fvsysid shortcourse 7 examples

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

Examples of Flight Vehicle System Identification

DO-328: Proof of Match

X-31A: High Angle of Attack Modeling

C-160: Aerodynamic Data Base

Rotorcraft: High Bandwidth Models

Phoenix: RLV


This page is left intentionally blank.


General Concept of Aerodynamic Model Identification

Normal Flightregime

Landinggear

Ramp door

Groundeffect

Airdrop

High speedregime

Stall approachand stall

Take-offlanding

Singleengine

Groundhandling Engine


Typical Flight Test Program for System Identification (I)

Test Case: C-160 Transall

FL 300

FL 260

FL 160

FL 80

FL 20

100 150 200 250 300 True Airspeed (Kts)

0.2 0.3 0.4 0.5 Mach No.

Alt

itu

de

80 K

CAS

100

KCAS

120

KCAS

160 K

CAS

195 KCAS

277 KCAS230

KCAS

140 K

CAS

Elevator 3-2-1-1

Short Period

Elevator pulse

Phugoid

Bank angle

Level Turn Maneuver

Aileron/Spoiler

Bank to BankManeuver

Rudder Doublet

Dutch Roll

Thrust Doublet


Typical Flight Test Program for System Identification (II)Test Case: C-160 Transall

Noof Flights Test Purpose Flight

Hours

1

1

2

14

2

1

2

4

3

30

2

1,5

8,5

42,5

4,5

3

3,5

7,5

5

78

Check Flight Test Instrumentation

Envelope Expansion with Trailing Cone

Calibration of Airdata System

System Identification and Model Validation(4 Altitudes, 5 Speeds, 37 Configurations)

Identification of Ground Effects

22 Stall Maneuvers with 5 Configurations

Ground and Taxi Tests

Noise Recording in Hangar, on Runway and in Flight

Special Tests: Load Drop, Takeoff and Landing on Unprepared Runway and Runway with Snow

Flights with ~ 1000 Maneuvers and 37 configurations


C-160: High-Fidelity Simulator Data Base

Aerodynamic data base valid overthe entire operational envelope - Nonlinear aerodynamics - Interference and coupling effects

Identification of C-160 specificoperational characteristics - Ramp door interference, - air drop, etc.

Identification of dynamic stall - Unsteady flow separation

Identification of - Ground effect - Landing and Take-off - Failure states

Validation of flight estimated database - FAA Level-D

Flight estimate of dihedral effect

Point ID: Single trim pointsMulti-Point ID: Several trim conditions

-0.12

-0.18

-0.24-6 0 6 12deg

Point IdentificationMulti-point Identification

C lβ

η = 20°K

Angle of Attack

LandingFlap

η = 0°K

η = 30°K

η = 40°K


Identification of Elevator Control EffectivenessTest Case: Transall C-160

elevatordeflection

0 10 20 30time

s-18

2deg

Linear model

0

m/s2

deg/s

deg

Verticalacceleration

pitch rate

angle ofattack

-6

-128

-818

6

Accounting for nonlinearity

0

m/s2

deg/s

deg

Verticalacceleration

pitch rate

angle ofattack

-6

-128

18

6

Deflection

Effectiveness


Identification of Downwash Lag: Speed Brakes (1) Test Case: Transall C-160

Two-point aerodynamic model:Consider longitudinal motion:The lift and drag forces at the Wing and Tail are considered separately.

Knowing the forces the pitching moment can be computed readily:force times lever arm

In a general case,

[ ] eeLHLH

LLL CittCS

StCCCHW

δτααα δαε

αα ++−−++= ∂∂ )()()(0

[ ] VcqCCittC

SS

cl

CC WmqeeLHLHt

mm H 2)()(0 +++−−−= ∂

∂ δταα δαε

α

V/lt=τ Time required for the downwash to reach the Tail.

Other sources: Landing flaps; Direct-Lift-Control flaps; Wing mounted engines, and Speed brakes


Identification of Downwash Lag: Speed Brakes (2)

Test Case: Transall C-160

Flight tests: δf = 0°, 30°, 60°

Test procedure:Starting from horizontal level flight,apply 40% (100%) of speed brakes, holdfor some time, then retract the brakes.

Basic aerodynamic model augmentedwith incremental effects:ΔCLSB, ΔCDSB, ΔCmSB

For δf = 0°, speed brakes work primarilyin a classical sense as a drag inducingdevice.

Flight measured

Estimated

δf = 0°



For δf = 30° and 60°, time lag effectincreases proportionally

δf = 60°δf = 30°



Speed brakes consists of a lower and upperflaps on each wing;Deflected symmetrically.

Model augmentation:Downwash with transit time effect

Angle of attack at the tail:

are known (basic aerodynamic model)

Estimate of linearly dependent on flap deflection.

⎥⎦⎤

⎢⎣⎡ τ−α+τ−+τ−α−+α=α αδ∂

ε∂∂ε∂

αα∂ε∂ )t()t(C)t(i

SBS CSSCHH

SCand ∂ε∂

α∂ε∂

SBδ∂ε∂



Augmented aero model

incremental effects:

ΔCLSB, ΔCDSB, ΔCmSB

and

with transit time effect

adequately characterizes the Speed brake characteristics.

SBδ∂ε∂

δf = 60°δf = 30°


Modeling of Landing Gear Effects (1)Test Case: Transall C-160

Modeling and Experimental Aspects

Important for simulation of take-offs and landings

Longitudinal and lateral-directionalmaneuvers with gear down

8000 ft and 16000 ft120, 140 and 160 kts

Basic aerodynamic model: Discernible deviations in - longitudinal motion - lateral-directional motion variables

1.2

.010

0

-813

0-75

08

0

-80 20 40 60

Neglecting Landing Gear Effects

Time

m/s2

β

x

r

θ

α

a

deg/s

deg

deg

deg

Flight measurement (C-160 Transall)Model identification

s


Modeling of Landing Gear Effects (2)Test Case: Transall C-160

Modeling of Aerodynamic Effects due to LG

Incremental aerodynamic modeling

Longitudinal motion:Lift, drag and pitching moment coeff.ΔCLLG , ΔCDLG , ΔCmLG

Lateral-Directional motion:- Increased weathercock stability ΔCnβLG

- Sideforce due to sideslip ΔCYβLG

Accounting for Landing Gear Effects

Flight measurement (C-160 Transall)Model identification

0 20 40 60Time

β

x

r

θ

α

a

1.2

.010

0

-813

0-75

08

0

-8

deg

deg

deg

m/s2

deg/s

s


Vertical-acceleration

Pitchrate

Pitchattitude

Pitchacceleration

CG-location

-8

-135

-5

8

-28

-16

50

20

-8

-135

-5

6

28

-16

50

20

m/s2m/s2

deg/s deg/s

degdeg

2deg/s 2deg/s

% %

0 5 10 15Time (sec) 0 5 10 15

Neglecing Variations in Aircraft MassCharacteristics

Accounting for Variations in theAircraft Mass Characteristics

MeasurementSimulation

Time (sec)

C-160: Load Drop (4.6 t)


Do-328: Stand-alone versus Integrated Models

ReversibleFlight Control

Dynamics

Aircraft MotionVariables

Pilot InputForces

Control SurfaceDeflect.

Aircraft MotionVariablesRigid Body

Dynamics

Flight controls stand-alone

ReversibleFlight Control

Dynamics

Rigid BodyDynamics

Integrated model


Aircraft MotionVariables

Pilot InputForces


Rigid-body stand-alone

measured data simulated data


Validation Example 1: Steady Sideslip (DO 328)Rigid-body Stand-alone Integrated Model: End-to-end Match

12

-1218

-184

-42

-220

-20

deg

deg

deg/s

deg/s

deg

β

φ

p

r

δr

0 25 50time s

β

φ

p

δr

12

-1218

-184

-42

-220

-20

deg

deg

deg/s

deg/s

deg

r

0 25 50time s


High activity task:

Single maneuver:

Tolerances: Ground effect:

Wind:

No closed-loop controller

Landing characteristics reproduced in thedatabase conform to the airplane.Complete sequence as a single time segment(starting from 200 ft AGL, flare, touch down,derotation, and initial ground roll)FAA: Landing phase may be split into two(approach and derotation after touch down)

3 kt on airspeed, 10 ft on altitude1.5 deg on pitch attitude, 2.0 deg on bankAnalytical function (tanh-approximation),Continuous transition from in-flight regime toon-ground

Flight card noted windWind components as the difference betweenmeasured tracking speed provided by IRS andthe true airspeed transformed in earth-fixedcoordinate system.

Validation Example 2: Normal Landing (DO 328)


Normal Landing

Flight measured (DO 328)Model identifiedFAA AC 120-40C tolerances

δe

Expanded View (Touch down)

θ

φ

14 16

-5

52

80

60

0

-10

ft

deg

deg

deg

h

Time (sec)

1.5 deg

2 deg

10 ft

18

130

0 10 20-5

10-10

20-10

5-5

100

25090

kt

ft

deg

deg

deg

deg

V

h

θ

φ

δe

δr

1.5 deg

10 ft

3 kt

2 deg

Complete Landing Phase

Time (sec)


Engine failure during the critical phase of take-off

Response to rudder and aileron important

Complete sequence as a single timesegment (stand-still, acceleration, rotation,and climb to 200 ft)

No closed-loop controller

Tolerances: 3 kt on airspeed20 ft on altitude

1.5 deg on pitch attitude2.0 deg on bank

Validation Example 3: Critical Engine Failure (DO 328)

Flight measuredModel identified

kt

ft

deg

deg

deg

deg

150

-500

300

-1000

15

-50

-5

0

10

30

-15

0

10

-20

0

0

-2000

4000daN

0 10 20 30 stime

left engine shut off

V

h

θ

φ

δe

δr

FL , FR


Experimental Aircraft X-31

Thrust vector control

What is X-31?- First international „X-System“- Technology Demonstrator

Goals- Enhanced Maneuverability (up to 70°)- Tactical advantages through Flight

beyond the limits

New Technologies- Thrust vector control- Aerodynamic design - Integrated Flight control system

Tasks- Flight envelope expansion- Development of Data base for

Simulation and FCS design- Handling qualities evaluation

Folie Nr.23


Control Surfaces of the X-31A

Thrust VectoringVanes (3)• -60° bis +35°• 60°/sec

Thrust VectoringVanes (3)• -60° bis +35°• 60°/sec

Inlet• 0° to -26°• 20°/sec

Inlet• 0° to -26°• 20°/sec

Trailing Edge Flaps (4) • ±30°• 80°/sec

Trailing Edge Flaps (4) • ±30°• 80°/sec

Canard (2)• -70° to +20°• 60°/sec

Canard (2)• -70° to +20°• 60°/sec

Leading Edge Flaps (2) • 0° to -40°• 25°/sec

Leading Edge Flaps (2) • 0° to -40°• 25°/sec

Speed Brakes (2) • 0° to +46°• 20°/sec

Speed Brakes (2) • 0° to +46°• 20°/sec

Rudder• ±30°• 80°/sec

Rudder• ±30°• 80°/sec


Flight Test Program

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Mac

h nu

mbe

r

Angle of Attack, deg0 10 20 30 40 50 60 70 80-10

Longitudinal motion

High Angle of AttackSupersonicLanding configurationData conditioningSeperate Surface Excitation

Longitudinal motion


Challenges of Flight in Post-Stall Regime

Basic aircraft is highly unstable;Resulting from aerodynamic design.

Motion variables and controls are highly correlated;Resulting from integrated flight control system.

Controller Suppresses the oscillatory and transient motion;Reduces drastically the information content.

Post-Stall Maneuver with large amplitudes;Conventional model structures inappropriate for analysis.

Determination of Air-Flow variables extremely critical; However, necessary for Stabilization of Flight systems.


Identification of controlled unstable aircraft

Problems- Increased Modeling effort for closed loop system- Numerical Problems in identification of open loop plant- Feedback of measured variables introduce input noise (stochastic system)

Parameter estimation methods- Equation error method with optional Data-Partitioning- Filter error method for problems with Measurement and Process noise- Extended Kalman filter

ControllerController UnstableAircraft

UnstableAircraft

Identificationin open loopIdentificationin open loop

Pilot

MeasuredControl inputs

MeasuredResponse

Noise

u z


AerodynamicControl surfaces

Pilotinputs

Thrust vector

Sensors

FCCFlight Control

Computer

FCC RedundancyManagement Signals

FTBFlutter test box

X-31Aircraft dynamic

Control commands

States

Realization of Separate Surface excitation (1)


Realization of Separate Surface excitation (2)

AerodynamicControl surfaces

Pilotinputs

Thrust vector

Sensors

FCCFlight Control

Computer

FCC RedundancyManagement Signals

FTBFlutter test box

X-31Aircraft dynamic

Control commands

States

PilotTrigger Signal generatorSignal generator


Correlated Inputs (1)

X-31A: Pilot Input and Separate Surface Excitation α σδTEδcan

deg

deg

deg

deg

20

35

0

2

-15

-4520

-20

time s200 10 15 255

PID command

pitch command

angle of attack

canard

sym. trailing edge flaps

TV deflection in pitch

2.5

-2.5

deg20

-20

deg

pilot inputpitch doublet

canard 3211

elevator 3211

separate surface excitation (SSE)


20 40 60 80Angle of Attack, deg

0.6

0.4

0.2

0

-0.220 40 60 80

Angle of Attack, deg

Pilot Input Separate Surface Excitation

Single maneuverData partitioningWindtunnel predicted

EstimatedWindtunnel

Cmδcan

X-31A: Canard Effectiveness

α σδTEδcan

Correlated Inputs (2)


correlated state andcontrol variables

Derivatives that cannot be identifiedindependently from pilot input maneuvers

α, δC , δe and σ,

δa , δr and as well as p and rCm α , Cm , Cm δe and Cm σ ,Cn δa , Cn δr and Cnκ Clp and Clrκ as well as

δC

• relatively large standard deviations and uncertainties

• use fixed values from the X-31 database for some parameters

• combined roll/yaw-damping

with

ppr

lrClpCplpC ⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+=⋅*

αtan=pr

for the velocity vector roll0 5 stime

angle ofsideslip

deg5

-5

rollcommand

1

-1

deg

TV-deflectionin yaw -20

20diff. trailingedge defl.

deg/s

yaw rate

roll rate

-20

20

Roll Doublet

PID with Pilot Input -- Single Maneuver (1)


PID with Pilot Input (2)Bank-to-bank maneuver at 54° angle of attack: LS and Filter error methods


PID with Pilot Input (3)Estimates of aerodynamic derivatives: LS and Filter error methods


X-31 Database Update (1)

-0.4

-0.3

-0.2

-0.1

0

0 20 40 60 80

Pilot Input

original data setsingle maneuverdata partitioningPID2 update

angle of attack, deg

C lβ

1/rad

0 20 40 60 80

Single Surface Excitation (SSE)

original data setflutter test boxPID2 update

angle of attack, deg

Dihedral Effect


X-31 Database Update (2)

Directional Stability

! " " #$

"

#

%

&

& ' ' ( )

"

! " " #$

"

#

%

&

& ' ' ( )

"


ReferenceMission:

Flight phases upon release:1) Acquisition2) Approach3) Flare4) Alignment5) Derotation6) Rollout

Launch at40m/s EAS

flare

118m/s

runway

acquisition dive

altitude

RLVapproachpath -23o

510m

2.65km6.6km

touch down71m/s

Towed to establish initial conditions

Phoenix freeflight profile

45m x 2100m

release Phoenixfrom helicopter

touchdown

lift-off

ground track

Launch at40m/s EAS

flare

118m/s

runway

acquisition dive

altitude

RLVapproachpath -23o

510m

2.65km6.6km

touch down71m/s

Towed to establish initial conditions

Phoenix freeflight profile

45m x 2100m

release Phoenixfrom helicopter

touchdown

lift-off

ground track

Phoenix: Reusable orbital glider (1)


Overview and goals

Phoenix:Flight test vehicle developed and tested within German ASTRA program

Experimental steps towards the development of next generation space transportation systems

Primary Objectives:To demonstrate un-powered automatic landing of RLV configuration

Secondary Objectives:To generate flight validated database and representativemodels (vehicle + subsystems) as developmental tool for future applications



Phoenix Configuration

Typical characteristics of RLV configurations (Phoenix):Low L/D -- causes steep approach path (= 5.5)Low achievable CL -- high landing velocity (=71 m/s)Small wing span -- high roll sensitivityAft CG position -- statically unstable configuration

(time to double < 0.5 s)

Overall length = 7.8 m (including noseboom)Span = 3.84 mOverall height = 2.56 m (retracted landing gear)Mass = 1200 kgCG position = 70 % of bare fuselage length



Aerodynamic Database

Wind-tunnel tests:DNW German-Dutch wind tunnel

Test program:171 quasi-static polar curves,25 dynamic polar with

rapid control deflections29 polar curves in ground effect

Scaled models and full scale flight vehicle



Wind-tunnel testing in August 2003

Pre-flight checks: April 2004

calibration of flow angles:

α-error nonlinear: quadratic or piecewise linear

Accuracy:AoA and AoS: < 0.5°Horizontal velocity: 0.5 m/s


-10 -5 0 5 10 15 20 25-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

alpha

Alph

a-er

ror

afte

rlin

ear c

alib

ratio

n

40 m/s70 m/s100 m/s

deg

deg

offsetc

d

c

dqp

korrqK

pα++=α β

βα

α


Free flights:Maiden flight on 8-May-2004Repeat flight on 13-May-20043rd flight with Offset on 16-May-2004

Configuration:Delta Wing, relatively low wing span3 controls (flaperons and rudder)Body flap and speed brake1200 Kg7m long3,48 m span

Highly dynamic behaviorHigh bandwidth control loops

Video free flight 1:



Aerodynamic DatabaseVerification and Update -- Principle


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

FlightCX, CY, CZCLX, CMY, CNZ

Windtunnel Database(…V31.txt)

Measureddero, delo,dari, deli,dr, dbf, dsb,p, q, r,al, be

WT-PredictionCX, CY, CZCLX, CMY, CNZ

Δs

SysID

Corrections


Flight derived and WT predicted aero coefficients

-0.06

-0.03

0

0.03ZA03 ZA06 ZA05

CXCX

-0.03

-0.015

0

0.015

0.03ZA03 ZA06 ZA05

CYCY

-0.5

-0.25

0ZA03 ZA06 ZA05

CZCZ

-4

-2

0

2

4x 10

-3

ZA03 ZA06 ZA05

CLXCLX

-12

-6

0

2x 10

-3

ZA03 ZA06 ZA05

CMYCMY

0 50 100 150-4

-2

0

2

4x 10

-3

t in s

ZA03 ZA06 ZA05

CNZCNZ

-0.02

-0.01

0

0.01ZA03 ZA06 ZA05

dCX

-0.02

-0.01

0

0.01

0.02ZA03 ZA06 ZA05

dCY

-0.1

-0.05

0

0.05

0.1ZA03 ZA06 ZA05

dCZ

-2

-1

0

1

2x 10

-3

ZA03 ZA06 ZA05

dCLX

-4

-2

0

2

4x 10

-3

ZA03 ZA06 ZA05

dCMY

0 50 100 150-2

-1

0

1

2x 10

-3

t in s

ZA03 ZA06 ZA05

dCNZ



0 0.05 0.1 0.15 0.2 0.25-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

Angle of attack (rad)

Tota

l CX

ff-n1 flight measurementsff-n2 flight measurementsff-n3 flight measurementsff-n1 wind-tunnelff-n2 wind-tunnelff-n3 wind-tunnel

Flight derived and WT predicted longitudinal force coefficient

Flight data

Pre-flight ADB



0 0.05 0.1 0.15 0.2 0.25-0.5

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0


Tota

l CZ

ff-n1 flight measurementsff-n2 flight measurementsff-n3 flight measurementsff-n1 wind-tunnelff-n2 wind-tunnelff-n3 wind-tunnel

Flight derived and WT predicted vertical force coefficient

Rough order of discrepancies:CZ: 9-10%

Cm: < 3%

CD: ~10% Nonlinear

Pre-flight ADB

Flight-derived



sbsbref

q CXVL

qCXCXCXCX δα δα +++=Δ 0

bfbfref

q CZVL

qCZCZCZCZ δα δα +++=Δ 0

sbsbee CMCMCMCMCMY δδα δδα +++=Δ 0

12 Parameters CZ(), CX() and Cm() are estimated to reduce the deviations between flight measurements and WT-predictions.

Aero model update (In-Air)



Flight derived and updated database aero coefficients

-0.06

-0.03

0

0.03ZA03 ZA06 ZA05

CXCX

-0.03

-0.015

0

0.015

0.03ZA03 ZA06 ZA05

CYCY

-0.5

-0.25

0ZA03 ZA06 ZA05

CZCZ

-4

-2

0

2

4x 10

-3

ZA03 ZA06 ZA05

CLXCLX

-12

-6

0

2x 10

-3

ZA03 ZA06 ZA05

CMYCMY

0 50 100 150-4

-2

0

2

4x 10

-3

ZA03 ZA06 ZA05

CNZCNZ

-0.02

-0.01

0

0.01ZA03 ZA06 ZA05

dCX

-0.02

-0.01

0

0.01

0.02ZA03 ZA06 ZA05

dCY

-0.1

-0.05

0

0.05

0.1ZA03 ZA06 ZA05

dCZ

-2

-1

0

1

2x 10

-3

ZA03 ZA06 ZA05

dCLX

-4

-2

0

2

4x 10

-3

ZA03 ZA06 ZA05

dCMY

0 50 100 150-2

-1

0

1

2x 10

-3

t in s

ZA03 ZA06 ZA05

dCNZ



0 0.05 0.1 0.15 0.2 0.25-0.5

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0


Tota

l CZ

ff-n1 flight measurementsff-n2 flight measurementsff-n3 flight measurementsff-n1 wind-tunnel + Updatesff-n2 wind-tunnel + Updatesff-n3 wind-tunnel + Updates

Flight derived and Updated database vertical force coefficient



Delta CZ versus AoAwithout and with update

Important Inferences:- lift generated in flight is higher - component due to pitch rate in lift and drag is not adequately accounted for. - basic longitudinal force coefficient for clean configuration underestimated,- impact of speedbrakes overestimated.

0 0.05 0.1 0.15 0.2 0.25-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03


Del

ta C

Z

ff-n1ff-n2ff-n3

0 0.05 0.1 0.15 0.2 0.25-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03


Del

ta C

Z

ff-n1ff-n2ff-n3

Flight derived and Updated database (Continued)Phoenix: Reusable orbital glider (14)


Flight derived and WT predicted In-Air + Landing Gear

0 0.05 0.1 0.15 0.2 0.25-0.015

-0.01

-0.005

0

0.005

0.01


Del

ta C

X

ff-n1ff-n2ff-n3In-Air

Land

ing

Gea

r



LGLGsbbsref

q CXCXVL

qCXCXCXCX δαδα αδα ++++=Δ 0

LGLGbffbref

q CZCZVL

qCZCZCZCZ δαδα αδα ++++=Δ 0

LGLGsbbsee CMCMCMCMCMCMY δαδδα αδδα ++++=Δ 0

Aero model update: In-Air + Landing Gear-Effects)

In-Air updates fixed from initial 50 s maneuver



Delta CX versus AoAwithout and with update

Landing GearAero effect

Aero model update (In-Air + Landing Gear-Effects)

0 0.05 0.1 0.15 0.2 0.25-0.015

-0.01

-0.005

0

0.005

0.01

Del

ta C

X

ff-n1ff-n2ff-n3

0 0.05 0.1 0.15 0.2 0.25-0.015

-0.01

-0.005

0

0.005

0.01


Del

ta C

X

ff-n1ff-n2ff-n3



Rotorcraft Modeling (1)

Integrated Approach to Rotorcraft Modeling and SimulationSID Models SIM & SID Models SIM Models

Classical SID approachDerivative modelsLinear/NL aerodynamicExtensive flight datafor point-model IDand validationStability & Controlanalysis andcontrol system design

Advanced integrated approachGeneric model Augmented with parametric submodelsNonlinear aerodynamicFlight data for sub-model ID and globalmodel validation

Classical SIM approachGeneric models based onmodular elements Nonlinear aerodynamicFlight data only formodel validationSimulation, performanceAnd vehicle design

System Identification System SimulationSystem Simulation &Identification

High Fidelity SimulationState Space Models



SID: based on classical 6 DOF motionrigid-body, small excursions: linear modellarge excursions NL derivatives

States:

Inputs:

Outputs:

Example: EC-135,60 kts forward speed

Trqpwvux ][ θφ=

Tcolpedlatlonu ][ δδδδ=

Tzyx rqprqpwvuaaay ][ &&&θφ=



SID: based on classical 6 DOF motionExample: EC-135, 60 kts forward speed

- Gauss-Newton method- concatenate several dynamic multistep inputs as well as frequency

sweeps with longitudinal, lateral, collective, and pedal inputs

1st and 2nd row: linear derivatives3rd and 4th row: a and b dependenciesweathercock stability parameter Cnβ (NV) for +/-ve side slipping

lonlonlonlon

pedpedpedpedrv

colcolpedpedlatlatlonlon

rqpwvu

NN

NNrNvN

NNNN

rNqNpNwNvNuNNN

δβδα

δβδααα

δδδδ

βδαδ

βδαδαα

δδδδ

++

++++

++++

++++++= 0~



SID: classical 6 DOF motionExample: EC-135, 60 kts forward speed

Model predictive capability:- Pedal and lateral inputs- low-frequency models- Flying qualities investigations

time

rad/s0.3

-0.5

0p

rad/s0.3

-0.3

0q

rad0.2

-0.2

0α

rad0.3

-0.3

β 0

0 10 20 30 40s

75

35

%δlat,δped

rad/s0.3

-0.3

0r


ModelInversion

Analysisof FlightTest Data

SystemIdentification

Model ofHelicopterDynamics

ModelValidation

HelicopterResponse

RequiredResponse

ControlLaw

Pilot CommandModel

ActualHelicopterDynamics

ControllerInputModel of

HelicopterDynamics

-1

Feed-forward

Response Error

PI-Controller

-+

Feed-back

High bandwidth models:In-flight simulation: Explicit Model Following Control Design:Based on feed forward regulation, for more accurate mode control



Rotorcraft Modeling (6)High bandwidth models:

Extension of 6DOF model through additional time delay:- easier to deal with; no difficulties in parameter estimation- not suitable for model following control:(inversion of time delay amounts to time lead – not realizable

Extension of 6h rotor degrees of freedom:1) implicit first-order approximation of the main rotor2) explicit equations for the rotor degrees of freedom

Basic equation for roll response can be written as:

step input results in a step response in the roll acceleration

controlpp LpLp δδ+−=& Eq. 12.45


Rotorcraft Modeling (7)High bandwidth models -- implicit first-order approximation

First order approximation of main rotor:based on high correlation between the flapping motion of the rotor tip path plane (lateral and longitudinal flapping) and the body-fixed rotational (roll and pitch) accelerations.

Correlation between roll acceleration and lateral flapping(rigid rotors and high hinge offset):

where is the lateral flapping, the control input at the blade root, and a flapping time constant.

This coupled differential equation indicates that a step into the control input leads to a first order response of the rotor itself coupled with the body response driven by the rotor flapping.

11 bLp b=&

controlb

b

b

Lpbb δ

ττδ+−−= 11

1&

1b controlδbτ

Eq. 12.47

Eq. 12.46


Rotorcraft Modeling (8)High bandwidth models -- implicit first-order approximation

Differentiating (12.46), substituting (12.47) and then using again (12.46)leads to a second order differential equation for rotor/body motion:

Which can be equivalently formulated as:

where denote the new set of lateral system parameters.

Thus, either the two first order equations (12.46) and (12.47) are now used to model the roll motion and lateral flapping, or depending on the application in the control system design the equivalent second order equation (in roll rate p), Eq. (12.49), can be used for system identification.

controlb

bbb

bb

LLpLpbLp δ

ττδ1

1111

+−−== &&&&

controlppp LpLpLp δδ~~~)( +++= L&&& &

()~L

Eq. 12.48

Eq. 12.49


Rotorcraft Modeling (9)High bandwidth models -- implicit first-order approximation:

The derivatives appearing in Eq. (12.49) are not the same as those in the classical rolling motion equation of the rigid-body motion.

Thus, when we use Eq. (12.49) for parameter estimation purposes, the classical parameters gets scaled through the flapping time constant and the flapping effects appear indirectly through these scaled parameters.

Incorporation of these second order models in the parameter estimation is little tricky, because the estimation programs require models postulated as first order differential equations. This is elegantly done by treating and as the state variables, leading to a state vector given by:

compared to that for pure rigid-body:

b

bb

b

ppb

b

pp

bp

LLLLL

LLL

ττττδδ

δ1

1~,~,1~ ==−=−=−=&

Trqqppwvux ][ θφ&&=

p& q&

Trqpwvux ][ θφ=


( )pp L p L tδδ= +&

Conventional first order- rigid body only -

bp L b=&

( )b L tb pδ δτ

− += −&

Extended second order- rigid body & first order rotor-

( )p pp L p L p L tδ δ= + +&% % %&& &

Equivalent second order rigid body

Extended model formulation: Summary



Rotorcraft Modeling (11)High bandwidth models -- implicit first-order approximation :The main advantage of this approach is that the extended model implicitly represents dynamics of the rotor degrees of freedom as a first order system. Together with the 8th order state vector of the rigid-body motion defined earlier, above approximation of the rotor coupling in the pitch and roll leads to a 10th order model, covering a wider frequency range. As rotor dynamics are implicitly modeled, the time delays are significantly reduced to the pure influence of the actuator dynamics.

High bandwidth models -- Explicit rotor degrees of freedom:Considering the blade flapping motions in terms of the tip path plane variables, the states of the rigid-body motion are extended by:

where and denote the longitudinal and lateral flapping, and the coning motion, each of which is modeled as a second order system, leading to an extended model with nine degrees of freedom.

Ta abaabax ][ 011011 &&&=

1a 1b 0a


State Matrix States

= +

rigid body

FUSELAGE

ROTOR

rotor

body/rotorcoupling

rotor / bodycoupling

x

y

o

TR

δ

δ

δδ

ControlMatrix Controls

a0.

v.

p.

q.

u.

w.

r.

.

..

.

.

a1.

b1

.

.

..

u

v

w

p

q

r

a1

b1

a0

Extended Model Structure Approach



BO 105 Time Histories (Linear Simulation and Flight Data)

Control Inputlateralstick

%

-10

10

Flight Data6 DoF Rigid Body

rollrate

rad/s

-0.3

0.3

rollacc.

2.0

-2.0

rad/s2

0 10time

s5

6 DoF Rigid Body

time

lateralflapping

.015rad/s

0 10s- .015 5

rollrate

rad/s

-0.3

0.3

rollacc.

2.0

-2.0

rad/s2

9 DoF Rigid Body + Rotor

9 DoF Rigid Body + Rotor



BO 105 Time Histories - Quality Control

9 DoF Rigid Body/Rotor Roll Acceleration

6 DoF Rigid Body Roll Acceleration




Frequency

dB

10

deg

Mag

nitu

dePh

ase

rad/s

-1045

0

-900.3 1 10

0

Rigid-body 6 DOF GenericNL model

9 DOF withrotor dynamics

Rigid-body 6 DOFGenericNL model

9 DOF withrotor dynamics

Boundaries of unnoticable dynamics

Rat

io o

f rol

l rat

e re

spon

ses

BO 105 model validation in frequency domain


Rotor Wake Modeling

Accurate Prediction of Off-axis Response- At hover and at low speeds;a long standing problem

- asymmetrical vortex compressionand dilation act on the induced velocity field.

- Gyroscopic behavior leads tostrong cross- coupling effectsdue to wake distortion

- Complex models based on geometricallyprescribed or free wake formulationwith discrete vortices; or equivalent vortex ring/sheet formulation.

- Simpler models based on local phenomenon -- Parametric extensions for the dynamics of the inflow

Pure Hover

Pitching motion in Hover



Rotor Wake Modeling

M :Apparent mass matrix associated with theacceleration terms from momentum theory

L : gain matrix, λ (= [λ0, λs, λc]T) the inflow ratiodescribing the first harmonic terms

c (= [cT, c1, cm]T): rotor load coefficients wrt rotor thrust and aerodynamic pitch and roll moment,

Ω: main rotor rotation speedKp and Kq: The wake distortion parameters for

longitudinal and lateral distribution of theinduced velocity.

The last term on the RHS is the parametric term that feeds back the total roll and pitch rates of the rotor tip path plane wrt to the surrounding air to the induced velocity distribution over the rotor disk.

Estimate Kp and Kq

4444444444 34444444444 21

&

&

444 3444 21

&

dynamicsdistortionWakeInflow

dynamicsInflowPetersPitt

cqqKsppKLcLM

+

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−−

Ω+=

−+

)(

)(0

1ˆ11ˆ

&

β

βλλ


Parametric extension of Pitt and Peters dynamic wake model:

Theoretical estimates of wake distortion parameters:

)/( RVH Ω=μVH: forward speed in m/s, Ω: main rotor rotation speed in rad/s,R: rotor radius in meter

.


Rotor Wake Modeling:

Hover:

Simulation fidelity withTheoretical and flightIdentified WD parameters:


Lateral Inp

utLongitudinal

Input

Roll Rate

Pitch Ra

te

deg/s

deg/s

deg

20

0

-30

30

0

20

-20

2

0

-3

time20 25 30 35

-20

deg4

0

-1

2

s

Flight case #1 Flight case #2with theoreticalWD-parameters

with flightidentified WD parameters


Rotor Wake Modeling:

Hover:

Off axis response without (i.e. inflow dynamics only) and with flight identified WD parameters


20

10

-10

-20

60 64 68stime

deg/s

Inflow and WakeDistortion

0

20

10

0

-10

-20

60 64 68stime

deg/s

PitchRate

Inflow Dynamics

Flight DataSimulation


Rotor Wake Modeling:Forward speed of 40 m/s:

Kp = 1.1; Kq = 1.6

Estimates do not conform to the wake prediction theory (they should be roughly zero).

classical issue often faced in modeling applying system identification methods:

estimated parameters do not represent the wake distortion phenomenon which mainly occurs at hover and at low speeds, rather they account for some other unmodeled effects, for example those resulting from rigid blade formulation as assumed in the present investigations.


with PWD

without PWD

time

Lateral Inp

utLo

ngitu

dina

lInpu

tRo

ll Rate

Pitch Ra

te

deg/s

deg/s

deg

deg

2

15

0

-10

20

0

-20

-40

-1

-3

-5

4

00 2 4 6 8 10s

Flight case #1 Flight case #2


References (1)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 of Aircraft, Vol. 33, No. 1, 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.

Jategaonkar, R. V., Fischenberg, D., and von Gruenhagen, W., “Aerodynamic Modeling and System Identification from Flight Data – Recent Applications at DLR,”Journal of Aircraft, Vol. 41, No. 4, 2004, pp. 681-691.

Jategaonkar, R. V., Mönnich, W., Fischenberg, D., and Krag, B. “Identification of Speed Brake, Air-Drop,and Landing Gear Effects from Flight Data”, Journal of Aircraft, Vol. 34, No. 2, March-April 1997, pp 174-180.

Jategaonkar, R. V., Mönnich, W., Fischenberg, D., and Krag, B. “Identification of C-160 Simulator Data Base from Flight Data”, Proceedings, 10th IFAC Symposium on System Identification, Copenhagen, Denmark,July 1994, pp. 3.67-3.74.

Jategaonkar, R.V., Mönnich, W., “Identification of DO-328 Aerodynamic Database for a Level D FlightSimulator”, AIAA 97-3729, 1997.

Mönnich, W., Jategaonkar, R.V., “Database Development for Level D Simulators - Lessons Learned”,RTO SCI Symposium on ‘System Identification for Integrated Aircraft Development and Flight Testing’,May 5-7, 1998, Madrid, Spain, Paper 14.


N.N., “Airplane Simulator Qualification”, FAA Advisory Circular, AC 120-40C, Interim Version, Jan. 1995.

N.N., “Joint Aviation Requirements - Aeroplane Flight Simulators”, JAR-STD 1A, Westward Digital Ltd.,Cheltenham, England, April 1997.

Jategaonkar, R. V., Behr, R., Gockel, W., and Zorn, C., “Data Analysis of Phoenix RLV Demonstrator Flight Test,” AIAA Paper 2005-6129, Aug. 2005.

Rohlf, D., Plaetschke, E., Weiss, S., “X-31A System Identification Applied to Post Stall Flight - Aerodynamics and Thrust Vectoring”, AGARD CP-548, March 1994, Paper 14.

Weiss, S., Friehmelt, H., Plaetschke, E., and Rohlf, D., “X-31A System Identification using Single Surface Excitation at High Angles of Attack”, Journal of Aircraft, Vol. 33, No. 3, May-June 1996, pp. 485-490.

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.

Tischler, M.B., “System Identification Methods for Aircraft Flight Control Development and Validation”,NASA TM 110369, Oct. 1995.

Kaletka, J., von Grünhagen, W., “System Identification of Mathematical Models for the Design of a Model Following Control System”, Vertica, Pergamon Press, Oxford, Vol. 13, No. 2, 1989, pp. 213-228.

Anon, “Rotorcraft System Identification”, AGARD, AR280, Sept. 1991.

Hamel, P.G., Kaletka, J., “Rotorcraft System Identification - An Overview of AGARD FVP Working Group 18”,AGARD CP-552, 1995, Paper 18.

N.N., “Helicopter Simulator Qualification”, FAA Advisory Circular, AC 120-63, Oct. 1994.

Rohlfs, M., von Grünhagen, W., Kaletka, J., “Nonlinear Rotorcraft Modeling and Identification”, RTO SCI Symposium on ‘System Identification for Integrated Aircraft Development andFlight Testing’, May 5-7, 1998, Madrid, Spain, Paper 23.

References (1)

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