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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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


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


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


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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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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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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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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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)

fvsysid shortcourse 1 introduction1

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