1/44 Laboratoire de l’Intégration du Matériau au Système IMS - UMR 5131 CNRS – Département LAPS Université Bordeaux I http://www.laps.u-bordeaux1.fr/aria - Phd student: Alexandre Falcoz - Academical supervisors: - Dr. David Henry (HDR) - Pr. Ali Zolghadri - Industrial supervisors: - Eric Bornschlegl (ESA / ESTEC) - Martine Ganet (EADS Astrium) P P A A S S L L ARIA ARIA On the design of a robust model-based On the design of a robust model-based fault diagnosis unit fault diagnosis unit for Reusable Launch Vehicles for Reusable Launch Vehicles Final Presentation of A. Falcoz Phd activities: March 16-09 – ESA/ESTEC [email protected]
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Final Presentation of A. Falcoz Phd activities: March 16-09 – ESA/ESTEC
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. - PowerPoint PPT Presentation
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Laboratoire de l’Intégration du Matériau au SystèmeIMS - UMR 5131 CNRS – Département LAPS
Université Bordeaux I http://www.laps.u-bordeaux1.fr/aria
- Phd student: Alexandre Falcoz
- Academical supervisors: - Dr. David Henry (HDR) - Pr. Ali Zolghadri
- Industrial supervisors: - Eric Bornschlegl (ESA / ESTEC) - Martine Ganet (EADS Astrium)
PPAA SSLLARIAARIA
On the design of a robust model-based On the design of a robust model-based fault diagnosis unitfault diagnosis unit
for Reusable Launch Vehiclesfor Reusable Launch Vehicles
Final Presentation of A. Falcoz Phd activities: March 16-09 – ESA/ESTEC
- RLV mission presentation – faulty situations,- RLV mission presentation – faulty situations,- Why model-based fault diagnosis??- Why model-based fault diagnosis??- requirements of the fault diagnosis unit, - requirements of the fault diagnosis unit,
• Diagnosis of the RLV actuator faults
. . Auto-landing phase
- modelling of the HL-20 dynamics - modelling of the HL-20 dynamics - formulation of the fault diagnosis problem : H- formulation of the fault diagnosis problem : H ∞ ∞ /H/H- - settingsetting
- post-analysis of the results - experimental results,- post-analysis of the results - experimental results,
. . TAEM Phase Some new results Some new results
- a more sophisticated GNC and modelling process- a more sophisticated GNC and modelling process- design – robust performances – simulation results- design – robust performances – simulation results
Restricted operating flight envelope (True air speed, Mach-AOA trim map,…),
Fault occurrence prominent risk of stall
• Statement of Atmospheric
re-entry problem
• Faulty scenarios
• Diagnosis of the HL-20
actuators
• Conclusion & perspectives
Atmospheric re-entry presentation
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Why model-based fault-diagnosis?
• Statement of Atmospheric
re-entry problem
• Faulty scenarios
• Diagnosis of the HL-20
actuators
• Conclusion & perspectives
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.
Mass
autonomy
Mod
el-b
ased
FDIR
FDIR
/ ha
rdaw
re
dup
licat
ion
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
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To be a potential candidate: TheTo be a potential candidate: The fault diagnosis strategy must fault diagnosis strategy must meet the following requirements: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,
- 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
Requirements of the fault diagnosis unit
-Systematic post-analysis procedure
- Mathematical proof of the robust performances (CNS!)
- provide the worst combination of the considered uncertainty parameters!
bridge exists: if -tests fails then Monte Carlo tests fails also!!
Advantage: - test is less time consuming
- Probabilistic proof of robust performances,
- How many simulations are needed to ensure
that the worst combination has been drawed?
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
g/
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Diagnosis of the HL20 actuator faults- Application to the auto-landing phase -
– Modelling
– Problem setting
– Solution of the problem
– Experimental results
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Residual generators
Decision
making
Faulty actuator
Nonlinear estimation
General overview of the Faut Detection Isolation and Identification architecture uncertainties
Navigation
Path
planner
Guidance loop Flight controllerVehicle dynamics
FDIR
Requirements of the fault diagnosis unit
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Actuator faulty situations- selection and modelling -
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HL-20 modelling
Vehicle dynamics:
Hypothesis:
• Non-rotative and flat earth:
• RCS not used during the landing phase:
• Inertia matrix assumed to be constant and diagonal:
with:
• Statement of Atmospheric
re-entry problem
• Faulty scenarios
• Diagnosis of the HL-20
actuators
• Conclusion & perspectives
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Modélisation du HL20: coefficients aérodynamiques (1/3)
• Strored into Simulink look up tables,• need to derive an analytical model
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Aerodynamic coefficients in “clean configuration”
• 2-Dimensional mapping using SVD decomposition
with:
modelling error
HL-20 modelling: Aerodynamic coefficients (1/2)
with:
• Statement of Atmospheric
re-entry problem
• Faulty scenarios
• Diagnosis of the HL-20
actuators
• Conclusion & perspectives
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Aerodynamic components linked to the aero-surfaces deflections and body angular rates:
• polynomial interpolation
• sensitivity analysis of the modelling errors
Integration of the modelling errors:
Approximation error
• Statement of Atmospheric
re-entry problem
• Faulty scenarios
• Diagnosis of the HL-20
actuators
• Conclusion & perspectives
HL-20 modelling: Aerodynamic coefficients (2/2)
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with:
Nonlinear representation of the HL20 dynamics:
• Statement of Atmospheric
re-entry problem
• Faulty scenarios
• Diagnosis of the HL-20
actuators
• Conclusion & perspectives
HL-20 modelling
(1)
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Question: Do the remaining healthy control effectors are able to maintain the vehicle control following an actuator fault?
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:
Problem formulation:
Selection of the faulty scenarios to be studied: non-destabilizing faults!!
Impact of faults on the system
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Fault free situation Faulty situation:
Faulty situation:
free -30° -15° 0° 15° 30°
free
-30°
-15°
0°
15°
30°
Impact of faults on the system
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Diagnosis filters synthesis
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Faults impact modelling –Left and right wing flaps faults *
1 – abnormal behavior of the control signals:
2 –abnormal variation of the aerodynamic coefficients due to the GNC performance level: depends on the use GNC
Modelling
Ex 2: runaway of the ith actuator:
Abnorrmal variation following a faultAbnorrmal variation following a fault
* Faults which satisfy the trimmability conditions
• Statement of Atmospheric
re-entry problem
• Faulty scenarios
• Diagnosis of the HL-20
actuators
• Conclusion & perspectives
Ex 1: jamming of the ith actuator:
Landing phaseTAEM phase
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Polynomial function depending on the reference flight velocity: i.e.
Linearization around the reference flight trajectory:
hypothesis: slow variation of the reference flight velocity during the Auto-landing phase
LPV LTI (uncertain)
Modelling
• Statement of Atmospheric
re-entry problem
• Faulty scenarios
• Diagnosis of the HL-20
actuators
• Conclusion & perspectives
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Procedure: Open-loop frequency domain (principal gain) and time domain (poles) analysis depending on :
Modelling
Model:
A posteriori checkout of the LTI hypothesis
Can we use an appropriated, single and simplified model for the design of the fault diagnosis algorithm?
• Statement of Atmospheric
re-entry problem
• Faulty scenarios
• Diagnosis of the HL-20
actuators
• Conclusion & perspectives
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Formulation and resolution of the fault diagnosis design problem
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++--
++
++
FiP
KyM
uM
)M,M(P uiyi2
F
Generate a residuals vector such as:
robust against exogeneous disturbances robust against exogeneous disturbances (measurement noises, winds, guidance signals)(measurement noises, winds, guidance signals)
sensitive wrt faults to detect sensitive wrt faults to detect
guarantying robust performances for all the considered guarantying robust performances for all the considered uncertainties uncertainties (mass, inertia, aerodynamic coefficients,…)(mass, inertia, aerodynamic coefficients,…)
context
context
Looking for an optimal static combination of all available Looking for an optimal static combination of all available measurements (i.e. compute measurements (i.e. compute My, Mu) My, Mu) andand a dynamic filtera dynamic filter F F for filtering for filtering purpose to make r:purpose to make r:
• Statement of Atmospheric
re-entry problem
• Faulty scenarios
• Diagnosis of the HL-20
actuators
• Conclusion & perspectives
Formulation of the fault diagnosis problem
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Let be a stable and invertible dynamic filter associated to the sensitivity objectives such as:
Let be a stable and invertible dynamic filter associated to the robustness objectives such as:
SDP problem in My, Mu, AF,BF,CF,DFSDP problem in My, Mu, AF,BF,CF,DF
• Statement of Atmospheric
re-entry problem
• Faulty scenarios
• Diagnosis of the HL-20
actuators
• Conclusion & perspectives
Formulation of the fault diagnosis problem
(D. Henry & A. Zolghadri, 2005):
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)s(P
)s(
Performances post-analysis
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
)(sF
)(sK
1fW
1dW
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:
Theorem (D. Henry & A. Zolghadri, 2005):
yM
uM
)s(d
)s(f
)(sN
Fig.b
df
Maximisation part
Minimisation part
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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)
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
Filters order: 9
Performances post-analysis
every 2 m/s 30 LFT
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Temporal simulations
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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:
Temporal simulations
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Fault on the Left wing flap: 300 Monte-Carlo runs
Temporal simulations
Fault on the Right wing flap: 300 Monte-Carlo runs
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Diagnosis of the HL20 actuator faults- Application to the TAEM phase -
– Aerodynamics modelling
– Problem setting - preliminary
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Residual generatorsDecision
making
Faulty actuator
Position control loop
FDI
Path
planner
Position control loop
Attitude control loop
Allocation
GNC
uncertainties
Navigation
Vehicle dynamics
-
-
- -
Outer loop
-
-
Inner loop
+
Position control loop algorithm
TAEM GNC/FDIR architecture
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Residual generatorsDecision
making
Faulty actuator
Attitude Control loop
FDI
Path
planner
Position control loop
Attitude control loop
Allocation
GNC
uncertainties
Navigation
Vehicle dynamics
-
-
+ +
Outer loop
-
-
Inner loop
-
s
)(IK ref1
Attitude control loop algorithm
TAEM GNC/FDIR architecture
33/44
Residual generators
Decision
making
Faulty actuator
Allocation Algorithm
FDI
Path
planner
Position control loop
Attitude control loop
Allocation
GNC
uncertainties
Navigation
Vehicle dynamics
On-line Allocation algorithm
1
2
Analytical model of the aerodynamic coefficients use of Neural Network
Vector coming from Guidance & Control loops
Off-line precomputed and parameterized w.r.t to the dynamic pressure Previous control input vector
TAEM GNC/FDIR architecture
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• Statement of Atmospheric
re-entry problem
• Faulty scenarios
• Diagnosis of the HL-20
actuators
• Conclusion & perspectives
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?
)s(M i
i
)s(Pi
i
)s(K i
Robust stability of the designed GNC is “guaranteed” all along the flight trajectory
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Aerodynamic database modelling
Aerodynamic coefficients modelling by means of neural network:
Two kind of nonlinear dependency:
1: Terms having a nonlinear dependency wrt to the mach number and
number of neurons in the hidden layer
number of inputs
Hidden layer Outer layer
2: Terms having a nonlinear dependency wrt to the mach number, and
3 dimensional aerodynamic terms linked to the actuator components
Aerodynamic database modelling
37/44
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)s(N i
id
f
1
2
3
4Gridding of the flight trajectory
every 5 m/s so that:
LFT
Formulation of the fault diagnosis problem
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Evaluation of for different vehicle flight velocities along the reference flight trajectory
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
Performances post-analysis
every 5 m/s 80 LFT
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Some preliminary results……in detection
Temporal simulations
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)
Jamming of the left wing flapRunaway of the left wing flap
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Actuator faults characterisation
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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
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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.
Problematic: Optimization of the EKF-based estimator parameters, i.e. Q and R
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
Faults estimation
Considered methodology:
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Simulation results
Right wing flap jamming Left wing flap runaway
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Conclusion Fault Detection and Isolation of the HL20 actuator
Design of two diagnosis filters of order 9 for Fault detection and isolation during AL phasePerformances analysis of the filters using the function along the flight trajectory
Faulty situations determined following a trimmability deficiency analysis
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.
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Thanks for your attention
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Residual generators
Decision
making
Faulty actuator
Nonlinear estimation
General overview of the Faut Detection Isolation and Identification architecture uncertainties