fvsysid shortcourse 5 models

AIAA Short Course: Flight Vehicle System Identification in Time Domain, Aug. 2006 Models/1Dr. Ravindra Jategaonkar

ParameterAdjustments

Model Response

ResponseError

ActualResponseInput

Maneuver

ModelValidation

ComplementaryFlight Data

Identification Phase

Validation Phase

OptimizedInput

Flight Vehicle

IdentificationCriteria

EstimationAlgorithm /Optimization

MathematicalModel /

Simulation

Data Collection& Compatibility

easurementsM

ethodsM

odelsM

A Priori Values,lower/upperbounds

Model Structure

Models for Flight Vehicle System Identification

-+


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0 20 40 60 80

Angle of Attack, deg

0

-0.05

-0.1

-0.15

-0.2

-0.25

1/rad

Quasisteady Aerodynamics

Point identification

Linear aerodynamic model(e.g. Rolling moment coefficient)

C δ a

aaCrrCppCCC δδ+++ββ=lllll

l

X-31A

original datasetsingle maneuverdata partitioning

Equations of Motion

Newtonian Mechanics

Differential Equations of Motion- Longitudinal motion (3 DOF)- Lateral-directional motion (3 DOF)- 6 DOF coupled motion

State Space Representation

Fundamental AssumptionForces and moments acting on the flight vehicle can be synthesized.

)0(x0x),,u,x(f.x =β=

),u,x(gy β=

General Aspects


Multipoint and Nonlinear modelsAoA dependency and Nonlinearities in control surface effectiveness(e. g., Tail lift coefficient)

Advanced Models (1)

[ ]dynHH

eeLHLLHLL

LH

LL

ittt

CCCCC

CS

SCC

eeeTH

TWB

ατααεαα

δδαα δαδδα

++−∂∂

−=

+++=

+=

)()()(

23

α dependency NL in control effectivenessat large deflections

Local AoA downwash time lag

Example will be Presented later

dynSBSB

HCSS

S

HHHH ttC

Cti ατδ

δε

τε

ταα

εαα αα +−

∂∂

+−∂∂

+−∂

∂−+= )()()(

Downwash due to Speed brakes and Thrust variation:

Example will be Presented later


Unsteady Aerodynamics

Lα

X =1/2 {1 - tanh [ a1(α − τ α − α ∗ ) ]}

a : airfoil static stall characteristicτ2 : time constant accounting for

unsteady aerodynamic effectsα∗ : break point (α for X = 0.5)

: lift curve slope: flow separation point (0 < X < 1)

CX

1

2

Estimate a ,1 τ2 and α∗

Advanced Models (2)

CL (α, x) = CLα

1 + x2

α2

Lift coefficient

Flow Separation Pointxα

x = 1

x = 0),( xCL α

Topic of extensive research:- CFD, Wind-tunnel tests, semi-empirical models- Common approach based on indicial functions- basis for analytical investigations of the complex flow phenomena

Alternative approach to describe analytically the flow separationincluding stall hysteresis as a function of an internal state variable.



Advanced Models (3)

αα α

2

0 21),(

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧ +

+=XCCXC LLL

)1(),(1 20 X

XC

XCe

CC DLDD −

∂∂

+Λ

+= απ

)1(0 XX

CC

VcqCCCC m

eemmqmmm −∂

∂++++= δα δα

Example:Flight data: h=16000 ft, clean configuration quasi-steady stall.

Run the test case:/FVSysID/chapter04/test_case = 27


Time Responses

-8 0 8 24

1.0

2.0

3.0

0.0

CL

16

Flight measured Model identified

αAngle of Attack , deg

DO 328

time0 20 40

deg

deg

deg

α

a Z

θ

V

δe

g

kt

-100.0

-1.220

-40140

8020

-30

25

60sec


Advanced Models (4)

Lift Coefficient


Principle of Lateral Stall Modeling

Asymmetric Flow Separation

Flow separation pointXright= f (α, α, t)

Flow separation pointXleft = f (α, α, t)

Lift coefficientCL = CL,right+ CL,left

Rolling moment coefficient

Cl = (CL,right- CL,left) Δy

right wing left wing

Δy

Unsteady Aerodynamic Model

CL (α, x) = CLα1 + x

2

α2

Lift coefficient

Flow Separation Pointxα

x = 1

x = 0),( xCL α

Advanced Models (5)


C-160 Lateral Stall Model Identification

flight test data

model response

Bank angle excursion during stalldue to asymmetric flow separation

Aircraft and Model Responses

-30

0deg

-10

5deg

5

25deg

-5

20deg

-20

10deg

elevator

aileron

AoA

pitch attitude

bank angle

flow separation point

1

00 20 40time (s)

right wing

left wing

Advanced Models (6)


Ground Effect Modeling

Advanced Models (7)

Physical phenomenon: resulting from proximity of moving vehicle to ground

- close to the ground the downward flow is interrupted. - for altitudes above ground level lower than the wing span.

Dominant influence on the aircraft landing and takeoff performance.- Reduced downwash angle at the tail.- Increase in the wing-body and the tail lift curve slopes.- Reduction in the induced drag

Loosely speaking, GE leads to reduction of the wing-tip vortices, - equivalent to a reduction of the induced angle of attack.

This implies that for a constant geometrical angle of attack the lift coefficient will increase as the aircraft approaches ground.

The reduction in the induced angle of attack results consequently in areduction of the induced drag.


Under ideal conditions (wing with elliptical lift distribution) the induced drag in terms of a GE influence function σ:

To enable parameter estimation

Three important aspects critical to determination of ground effect from flight data:

- Flight test technique:Landings, Takeoffs, Touch and go, Tower flyby over runway at different height AGL (e.g.,100, 40, 20, 10 ft), Tower flybys with small dynamic inputs

- Accurate height AGL signal.- High fidelity in-air aerodynamic model including landing gear effects.

Ground Effect Modeling

Advanced Models (8)

Λ−=

πσ

eCC L

Di

2)1(

10 5 32

1,5

h/b0 0.2 0.4 0.6 0.8 1 1.2 1.4

0

0.2

0.4

0.6

0.8

1

σIncreasing a1

GE influence functionPrandtl theory

⎟⎠⎞

⎜⎝⎛−=

bha1tanh1σ


Ground Effect Modeling from flight data: example

Advanced Models (9)

Drag coefficient CD Angle-of-attack α Pitching moment Cm

0 0.1 0.2 0 10 20 0 0.5-0.5

Lift

coef

ficie

nt C

L

0

1

2

3 h/b = 0.1h/b = 0.2 h/b = 0.5 h/b = ∞

deg

dragreduction

pitch down

liftincrease

1,0,2525

2_,,1_,,

σ

σασα αα

GEmbasicmm

HHGELbasicHLHLGELbasicWBLWBL

CCC

CCCCCC

+=

+=+=


Global model

Model structure determination- Large number of point ID

Multi-run evaluation

Homogeneous model throughsystematic approach- Normal flight regime,

symmetric flight- Aerodynamic coupling- Control system dynamics- Special effects

(landing gear, engine-out,ground effect, etc.)

Incremental update

A priori simulation model

Incremental coefficients (Δ)(e.g. pitching moment)

Identification of ΔC

C = C + ΔCmaero msim m

m

- Wind tunnel predicted database- Analytical predictions

- Engineering judgement- Highly interactive- Can be as involved as global model ID

Models with Global Validity


Trim point models versus Global model

Point-identification yields models related to specific trim conditions.

Extend aerodynamic model to include angle of attack, Mach numberand angle-of-sideslip dependencies, coupling derivatives, and nonlinearities.

multi-point-identification:several flight conditions are analyzed simultaneously.

Normal flight regime.

Submodels for other Aero effects:landing gear,ground effect, stall approach and quasi-steady stall,takeoff and landing,single engine etc.

Normal Flightregime

Landing gear

Ramp door

Ground effect

Airdrop

High speedregime

Stall approachand stall

Take-offlanding

Singleengine

Groundhandling Engine

Incremental update versus global model (2)


Incremental update versus global model (1)

MeasuredAX, AY, AZ,p, q, r,Pdyn, . . .

p_dot, q_dot, r_dot

AX_cg, AY_cg, AZ_cg

X, Y, Z, L_cg, M_cg, N_cg

X, Y, Z, L_ac, M_ac, N_ac

Flight derivedCX, CY, CZCLX, CMY, CNZ

Wind-Tunnel DatabaseMeasureddero, delo,dari, deli,dr, dbf, dsb,p, q, r,al, be, . . .

WT-PredictionsCX, CY, CZCLX, CMY, CNZ

Δs

SysID

Corrections

The two approaches of database generation, verification and update are more or less equivalent. The choice between the two is mainly dictated by the familiarity and background of the team of engineers involved in this task.

The quality of the a-priori model will also be a decisive factor, so also the form (table look-up or derivative) because of the significant differences in the computational overhead.


LOES

• Primarily for augmented aircraft

• Lower order description of the higher-order augmented system

• To extend the applicability of MIL-STD 1797A developed for flying qualities of classical piloted a/c to augmented a/c

• Linear model with time delays

Low Order Equivalent System

AircraftMotion

Flight Control

Surfacedeflections

Pilotinputs

Closed LoopBasic Airframe


ReferencesJategaonkar, 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

Fischenberg, D., “Identification of an Unsteady Stall Model from Flight Test Data“, AIAA 95-3438, Aug. 1995.

Fischenberg, D., Jategaonkar, R.V., “Identification of Aircraft Stall Behavior from Flight Test Data”,RTO SCI Symposium on ‘System Identification for Integrated Aircraft Development andFlight Testing’, May 5-7, 1998, Madrid, Spain, Paper 17.

Singh, J. and Jategaonkar, R. V., “Identification of Lateral-Directional Behavior in Stall from Flight Test Data“, Journal of Aircraft, Vol. 33, No. 3, May-June 1996, pp. 627-630.

Rohlf, D., “Direct Update of a Global Simulator Model with Increments via System Identification”,RTO SCI Symposium on ‘System Identification for Integrated Aircraft Development andFlight Testing’, May 5-7, 1998, Madrid, Spain, Paper 28.

Hodgkinson, J., Lamanna, W. J., and Heyde, J. L., “Handling Qualities of Aircraft with Stability andControl Augmentation Systems - A Fundamental Approach”, Aeronautical Journal, Vol. 80,Feb. 1976, pp. 75-81.

Mitchell, D. G. and Hoh, R. H., “Low-Order Approaches to High-Order Systems: Problems and Promises”,Journal of Guidance, Control, and Dynamics, Vol. 5, No.5, Sept.-Oct. 1982, pp. 482-489.


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