Final Presentation of A. Falcoz Phd activities: March 16-09 – ESA/ESTEC

1. L A P S Final Presentation of A. Falcoz Phd activities: March 16-09 – ESA/ESTEC Laboratoire de l’Intégration du Matériau au Système IMS - UMR 5131 CNRS – Département LAPS Université Bordeaux I http://www.laps.u-bordeaux1.fr/aria ARIA On the design of a robust model-based fault diagnosis unitfor Reusable Launch Vehicles - Phd student: Alexandre Falcoz - Academical supervisors: - Dr. David Henry (HDR) - Pr. Ali Zolghadri - Industrial supervisors: - Eric Bornschlegl (ESA / ESTEC) - Martine Ganet (EADS Astrium) Alexandre.falcoz@ims-bordeaux.fr

2. OUTLINE • Statement of the problem - RLV mission presentation – faulty situations, - Why model-based fault diagnosis?? - requirements of the fault diagnosis unit, • Diagnosis of the RLV actuator faults . Auto-landing phase - modelling of the HL-20 dynamics - formulation of the fault diagnosis problem : H∞ /H- setting - post-analysis of the results - experimental results, . TAEM Phase Some new results - a more sophisticated GNC and modelling process - design – robust performances – simulation results • Faults characterization - methodology description, - simulation results,

3. Statement of the problem

4. Injection point Hypersonic phase TAEM phase Autolanding phase Atmospheric re-entry presentation • Splitted into 3 successive paths: • 120 km  Mach 2 hypersonic • Mach 2  Mach 0.5 TAEM • Mach 0.5  touch-down Landing TEP Earth Horizon Zrunway • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives Orbiter ground track NEP Xrunway Runway Yrunway HAC radius

5. Extended Parabolic trajectory Intercept inner glideslope Begin constant “G” pullup Constant “G” Pullupmaneuver Inner glideslope flight path angle Runway threshold Atmospheric re-entry presentation • Auto-Landing path characterized by: • Restricted operating flight envelope (True air speed, Mach-AOA trim map,…), • Fault occurrence  prominent risk of stall HL-20 Autolanding handover Outer Glideslope flight path angle Aimpoint • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives Touchdown Final flare Runway Runway plane

6. Why model-based fault-diagnosis? • Model-based algorithms: • Why? • «mass free and non intrusive Intelligent sensors » • How? • data fusion of already available measurements for the design of • residual generators (activities similar to control design process) • resulting in a software FDI filter • Great Advantages: Perturbations/uncertainties modelling • Possibility to distinguish between faults and • various operating conditions autonomy Model-based FDIR FDIR / hardawre duplication Mass • global optimization of the spacecraft/aircraft design programs: • . Reduction of the in placed hardware redundancy •  reduction of the maintenance costs and times, •  reduction of the vehicles empty mass: • . aeronautic applications:  operating cost reduction • (airline price ticket?? ) • . space applications:  increase of the orbital payload • (for launcher)  satellite cycle life. •  decrease of the mission costs • because sometimes we have not the choice: • Military UAV applications with stringent weight constraints: •  actuators and sensors reduced to the bare necessities , •  no hardware/software redundancy to diagnose and recover • faulty situations Model-based FDI/FTC techniques appear to be an attractive solution. • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives

7. Requirements of the fault diagnosis unit analysis must be understood as a powerful tool for: 1: the a posteriori checkout of the FDI/controller robust performances 2: a driving lines fo the synthesis!! 3: a driving lines for ‘targeted’’ Monte Carlo analysis • To be a potential candidate: The fault diagnosis strategy must • meet the following requirements: • non detection and false alarms rates must be extremely rare (ideally zero), whilst guaranteeing, at the same time, a large fault coverage with a low detection time delay, • - exogeneous disturbances: wind gusts, turbulences, measurement noises, • guidance signals, • - endogeneous disturbances: innacurate knowledge of the vehicle parameters (mass, Center-of-gravity, inertia, aerodynamic coefficients) • the performances must be guaranteed over the whole vehicle flight trajectory • Two different way: • Monte-Carlo simulations Generalized structured singular value • Robustness constraints to be met: • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives • Systematic post-analysis procedure • Mathematical proof of the robust performances (CNS!) • provide the worst combination of the considered uncertainty parameters! • Probabilistic proof of robust performances, • How many simulations are needed to ensure that the worst combination has been drawed? bridge exists: if -tests fails then Monte Carlo tests fails also!! Advantage: - test is less time consuming

8. Diagnosis of the HL20 actuator faults- Application to the auto-landing phase - • Modelling • Problem setting • Solution of the problem • Experimental results

9. Requirements of the fault diagnosis unit • General overview of the Faut Detection Isolation and Identification architecture uncertainties Vehicle dynamics Path planner Guidance loop Flight controller Navigation • FDIR Residual generators Faulty actuator Decision making Nonlinear estimation

10. Actuator faulty situations- selection and modelling -

11. HL-20 modelling • Vehicle dynamics: with: • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives • Hypothesis: • Non-rotative and flat earth: • RCS not used during the landing phase: • Inertia matrix assumed to be constant and diagonal:

12. Modélisation du HL20: coefficients aérodynamiques (1/3) • Strored into Simulink look up tables, • need to derive an analytical model

13. HL-20 modelling: Aerodynamic coefficients (1/2) • Aerodynamic coefficients in “clean configuration” • 2-Dimensional mapping using SVD decomposition with: with: • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives modelling error

14. HL-20 modelling: Aerodynamic coefficients (2/2) • Aerodynamic components linked to the aero-surfaces deflections • and body angular rates: • polynomial interpolation Approximation error • Integration of the modelling errors: • sensitivity analysis of the modelling errors • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives

15. HL-20 modelling • Nonlinear representation of the HL20 dynamics: • with: • (1) • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives

16. Impact of faults on the system • Selection of the faulty scenarios to be studied: non-destabilizing faults!! • Question: Do the remaining healthy control effectors are able to maintain the vehicle • control following an actuator fault? • Problem formulation: • Consider the model given by equation (1). The problem of finding a non-saturated control input combination which ensures the static equilibrium of the vehicle around its center-of-gravity can be formulated according to the following minimization problem:

17. Impact of faults on the system • Faulty situation: • Fault free situation • Faulty situation:

18. Diagnosis filters synthesis

19. Modelling • Faults impact modelling –Left and right wing flaps faults* • 1 – abnormal behavior of the control signals: • Ex 1: jamming of the ith actuator: • Ex 2: runaway of the ith actuator: • 2 –abnormal variation of the aerodynamic coefficients due to the GNC performance level: depends on the use GNC • Landing phase • TAEM phase • Abnorrmal variation following a fault • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives • * Faults which satisfy the trimmability conditions

20. Modelling • Linearization around the reference flight trajectory: Polynomial function depending on the reference flight velocity: i.e. • hypothesis: slow variation of the reference flight velocity during the Auto-landing phase • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives LPV LTI (uncertain)

21. Modelling • Can we use an appropriated, single and simplified model for the design of the fault diagnosis algorithm? • Procedure: Open-loop frequency domain (principal gain) and time domain (poles) analysis depending on : Model: • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives • A posteriori checkout of the LTI hypothesis

22. Formulation and resolution of the fault diagnosis design problem

23. Formulation of the fault diagnosis problem - + + + • Generate a residuals vector such as: • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives • Looking for an optimal static combination of all available measurements (i.e. compute My, Mu) anda dynamic filter F for filtering purpose to make r: • robust against exogeneous disturbances • (measurement noises, winds, guidance signals) • sensitive wrt faults to detect • guarantying robust performances for all the considered • uncertainties (mass, inertia, aerodynamic coefficients,…) • context • context

24. Formulation of the fault diagnosis problem • Synthesis objectives formulation: ‘’shaping filters’’ • Robustness objectives: Let be a stable and invertible dynamic filter associated to the robustness objectives such as: • with: • Sensitivity objectives : • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives Let be a stable and invertible dynamic filter associated to the sensitivity objectives such as: (D. Henry & A. Zolghadri, 2005): SDP problem in My, Mu, AF,BF,CF,DF

25. Performances post-analysis Fig.b • Minimisation part • Maximisation part • Theorem (D. Henry & A. Zolghadri, 2005): • Let consider the scheme of Fig (b). Let and • two fictitious uncertainty blocks introduced to close the loop between respectively d and r and f and r. Let then, the robustness and sensitivity objectives are achieved iff: • sufficient condition in the synthesis process • is not taken into account during the synthesis procedure: an a priori choice for reduced FDI filters (less time and consuming FDI algorithms) • A posteriori checkout of the LTI hypothesis • Do the robustness requirements against d and sensitivity objectives w.r.t f are fulfilled and all along the flight trajectory? • Generalized structured singular value

26. Performances post-analysis • Evaluation of for different vehicle flight velocities along the reference flight trajectory taking into account the uncertainties (i.e. a robust performances analysis test for for FDI algorithm generalized to any LTI FDI algorithm, see (Henry 2007) • Filters order: 9 • every 2 m/s  30 LFT • achievement of the robustness/sensitivity objectives w.r.t the considered exogeneous disturbances vector and model uncertainties, • The diagnosis filter performances are guaranteed all along the flight trajectory, i.e

27. Temporal simulations

28. Temporal simulations • Temporal simulations: 300 Monte-Carlo runs • implementation of the two dedicated diagnosis filters into the simulator, • implementation of a Wald sequential test for the decision making issue: - False alarm probability: - Non detection probability:

29. Temporal simulations • Fault on the Left wing flap: 300 Monte-Carlo runs • Fault on the Right wing flap: 300 Monte-Carlo runs

30. Diagnosis of the HL20 actuator faults- Application to the TAEM phase - • Aerodynamics modelling • Problem setting - preliminary

31. TAEM GNC/FDIR architecture • Position control loop • algorithm - - - - + - - • Inner loop • Outer loop • Position control loop uncertainties • GNC Path planner Position control loop Vehicle dynamics Allocation Attitude control loop Navigation • FDI Faulty actuator Decision making Residual generators

32. TAEM GNC/FDIR architecture + + - • Attitude control loop • algorithm - - - - • Inner loop • Outer loop • Attitude Control loop uncertainties • GNC Path planner Position control loop Vehicle dynamics Allocation Attitude control loop Navigation • FDI Faulty actuator Decision making Residual generators

33. TAEM GNC/FDIR architecture • On-line Allocation algorithm 2 1 • Analytical model of the aerodynamic • coefficients  use of Neural Network • Off-line precomputed and parameterized • w.r.t to the dynamic pressure • Previous control input vector • Vector coming from Guidance & Control loops • Allocation Algorithm uncertainties • GNC Path planner Position control loop Vehicle dynamics Allocation Attitude control loop Navigation • FDI Residual generators Faulty actuator Decision making

34. Robust stability analysis of the GNC architecture • Evaluation the GNC robust performances for the considered parameter uncertainties and all along the reference flight trajectory: • every 10 m/s  40 LFT • Does the closed-loop system remains stable for all values of in the • considered variation range? • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives • Robust stability of the designed GNC is “guaranteed” all along the flight trajectory

35. Aerodynamic database modelling • Aerodynamic coefficients modelling by means of neural network: • number of neurons in the hidden layer • number of inputs • Outer layer • Hidden layer • Two kind of nonlinear dependency: • 1: Terms having a nonlinear dependency wrt • to the mach number and • 2: Terms having a nonlinear dependency wrt • to the mach number, and

36. Aerodynamic database modelling • 2 dimensional aerodynamic terms: clean configuration • 3 dimensional aerodynamic terms linked to the actuator components

37. Formulation of the fault diagnosis problem 1 2 3 4 Extraction of a ‘judicious’ certain LTI model of the vehicle dynamics: Objective design formulation: Fault diagnosis problem formulation and resolution of the SDP problem Post-analysis – analysis procedure • LFT • Gridding of the flight trajectory • every 5 m/s so that:

38. Performances post-analysis • Evaluation of for different vehicle flight velocities along the reference flight trajectory • every 5 m/s  80 LFT • achievement of the robustness/sensitivity objectives w.r.t the considered exogeneous disturbances vector and model uncertainties, • The diagnosis filter performances are guaranteed all along the flight trajectory, i.e

39. Temporal simulations • Some preliminary results……in detection Jamming of the left wing flap Runaway of the left wing flap Some a posteriori important conclusion about the “TAEM feasibility” study: • A need of modelling more accurately the faults impact •  Isolation task is not performed at this time! • The LTI technique seems to be appropriated ( -test reveals robust performances)

40. Actuator faults characterisation

41. Faults estimation • Nonlinear state-space model used for the estimation process: • with: • et denote respectively the process and measurements noises which are assumed to be uncorrelated white noise processes with covariance matrices Q et R such as: • Objective: Estimate the position of the unknown inputs using the following nonlinear observer-scheme: • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives

42. Faults estimation • Problematic: Optimization of the EKF-based estimator parameters, i.e. Q and R • Considered methodology: • Particle Swarm Optimization algorithm (James Kennedy and Russell Eberhart) • Integrated in the class of evolutionary algorithms and very efficient to deal with multi-parameters, non-linear and discrete-type optimization problems, • Algorithm quite easy to understand, to code and to use. • Off-line Minimization of the root mean square of the state estimate errors • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives

43. Simulation results • Left wing flap runaway • Right wing flap jamming

44. Conclusion • Fault Detection and Isolation of the HL20 actuator Faulty situations determined following a trimmability deficiency analysis Design of two diagnosis filters of order 9 for Fault detection and isolation during AL phase Performances analysis of the filters using the function along the flight trajectory • Estimation of the faulty deflections once the FDI task has been achieved EKF-based estimator (DD1 filter) • Statement of Atmospheric re-entry problem • Faulty scenarios • Diagnosis of the HL-20 actuators • Conclusion & perspectives IF it is very carefully chosen: A single LTI model is sufficient to deal with the FDI task during the A-L and TAEM phases • LPV techniques have not to be excluded!! But a trade-off between the design complexity, the onboard computational burden and the FDI performances must be studied.

45. Thanks for your attention

46. Requirements of the fault diagnosis unit • General overview of the Faut Detection Isolation and Identification architecture uncertainties Vehicle dynamics Path planner Guidance loop Flight controller Navigation • FDIR Residual generators Faulty actuator Decision making Nonlinear estimation