SEC PI Meeting 06/00 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

SEC PI Meeting 06/00 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

SEC PI Meeting 06/00 What to model?

SEC PI Meeting 06/00 System Architecture Tools/components are model-based

SEC PI Meeting 06/00 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 behavior Dynamic Physical Systems

SEC PI Meeting 06/00 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.

SEC PI Meeting 06/00 Plant modeling: Nominal behavior Switched Bond-Graph Implementation Switched Bond-graph Model Switched 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

SEC PI Meeting 06/00 Plant modeling: Nominal behavior Hybrid System Model: State-space + switching 9 tuple: H= 9 tuple: H= xx ss x Continuous model: Discrete Model I: modes  events Interactions    y ( y + )   Multiple mode transitions may occur at same time point t 0 results in and which causes further transitions.   ff g hh   yy+y+ x+x+ u. x i j i x+x+ (State mapping) (Event generation)

SEC PI Meeting 06/00 Plant modeling: Nominal behavior Non-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

SEC PI Meeting 06/00 Plant modeling: Nominal behavior Implementation of the observer switching Embedded Switched Bond-graph Model Embedded Switched Bond-graph Model Generate Current State-Space Model (A,B,C,D) Recalculate 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)

SEC PI Meeting 06/00 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 Sf1Sf C1C2 C3 R1 R2R12nR23n h 3  H 3 or h 4  H 4 ON OFF 6: h 1  H 1 or h 2  H 2 ON OFF 4: h 1 <H 1 and h 2 <H controlled junctions (1,2,3,5,7,8) 2 autonomous junctions (4,6)

SEC PI Meeting 06/00 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

SEC PI Meeting 06/00 Plant modeling: Faulty behavior Fault 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)

SEC PI Meeting 06/00 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

SEC PI Meeting 06/00 FDI for Continuous Dynamic Systems Fault detection: Faults with quantifiable effects State-Space Models (A,B,C,D) Quantitative Fault-effect Model (R 1,R 2 ) Residual Generator Design Residual Generator y meas y est r System Generation

SEC PI Meeting 06/00 FDI for Continuous Dynamic Systems Qualitative FDI Detect discrepancy Generate faults Predict behavior progressive monitoring rrsrs fhfh f h, p fhfh Magnitude: low, high Slope:below, above normal discontinuous change e 6 - =>R - leak, I + rad-out, R - hy-blk R - leak --> e 6 = 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

SEC PI Meeting 06/00 FDI for Continuous Dynamic Systems Quantitative Analysis: Fault Refinement,Degradations True Fault (C 1 ) Other hypothesis (R 12 ) fhfh fh’fh’ Multiple Fault Observers

SEC PI Meeting 06/00 Hybrid Diagnosis Issues 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

SEC PI Meeting 06/00 Plant modeling: Faulty behavior Faults with discrete effects FM1 FM2 FM3 FM4 C1 DY4 DY3 DY6 DY7 DY8 DY5 DY2 DY1 DY9 DY10 DY11 DY12 C2 Failure ModeDiscrepancy“Alarmed” Discrepancy F1 F3 F2 Qualitative fault description, propagations

SEC PI Meeting 06/00 Plant modeling: Faulty behavior Degradations and precursors leading to discrete faults Hard/soft failures DegradationPrecursorFailure mode DE1 Behavioral equation DE2 FM Degradations accumulate to a failure mode PC2PC1 Sequence of precursors leading to a failure mode

SEC PI Meeting 06/00 Plant modeling: Faulty behavior OBDD-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

SEC PI Meeting 06/00 OBDD-based discrete diagnostics Relations Between Sets R 1, R 2, R 3  P (A)  P (B) relations between subsets of A, B Relational Product R1 = R2 ; R3 R 1 = { |  b  R 2   R 3 } Intersection R1 = R2  R3 R 1 = { |  R 2   R 3 } Superposition R 1 = R 2  R 3 R 1 = { s | (s  R 2 )  (s  R 3 )   s 2,s 3 ((s 2  R 2 )  (s 3  R 2 )  (s =s 2  s 3 )}

SEC PI Meeting 06/00 OBDD-based discrete diagnostics Hypothesis Calculation H k =( A k ; Q )  ((H k-1  T) ; P) All disjunctions Previously Hypothesized Set of Alarm Instances Ringing Alarms Next Hypothesized Set of Alarm Instances P H k-1 Previously Hypothesized Set of Failure Modes T Any Set of Failure Modes Set of Failure Mode Instances Q

SEC PI Meeting 06/00 Transient Management Topics 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

SEC PI Meeting 06/ Time (sec) Controller output state zeroing scaled SS direct form Time (sec) Plant output

SEC PI Meeting 06/ Time (sec) Controller output state zeroing scaled SS direct form Time (sec) Plant output

SEC PI Meeting 06/ Time (sec) Controller output state zeroing scaled SS direct form Time (sec) Plant output

SEC PI Meeting 06/ Time (sec) Controller output state zeroing scaled SS direct form Time (sec) Plant output

SEC PI Meeting 06/00 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

SEC PI Meeting 06/00 Backup slides

SEC PI Meeting 06/00 Plant modeling: Nominal behavior Hybrid 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

SEC PI Meeting 06/00

SEC PI Meeting 06/00 First-order direct structure

SEC PI Meeting 06/00 First-order resonator-based structure

SEC PI Meeting 06/00 Second-order direct structure

SEC PI Meeting 06/00 Second-order resonator-based structure

SEC PI Meeting 06/00 Sixth-order direct structure

SEC PI Meeting 06/00 Sixth-order resonator-based structure