fvsysid shortcourse 1 introduction1
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Dr. Ravindra Jategaonkar AIAA Short Course: Flight Vehicle System Identification in Time Domain, Aug. 2006 Introduction/1
One-Day Tutorial on
Flight Vehicle System Identification in Time Domain
AIAA Professional Development Tutorial, Keystone, CO
24 August 2006
Dr. Ravindra JategaonkarInstitute
of
Flight
SystemsDLR
- German
Aerospace
CenterLilienthalplatz 738108
Braunschweig,
Germany
Email: [email protected]: +49
531
295-2684Fax: +49
531
295-2647
?
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Objectives and Key Topics of the Tutorial
Overview of key methods of parameter estimation in time domain
Not highly mathematical, rather emphasis on practical utility
Large scale systems
Cover aspects of parameter estimation and model validation
Several examples from real flight data to bring out wide applicability
of time domain methods to highly nonlinear phenomenonReview some available tools
Goals:
- Better understand the importance of coordinated Quad-M approach- Get to know the intricacies in the application of time domain method
- Be in a better position to address individual problems
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Classification of Problems in System Theory
Inputs Outputs
u z / y
State Equationsx = f (x, u, ).
Classical problem (Simulation):
given u and f, find y
Control problem:
given y and f, find u
Identification problem:
given u and z, find f
What is System Identification? (1)
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What is System Identification? (2)
AIM:
To determine unknown model parameters such that the model response y matches wellwith the measured system response z.
Dynamic Systemu z
Mathematical Modelu y
)),(),(()()),(),(()(
tutxgtytutxftx
==
&
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(1) System Identification
Concerned with the mathematicalStructure of a flight vehicle model
(2) Parameter EstimationQuantifying of parameters for aselected flight vehicle model?
Given the answer, what are the questions,
i.e., look at the results and try to figure outwhat situation caused those results.
Iliff1994
Philosophical Definition
What is System Identification? (3)
Zadeh 1962
System Identification is the determination,
on the basis of observation of input and
output, of a system within a Specified classof systems , to which the system under test
is equivalent.
Technical Definition
In the commonly used terminology PID appropriate?
SysID: an Inverse Problem
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Dynamic System
Mathematical Model ?
?
Definitions: Simulation, Parameter Estimation, and System Identification
What is System Identification? (4)
Modelstructure
fixed
Model structureand parametersknown a-priori
Concerned with thecomputation ofsystem responses
Numerical integration
Simulation
Concerned with thequantification ofparameter values
Statistical estimationof parameters
Parameter estimation
Concerned with themodel structuredetermination andestimation ofparameters
System identification
Model structureand parametersunknown
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TransferFunction
(Magnitude)
Low Order Dynamics Higher Order Dynamics
Nominal Model
Envelope of"True" Systems
Possible"True" System
ModelStructureUncertainty
Model ParameterUncertainty
Frequency
Flight Mechanics Modeling
Flight Control Modeling
Structural Dynamics Modeling
Aeroservoelastic Modeling
What is System Identification? (5)
Interdisciplinary Flight Vehicle Modeling
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What is System Identification? (6)Block Schematic of System Model
Dynamic Systemu z
Aircraft masscharacteristics
Aerodynamics
(unknownparameters)
Sensorlocations
Sensor model
(calibration factors,bias errors)
Inputs States
Process noise(turbulence)
Measurementnoise
Outputs
State Equations Measurement Eq.
)),(),(()( tutxgty =)),(),(()( tutxftx =&
AIM: To determine unknown model parameters such that the modelresponse y matches well with the measured system response z.
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Some Fundamental Assumptions
True state of dynamic system is deterministic (unchanging):- real valued system functions
- iterative experimentation and data analysis converges to the truthIt is possible to carry out specific experiments:
- different modes of dynamic motion (flight vehicle; economic systems?)
- design experiments
Measurements of system inputs and outputs are available:
- directly measured or derived quantities
Physical principles underlying the dynamic process can be modeled:
- model implies mathematical description of the process
- phenomenon purported to underlie the process
- black-box models (Neural networks)
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Model Characterization (1)
Model characterization: a critical aspect of paramount importance
1) Phenomenological models:
- knowledge based,- built from basic principles,- involves physics of the process
2) Behavioral models
- approximate observed behavior,- no physical meaning
Phenomenological Behavioral
Parameters physical meaning no concrete meaning
Simulation complex and difficult quick and easy
A priori info included not necessary
Validity large restricted
a) Parametric models:- model structure and order assumed,- state space models, transfer functions
b) Nonparametric models- No model structure or order assumed,
- impulse response, frequency response
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Model Characterization (2)Three types of models
White Box models
- Derived from theoretical formulation of phenomenon purportedunder lie the process under investigation(Newtonian mechanics, parameters having physical interpretation)
- To reproduce system structure and match the system response
Black-Box models- Input-Output subspace matching
(Neural networks)- To Reproduce the system response
Grey-Box models- Combination of above two models
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Model Characterization (3)Parsimonious models
Principle of parsimony (Principle of Simplicity; Ockhams Razor)
The number of entities should not be increased beyond what isnecessary to explain anything.
Methodological principle
- minimizes redundancies and inconsistencies in the model
- helps to determine the best model- model representation with minimum number of parameters,yet having fidelity within specified tolerances
Ockham: English theologian and Philosopher, early 14th Century
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Why System Identification?
Need and quest to better understand the system
- Cause-effect relationship purported to underlie the physical phenomenon
Mathematical models required for:- Investigation of system performance and characteristics
- Aerodynamic databases valid over operational envelope for flight simulators
- High-fidelity / high-bandwidth models for in-flight simulators
- Flight control law design- Analysis of handling qualities compliance
Aerodynamic databases from flight data
- Analytical estimates: validity and inadequate theory !- Wind-tunnel predictions: model scaling, Reynold's number,
dynamic derivatives, cross coupling,
aero-servo-elastic effects !!
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Historical Background (1)
C. F. Gauss (1777-1855):problem during evaluation of astronomical measurements:
True values q1, q2, ...., qr of physical constants are unknown (trajectoryparameters of a planet). q
1, ...., q
rare however not measured.
Related parameters are observed, whose true values f1, ...., fr dependon q1, ...., qr according to some rule: fi = fi(q1, ...., qr ).
Q: Which values of i define the observations at best?
Least Squares method (1795)
The Apple and Newtonian gravity:
Sir Isaac Newton (1642-1727):Observed process => model => numerical values
Daniel Bernoulli (1700-1782):
The most probable choice between several discrepantobservations and the formation of the most likely induction (1777)
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Historical Background (2)
Time-Vector Method
Analysis of Dutch Roll Oscillation:
- Graphical method- Time invariance of amplitude and phasebetween the degrees of freedom
l , lp, lr - C C C : Only two derivatives
1/2V Sb2
xz-I r
r-
r
-Cl rr
r
r
p
1/2V Sb2
xxI p
r-
p
-Cl pp
r
-Cl
r
Dynamic Response Flight Testing
1919 -1923 (Glauert, Norton)
Step input:- Sand Dropping from Wing Tips
1940's (Milliken)
Steady State Sinusoidal Response- Circle Diagram: Effective Damping
and Spring Constant
- Analytical Method - Aero. DerivativesEarly 1950 (Seamans)
Pulse Transient Response- Fourier Transformation- Electro-mechanical Synthesizer
1950's (Doetsch, Breuhaus, Wolowicz)
Time Vector Method
1960's (Rampy)
Analog Matching
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Historical Background (3)
Estimation of Damping-in-Roll Derivative:NACA Report 167, by F. H. Norton, 1923
Flight Test Technique:
- Load sand boxes on each wing tip,one pound each, distance to CG 14.7 ft
- Steady flight
- Excitation:
Suddenly release sand in one box,box emptied in < 0.5 sec
- Allow aircraft to roll up to 90 bankwith neutral controls
- Rudder was kicked over and then
other box emptied.- Tests were carried out in smooth air
- Carefully executed repeat runs(test to test scatter within 0.01 rad/s)
Sand box
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Historical Background (4)
Recordings:
- angular rate: electrically driven gyro- Angular velocity recorder;
was calibrated frequently on arevolving table, accuracy 0.01 rad/s
Aircraft mass characteristics:- Sand was weighed out in everycase to within 1%
Methods and Models:- Simple basic formula for estimation:
Lp = M / (mass*p) ==> M =150 x 14.7
Results- Flight estimate 40% lower than the
WT prediction from small oscillations
Estimation of Damping-in-Roll Derivative:NACA Report 167, by F. H. Norton, 1923
Perceptions of SysID 80 years back !
C-160 Example will be shown later
More complex methods and modelsin the modern Era 1966-2006
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Historical Background (5)
Simplified-Equations and Analog-Matching Methods
Simplified-Equations Method
Principle:
For selected types of responses theeffect of only a few coefficientsdominates.
r
rr
N
&
Ruder pulse
a
ppL
a
pa
L
&
Aileron pulse
pa
aLpL
Aileron step
d
ada
Ld
rr
LL Steady sideslip
+
L2d
N Dutch roll
Analog-Matching Method
Principle:
Solve equations of motion onanalog computer; manually tuneparameters to match the responseto flight data.
- limited to a few primary derivatives- time consuming- ingenuity of operator
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Transition Phase
Late 1960'sClassical Approach1919 - mid 1960's
Modern Era1966 - 2006
AdvancedMethods
- Statistical analysis
- Time domain- Frequency domain
- Digital computation
- Deterministic- Graphical
(Paper & Pencil)- Frequency domain
- Analog computation
ClassicalMethods
Fortran
MatlabLaptops
DinosauricDigital
Computation
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Unified Approach to Flight Vehicle System IdentificationQuad-M Basics
ParameterAdjustments
Model Response
Response
Error
-
ActualResponseInput
Maneuver
ModelValidation
ComplementaryFlight Data
Identification Phase
Validation Phase
Optimized
Input Flight Vehicle
IdentificationCriteria
EstimationAlgorithm /
Optimization
MathematicalModel /
Simulation
Parameter Estimation
Data Collection
& Compatibility
easurementsM
ethodsM
odelsM
A Priori Values,lower/upper
bounds
ModelStructure
+
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References (1)
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Jategaonkar, R. V.,Flight Vehicle System Identification: A Time Domain Methodology,Volume 216, AIAA Progress in Astronautics and Aeronautics SeriesPublished by AIAA Reston, VA, Aug. 2006, ISBN: 1-56347-836-6http://www.aiaa.org/content.cfm?pageid=360&id=1447
Hamel, P. G. and Jategaonkar, R. V., Evolution of Flight Vehicle System Identification, Journal ofAircraft, Vol. 33, No. 1, Jan.-Feb. 1996, pp. 9-28.
Hamel, P. G. and Jategaonkar, R. V., The Role of System Identification for Flight Vehicle Applications -Revisited, RTO-MP-11, March 1999, Paper No. 2.
Iliff K. W., Parameter Estimation for Flight Vehicles Journal of Guidance, Control, and Dynamics,Vol. 12, No. 5, Sept.-Oct. 1989, pp. 609-622.
Klein, V., Estimation of Aircraft Aerodynamic Parameters from Flight Data, Progress in AerospaceSciences, Vol. 26, Pergamon, Oxford, UK, 1989, pp. 1-77.
Maine, R. E. and Iliff, K. W., Identification of Dynamic Systems, AGARD AG-300, Vol. 2, Jan. 1985.
Maine, R. E. and Iliff, K. W., Identification of Dynamic Systems - Applications to Aircraft. Part 1:The Output Error Approach, AGARD AG-300, Vol. 3, Pt. 1, Dec. 1986.
Walter, . And Pronzato, L., Identification of Parametric Models, Springer, Berlin, 1997.
Jategaonkar, R. V., (Guest ed.), Special Section: Flight Vehicle System ID - Part 1,Journal of Aircraft, Vol. 41, No. 4, 2004, pp. 681-764.
Jategaonkar, R. V., (Guest ed.), Special Section: Flight Vehicle System ID - Part 2,Journal of Aircraft, Vol. 42, No. 1, 2005, pp. 11-92.
References (2)