults • Hard/soft failures Sequence of precursors leading to a failure mode Degradations accumulate to a failure mode PC1 PC2 FM DE1 FM DE2 Degradation Precursor Failure mode Behavioral equation

21. Plant modeling: Faulty behaviorOBDD-based discrete diagnostics • OBDD-based reasoning can rapidly calculate next-state sets (including non-deterministic transitions) • All relations are represented as Ordered Binary Decision Diagrams

22. OBDD-based discrete diagnosticsRelations Between Sets R1, R2, R3P(A) P(B) relations between subsets of A, B Relational Product R1 = R2 ; R3 R1= { <a,c> |  b <a,b>  R2  <b,c>  R3 } Intersection R1 = R2  R3R1 = { <a,b,c> | <a,b>  R2  <b,c>  R3 } Superposition R1 = R2R3R1 = { s | (s  R2)  (s  R3)   s2 ,s3 ((s2  R2)  (s3 R2)  (s =s2 s3)}

23. OBDD-based discrete diagnostics Hypothesis Calculation Previously Hypothesized Set of Alarm Instances Previously Hypothesized Set of Failure Modes All disjunctions Hk-1 P Any Set of Failure Modes Next Hypothesized Set of Alarm Instances Set of Failure Mode Instances T Q Ringing Alarms Hk=( Ak ;Q )  ((Hk-1  T) ; P)

24. Transient ManagementTopics • Transients in simple cascade compensation control loops using a reconfigurable PID controller • Experimental testbed: two-link planar robot arm for testing controller reconfiguration transients in highly nonlinear control loops • Preliminary investigation of transients in model-based controllers

25. Controller output 4 state zeroing 3 scaled SS direct form 2 1 0 -1 0 50 100 150 200 250 300 350 400 450 500 Time (sec) Plant output 2 1.5 1 0.5 0 0 50 100 150 200 250 300 350 400 450 500 Time (sec)

26. Controller output 4 state zeroing 3 scaled SS direct form 2 1 0 -1 0 50 100 150 200 250 300 350 400 450 500 Time (sec) Plant output 2 1.5 1 0.5 0 0 50 100 150 200 250 300 350 400 450 500 Time (sec)

27. Controller output 4 state zeroing 3 scaled SS direct form 2 1 0 -1 0 50 100 150 200 250 300 350 400 450 500 Time (sec) Plant output 2 1.5 1 0.5 0 0 50 100 150 200 250 300 350 400 450 500 Time (sec)

28. Controller output 4 state zeroing 3 scaled SS direct form 2 1 0 -1 0 50 100 150 200 250 300 350 400 450 500 Time (sec) Plant output 2 1.5 1 0.5 0 0 50 100 150 200 250 300 350 400 450 500 Time (sec)

29. Conclusions • Summary • Experimental hybrid observer • Prototype discrete diagnostics algorithm • First cut of model building tool • Transient management experiments • Finish modeling tool • Develop integrated software • Controller selection component • Integrated demonstration • Cooperation with Boeing IVHM • Fuel system example

30. Backup slides

31. Plant modeling: Nominal behaviorHybrid Observer for Tracking Behavior • Switched Bond-Graph Implementation • Algorithmically generate a hybrid automata from the switched bond-graph. The states of the HA will represent the discrete mode-space of the plant • Derive standard state-space models for each mode and use a standard observer (e.g. Kalman filter) to track the plant in that mode • When a mode-change happens, switch to a new observer

33. First-order direct structure

34. First-order resonator-based structure

35. Second-order direct structure

36. Second-order resonator-based structure

37. Sixth-order direct structure

38. Sixth-order resonator-based structure