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177943,

Volume [I

D

ANALYSIS OF FLEXIBLE AIRCRAFT LONGITUDINAL DYNAMICSANDHANDLINGQUALITIES VOLUMEII

Martin

DATA

R. Waszak and David K. Schmidt

(NASA-C_-I77943-Vol-2} ANALYSi3 OF FLEXIBLB AIRCHAFT LONGITUDINAL DYNAMICS AND HANDLING QUALITITS, VOLU._E 2 : DATA (Purdue Univ, ) 243 p HC &II/MF &01 CSCL _,IC

N85-352_13

_3/[8

Unclas 22275

PURDUEUNIVERSITY !Vest Lafayette, Indiana

Grant NAGI-254 June 1985

_"__"3

,_

i

NationalAeronauticsand Space Administration

:"! j •

LangleyResearchCenter Hampton,VPrgJnJa 23665

_.

ANALYSIS OF FLEXIBLE AIRCRAFT LONGITUDINAL DYNAMICS AND IIANDI.ING QUALITIES w

VOLUME II - DATA

Martin R. Waszak " David K Schmidt "

School of Aeronaulics and Astronautics Purdue University West Lafayette, IN

June 1985

* Graduate Student ** Professor

"

;4

ACK NOWLEDGMENTS

This research was supported by the NASA l,angley Research Center under gran', number NAG-I-25-t. Thanks go to Mr. William Grantham and Mr. Jerry Elliot who have served as technical monitors. Addflional thanks go to J.B. Davidson and F.A. Leban for advice and assistance which aided this research.

i

.°°

111

TABLE OF CONTENTS

Page

LIST OF TABLES ...........................................................................................

v

IAST OF FIGURES ........................................................................................

vi

LIST OF S'_%,1BOLS......................................................................................

ix

SUMMAI_ Y....................................................................................................

xii

VOL[JME I CtL_I'TER

" I I INTRODUCT.ON .....................................................................

1

CIL'O'TEIt II BACKGROUND .....................................................................

3

CItAPTER IIl EXPERIMENTAL DATA BASE ..........................................

10

CHAPTER IV OPEN-LOOP MODAl. ANALYSIS .....................................

19

Modal Analysis .......................................................................................... Vehicle Model ............................................................................................ Application to Data Base Configurations .................................................. Numerical Results ..................................................................................... CttAPTEP

V CLOSED-LOOP ANALYSIS ................................................

NeaI-Smith/Bacon Methodology ............................................................... Extension of Neal-Smith/Bacon Methodology ........................................... Application of the NeaI-Smith/Bacon Analysis to the Data Base Configurations .............................................................. Numerical Results ..................................................................................... CHAPTER

VI

CONCLUSIONS

...................................................................

LIST OF REFERENCES ..............................................................................

PRECEDING PAGE BLANK NOT FILMED

19 24 28 32 52 52 61 68 76 85

"

87

_

iY

Page APPENDICES Appendix A.I Scaling Transformation for Mode Identification .........................................................................

89

Appendix A.2 nz in Terms of Vehicle States ............................................

92

VOLUME II Appendix A.3 Vehicle Configurations and Modal Analysis Results ..................................................................

96

Configuration 1 .................................................................................... Configuration 2 .................................................................................... Configuration 3 .................................................................................... Con figurat.,ion 4 .................................................................................... Configuration 5 .................................................................................... Configuration 6 .................................................................................... Configuration 7 .................................................................................... Configuration 8 ....................................................................................

100 11g 137 155 173 19I 209 227

Appendix A.4 Aeroelastic-Structural Appendix A.50CM

Mode Shapes ................................

Frequency Responses .............................................

Append!x A.6 Listing of Source Code for Modal Analysis Program ...............................................................

2,15 251

28!

LIST OF TABLES

Table

6

Page

3.1

Summary of Data Base Configurations ................................................

12

3.2

Summary of Tracking Error, Pilot Rating and Pilot Comments ...................................................................................

14

4.1

Summary of Navion Longitudinal Dynamics .......................................

23

5.1

Comparison of Resonance Peak and SP Values ..................................

67

5.2

Summary of Closed-Loop Analysis Inputs ...........................................

75

5.3

Summary of Closed-Loop Analysis of Data Base Configurations ....................................................................

82

vi

LIST OF FIGURES t

Figure

Pal_e

2.1

Pole-Zero Plot of Typical Flexible Aircraft ............................................

4

2.2

Pole-Zero Plot, of Simple Example ..........................................................

5

3.1

Geometry of Dala Base Configurations .................................................

il

3.2

Rigid and Elastic Pitch Angles .............................................................

13

3.3

Simulation Visual Display .....................................................................

15

3.4

Simulation Tracking Errors ..................................................................

16

3.5

Simulation Pilot Ratings ......................................................................

17

4.1

Rigid and Elasiic Pitch Angles .............................................................

30

4.2

Pilot Impulse Residue Magnitudes-

qonfig. 1......................................

33

4.3

I'ilot l_mpulse Residue Magnitudes - Config. 2 ......................................

3,1

4.4

Pilot Impulse Residue Magnitudes - Config. 3 ......................................

35

4.5

Pilot hnpulse Residue Magnitudes-

Config. 4 ......................................

36

4.6

Pilot Impulse Residue Magnitudes-

Config. 5 ......................................

37

4.7

Pilot Impulse Residue Magnitudes-

Config. O.....................................

38

4.8

Pilot Impulse Residue Magnitudes-

Config. 7 ......................................

39

4.9

Pilot Impulse Residue Magnitudes-

Config. 8 ......................................

40

\

vii

Figure

Page

4.10

Gust Impulse Residue Magnitudes - Config. 1 .....................................

43

4.11

Gust Impulse Residue Magnitudes - Config. 2 .....................................

44

4.12

Gust Impulse Residue Magnitudes - Config. 3 .....................................

45

4.13

Gust Impulse Residue Magnitudes - Config. 4 ....................................

46

4.14

Gust Impulse Residue Magnitudes - Config. 5 .....................................

47

4.15

Gust Impulse Residue Magnitudes - Config. 6 .....................................

48

4.16

Gust Impulse Residue Magnitudes - Config. 7 .....................................

40

417

Gust Impulse Residue Magnitudes - Coufig. 8 .....................................

50

5.1

Neal-Smith Model Structure .................................................................

54

5.2

Frequency Response Specifications .......................................................

55

5.3

Neal-Smith Criteria ..............................................................................

57

5.4

OCM Block Diagram ............................................................................

50

5.5

Resonance Peak Adjustment ................................................................

62

5.0

Neal-Smith/Bacon

Pilot Compensation ................................................

63

5.7

Neal-Smith/Bacon

Criteria ...................................................................

64

5.8

Pilot Rating ve:sus Bandwidth for Neal-Smith/Bacon Configurations ........................................................

65

5.9

SP versus PC for Neal-Smith Configurations .......................................

6g

_:

5.10

Dynamics of Neal-Smith Configurations ..............................................

70

_

5.11

Dynamics of Flexible Configurations ....................................................

71

:_

5.12

Block Diagram of Tracking Analysis ....................................................

74 ',%

,,,

VIII

Figure

Page

5.13

Example: OCM Frequency Response - Config. 8 .................................

77

5.14

PR versus BW for Data Base Configurations ......................................

81

5.15

SP versus PC for Data Base Configurations ........................................

83

Appendix Figure

l ! ;

A.4.1 Mode Shape Sign Conventions ..........................................................

246

A.4.2 Aeroelastic-Structural Mode Shape - Mode I.....................................

247

A.4,3 Aeroelastic-Structural Mode Shape - Mode 2.....................................

248

A.4.4 Aeroelastic-Struetural Mode Shape - Mode 3 .....................................

2.19

?,.4.5 Aeroelastic-Structural Mode Shape - Mode 4 .....................................

250

A.5.10CM

Frequency Responses - Config. 1..............................................

252

A.5.20CM

Frequency Respc,nses- Config. 2 ..............................................

256

A.5.30CM

Frequency Responses - Config. 3 ..............................................

260

A.5.40CM

Fr_.queney Responses - Config. 4 ..............................................

264

A.5.5 OCM Frequency Responses - Config. 5 ..............................................

268

A.5.60CM

272

Frequency Responses - Config. 6..............................................

,

#L

A.5.7 OCM Frequency Responses - Config. 7 ..............................................

276

A.5.80CM

280

Frequency Responses - Config. 8 ..............................................

ix

LIST OF SYMBOLS

Symbol



4

Meaning

A(.) .....................................

plant matrices

B(} ..................................... B ....................................... BW ................................... C ........................................ (_ .......................................

control matrices modal controllability matrix bandwidth frequency output matrix (for states) modal observability matrix

DI.) ..................................... D ....................................... E ........................................ F ........................................

disturbance matrices modal disturbability matrix output matrix (forcontrols) output matrix (for disturbances)

G(.) ..................................... G(s) .................................... It(s) ....................................

control matrices plant transfer functions pilot transfer function

Jp ....................................... Kp ...................................... Kx ....................................

pilot objective functional pilot gain (feedforward) optimal control gains

AK ..................................... OCM .................................. PC ...................................... Q ........................................

incremental change in pilot gain Kp Optimal Control Model of the pilot pilot compensat ion wcighling matrix for output vector

Ji'l.) ..................................... SP ...................................... T ........................................

impulse residue sensilivity parameler modal matrix

VI.I......................................

in'.-.nsity of white noise (.)

g .........................................

weighting ¢_,:_ pilot input rate {tip}

Ix ........................................

distance from e.g. to pilot station

\

Symbol

Meaving

n z......................................

plunge acceleration

Pl) ...................................... it ........................................

pole of a transfer function modal state vector

r ......................................... u ....................................... i! .........................................

weighting on pilot input (up) perturbed forward velocity ([t/sec) input vector

v m......................................

motor noise

vy ....................................... w ......................................

obser,, ation noise Gaussian white noise

w ........................................

disturbance

x ......................................... _. .......................................

state vector state estimate

E ........................................

output

z() .......................................

zero of a transfer

_(.) .................................... .......................................

phase of impulse residue, R(.) angle of attack, (rad)

......................................

(g's)

vector vector

vector function

flight path angle, (rad)

b(.)...................................... ......................................... _"..........................................

control surface deflection attitude tracking error (0-0c) damping ratio

q .........................................

generalized

0_)...................................

attitude

),(.) .....................................

eigenvalue

vl. ) ................................... _"..........................

eigenvector damping ratio

a .......................... r ...................

real part ,,f eigenvalue. time delay. (see)

rn................................

neur,,-m, qor lag. Feel

o j .................................. 0'1) ................................. ._...............................

mode shape, Ift) mode slope, (ft/ft) imaginary part of eigenvalue.

deflection,

(dimensionless)

angle, (tad)

3,

X

xi

Symbol

Meaning operations

E{'} ....................................

expected value operator

]'1 .................................... [':'J....................................... l (-) .................................... (:) .......................................

magnitude of (.) complex conjugate of (-) phase angle of (.) time derivative of (.)

subscripts C ........................................

commanded

R .......................................

rigid-body

T ....................................... g ......................................... p ........................................ v. ........................................

total [rigid-body + elastic) gust pilot vehicle

y. ...................................

output or measurement

xi _

SU_4ARY

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As aircraft become larger and lighter due to design requirements for increased payload and improved fuel efficiency, they may also become much more fl_,xible. For highly flexible vehicles, the handling qualities may not be accurat_,ly predicted by conventional methods. This study applies two allalysis methods to a family of flexible aircraft in order to investigate how and when str,et_lral (_pecially dynamic aeroelastic} effects affect the ,;ynamic characteristi

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2,15

Appendix Aeroelastic-Structural

A.4 Mode

Shapes

The mode shapes of the data base configurations are defined to be (l['fl(,('ti,,n_ in feet n¢)rm_.!ized so that for each mode the deflection at the n()s(, (i._'. F.S. 0) is (me f(),)t. The deflecti(,ns

are to a set of

1,