Development of an advanced pitch active control system for a wide body jet aircraft

TABLE OF CONTENTS Section Page v SUMMARY , • • • • • - • • • • . • • • • • • • • • • • t • • LIST OF FIGURES ...................... ix LIST OF TABLES ...................... xiii LIST OF SYMBOLS ................... xv I.I 1 Background .......................

1.2 2 Program Objective ...................

1.3 2 Scope of Program ...................

3.1 9 Advanced PACS Design Objectives ............

3.2 Control Law Synthesis .................

3.2.2 Baseline Aircraft Model ...............

3.2.3 Feedback Loop Synthesis ...............

3.2.4 23 Feed-Forward Loop Synthesis .............

3.2.5 23 Primary Gain Scheduling ...............

3.2.6 23 Secondary Gain Scheduling ..............

3.3 Control Law Mechanization ................

3.3.1 28 Control Column and Actuator System .........

3.3.2 28 Feedback Loops ...................

3.3.3 3O Feed-Forward Loops .................

3.4 3O Control Law Analysis ..................

3.4.1 Poles and Zeros ................... 3O 3.4.2 35 Nyquist Plots ...................

5. 49 FLYING QUALITIES ANALYSIS .................

5.1 49 Speed Stability ....................

5.2 5O Maneuver Stability. • ................

r,_r,"cer',;_'CG 2Ai3E BLANK NO_ EILN'ED_

\

TABLE OF CONTENTS (Continued) Page Section 5.2.1 Takeoff Maneuver Stability ..............

5.2.2 Cruise Maneuver Stability ............

5.3 Dynamic Stability ..................

5.3.1 Linear Analysis ...................

5.3.2 Nonlinear Analysis ..................

5.4 Trimmability and Stabilizer/Elevator Limits ....

6. PILOTED FLIGHT SIMULATION TEST .............

6.1 NASA Flight Simulator Center ..............

6.2 Simulation Math Model ..................

6.3 Flight Conditions ....................

6.4 Evaluation Tasks ............ • ......

6.5 Evaluation Guidelines ............. • • • • 6.6 Simulation Test Results .................

6.6.1 Flight Condition i0: 6.6.2 Flight Condition 15: Maximum Range Cruise ......

6.6.3 Flight Condition 7: High W/6 Cruise .........

I00 6.6.4 Flight Condition 16: High Speed ...........

I00 6.6.5 Flight Condition 18: Landing ............

I00 6.6.6 Flight Condition 17: Holding .............

6.6.7 Takeoff .............

Flight Condition 19: 6.6.8 Summary of Simulation Test Results ..........

7. PACS ARCHITECTURE ....................

CONCLUSIONS .........................

APPENDIX A - AERO DATA ........................

APPENDIX B - BASELINE AIRCRAFT MATH MODEL ...............

APPENDIX C - MODAL CONTROL METHOD ...................

APPENDIX D - PITCH ATTITUDE LOOP LAG-LEAD CIRCUIT ...........

APPENDIX E - FEED-FORWARD LOOP CONTROL LAW ..............

APPENDIX F - PRIMARY GAIN SCHEDULING .................

APPENDIX G - SECONDARY GAIN SCHEDULING ................

APPENDIX H - PITCH ATTITUDE LOOP SYNCHRONIZER CIRCUIT .........

151 _ REFERENCES .........................

viii

LIST OF FIGURES

Figure Page

Longitudinal control system with the advanced PACS.......

PACSload path diagram .....................

Schematic of the L-1011 control system with the advanced PACS

I0

PACS dynamic stability design objectives ............

II

PACScolumn force gradient design objective ...........

II

Blended normal-acceleration/pitch-rate response objective ....

Control law synthesis ......................

I0 18

Flap-up eigenvalues .......................

ii 19

Flap-down eigenvalues ......................

i2

Plots of compensatedpitch rate _eedback gains, flap-up

Plots of feed-forward gains flaps-up conditions .........

Scheduled feedback gain curves, flap-up conditions .......

AdvancedPACS block diagram...................

s - plane nomenclature for poles and zeros tables ........

Nyquist plots ..........................

19 38

Openloop column force in turns .................

20 40

Full gain PACS,column force gradients .............

21 40

Partial gain PACS,column force gradients ............

22 42

PACS without feed-forward, column force gradients ........

23 42

One-g gain PACS,column force gradients ............

24 43

Quasi-steady PACScolumn force gradients ............

25 46

Time history plots, flight condition 7 .............

26 51

AdvancedPACS modified block diagram ..............

27 52

Hach trim compensation .....................

28 53

Hach compensation circuit servo offset schedules ........

ix LIST OF FIGURES Figure Page PACS configured aircraft speed stability column force Baseline aircraft takeoff maneuver stability column forces 56 AACS engagement and pitch rate impact on pitching moment _ takeoff 57 Baseline aircraft takeoff maneuver stability stabilizer position PACS configured aircraft maneuver stability column force Baseline aircraft maneuver stability column characteristics Aircraft pitching moment versus angle-of-attack characteristics AACS engagement and pitch rate impact on pitching moment Baseline aircraft cruise maneuver stability stabilizer position PACS configured aircraft maneuver stability column force Comparison of aircraft response with and without PACS engaged Comparison of aircraft response with and without PACS engaged Stabilizer deflection trim range for various flight conditions . 73 Modified trim stabilizer position versus trim servo x

LIST OF FIGURES

Figure Page

5O

L-1011-1S/N i001 high-speed pitching moment characteristics . 81 Cooper-Harper rating for flight condition i0, moderate Pilot 5 Cooper-Harper rating for flight condition 15, calm air 93 Pilot 5 Cooper-Harper rating for flight condition 15, moderate Cooper-Harper rating for flight condition 7, moderate Flight condition 7 comparison of damping response characteristics with PACS on and off, c.g. at 39 percent mac 97 Flight condition 7 comparison of damping response characteristics with PACS on and off, c.g. at 43 percent mac . 98 Flight condition 7 comparison of damping response characteristics with PACS on and off, c.g. at 50 percent mac . 99 Cooper-Harper rating for flight condition 16, calm air ..... I01 Cooper-Harper rating for flight condition 16, moderate Cooper-Harper rating for flight condition 18, moderate xi

LIST OF FIGURES

Figure Page

74 105

Cooper-Harper rating for flight condition 17, calm air. .

Cooper-Harper rating for flight condition 17, moderate

I08

Cooper-Harper rating for flight condition 19, calm air.

Cooper-Harper rating for flight condition 19, moderate

Summary of Cooper-Harper ratings for cruise and high

II0 speed flight conditions ...................

AdvancedPACSinterface block diagram ............

80 115

AdvancedPACS componentdiagram ...............

PACS lag-lead circuit block diagram .............

PACS feed-forward loop block diagram ............

PACS equivalent feedback gain block diagram for N Z signal

PACS secondary gain controller ...............

PACS pitch synchronizer operation modes ...........

xll

LIST OF TABLES

Table

Page

i

2 FLIGHT CONDITIONS FOR ADVANCED FLIGHT CONTROL SYSTEM

3 17

FEEDBACK GAIN MATRIX (GI)

4 20

COMPENSATED FEEDBACK GAIN MATRIX (G2) ............

5 22

6HT AND q TRIM CONDITIONS FOR EACH FLIGHT CASE .......

6 25

PACS GAIN SCHEDULE EQUATION COEFFICIENTS ..........

7 31

SHORT PERIOD FREQUENCY CHARACTERISTICS ............

8 32 PHUGOID FREQUENCY CHARACTERISTICS ..............

9 33 CONTROLLER FREQUENCY CHARACTERISTICS .............

I0 OPEN LOOP CASE POLES IN THE RIGHT-HAND SIDE OF THE s PLANE. 35 ]'4 . . . . . . . . . . . . . . . , _ l _ n _ _ U _ U [ _ i 0 , C A L M AIR . . . . . . . .

14 SUMMARY OF COOPER-HARPER RATINGS WITH PACS ON ........ III 15 120 LONGITUDINAL AERO DATA, CASE 7b ...............

18 PACS PITCH SYNCHRONIZER SWITCH POSITIONS AND ATTITUDE REFERENCE ..........................

xiii

LIST OF SYMBOLS

A

State-space equation dynamic matrix of aerodynamic data

AACS

Aileron Active Control System Aircraft A/C ACEE Aircraft energy efficiency AFCS Automatic flight control system B State-space equation input distribution matrix C State-space equation odtput distribution matrix c Blended normal-acceleration/pitch-rate parameter Aircraft drag coefficient CD L-1011 longitudinal control system feel spring CF Aircraft lift coefficient CL C Pitching moment coefficient m C Pitching moment coefficient about a particular aircraft m c.g. center of gravity C Pitching moment coefficient about the wing 25% mac m •25mac Coefficient of the bank angle term for secondary gain c, scheduling C.A.

Calm air atmospheric conditions Aircraft center of gravity c.g.

CL Closed loop (feed-forward or feedback) Col--in Control column movement-inches c.p. Wing aerodynamic center of pressure D State-space equation feed-forward matrix dB' Decibel

dei

Degrees xv PRECEDING PAGE BLANK NOT FILMEI3 Denominator of transfer function (determinant of baseline aircraft D(s) state-space equation in Laplace domain) F State-space equation feedback matrix Control column force F C Transfer function FT FCES Flight control engineers service panel FRL Fuselage reference line ft Feet Fwd Forward G Gain, general representation on Nyquist diagrams Acceleration of gravity g Computed feedback gains G I J-curve compensated feedback gains G 2 Computed feed-forward gains G 3 Computed feedback gains after elimination of velocity sensor G 4 signal SchedOled gains (Feed-forward and Feedback) G 5 h Altitude in. Inches I Aircraft inertia about roll axis X I Aircraft inertia about pitch axis Y I Aircraft inertia about yaw axis Z J J-curve (relationship between control column displacement and horizontal stabilizer rotation) Unit imaginary number (-I) J!

Space derivative of J-curve K Aileron cross feed loop gain a K (i) Coulomb friction, (2) normalizing constant = 2.5 c xvi Detent spring rate

Kd

Feedback gain

KFB

Feed-forward gain KFF Total loop gain of closed-loop system Mach compensation loop gain Normal acceleration gain iKNz Yaw rate loop gain Spring rate Ks K Velocity gain u Viscous friction K Angle of attack augmented gain c_ Pitch attitude gain :K e K.

Pitch rate gain tj K Bank angle augmented gain Combined pitch-attitude/velocity gain K3 KEAS Knots equivalent air speed Kts Knots lbs Pounds L.I01I Lockheed wide body commercial transport M Mach number Dive Mach number M Maximum operation mach number mo mac Mean aerodynamic chord MCT Maximum continuous thrust MTO Maximum takeoff thrust xvii Structural load factor limit

nL

Normal acceleration feedback signal N z Filtered normal acceleration feedback signal NZ F Nose down ND N(s) Numerator of transfer function of baseline aircraft in Laplace domain NU Nose up OL Open loop (PACS not engaged) PACS Pitch active control system PLF Power for level flight Dynamic pressure q Yaw rate measured by tilted gyro R G Radian rad rms Root mean square of the air turbulence RSS Relaxed static stability RT Right turn s Laplace transform operator Second sec S.L. Sea Level English system unit mass equal to 32.2 ib slug m Serial number S/N T Turbulent atmospheric conditions TE Trailing edge TED Trailing edge down TEU Trailing edge up TR Stabilizer trim rate u State-space equation input vector xviii

V

Aircraft Velocity

V

Aircraft equivalent air speed e V Aircraft maximum operating speed NO V Aircraft stall speed s Aircraft velocity at trim V T VAC Alternating current voltage VDC Direct current voltage W Aircraft weight w Input vector from pilot Turbulence gust value ' WGUST Peak turbulence gust value WpEAK GUST State vector x Time derivative of state vector Electronic input signal to series servo XA Control column displacement X C Simulator column reference position XC Output displacement of series servo X S Output displacement of column trim

xT

X Initial dynamic state of aircraft o State-space equation feedback signals Y Z State-space equation feed-forward signal Angle of attack Angle of attack relative to fuselage reference line C_FR L Pressure of air at aircraft altitude/Pressure of air at sea level Symmetric outboard aileron deflection Total differential inboard aileron angle xix Elevator deflection e Wing flap deflection _F Horizontal stabilizer angle 6H Signal to power actuator _H c -4.

Horizontal stabilizer trim angle _HT Modified horizontal stabilizer feedback gain signal for secomdary _HT gain scheduling Rudder deflection _R Control pedal displacement _RP Spoiler deflection _SP Control wheel displacement w Secondary scheduling angle-of-attack gain 6_ Incremental pitching moment coefficient due to engagement of the ACmAACS AACS Increment in pitching moment coefficient ACmc.g.

A_ Math trim compensation c A_ Mach trim servo offset schedule o Principal inertia axis Short-period and phugoid mode damping Short-period mode damping _SP Pitch attitude feedback signal Pitch rate feedback signal t,e e Time derivative of pitch rate signal Filtered pitch attitude feedback signal Filtered pitch rate feedback signal

;F

Lagged component of pitch attitude feedback X State-space equation eigenvalues State-space equation eigenvectors i xx Turbulence level of wind gust or _n Time constant, general designation Force sensor filter time constant T C Mach trim compensation filter time constant TM Power actuator time constant Tp Series servo time constant T S Normal acceleration feedback signal filter time constant T Z Pitch rate feedback signal filter time constant Numerator time constant of lag-lead transfer function X 1 Denominator time constant of lag-lead transfer function T 2 ¢ (I) Bank angle, (2) phase angle on Nyquist diagrams hl _hort-per_ or _,,_ -^_ _4 ..... I ....

.... _,._o_ ,,,_= _LUU_dL _requency Short-period or phugoid mode damped circular frequency md LO Short-period or phugoid mode natural circular frequency n Short-period mode circular frequency _SP Reference short-period mode circular frequency for the specific flight condition xxi

i. INTRODUCTION

i.i Background

Jet aircraft fuel cost has increased from 12¢ per gallon in 1972 to

$1.00 or more in 1983. As a result, the fuel cost portion of aircraft direct

operating cost has increased from 25 percent to nearly 60 percent. This trend

was recognized early by aircraft manufacturers and government leaders. There-

fore, in 1975 the U.S. Congress requested NASAto establish a program to develop

fuel saving technology for commercial transports.

The NASA Aircraft Energy Efficiency (ACEE)program was initiated in 1976.

In February 1977 Lockheed received an ACEE program contract for "Development

and Flight Evaluation of Active Control Concepts for Subsonic Transport

Aircraft" (NASAContract NASI-14690). The contract resulted in the develop-

ment of an aileron active control system (AACS)which provided wing load

alleviation. The AACS allowed a 5.8 percent wing span increase for the

L-1011-500 (in service date 1980) which decreased fuel consumption by approxi-

mately 3 percent (Reference 2). Also, studies were conducted under the con-

tract to evaluate benefits of a pitch active control system (PACS). Piloted

flight simulations were conducted on a moving base simulator with an L-1011

• cab. These tests showedthat with static longitudinal stability relaxed to

near neutral and in heavy turbulence a lagged pitch _ate damper provided flying

qualities which are equivalent to those of the baseline aircraft. The aft

c.g. simulation results provided a sufficient basis for proceeding to a flight

evaluation of the PACS.

In December1978 Lockheed was awarded the current contract for "Develop-

ment and Flight Evaluation of an AugmentedStability Active Control Concept

with a Small Tail". A small horizontal tail was to be built and installed on

an L-1011; the center of gravity was to be movedaft to provide flight at

relaxed longitudinal static stability; and a PACS was to be installed to pro-

vide satisfactory flying qualities. As the program progressed wind tunnel

tests showeddrag reductions of the small tail to be less than were predicted.

Also, analyses and wind tunnel tests on other programs had shown that signi-

ficant fuel savings could be achieved by flying an L-1011 aircraft at near

neutral static stability. Therefore, in May 1980 the program was restructured

to concentrate on development of near-term, advanced, and future PACStech-

nology for flight at near neutral to negative static stability margins, and

to continue small tail drag reduction evaluations by analyses and wind tunnel

tests. The near-term and advancedPACSsystems were to be developed, installed

on a L-1011 and flight tested; and future PACS studies were to include assess-

ment of componenttechnology for future aircraft. The near-term PACS was to

provide satisfactory flying qualities at static stability margins near neutral

within the linear static stability flight envelope. The advance PACS was to

provide good flying qualities to a negative I0 percent static stability mar-

gin and for high-Mach/high-g flight conditions. However, flight tests of the

advanced system were to be limited to flight at a negative 3 percent static

stability margin because of the L-1011 flight test aircraft structural and

c.g. management limitations.

In the fall of 1981 Lockheed decided to phase-out production of the L-1011.

Consequently, in Decemberof 1981 the scope of the program was reduced. The

near-term PACS development was to be continued as previously planned; the

advanced PACS development was to be continued through piloted flight simulation

tests; and the future PACS studies were to be stopped. Also, scope of the small

tail wind tunnel program was reduced. Tests of future aircraft small tail con-

figurations were deleted from the wind tunnel test program.

The near-term PACS program is reported in Reference i; the advanced PACS

program is reported herein_ and the small tail program is reported in Reference 3.

1.2 Program Objective

The advancedPACS program design objective was to develop technology for

a PACS which would provide flying qualities at negative static stability mar-

gins that were equivalent to those of the baseline aircraft with a mid c.g. posi-

tion (25 percent mac). Also, the PACS was to compensate for high-Mach/high-g

instabilities that degrade flying qualities during upset recoveries and maneuvers.

1.3 Scopeof Program

The advancedPACS program consisted of control law development, flying

qualities analysis, piloted flight simulation testing on a moving base simulator,

and architecture development of a PACSthat could be used for a flight test

program.

ORIGINAE PAG_ _ OF POOR QUALITY

2. L-1011 CONTROL SYSTEM DESCRIPTION

This section describes the longitudinal control system of an L-lOll air- craft equipped with a PACS. A simple block diagram of the longitudinal control system is given in Figure i. The baseline aircraft control system is repre- sented by the dashed lines and the PACS is represented by solid lines.

The controller is a digital computer with the input signals shown (Table I). The controller output signal is sent to the two series servos which have a position summed output that is added to the control column displacement.

Control authority of the PACS is limited to a stabilizer rotation of ±1.5 degrees at a cruise trim setting of -I degree. The control authority varies with trim setting to approximately ±4 degrees at a trim setting of -i0 degrees.

A PACS loads path block diagram is shown in Figure 2. The control system is an irreversible hydro-mechanical system which consists of the following: • Control column • Feel and trim system I I I I .

_ [HE PACSAUTHORITY _ ,i...,..--_ AT-ldegTRIMSETTING | --..--_t O --I ,w,.r.,, I IS -+1.5deg _ ........ II t IF 1 I i _' ............... STABILIZER I" - -'__j _ _J I I _ it HORIZONTAL ! ' ' I ,Ik T I

1 I

I SERVO SERIES I

I 'c ] I =

!

t

'_I CONTROLLER [ Figure I. - Longitudinal control system with the advanced PACS.

TABLE i. - PACS CONTROLLER INPUT SIGNALS SYMBO L SIGNAL TYPE USE F C Column force Feed-forward Column force gradient NZ Normal acceleration Short period mode Pitch rate Feedback Pitch attitude Phugoid mode q Dynamic pressure Compensation for Primary 9ain flight condition Horizontal stabilizer trim scheduling changes Angle of attack Ol Compensation for Secondary gain pitch-up and AACS ¢ Bank angle scheduling outboard aileron M Mach number operation • Autopilot • Stabilizer power servo system A schematic diagram of the control system is shown in Figure 3. The solid black linkage system shown in the figure represents the PACS series servo tie- in mechanism. This tie-in arrangement allows the series servo output to pro- vide input to the stabilizer actuators via a nonlinear mechanical linkage and hydraulic servo valve without moving the control column.

The nonlinearizer in the mechanical linkage consists of four bars: the three indicated in Figure 3 and the airframe structure. This nonlinearizer changes the stabilizer rotation (_H) sensitivity with relation to control column displacement (Xc) as shown in Figure 4. This relationship is called the J curve. Two _H versus X C curves are shown in the figure: the curve on the right for a stabilizer trim setting (_HT) of zero and the curve on the left for a trim setting of -I0 degrees, The dashed line provides a locus of trim points. Thus, a family of J curves exists over the range of trim settings, and every trim setting has a different column to stabilizer gain about trim which must be considered in computing the PACS feedback gains; U'J'_ i_-.a .H 4-1 rj .< I o,,I _J i,.i..11._1 _) .H

_1

I°° 1

u. I-,- I,-- z =.

O :> t0 .,-I "El C_ :> "O c_ ..c: 4J 4J 4J O O U O I 4-1 u_ O U ",-I • ._ c_

/

U I (11

°I

E -,-t _-_ _ _._ !_ OF POOR Qu_L_y -14 -12 -10 XC -8 LIMIT _HT _ deg -6 _H _ deg -4 rRIM LINE -2 / 6 H LIMIT +2 4 6 8 12 XC _'in. • Figure 4. - J curve.

3. CONTROL LAW DEVELOPMENT

Design criteria were developed for the short period modeand phugoid mode

frequency and damping, for the blended normal-acceleration/pitch rate (C*) time

history, and for the column force gradient.

The control law synthesis procedure utilized the modal control method of

modern control theory to determine feedback gains which satisfied the prescribed

stability criteria for the complete envelope of L-1011 flight conditions.

Matrix algebra was applied to the state-space equations to determine the corres-

ponding set of feed-forward gains. Primary gain scheduling was accomplished by

expressing the feedback and feed-forward gains as second-degree polynominals

in terms of the dynamic pressure (q) and the horizontal stabilizer trim angle

(6HT). Secondary gain scheduling was provided by a modified stabilizer trim

signal (6_T) for pitch-up and AACSoperating conditions.

Mechanization of the control laws included the specification of signal

filter requirements, defined lag-lead and pitch synchronizer circuits, and

designated values for bias switches.

Closed-loop poles were evaluated for 56 selected cases. Nyquest plots

were used in 13 selected cases to determine the phase and gain margins.

Details of the control law development are given in the following

sections.

3.1 AdvancedPACS Design Objectives

The PACSconfigured aircraft wasdesigned to have the capability to operate

over the full flight envelope with static stability margins to -i0 percent

(c.g. at 50%mac) and to have flying qualities equivalent to those of the base-

line aircraft with the c.g. at 25%mac. The 25%mac c.g. location represents

the existing L-1011 baseline configuration which is considered to have excellent

flying qualities.

The PACS design objectives were as follows:

• The short-period and phugoid modesfrequency and damping character-

istics should fall within the shaded s-plane areas given in Figure 5.

The column-force gradients should fall within the column-force versus

load-factor boundaries designated in Figure 6 and have nearly constant

slope.

The blended normal-acceleration/pitch-rate (C*) time history response

to a step command should fall within the limits designated in

Figure 7.

p.p_cEDIIqG pAGK BLANR lqOT FILleD ORIGINAL P_'_,G_ _g OF POOR QUALITY _'- 0.5 _'-0 THE MINIMUM SHORT-PERIOD ..

FREQUENCY03o'O_ sp @ 25% mac 030 OPEN-LOOP CONDITION SIN 1 _" -o r A. SHORT PERIOD MODE _'- 0.1 THE MINIMUM PHUGOID - . 10.1 6 PERIOD = 40 sec SIN'I_ " -or t ,' ) B. PHUGOID MODE Figure 5. - PACS dynamic stability design objectives.

!3 ORIGINAL PAGE _'S OF POOR QUALITY I ,= U _J C_ ,_ 4J _J U _J OJ I 0 0 0 "00J OJ _J I I I OJ _0 -PI 4J e_ m

;=

_0 OJ I.-- _> M.

q_ 4-1 cJ ,< .-I .._ ,.-I 0 _J o_ .-I I ,d r-_ 3.2 Control Law Synthesis The control law synthesis process was accomplished as shown in Figure 8.

Each block in the synthesis process is described briefly in tile following paragraphs.

3.2.1 Aero Data. - The synthesis process started with a separate set of aero data for each of the flight cases listed in Table 2. Each case is defined by the flight condition number shown in the first column of the table and a letter (a through e) representing one of the c.g. locations in the next five columns.

Thus, the case numbers are la, ib, ..., le, 2a, 2b, ..., 2e, etc. The aero data consist of the trim condition parameters and the derivatives at trim given in Appendix A.

3.2.2 Baseline Aircraft Model. - The PACS control math model in state-space form is shown in Figure 9. The baseline math model (Appendix B) was the state- space equation of the system with the control loops open (Eq. I).

(Eq. i)

= [A] {x} + [B] {u}

Equation 1 was used to obtain a set of eigenvalues (%i) i and eigenvectors i)i for each of the 14 flight conditions with c.g. lo_ation at 25% mac.

Thes_ 14 sets (j = I, 2 .... , 14) of eigenvalues and eigenvectors are called the reference eigenstructure (%i,_i)j for the respective flight conditions.

Each set of the eigenstructure complmes with the design objectives given in Figures 5 and 7.

3.2.3 Feedback Loop Synthesis. - The feedback !OOD synthesis for each flig}it condition was accomplished in three steps: • Modal control synthesis (computation of feedback gains) • J curve compensation • Deletion of velocity signal With the feedback loop in Figure 9 closed, the modal control synthesis method (see Appendix C) yields the set of feedback gains represented by G I in Figure 8. The closed-loop state-space equation of the system in Figure 9 is: (Eq. 2) {_} = ([A] + [B][F][C]){x} ORIGINAL p,_ _._- OF POOR QUALITY == ..=.

..=. _= ==

_,,>_ ..=.

_o.=.

u,.= u.j ¢-_ (U L ;i_ ¢/) Q,. u.I

==P=

=

;=

.,_=E uk. ,¢_ ..=._ M.

O m- .-T..

¢O I ...,__ __.E i._ ,T.

Z I,- u,.Z 5¢_Z Z 0m ;,._ r,.. p

=_==_

i3 ORIGfNAL PAGE l_ OF POOR QUALITY Z Z Z Z Z Z Z _j 0 0 i-- _- _- 1.4- u. u. u. u. u. u. u. 1.1.

I--I r._ i-- _-- N C_ _ N N N N N N _ P I-- • _ 0 _'_ _ 0 _ _ _ (_ 0 0 0 0 0 0 0 0 0 r._ _ U_ m m _ m _ _ M M U_ z o 0 _ 0 _) 0 0 0 0 e-_ e_ 0 0 _ 0 u -r 0 _ 0 _ _ 0 0 _ 0 _ _ 0 _ 0 ,:::) ,:::) ,::) c_ ,:::_ ,::) ,::_ c::_ c:::) c) ,::) ,::) (:_ (:::_ U.I -- r_ Z e_ o _ o o e_ o o o r_ I ! _ _ _ _ _ _ _'_ _ _ I I I o r_ Z o • Z o u • ° ° <o Q,.

,.-1 I _ {_1 N {"',,I {",,,,I C_I N N C",,I C",,,I N _ M •-- ,--' I I I I I I I I I "-- _ N ::=: I'-- ORIGINAL PAGE |g OF POOR QUALITY x o

k

Figure 9. - PACS control model.

The reference eigenstructure for each flight condition was assigned to the matrix ([A] + [B][F][C]) for each of the corresponding e.g. locations in accordance with the standard eigenvector equation:

([A] + =

(Eq. 3) ±.I 1.1 Z.l Each element of Equation 3 is known except the gain matrix F. Values of the matrix elements for matrices A, B, and C are different for each c.g. location, whereas the desired values of (%i)_ and (_i)j remain unchanged over the c.g.

range for each specific flight condition.

Steps performed for computing the feedback gains from Equation 3 are: • Insert a set of eigenvalues and truncated eigenvectors for a specific flight condition.

• Insert a corresponding set of aero data for a specific c.g. location.

• Partition the matrices (Appendix C).

• Solve the partitioned equation' explicitly for matrix F.

This process was performed for each flight case to produce the 56 x 4 feedback matrix (GI) in Table 3.

The table headings consist of velocity gain (Ku), pitch attitude gain (Ke) , normal acceleration gain (KNz), and pitch rate gain (K6). The table shows gains for only four c.g. locations for each flight condition. For the flap-down flight conditions (numbers i, 2, 12, 13, and 14), gains for c.g.

locations a through d of Table 2 are given; and for the flap-up flight condi- tions, gains for c.g. locations b through e are given. The discarded gain values were least important for the respective flight conditions. Eliminating one c.g. position reduced the number of points to be used for gain scheduling and permitted a more accurate curve fit of the remaining four points.

An evaluation of the feedback equation pole placement was made by com- paring the closed loop poles with the design objectives given in Figure 5 and with the poles of the open loop cases. Figures i0 and ii show the dominant pole placements for 36 flap-up and 20 flap-down flight cases, respectively.

These cases are the 56 that were selected for gain scheduling. Open and closed-loop poles in the short_-period mode frequency range are shown at the top of the figures and those in the phugoid frequency range are shown at the bottom. The closed-loop damping scatter is due to gain scheduling tradeoffs.

A few of the closed-loop, short-period, flap-up eigenvalues slightly missed the corresponding boundaries in Figure i0. However, they were considered acceptable because the criteria were objectives and not rigid requirements.

The feedback gains were adjusted to compensate for the nonlinearizer (J curve) in the L-1011 control system. Figure 8 shows the _HT input to the J-curve model from the aero data. The J-curve model is a set of equations that was curve fitted to the family of curves shown in Figure 4. The output of the J-curve model was the J-curve derivative (J') corresponding to _HT for the specific flight condition being evaluated. The slope of all members of the J-curve family is the same for any specified value of 6HT. The com- pensated feedback gain matrix (G2) given in Table 4 was determined by applica- tion of Equation 4.

(Eq. 4)

[G2]= [j,]-i[G1]

J' is a diagonal matrix of 56 J-curve derivatives. A plot of the compensated pitch rate gain (K6) is shown in Figure 12 for the flap-up flight conditions to illustrate the compensated gain values. This figure is a plot of the K0 flap-up values in Table 4 as a function of the corresponding _HT values of Table 5 for each dynamic pressure, q.

Control of the phugoid mode requires a velocity gain component. Because of frequent velocity changes associated with changing trim conditions, use of a velocity signal is undesirable. Consequently a method was devised (Appendix D) where the velocity gain (Ku),and the pitch attitude gain (Ke) could be combined to eliminate the need for a velocity signal. Thus, instead ORIGINAL PAGE |9 OF POOR QUALITY TABLE 3. - FEEDBACK GAIN MATRIX (GI) KN Z CASE K u deg/g K8 K_ -sec 1A 0.0692 -0.116 -0.9855 -0.434 18 0.104 -0.119 -1.8850 -0.444 1C 0.172 -0.134 -3.6039 -0.524 1D 0.227 -0.144 -5.0420 -0.584 2A 0.0718 -0.138 -1.4782 -0.595 2B 0.140 -0.144 -3.2143 -0.628 2C 0.257 -0.175 -6.3025 -0.796 2D 0.391 -0.209 -9.7403 -0.994 3B 0.0541 -0.0397 -0.1988 -0.130 3C 0.0747 -0.041 -0.2830 -0.155 3D 0.0863 -0.0402 -0.6188 -0.167 3E 0.142 -0.0446 -1.7991 -0.242 4B 0.00534 -0.011 0.1450 -0.0484 4C 0.0189 -0.0104 -0.1381 -0.0733 4D 0.0269 -0.00996 -0.3088 -0.0894 4E 0.043 -0.00962 -0.6303 -0.126 5B 0.00719 -0.0091 -0.1083 -0.0279 5C 0.0187 -0.00827 -0.1306 -0.0510 5D 0.0271 -0.00777 -0.2956 -0.0697 5E 0.0381 -0.00754 -0.5025 -0.0974 6B 0.0247 -0.0129 -0.04927 -0.162 6C 0.0126 -0.0127 0.09397 -0.154 6D 0.0241 -0.0125 -0.27674 -0.170 BE 0.0659 -0.0136 -1.4954 -0.252 78 0.0612 -0.0144 2.1830 -0.118 7C 0.0873 -0.164 0.09397 -0.145 7D 0.0987 -0.0175 -0.25382 -0.159 7E 0.148 -0.024 -1.3997 -0.240 8B -0.0037 -0.00949 0.43831 -0.108 8C 0.0180 -0.0104 0.01415 -0.125 8D 0.0351 -0.0112 -0.32429 -0.150 8E 0.0849 -0.0124 -1.3407 -0.217 98 0.0356 -0.000699 -0.04956 -0.108 9C 0.0536 -0.00115 -0.50764 -0.141 9D 0.0674 -0.00146 -0.77922 -0.163 9E 0.101 -0.00205 -1.5871 -0.221 -0.0378 -0.00881 0.28533 -0.130 10C -0.0178 -0.00858 -0.20168 -0.158 10D -0.00551 -0.00891 -0.52426 -0.136 10E 0.0201 -0.00906 -1.1345 -0.237 11B 0.0358 -0.00817 0.19022 -0.0769 11C 0.0548 -0.00843 -0.16902 -0.110 11D 0.0665 -0.00816 -0.432O1 -0.133 11E 0.0834 -0.8821 -0.76203 -0.169 12A 0.0496 -0.0876 -0.64744 -0.393 12B 0.0957 -0.0938 -1.7704 -0.424 12C 0.170 -0.108 -3.5351 -0.501 12D 0.238 -0.124 -51.4516 -0.588 13A 0.0363 -0.0876 -0.82506 -0.420 13B 0.0876 -0.0945 -2.0798 -0.453 13C 0.162 -0.108 -3.8847 -0.528 13D O.239 -0.124 -5.7869 -0.629 14A 0.0985 -1.1860 -0.114 -0.459 14B 0.157 -25.9550 -0.120 -0.478 14C 0.234 -0.136 -43.2583 -0.543 14D 0.319 -0.156 -6.1879 -0.634 OF POOR O!'-_ .I':"4 OPENED LOOP CLOSED LOOP 0.20 2.00 D 0.16 1.60( O O m 0.12 1.20 0.08 0.80 0.04 0.40 - 1.60 - 1.20 -0.80 -0.40 0 0.4 - 1.60 - 1.20 -0.80 -0.40 0 _'_n- sec-1 _'_n _ sec-1 A. SHORT PERIOD MODE 2.00 1.60 -- 1.20 -- joo d O joo d sec-1 -I sec 0.80 -- 0.40 -- 00.

0.04 -0.16 _'_o n - sec-1 _'_n - sec-1 B. PHUGOID MODE Figure i0. - Flap-up eigenvalues.

ORiGINAl- __ OF POOR QUALIFY OPENED LOOP CLOSED LOOP 2.00 1.60 -- 1.20 _ J_°d1.20 -- 0_0_ sec-1 0.80- 0.40

oo]

-1.60 -1.20 -0.80 -0.40 0 -1.60 -1.20 -0.80 -0.40 _'oo n - sec-1 _'oj n - sec-1 A. SHORTPERIOD MODE 0.20 0.20 0.16 R 0.16 -- 0.12 0.12 -- O, joo d J_d ~ sec -1 sec -1 0"081 0.08 -- O.O4 0.04 --

0.00 I

0.00 -0.16 -0.12 -0.08 -0.04 0.00 -0.16 0.00 _'oo n - sec-1 B. PHUGOID MODE Figure Ii. - Flap-down eigenvalues.

TABLE 4. - COMPENSATED FEEDBACK GAIN MATRIX (G2) KN z CASE K u K8 deg/g K_ - sec 1A 0.079861 -0.133871 -0.500861 -1.1373 1B 0.130845 -0.149717 -2.37159 -0.558608 1C 0.253478 -0.197477 -5.31109 -0.772224 1D 0.389597 -0.247145 -1.002310 -8.65355 2A 0.080263 -0.154267 -0.665136 -1.65247 2B 0.187112 -0.192458 -4.29592 -0.0839331 2C 0.454108 -0.309218 -11.1363 -1.406497 2D -0.541814 -25.2508 -2.576858 1.013633 3B 0.104016 -0.076330 0.38228 -0.249947 3C 0.159097 -0.087322 -0.60281 -0.330121 3D 0.199221 -0.092800 -1.42844 -0.385515 3E 0.428737 -0.137800 -5.55861 -0.747706 4B 0.012824 -0.026417 -0.34813 -0.116235 4C 0.049774 -0.027389 -0.36366 -0.193039 4D 0.075318 -0.027887 -0.86471 -0.250313 4E 0.135468 -0.030307 -1.98559 -0.396952 5B 0.017773 -0.022495 0.26769 -0.068967 5C 0.050394 -0.022287 -0.35203 -0.137439 50 0.077784 -O.O223O2 -0.84861 -0.200058 5E -0.119027 -0.023556 -1.56979 -0.304285 6B 0.046369 -0.024217 0.09402 -0.304118 6C 0.026743 -0.026955 0.19945 -0.326855 6D 0.055634 -0.028856 -0.63885 -0.392440 6E 0.206452 -0.042606 -4.68485 -0.789466 78 0.117311 -0.027603 -0.226188 1.31792 7C 0.188561 -0.035423 -0.313189 0.20294 7D 0.228629 -0.040952 -0.59399 -0.372078 7E 0.462363 -0.074978 -4.34960 -0.749778 8B -0.007373 -0.018910 0.87342 -0.207237 0.040389 -0.023336 0.03174 -0.280478 8D 0.085334 -0.027229 -0.78839 -0.364675 8E 0.273638 -0.039966 -4.32125 -0.699404 9B 0.072922 -0.001432 -0.10153 -0.241709 90 0.122554 -0.002629 -1.16070 -0.322390 90 0.165566 -0.003586 -1.91414 -0.400405 9E 0.318192 -0.006458 -4.99997 -0.696241 108 -0.079541 -0.018538 0.60040 -0.273552 10C -0.042236 -0.020358 -0.47853 -0.374895 10D -0.014284 -0.023098 -1.35911 -0.482189 10E 0.062620 -0.028226 -3.53429 -0.738350 11B 0.081237 -0.018539 0.43167 -0.174500 11C 0.138079 -0.021241 -0.42588 -0.277165 11D 0.182629 -0.022410 -1.18642 -0.365258 11E 0.256272 -0.025228 -2.34156 -0.519305 12A 0.058653 -0.103589 -0.76559 -0.464730 12B 0.128241 -0.125695 -2.37245 -0.568174 0.281634 12C -0.178920 -5.85655 -0.829992 12D 0.481169 -0.250693 -10.40205 -1.88770 13A 0.042143 -0.101701 -0.95787 -0.487609 13B 0.117594 -0.126856 -2.79197 -0.608104 13C 0.272417 -0.181611 -6.43241 -0.887878 13D 0.523655 -0.271687 -12.67921 -1.378156 14A 0.110854 -0.128310 -1o33488 -0.516615 14B 0.210756 -0.161087 -3.48416 -0.641664 14C 0.393492 -0.228696 -7.27427 -0.913102 14D 0.698938 -0.341800 -13.55980 -1.389111 ORIGINAL PAGE IS CASES OF POOR QUALITY 0 3.

• 4.

+ 5.

X 6.

07.

4L 8.

X 9.

Z 10.

Y 11.

m -0.16 265,0 203.0 -0.31 i B -0.48 m m -0.64 I I I I I I I I I -0.80 -3.6 -2.8 -2.0 -1.2 -0.4 _HT_ deg Figure 12. - Plots of compensated pitch rate feedback gains, flap-up conditions.

ORiGI_!AL PAGE lg OF POOR QUALITY TABLE 5. - _HT and q TRIM CONDITIONS FOR EACH FLIGHT CASE q _ ibs/ft2 FLIGHT CASE NUMBER GHT_deg 1A -8.35 1B -7.15 71.2 1C -5.39 10 .-4.07 2A -8.85 2B -6.42 51.2 2C -3.85 2D -1.63 '3B' -3.26 3C -2.63 255.0 3D -2.19 3E -0.92 4B -1.99 4C -1.56 457.0 4D -1.30 4E -0.85 5B -1.85 5C -1.46 457.0 5D -1.20 5E -0.88 ' -3.42 6B -2.65 6C 203.0 6D -2.19 6E -0.87 7B -3 28 7C -2.55 219.0 7D -2.12 7E -0.88 -3.03 8B 8C -2.34 235.0 8D -1.93 8E -0.77 -2.86 9B -2.24 9C 257.0 9D -1.88 -0.85 9E lOB -2.70 -2.05 10C 265.0 10D -1.63 -0.89 10E 11B -2.28 11C -1.76 284.0 11D -1.38 11E -0.94 12A -7.99 12B -6.39 75.2 12C -4.35 120 -2.94 13A -8 26 -6.37 68.3 13C -423 130 -2.47 14A -8.74 148 -6.37 55,5 14C -4.23 140 -2.47

ORIGINALpAGE iS

OF pOOR QUALI'i'Y

of scheduling K u and KO a new set of gains in terms of K 3, T I, and T 2 (see Appendix D) were selected for scheduling. Thus the revised set of compensated feedback gains to be scheduled was T2 _i K_, KNz, I/T2, T--_-I , and K 3-_ • 3.2.4 Feed-Forward Loop Synthesis. - The feed-forward loop synthesis con- sidered the feedback and feed-forward loops (Figure 9) to be closed. The control equation is now written as: {_} = ([A] + [B][F][C]{x} + [B][D]{w} (Eq. 5) IThis equation was solved by the method given in Appendix E to obtain a transfer !function of NZ/_ H which was combined with the feel spring characteristics shown in Figure 8. The resulting feed-forward gains (KFF) are plotted in Figure 13.

3.2.5 Primary Gain Scheduling. - The primary gain scheduling was accomplished in the same way for the feedback and feed-forward gains. A curve fitting pro- cedure (Appendix F) was used to express the gain curves (e.g. Figures 12 and 13) in terms of _ second degree polynominal as given by equation 6.

(Eq. 6) K : a + bq + cq 2 + d6HT + e_T A least squares curve fit computer program used the q and 6HT values in Table 5 to determine the equation coefficients which are given in Table 6. The q and _HT values are provided by the aero data as shown in Figure 8. Plots of the feedback pitch rate and the feed-forward scheduled gains for the flap-up con- ditions are shown in Figures 14 and 15, respectively. These gains are applica- ble to the complete flap-up flight envelope.

3.2.6 Secondary Gain Scheduling. - Secondary gain scheduling is required to compensate for: • Pitch up at high-Mach/high-g flight conditions • Outboard aileron symmetric activity when the AACS is activated.

OF POOR QUALITY CASES O 3.

• 4.

+ 5.

X 6.

O 7.

4L 8.

X 9.

0.048 Z 10.

Y 11.

0.032 KFF_!bs/in.

0.0016 8HT _ deg Figure 13. - Plots of feed-forward gains flaps-up conditions.

OF POOR QUALITY TABLE 6. - PACS GAIN SCHEDULE EQUATION COEFFICIENTS I FLAP SETTING COEF.

1/_- 2 - sec "1 K3 _-1h-2 KFF- in/Ib K_-sec KNz _ deg/g _'2/_'1 - 1 -1.4295 9.7718 2.2322 x 10 .2 -2.9433 x 10 -1.4028 x 10"1 2.1328 x 10.2 a 1.5023 x 10.3 8.96 x 10.3 -2.8474 x 10.5 2.9511 x 10"1 1.5431 x 10 .4 2.0571 x 10 .4 b -4.1698 x 10.4 0 -4.0915 x 10.7 FLAPS- C L 0 UP -5.0386 x 10 "1 -4.2834 x 10.2 2.6975 x 10-2 d 4.5098 4.2547 -7.4588 x 10.3 3.8428 x 10 .3 6.0459 x 10"1 -7.6620 x 10.2 e 0 0 -3.6149 36.2224 8.7222 x 10.2 -1.5771 -1.0483 3.2829 x 10"1 a 4.0909 x 10.3 2.4014 x 10.3 1.1658 x 10 .2 9.9013 x 10.2 -4.7143 x 10.4 1.8067 x 10"1 b 0 0 0 -1.4232 x 10.3 0 -3.5719 x 10.5 FLAPS c DOWN d -6.0629 x 10"1 7.0302 0 3.4827 x 10"1 -1.5772 x 10"1 6.8201 x 10 .2 -3.9313 x 10.2 4.3358 x 10"1 0 0 -9.7027 x 10 .3 4.0296 x 10.3 e K = a+bq+cq2+d_HT+e(_HT 2 The pitch-up phenomena is caused by a loss of lift at the wing tips during high-Mach/high-g flight conditions which causes the aerodynamic center of pressure (c.p.) to shift forward. Thus, the distance between the c.g. and the c.p. is shortened, and the static stability margin is reduced in a manner similar to when the c.g. is moved aft relative to a fixed c.p. Consequently, the scheduled gain curves already developed can be used to stabilize the pitch- up conditions. The feedback and feed-forward gain values are changed by augmenting the gain scheduling 6HT value by a required increment to provide a 6_T value (Appendix G). The modified value 6HT changes the feedback gains to provide the increased control command for the horizontal stabilizer, and changes the feed-forward gains to provide the desired column force gradients.

If the feed-forward gains were not provided, the column force gradients would be incorrect and might encounter severe reversals.

The AACS operates the outboard ailerons in a symmetric mode in response to normal acceleration of the aircraft c.g. and wing tips. This symmetric mode produces a C.po shift that is equivalent to an aft c.g. shift of about 5 per- cent mac. The change in pitching moment can be corrected in the same manner as for the pitch-up by providing the primary gain-scheduling signal _HT with an,augmented increment.

-0.00 -0.08 -0.16 -- -0.2_ -- -0.32 -- -0.40 -- K_) _ sec -0.48 -- -0.56 -- -0.64 -- -0.72 -- -0.80 I I I I I I I -3.6 -3.2 -2.8 -2.4 -2.0 -1.60 -1.20 -0.8 -0.4 _HT - deg Figure 14. - Scheduled feedback gain curves, flap-up conditions.

ORIGINAL P._.GE _S OF POOR QUALITY 0.56 0.48 CASES 0 5.

<> 6.

0.40 ® 7.

0 8.

10.

0.32 [] 11.

0.24 - 0.16 -- KFF "_ in/Ibs 0.08 - 0 -- -0.08 -- -0.16 -

I I I I I I I

-0.24 -0.40 -3.20 -2.80 -2.40 -2.00 -1.60 -1.20 -0.80 -3.60 _HT _ deg Figure 15. - Scheduled feed-forward gain curves, flap-up conditions.

The secondary gain scheduling method is discussed in Appendix G. The sensor signals required for secondary gain scheduling are angle of attach (a), aircraft bank angle (_), and Mach number (M), as shown in Figure I.

3.3 Control Law Mechanization The advanced PACS block diagram is shown in Figure 16. This diagram is considered to be divided into three parts for discussion: Control Column and actuator system: control column, column trim, series servos, J curve, stabilizer trim, and power actuator.

Feedback loops: pitch rate (_), normal acceleration (Nz) , and pitch attitude (e).

• Feed-forward loop: column force (Fc).

3.3.1 Control Column and Actuator System. - The control column displacement (Xc) and column trim (_) are summed along with the series servo outputs (X_).

The nonlinearizer represented by the J curve (J) changes the linear displacg- ments into stabilizer rotations which are dependent upon the trim condition.

In the model (Figure 16) stabilizer trim (_HT) is subtracted and leaves the linear signal (_Hc) to command the power actuator which rotates the horizontal stabilizer.

The column trim consists of the parallel trim which relieves the force on the control column and the series trim which places the control column at the desired location. The parallel trim and series trim are set simultaneously by a trim wheel (mechanical trim cable) as shown in Figure 3 or by a motor con- trolled by an electrical pitch feel and trim switch located on the control column.

The input to the series servos is an electric signal (XA) from the sunnned feed-forward and feedback loops. The transfer function I/(TSS+I) in each servo block represents the servo lag characteristics. The output of the series servos are position summed so that the control authority of each series servo is 0.75 degree at the cruise trim setting of -i degree. This provides a maxi- mum position summed output of 1.5 degree at the cruise trim setting. The series servos were position summed so that failure of one servo would not pro- vide a stabilizer hardover which results in loads greater than the aircraft limit loads.

The power actuator lag characteristics are presented by i/(TpS+1) as shown in the figure.

3.3.2 Feedback Loops. - The e and N Z feedback signals are used for control of the short-period modes. These signals are filtered through the first-order low-pass filters shown in Figure 16. The filter time constants _ and _Z are equal to 0.03 seconds. The filter time constants _ and T Z are equal to .03 seconds. The filtered signals 6F and NZF are subject to gains of K0 and KNz

ORX_r_AL P_C_ _3

OF. POOR QUALITy

_) _J ¢.J < n3 _J u '-a < I ,d °< respectively. The gain scheduling parameters q and 6HT are provided to set the desired gain values. A normalizing constant I/K^ is used in each feed- back loop so that the gain from the gain schedules t_rough the J curves for a 6HT setting of -i0 degrees is equal to I. The value of K c is 2.5 degrees stabilizer per inch of column.

The g feedback signal is used to control the phugoid mode. This signal is processed through a pitch synchronizer, a lag-lead circuit, and a gain amplifier. The pitch synchronizer suppresses the attitude hold during maneuvers and sets a new attitude reference at the synchronizer output when a control column force is applied (see Appendix H). The lag-lead circuit eliminates the need for a velocity gain sensor (Appendix D) that would be required for phugoid mode control. The gains to be scheduled are (see Table 6): T2 , - 1 , and K 3 T2 3.3.3 Feed-Forward Loop. - The feed-forward loop is used to provide the de- sired control column feed-forward gradients. The feel spring converts the column displacement (Xc) to pounds (Fc). The force sensor converts FC to an electric voltage. A flaps-up/flaps-down bias signal switches the time con- stant of the feed-forward low pass filter which is related to the reference baseline aircraft short-period mode. It provides the frequency variant part of the feed-forward transfer function (see Appendix E). The feed-forward signal is then passed through the gain amplifier (KFF) and summed with the feedback signals to provide the series servo input signal (XA).

3.4 Control Law Analysis Thirteen of the flight cases that were used for control low synthesis were selected for stability margin analysis. These were representative of all of the cases and included those that were expected to have the lease gain or phase margins. All closed loop poles of fifty six flight cases were checked.

3.4.1 Poles and Zeros. - The short period mode, phugiod mode, and controller characteristics for each of the 13 selected cases are shown in Tables 7, 8, and 9 respectively. The nomenclature for the Tables are shown in Figure 17.

Each Table shows the flight case number, specifies the control condition as open loop (OL) or closed loop (CL), and gives the poles and zeros. Table 9 also lists the open loop gain factor (K).

TABLE7. - SHORT PERIOD FREQUENCY CHAP_CTERISTICS

Flight Poles Zeros Case Control Number Cond. °_n _ 1/T O_ n Z_ 1/T 0.538 lb 0.615 OL 0.853 0.695 CL 1.18 ld 0L 0.719 0.655 1.06 CL 1.27 0.70O 4b OL 2.03 0.589 7.76 -0.198 CL 1.84 0.847 OL 1.41 0.881 2.99 4d CL 2.09 0.705 4e OL 2.51 -0.134 CL 2.18 0.641 OL 1.40 0.37 0.482 7b 0,296 CL 1.64 0.682 7d OL 0.960 0.571 1.17 CL 1.48 0.641 7e 0L 1.44 2.30 0.0515 CL 1.40 0.691 .337 10b OL 1.57 0.454 .354 CL 1.80 0.626 2.09 10d OL 0.972 0.764 CL 1.79 0.616 1.73 10e OL 0.0760 CL 1.78 0.613 13b OL 0.901 0.613 0.973 CL 1.30 0.679 0.828 1.54 13d OL 0.687 0.684 CL 1.49 TABLE 8. - PHUGOID FREQUENCY CHARACTERISTICS Flight Poles Zeros Case Control Number Cond. con _ lIT con _ lIT lb 0.155 0.716 OL 0.143 0.040 CL 0.148 0.303 ld OL 0.149 0.514 0.113 0.054 CL 0.141 0.368 4b OL 0.0416 0.066 -0.0873 +0.0468 CL 0.0648 0.176 4d OL -0.0328 0.0774 0.377 0.0414 CL 0.0483 0.336 4e OL 0.182 0.604 0.0652 0.300 CL 0.0415 0.476 7b OL 0.0679 0.188 0.0221 0.0330 CL 0.0734 0.358 7d OL 0.0771 0.156 0.0819 0.455 CL 0.0801 0.308 7e OL -0.0731 0.0748 0.284 -0.233 CL 0.289 0.0881 OL 0.0206 10b 0.0668 0.136 0.136 CL 0.0877 0.245 lOd OL 0.0839 0.090 0.0916 0.315 CL 0.0898 0.240 lOe OL 0.146 -0.876 0.0830 0.257 CL 0.0942 0.246 13b OL 0.150 0.060 0.161 0.650 CL 0.153 0.344 13d OL 0.0990 0.123 0.161 0.480 CL 0.153 0.405 TABLE 9, - CONTROLLER FREQUENCY CHARACTERISTICS PoleslIT Zeros lIT Flight Compen- Series Compen- Control Case Power sator Power Servo/ sator Series Number Cond. Gain Servo Poles Servo Sensor Zeros Servo Sensors lb OL 49.7 55.9 0.0611 6.23 20.1 33.0 0.0537 CL 5.04 20,5 32.9 0.O556 OL 287 0.0635 ld 6.23 20.1 33.0 0.0537 12.3 CL 5.39 0.0602 19.5 33.5 4b OL -82.0 6.23 0.00920 0.00830 20.1 33,0 CL 5.11 20.7 32.7 0.00886 4d OL 95.1 6.23 20.1 33.0 0.00920 28.5 0.00826 CL 5.50 20.3 33.0 0.00795 OL 3O0 6.23 4e 20.1 33.0 0.00920 5.30 11.5 0.00848 CL 6.07 19.5 33.5 0.00726 7b OL -35.6 6.23 20.1 33.0 0.0161 -77.1 CL 4.68 21.0 32.6 0.0167 7d OL 80.2 6.23 20.1 33.0 0.0161 39.6 0.0205 0.0183 CL 5.01 20.5 33.0 7e 20.1 33.0 0.0161 12.3 0.0217 OL 313 6.23 5.50 19.5 33.5 0.0212 CL -97.3 lOb OL -24.2 6.23 20.1 33.0 0.0148 0.0171 CL 4.86 20.9 32.7 20.1 33.0 0.0148 26.9 0.0196 lOd OL 131 6.23 5.18 20.3 33.1 0.0180 CL 0.0148 3.15 13.2 0.0192 OL 317 6.23 20.1 33.0 lOe 0.0187 CL 5.57 19.5 33.5 48.0 0.0605 20.1 33.0 0.0550 13b OL 61.8 6.23 20.4 33.0 0.0550 CL 5.07 11.9 0.0583 20.1 33.0 0.0550 13d OL 335 6.23 5,35 19.4 33.6 0.0579 CL OF pOOR Q UA_-_ J_d _- DAMPINGRATIO _n_n CLOSED LOOP °Jn" NATURAL FREQUENCY N \ r - TIME CONSTANT . N \ s - _'_n + i_d I _'o_ n 1 1" Figure 17. - s - plane nomenclature for poles and zeros tables.

The open loop transfer function is: N(s) (FT) = K D(s----_ (Eq. 7) OL The value of the numerator N(s) for each case is the product of terms cor- responding to the zero values in the frequency ranges of the short period mode, phugoid mode, and controller as given in Tables 7, 8, and 9 respectively. The value of the denominator D(s) is the product of terms corresponding to the pole values.

ORIQINAL p,_ _3 OF POOR QUALITY Any pole on the positive real axis or complex pair of poles that fall in the right-hand side of the s plane (Figure 17) represents an unstable mode.

Poles shown in Tables 7, 8, and 9 that fall in the right-hand plane represent the open loop cases listed in Table i0. Identification of these poles is necessary for evaluation of the Nyquist plots which will be subsequently discussed.

All of the closed-loop poles are in the left-hand plane. Most of the poles comply with the design objectives of Figure 5. The few closed-loop poles that fall outside the prescribed boundaries (see Figure i0) were judged to be acceptable for continuing with piloted flight simulation tests.

3.4.2 Nyquist Plots. - Nyqulst plots were used to evaluate the gain and phase margins of the PACS. The plots that were selected for illustration are shown in Figure 18. These plots represent a locus of gain-phase points (G, _) as the circular frequency (_) varies from negative to positive infinity. Only the half of the locus from zero to infinity is shown. Since the points are complex conjugate pairs, the other half of the locus is the mirror image with respect to the horizontal axis. The closed loop system is stable if and only if the number of counterclockwise encirclements of the locus about the -i point of the plot is equal to the number of open loop poles in the right-hand plane.

Plots a and b in Figure 18 for flight cases id and 4b, respectively, represent stable closed-loop systems where there are no open-loop poles in the right-hand plane and no encirclements of the -i point. If the gain in plot b were increased by a factor of 3 (9.5 dB) or if the phase had an addi- tional lag greater than 22 degrees there would be a clockwise encirclement of the -I point. This means that for this system the gain margin is 9.5 dB and the phase margin is 22 degrees.

In plots c and d for flight cases 4d and 4e, respectively, the locus makes one counterclockwise encirclement of the -i point. Consequently, these closed-loop systems are stable because the open-loop systems have a TABLE i0. - OPEN LOOP CASE POLES IN THE RIGHT-HAND SIDE OF THE s PLANE FLIGHT CASE SHORT'PERIOD MODE - sec'l PHUGOID MODE ~ sec -1 - 0.134 4.8 - 0.0328 4d - 0.0731,-0.233 7e 0.146d,_n "1 (-0.876)* 10e *TWO COMPLEX POLES SYMMETRIC WITH RESPECT TO REAL AXIS.

OF POOI_ q.]U_:'_:-: .-:' • '_ H c ASH c G _-_H 8

/ / _.Jo_ \ \ o_-,., ,_,.o

PHASE (A)FLIGHT CONDITION ld G ASHc G

' "'"',__ ) o) l/ _ \ \ °_'" -°'°

(C)FLIGHT CONDITION 4d (D)FLIGHT CONDITION 4e A_ Hc "_ Hc G 8 1 _~deg (E) FLIGHT CONDITION 7e (F)FLIGHT CONDITION l Oe Figure 18. - Nyquist plots.

ORIGII'_AL v_o_ oE POOR QUALn'_C pole in the right-hand plane as listed in Table I0. The phase and gain margins for these cases were determined to be: Ga in Phase Margin Case 4d -11.8 dB 51 deg Case 4e -3.9 dB 50 deg Plots e and f for flight cases 7e and 10e, respectively, have two counter- clock encirclements of the -i point (the one shown and one for the mirror image). This closed-loop system is stable because there are two open-loop poles in tlle right-hand s plane as listed in Table i0. The phase and gain margins for these cases were determined to be: Gain Margin Phase Margin Case 7e -11.3 dB 58 deg Case 10e -13.6 dB 55 deg 3.4.3 Feel-Force Gradients. - The baseline aircraft configuration maneuver (wind-up turn) column-force gradients are shown for flight conditions 6, 7, 9, and ii in Figure 19a through d respectively. These curves are typical of the column-force gradients for the other flight conditions and show how the gradients change significantly with c.g. location and are highly depen- dent on load factor. The force gradients decrease as the c.g. moves aft because of increased control sensitivity. The gradient for each flight con- dition is shown to be negative for the 50% mac c.g. location. This negative gradient is unacceptable and indicates the need for a PACS. Flight condition 7 was selected to illustrate comparison of six experimental PACS configura- tions that are listed in Table ii. Figure 19b represents the PACS configura- tion i, flight condition 7, column forces.

The full gain PACS (configuration 2) provides a maneuver (wind-up turn) column-force gradient that is nearly independent of the c.g. location and load factor. The column gradients for this configuration are shown in Figure 20.

The curves shown in the figure satisfy the column-force gradient objectives and are representative of the other Plight conditions.

The partial gain PACS (configuration 3) demonstrates the importance of bank angle gains on column-force gradients. The bank angle gain scheduling component is shown in Appendix G to be C_ _T (1-cos 9). The optimum C_ was determined to be 0.05 and this value was used for the full gain PACS. The partial gain case has no bank angle gain (C_ = 0). The force gradients for this configuration are shown in Figure 21. A comparison of the curves in Figure 21 with the desired force gradient curves in Figure 20 show the effect of deleting the bank angle from the secondary gain scheduling.

c.g. % mac 25.0 25- _33.1 20- 2O t 37.7 c.g.% mac Ibs 25.0 Fc _lbSlo

0 / o

31"1 -5 I I I I -5 I J 1.0 1.2 1.4 1.6 1.8 2.0 1.0 1.2 1.4 1.6 1.8 2.0 LOADFACTOR- g LOADFACTOR- g A. FLIGHTCASE6 B. FLIGHTCASE7 c.g.% mac 25 - 25 25.0 35.0 20; 20 15 c.g. % mac Fc _ Ibs _ 25.0 Fc _lbs 15 42.0 5 37.7 5 10 "_33.1 10 50.0

o i

-5 ,L I I I I J - 1.0 1.2 1.4 1.6 1.8 2.0 1.0 1.2 1.4 1.6 1.8 2.0 LOADFACTOR- g LOADFACTOR - g C. FLIGHTCASE9 D. FLIGHTCASE11 Figure 19. - Open loop column force in turns.

DE POOR qU_'_L_T'Y z v, v v v II

<

z I-- z Z r..r-1 i! II ,_r-i ,< i-1 p;,.

Z; O I,-I E-I I-- I-- 2 Z n- l--I o _._ Z ii II _D u u,. v _,_ I F- F- N Z c_ c_ v v N N N _ _,) Z Z Z II II v N N Ila _ z z a; _ v i11 I ,-4 v _ b-t z _ m u. z _ z ¢_ u_ m i.u ,_: l.u _.I I,-,= I.I,. ' uu _ _ uJ ,_ z _ <[: c_ =_ '_ •-; u. ,', ;[ _ C:l "_ 12,. G. r, O. O.

ORIGINAL PAGE _'S OF POOR QUALITY 3O FLIGHTCONDITION7 c.g. % mac o 25.0 A 33.1 [] 37.7 0 50.0 2O ¢,_1 LI DESIGNCRITERIA (SEEFIGURE6) o I I I 1.0 1.4 1.8 2.2 LOADFACTOR,'-.-, g Figure 20. - Full gain PACS, column force gradients.

FLIGHTCONDITION 2O I I o I 1.0 '1.4 1.8 2.2 LOADFACTOR,...-, g Figure 21. - Partial gain PACS, column force gradients.

4O For the PACS with feedback but without feed-forward (configuration 4),

the column-force gradient increases as the e.g. location is moved aft as

shown in Figure 22. This increase is due to excessive cancellation of the

stabilizing feedback loop gain signals. A comparison of Figures 22 and 20

show that for the 25%mac c.g. location the PACS without feed-forward pro-

vides a column force gradient that is less than desirable. As the c.g. is

movedto 38 and 50%mac, the force gradients are greater than desirable.

..... The one-g gain PACS(configuration 5) has all gains frozen at the maneu-

ver threshold value. This configuration permits undesirable column-force

reversals as shown in Figure 23. Comparisonof Figures 21 and 23 illustrates

a natural benefit that results (with gains not frozen) from the stabilizer

deflection commanding nose-up attitude during a turn.

The quasi-steady gain PACS(configuration 6) freezes all gains at the

maneuver threshold values except the increment due to the angle-of-attack

signal. The column forces for this configuration are shown in Figure 24. There

is only a slight improvement over the configuration 5 force gradients and

demonstrates that the _ signal does not have mucheffect on column forces.

It would have a significant effect if it were added to the (l-cos _) term in

the bank angle mechanization.

OF, POOR QUALITY 3O FLIGHTCONDITION7 c.g. % mac o 25.0 2O ,L 33.1 0 37.7 o 50.0 C=3 U.

0 I I I I 1.0 1.4 1.8 2.2 LOADFACTOR,---g Figure 22. PACS without feed-forward, column force gradients.

LBS FLIGHTCONDITION7 2O C.3 U.

J I 0 I 1.0 1.8 2.2 LOADFACTOR_ g Figure 23.

One-g gain PACS, column force gradients.

ORIGINAL P._GE _ OF POOR QUALITY.

3O FLIGHT CONDITION 7 25 - c.g. % mac o 25.0 A 33.1 o 37.7 20 - 50.0 15 - I.L

i

I I I 1.0 1.4 1.8 2.2 LOAD FACTOR_ g Figure 24. - Quasi-steady PACS column force gradients.

4. ANALYTICAL SIMULATION Analytical simulation was performed by using a computer program that has been developed over a period of several years. The program is called PICSS (Program for Interactive Continuous System Simulation). Drag, lift, and moment coefficients are input to the program for the clean aircraft configura- tion as functions of angle of attack and Mach number. These coefficients are incremented by pitch rate and angle-of-attack rate in maneuvering flight, by deflections of the ailerons and stabilizer, and by trim variations due to center of gravity travel. Also, ground effects, gear and flaps, direct lift control, and aerodynamic effects due to structural deflections are included in the program.

Time history outputs of the program include: N Z - Normal acceleration M - Mach number h - Altitude A6HT - Incremental trim position of horizontal stabilizer 6H - Horizontal stabilizer position - Angle of attack 0 - Pitch attitude - Pitch rate e_ - Lagged component of pitch attitude feedback C - Pitching moment coefficient m CD - Drag coefficient C L - Lift coefficient ACLAAC S - Incremental lift coefficient due to active AACS ACmAAC S - Incremental pitching moment coefficient due to active AACS The most significant time history parameters for flight condition 7 are plotted in Figure 25. Pitch rate is shown in part a. The solid line represents the open loop condition with c°g. at 25% mac (case 7b OL). This is the refer- ence case which represents the desired pitch-rate response. The dotted line represents the open loop condition with c.g. at 50% mac (case 7e OL). The pitch-rate amplitude response for this case is unacceptable. The dashed line represents the PACS-on condition with c.g. at 50% mac (case 7e CL). As shown in the figure the closed loop pitch-rate response with c.g. at 50% mac compares PRECEDING PAGE BLANK NOT. FILMED ORIGINAL P_G_ I$ OF POOR QUAL|'P( CASE -.____ 7b0L ...... 7e 0L _ ___ 7e CL 3.2 20 - e• /

/

,r / 2.4 16- /..., # I e t 1.6 i 12- o (_ "" dog ] sec e _, deg • ,o, • • .8 e- / ,_. "ee .-_l ,.aL _ h I I , I , I | I I , I I I I I J I , 4 8 12 16 0 4 8 12 16 TIME - sec TIME- sec A. PITCH RATE B. PITCH ATTITUDE - 2.0 1.8 1.6 NZ - g 1.4 C" '" "" "', . . ". 1.5 1,0 1.2 ,,j • ,,S ; 0.5 1.0

IS E ,,6..' .I / / DES, GN O ECT,VE

.8 , I , ,! , I , I I I I I 1 4 8 12 16 0 1 2 3 4 TIME- sec TIME- sec C. NORMAL ACCELERATION D. C* - BLENDED NZIO Figure 25. - Time history plots, flight condition 7.

favorably with the open loop pitch-rate response with c°g. at 25% mac. Parts b and c of Figure 25 show the pitch attitude and normal acceleration responses respectively. Part d of the figure shows how the blended normal-acceleration/ pitch-rate response (C*) compares with the design objective defined in Figure 7.

Similar responses were obtained for the other flight conditions. Con- sequently, the control law was considered to be valid.

OF POOR _ .......

5. FLYING QUALITIES ANALYSIS Speed stability, maneuver stability, dynamic stability, and controllability flying qualities were performed for the flight conditions listed in Table 12, as described in the following sections, to determine conformance of the PACS configured aircraft with FAR Part 25 and MIL-F-8785C criteria.

5.1 Speed Stability The speed stability analysis determines the column force required to main- tain the aircraft at a speed other than trim speed. FAR Part 25 defines satisfactory column force characteristics as follows: • A pull force shall be required to maintain speed below trim speed and a push force shall be required to maintain speed above trim speed.

• Stick forces shall vary monotonically with speed.

• The average stick force gradient shall be at least -i ib per 6 KEAS increase throughout the speed range.

Speed stability analysis of the PACS configuration (Figure 16) showed an abrupt column force reversal for the takeoff condition with the c.g. at 25% mac and unstable column force gradients for the 50% c.g. position. Also, unsatisfactory force gradients were shown to exist for the hold condition aft c.g. positions.

TABLE 12. - PILOTED FLIGHT SIMULATION TEST CONDITIONS Weight c.g. Altitude V e Flight Condition 1000 Ibs % mac 1000 ft KEAS 7. Cruise 408 25 to 50 37 W/_ = 1.9 x 106 Ibs (M = 0.83) 10. Cruise 360 25 to 50 33 260 W/$ = 1.4 x 106 Ibs) (M = 0.83) 15. Cruise 360 25 to 50 36 280 W/$ = 1.6 x 106 Ibs (M = 0.83) 350 25 to 50 25 16. Mmo/Vmo 335 25 to 50 17. Holding 10 250 330 25 to 50 18. Landing 2 135 (_F = 33 deg) (1.3 V s) 19. Takeoff 380 25 to 50 (_F = 26 deg) (1.2V s) PRECEDING PAGE BLANK NOT, FILMED The column force reversal for the takeoff condition is a result of the feed-forward gain schedule being a function of dynamic pressure and stabilizer deflection angle (Figure 13). Dynamic pressure increases with speed and decreases the feed-forward gain from positive to negative values. Negative gain causes the PACS series servo to oppose control column input and to reverse abruptly the column force at 50 knots above the trim speed. This problem was remedied by restricting the lower bound of the feed-forward gain (KFF) to zero.

The unstable column force gradients for the takeoff condition are associ- ated with the feed-forward loop that reduces the force needed to trim the air- craft and the small stabilizer deflection gradient that is required to trim the aircraft throughout the speed range. The unsatisfactory column force gradients for the hold condition were due to inadequate or contrary stabilizer gradients throughout the speed range. These problems were solved by adding a Mach compensation circuit that operates through the Mach trim system as shown by the dashed lines in Figure 26. The feed-forward gain restriction is also shown in the figure. Mach trim compensation (A_c) shown in Figure 27 was available as part of the baseline aircraft pitch and trim system.

The Mach compensation circuit consists of two elements: Mach trim servo offset schedule, and loop gain schedule. The Mach trim servo offset schedule (A_o) is different for the flap-down and flap-up flight conditions as shown in Figure 28. The Loop gain (KM) given in Figure 29 is scheduled with Mach num- ber and stabilizer angle to provide the desired speed stability column force gradient throughout the c.g. range. The stabilizer gain schedule input has a 20 second filter and the Mach trim offset schedule input has a i0 second filter to limit servo offset gain overshoot.

Speed stability column force characteristics for the reconfigured PACS (Figure 26) are shown in Figure 30 for the hold and cruise conditions. FAR Part 25 design criteria is shown for comparison. The hold condition column force gradients comply with the design criteria in all respects, whereas the cruise condition criteria does not vary monotonically with speed as desired.

However, the column forces were considered satisfactory to continue with piloted flight simulation tests.

5.2 Maneuver Stability The maneuver stability analysis determined the column forces required to maintain the airplane in steady wind-up turns or quasi-steady pushovers.

Satisfactory maneuver stability column forces according to the MIL-F-8785C are a steadily increasing pull to maintain positive load factors and a steadily increasing push to maintain negative load factors.

The upper and lower column force maneuver criteria boundaries for takeoff are: • Upper boundary = 120 ibs/g • Lower boundary = 1 ibs/g n L - OF. FO©i:_ _": ......... ' I- + I I-.

.,-4 ,--4 .r-I "0 n_ I ,d ORtG|_¢:%t. v:_ ......

OF POOR _'_- 1.2 0.8 -- A(_C- in 0.4 - I I 0.2 0.4 O.B 0.8 1.0 MACH NUMBER Figure 27. - Mach trim compensation.

The column force criteria for cruise are: • Upper boundary = nL _ 1 ibs/g • Lower boundary = Same as for takeoff The value of n L is 2.5 for the L-lOll aircraft.

ORIGINAL P_GE _g OF POOR QUALITY (COL-IN) -41 -3.

i_60 "" col-in.

-2 -1.

[ I J .15 .20 .25 .30 .35 MACHNUMBER A. MACH TRIM SERVO OFFSETSCHEDULE, FLAPSDOWN (COL-IN) -2 m A_ 0 _ col-in.

-1 I I j .2 .4 .6 .8 1.0 MACH NUMBER B. MACHTRIM SERVO OFFSET SCHEDULE, FLAPS UP Figure 28. - Mach compensation circuit servo offset schedules.

1.0 _* .8-- .6 KM .4

_2oL_,v/_ I

-5 -4 -3 -2 -1 0 -6 8 H _deg Figure 29. - Mach compensation gain .qeh_d,,le, fl_ps do,;.m..

ORIGINAL P._IG_ _1 OF POOR QUALITY 4O PULL FC _"lbs FAR PART 25 CRITERIA -1 Ib/6 Kt -20 t -40 I I I I I 200 240 280 320 Ve - KEAS A. FLIGHT CONDITION17: HOLD CONDITION 80- PULL 4O VTRIM MD F C _ Ibs FAR PART 25 CRITERIA -1 Ib/6 Kt -40 -- -80 - I I I I I I I 180 200 220 240 260 280 300 V e - KEAS • B. FLIGHT CONDITION 7: CRUISE Figure 30. - PACS configured aircraft speed stability column force characteristics.

ORIGIN,_L .,-,_=..r'_.¢'_'_ _ OF POOR QUALITY 5.2.1 Takeoff Maneuver Stability. - Maneuver stability analysis of the base- line aircraft in the takeoff configuration showed that the column forces were stable throughout the c.g. range. However, the gradients were very steep for the aft c.g. position compared to MIL-F-8785C guidelines shown in Figure 31.

The nature of these column forces can be attributed to the low speed aero- dynamics and control system characteristics.

The pitching moment characteristics for takeoff are shown in Figure 32.

The aircraft has close to zero static margin (neutral stability) for the center- of-gravity at the 50% mac position. However, it has a substantial positive maneuver margin because of pitching moment due to AACS engagement and due to pitch rate for the maneuver. Figure 33 shows the maneuver pitching moment increments of the aircraft due to pitch rate and the AACS. The maneuver margin is the nondimensional longitudinal distance from the center-of-gravity of the, aircraft to the maneuver point which is the c.g. where the column force per g is zero. The maneuver point is always aft of the neutral point and increases the aircraft stability. The AACS engagement is shown to have a small effect on pitching moment. The pitch rate effect makes the pitching moment substantially more negative as the load factor increases. Increased stabilizer deflection is required to counteract this increased stability and maintain load factor during maneuvers.

FLIGHT CONDITION 19 ,V 80 - AACS ON FEEL FORCE / PULL SATORAT,ON --, 60 - ,=\£-/ .t',,._ A _ F C ~lbs 40 -- MIL-F-8785C TAKEOFF GUIDELINES

<; I , //.,.d

t I I I I I 1.0 1.2 1.4 1.6 1.8 2.0 LOAD FACTOR - g Figure 31. - Baseline aircraft takeoff maneuver stability column forces.

OF. POOR QUALITY 0.4 _9. _. FLIGHTCONDITION 19

0.2

CmTRIM -0.2 [ I I I i I I 0 4 8 12 16 20. 24 O..FR L _deg Figure 32. - Baseline aircraft takeoff pitching moments.

-.12 FLIGHT CONDITION 19 -.08 A Cmc.g" -.04 I J I I I,, J 1.0 1.2 1.4 1.6 1.8 2.0 LOAD FACTOR - g Figure 33. - AACS engagement and pitch rate impact on pitching moment _ takeoff.

OF POOR QUALrI'Y The takeoff maneuver stabilizer gradient decreases slightly as the c.g.

is moved from 25% to 50% mac as shown in Figure 34.

Although the stabilizer gradient is higher at the forward c.g. than at the aft c.g., the control system characteristics causes the column force gradient to be higher at the aft c.g. than at the forward c.g. because the J-curve (Figure 4) was optimized to give good handling qualities for the L-1011 with c.g. range of 12% to 35% mac. The slope of the J-curve was designed to obtain a maneuver column force gradient at the aft c.g. similar to the gradient at the forward c.g. Thus, more control column displacement at the aft c.g. is required to obtain the same stabilizer displacement increment than at the for- ward c.g. Flaps down configurations which have a trim stabilizer setting of -4 degrees or less determined the upper portion of the curve, and the flaps up configurations which have a trim stabilizer setting at i degree or less deter- mine the lower portion of the curve. In the c.g. range of interest (35% to 50% mac) for the advanced PACS, the trim stabilizer setting is greater than -I degree (e.g., +I degree for the takeoff configuration with the c.g. at 50% mac). This setting falls outside the optimal range of the J-curve and results in a higher column force gradient with c.g. aft than with c.g. forward.

FLIGHT CONDITION 19 -16 -TEUP -12 -8 -4 | I I I I I 1.0 1.2 1.4 1.6 1.8 2.0 LOAD FACTOR - g Figure 34. - Baseline aircraft takeoff maneuver stability stabilizer position characteristics.

ORIG]NA_ PAGE ]g OF POOR QUALITY Figure 35 shows maneuver stability characteristics of the aircraft in the takeoff configuration with the advanced PACS (Figure 26). These data show that the PACS reduces the spread of the column force gradients for the complete c.g.

range so that they are similar to the baseline aircraft with c.g. at 25% mac.

5.2.2 Cruise Maneuver Stability. - Maneuver stability analysis of the base- line aircraft at cruise conditions (Figure 36) shows unsatisfactory column force characteristics for the complete c.g. range of 25 to 50% mac. The un- satisfactory force characteristics can be attributed to nonlinear high speed pitching moment characteristics and to the AACS.

The nonlinear pitching moment characteristics are illustrated in Figure 37.

The pitching moment for Mach numbers greater than 0.7 are a strong function of angle of attack. At angles of attack greater than 5 degrees, there is a sig- nificant nose-up pitching moment caused by shock-induced boundary layer separa- tion on the upper surface of the outer wing. This nose-up pitching moment for the angle of attack between 4.7 and 7.5 degrees causes a dip in the stabilizer displacement required to maintain load factor and results in column force lightening. The static stability of the airplane decreases as the c.g. is moved aft, and at 50% mac the c.g. location airplane is statically unstable.

The effect of pitch rate and the AACS on pitching moment characteristics are shown in Figure 38. The AACS reduces the maneuver margin by 4 to 5% mac AAcsFLIGHToNCONDITION 19 ,_ / 60 - PULL 40 - 20 - 0 -

I I I I I I

1.0 1.2 1.4 1.6 1.8 2.0 LOADFACTOR - g Figure 35. - PACS configured aircraft maneuver stability column force characteristics _ takeoff.

OF [;CO_ ,,z._._-_,_..., _' 80 -PULL FLIGHT CONDITION 7 AACS ON PMILf 8785C CRUISE GUIOELINES 4O 20 -- Fc_lbs 0-- -20 -- -40 -- - 60 - L. I I I I I I 1.0 1.2 1.4 1.6 1.8 20 2.2 LOAD FACTOR - g Figure 36. - Baseline aircraft maneuver stability column characteristics _ cruise.

.2 -- FLIGHT CONDITION 7 39% Cm ___-_,,_ TR!_' Cmc.g" -.2 - I I I I I I I 0 2 4 6 8 10 12 eFRL _ deg Figure 37. - Aircraft pitching moment versus angle-of-attack charanteristics _ _uise.

• 6O ORIGINAL p,_Q_. _,g OF POOR QUALITY .02 -- FLIGHT CONDITION7 AACS ON .01 - AC m DUE TO c.g CS ENGAGEMENT 0- ACre c.g ACmc.9" DUE TO RATE -.01 -- -.02'- I I I I I !

1.0 1.2 1.4 1.6 1.8 2.0 LOADFACTOR - g Figure 38. - AACS engagement and pitch rate impact on pitching moment _ cruise.

at high speeds and completely negates the 3 to 4% mac increase in maneuver margin contributed by the pitch rate. There is a net reduction in stabilizer gradient throughout the load factor range which reduces the column force gradient.

The cruise maneuver stability stabilizer gradients are illustrated in Figure 39. At the 50% c.g. position there is an adverse stabilizer gradient at the trimmed load factor, and all c.g. locations have a dip in the middle of the stabilizer displacement curve.

Maneuver stability characteristics of the airplane with the advanced PACS are shown in.Figure 40. These data show that the PACS completely removes the dip in column force gradient characteristics shown in Figure 36. This is accomplished primarily by the pitch-up controller which is scheduled with Mach number and angle of attack. These data show that the column force character- istics are satisfactory for all c.g. locations except for high load factors where the aircraft is very stable. The initial force gradients are essentially the same for the entire c.g. range.

5.3 Dynamic Stability Analyses were performed to determine characteristic roots of the linear system dynamic stability and to demonstrate nonlinear time histories of the longitudinal dynamic response for discrete vertical gusts and control column -6 - TE UP FLIGHT CONDITION 7 AACSON -4 - .,,..--- c.g.= 25% mac _ _ _H _deg -2 - 0 " 2 - I I I I I I 1.0 1.2 1.4 1.6 1.8 2.0 LOAD FACTOR - g Figure 39. - Baseline aircraft cruise maneuver stability stabilizer position characteristics.

FLIGHT CONDITION 7 AACS ON 60 - PULL F C _ Ibs I I I I I I 1.0 1.2 1.4 1.6 1.8 2.0 LOAD FACTOR - g Figure 40. - PACS configured aircraft maneuver stability column force gradients _ cruise.

step inputs. The linear analysis did not include the effects of aerodynamic and control system nonlinearities and is valid only for small disturbances about the trim condition.

5.3.1 Linear Analysis. - The purpose of the linear system analysis was to evaluate the dynamic stability characteristics of the aircraft for flight conditions and c.g. locations that were selected for piloted flight simulae:- tion tests (Table 12) and to determine effects of the Ma_N compensation loop (Section 1.4.1).

In general, an airplane that has satisfactory dynamic characteristics will have a short-period mode which is moderately damped and a phugoid mode which is lightly damped. Pitch angle and angle-of-attack perturbations are predominate for the short-period mode, and pitch angle and velocity perturbations are pre- dominate for the phugoid mode.

The linear system dynamic stability characteristics were obtained by cal- culating eigenvalues of the small disturbance equations of motion. MIL-F-8785C specifications were used as guidelines to evaluate the dynamic stability.

Figure 41 presents s-plane eigenvalues (cruise condition 7) for the baseline aircraft short-period (x) and phugoid (o) modes. The short-period modes do not meet the MIL-F-8785C criteria when the c.g. is aft of 25 percent mac. Also, the phugoid characteristics become unstable as the c.g. is moved aft and violates the requirement for a minimum damping ratio of 0.04. The time-to-double amplitude for the most unstable phugoid nonoscillatory mode is 1.5 seconds.

The baseline aircraft exhibits the same general characteristics for the holding condition except that the phugoid instability at the aft c.g. limit has an increased time-to-double-amplitude of 4.6 seconds. The short-period characteristics of the aircraft for the low-speed conditions with flaps extended, are unsatisfactory for all c.g. locations and the phugoid mode goes unstable at 50% c.g. position with a time-to-double-amplitude of i0 seconds.

Figure 42 shows that the d_amic Stability characteristics for the air- craft in cruise condition 7 with the advanced PACS engaged comply with MIL-F-8785C criteria. All of the flight conditions satisfied the dynamic stability characteristics except for the hold condition which has a mild phugoid instability with the c.g. at 25% mac. This instability resulted in a time-to-double-amplitude of 700 seconds and was considered acceptable.

5.3.2 Nonlinear Analysis. - Nonlinear aerodynamic and control system char- acteristics were modeled to compute responses of the aircraft with PACS on and off for discrete vertical gusts and column control step inputs. The analysis was concentrated on high altitude cruise flight (condition 7) be- cause of the aircraft variable stability characteristics at this condition.

The computer program used in the study consists of longitudinal equations of motion, nonlinear aerodynamic data, and models of the _ongitudinal control ORIGINAL PAGE; |g OF POOR QUALITY q = _ c.g. -43% mac/ .t.,,., .,,.., _..,.,_ / - 0.2 FLIGHTCONDITION7 34.5 AACS ON 0.1 I --,1 0 .1 .2 .

EXPANDEI SCALE OF PHUGOIDMODE MIL-F-8785C CRITERIA._._ --1.6 - 1 - 1.2 O_d-,sec c.g. = 25 - 0.8 < 34.5 .

- 0.4 39 43 34.5 _ 43 39 39

43 5 '2550 i, 5O

V_ I _---JO I /\ /\ /\

.2.o

-1.6 o .4 .8 - 1.2 -.8 -.4 j- o_ n -J sec- 1 Figure 41. - Baseline aircraft dynamic stability characteristics.

OF POOR QUALITY

z;- o.o4--

FLIGHT CONDITION 7 _ I 0"2 PACS ON c.g. = 25% mac = 0.1 AACS ON MACH TRIM ON 39 "--"_ [" "-0.1 50/_'° 0] 0.1 EXPANDED SCALEOF PHUGOID MODE MIL-F-8785C CRITERIA , oo d - sec:-1 _ %,_ c.g. = 25% mac 34.5 5O I I I -1.6 .4 .8 Figure 42. - PACS equipped aircraft stability characteristics.

OF POOR QUAL,'w_ ' and stability augmentation systems. Figure 43 shows the discrete vertical igust model used for the analysis. It was patterned after the model given in !MIL-F-8785C. Horizontal distance of the disturbance is equivalent to dis- tance the airplane travels during one cycle of a short-period response. A igust amplitude of -12 ft/sec is moderate and -54 ft/sec is a severe distur- ibance of heavy thunderstorm magnitude.

Satisfactory flying qualities are defined in terms of stable responses to external disturbances and pilot control inputs. After experiencing a discrete vertical gust, the aircraft should return quickly to its trim equilibrium con- dition and oscillations should be well damped. The airplane should respond predictably to a column force step input, and should quickly stabilize new equilibrium condition. The controls should give the pilot ability to change the pitch attitude precisely.

Figure 44 shows the response of the baseline airplane to a moderate verti- cal gust for various center of gravity positions. The aircraft is statically stable at initial trim conditions for the c.g. range of 25% to 43% mac. The angle-of-attack response is in the stable region for a disturbance of moderate magnitude and the aircraft returns to its initial trim condition naturally.

The aircraft with c.g. at 43% mac is close to being neutrally stable and its pitch rate response is very flat. The short-period response matches results of the linear dynamics analysis for the 25 to 43% mac range. The aircraft is statically unstable about its initial equilibrium trim condition for the 50% mac c.g. case. The aircraft diverges from its trim position for any external disturbance at this c.g. and seeks a new equilibrium condition at a high angle of attack where a region of strong stability is encountered.

FLIGHTCONDITION7 1.0 B WGUST WpEAKGUST .5 B I I I I I I I I -1000 0 1000 2000 3000 4000 5000 6000 HORIZONTAL DISTANCE "-ft Figure 43. - Flight condition 7: discrete gust model, cruise.

ORIGINAL P_,._ :; OF POOR QUALITY WpEAK GUST= -12 ft/sec 10 ¸ % mac ?

e I I I I I I | 0 4 8 12 18 20 24 TIME -- zec .,= 25% -2 I I I I / I I O 4 8 12 16 20 24 TWE_r,K 2.5 2.0 /__,, c.O" 50 % mzc 39% 1.5 1.0 _ 43.0'4 g o15 i I i I I I I 0 4 8 12 18 20 24 TIME _sec Figure 44. - Baseline aircraft response to a moderate vertical gust.

Figure 45 shows the baseline and PACS configured aircraft response to a -54 ft/sec gust. For this severe disturbance the baseline airplane with c.g.

at 25% mac will return to its initial trim condition. The aircraft diverges from its trim condition for a c.g. position aft of 25% mac and seeks a new equilibrium at high angle of attack. The disturbance is strong enough to drive the aircraft into the high angle of attack heavy buffet region where the aircraft is excessively stable. The response of the PACS configured aircraft to a severe vertical gust has well-behaved, stable, response characteristics.

The response characteristics were determined to be essentially the same for all c.g. positions from 25% to 50% mac as shown on the right side of Figure 45.

Figure 46 illustrates the aircraft response to various column force step inputs for the high altitude cruise condition with the c.g. at 50% mac. The baseline aircraft diverges quickly from its trim condition for any constant force input until it reaches a region of increased stability at high angle of attack.

The response of the PACS configured aircraft to column force step inputs show that the advanced PACS works to reduce excessive excursions in angle of attack and load factors.

5.4 Trimmability and Stabilizer/Elevator Limits This analysis was performed to determine changes to the baseline aircraft control system that were required for the advanced PACS configured aircraft.

Control system characteristics that were evaluated included: Stabilizer/ elevator deflection range, trim servo range, elevator versus stabilizer gearing, control column limits, and pitch feel-spring rate.

The control system design criteria were: • Capability must be provided to trim the aircraft for all flight conditions Sufficient control power must be provided to provide a minimum pitch angular acceleration of -5.73 deg/sec 2 for stall recovery from any flight condition • Control power must be provided to recover from maneuvers in high angle-of-attack regions.

The standard L-1011 has a c.g. range of 12% to 35% mac. The corresponding stabilizer/elevator deflection range that provides sufficient control at all flight conditions is from -14 deg/-25 deg to +I deg/0 deg. The stabilizer deflection range to trim the aircraft is -i0 to 0 degrees. The advanced PACS configured aircraft has a c.g. range of 25% to 50% mac. Analyses show that the advanced PACS system with its further aft c.g. travel required more nose down trim and control capability. Therefore, the stabilizer/elevator deflection range was changed to -14 deg/-20 deg aircraft nose up and to +4 deg/+5 deg air- craft nose down. The trim range was increased to +i degree aircraft nose down.

The modified elevator versus stabilizer gearing curve is shown in Figure 47.

ORIGIP_,AL FA_ _ OF POOR QUALITY FLIGTH CONDITION 7 WpEAK GUST " 16.46 MISEC (-54 FTISEC) 6ASELI_ AIRCRAFT PACSCONflGUREO AICRAFr I e I I I I l I I i .J i i l i i 0 4 8 12 18 20 24 O" 4 8 12 16 20 24 I_soc TIME _ z,c _A._It/c.g" = 50% mK ./34.5% M 2.

$ ?

•_ 0 -2 -2 -4 -4 t I l I I_ I I I I, I i l !

0 "4 B 12 18 20 24 0 4 8 12 16 20 24 TIME s_ TIME _ sic 2.5 c.g,= 25 % mac 2.0 ;+.o //34.5,+ ] / 50_ c.g. - 50 % mac 43% 1.5 3g% _, '.+ 1,0 1.0 +j 0,5 0.5 i I I l / 0 "-J e 0 4 6 12 I 24- I, i I I L I I 0 4 8 12 16 20 24 " TIME _c TINE_ sic Figure 45. - Comparison of aircraft response with and without PACS engaged for a severe vertical gust.

S._, _ t$ OF pOOR QuAL|TY FLIGHTCONDITION 7 AACS ON, c.g. AT 50% mac PACSCONFIGUflEO AIRCRAFT I0 / FC- 20 lbs _3 I I I I I I I [ I l I I I I O 4 8 12 16 20 24 0 4 8 12 16 20 24 -- TIME +sic TIME _sic FC: 10 Ibs 6 " / FC_020 Ibs ,) .

-2 -4 -4 l l t l I + , + ,', ,!,, 1o ,, o I , ,, ,'+ :_o 2', TIME +s_ TIME +sic 2,5 2,5 FC: 1o Ibs 2.0 2.0 1.5 1.5 1,0 1.0 =0 0.5 0.5 I I I J I l I o , o ,, ,+ ,o ,,-. .+ _ ; ,'+ ,'+ + ,_ TIME +r, ic TIME +sic Figure 46. - Comparison of aircraft respon_ with and without PACS engaged to various leve%s of control column step inputs.

ORIGINAL p_._- OF POOR QUALI'i'y I-- -30 -- -20 -- ® _- _ Z _Z _m

-f

°E

I I I I I I

4 0 -4 -8 -12 -16 _H "" deo Figure 47.

Modified elevator versus stabilizer gearing curve.

The PACSconfigured aircraft stabilizer deflection trim range for the

flight conditions which were to be evaluated by piloted flight simulation

tests is given in Figure 48. The +i degree increase in the trim limit is

required for the takeoff condition with the c.g. at the 50%mac position. The

J-curve modification required because of the increased trim limit is indicated

in Figure 49 by the dashed part of the curve. Travel of the trim servo dis-

placement is shownto be increased by 1.15 inches to provide the +i degree

stabilizer deflection increase. It was also necessary to alter the pitch feel

spring rate schedule as shown in Figure 50 by the dashed lines.

ORIGINAL p._,_,_ ;_ OF POOR QUALITY -4 TE UP -3 15: CRUISEWl_ - 1.6 - 106 Ib$ -2 ==, '10 I-- -,I.-.

r,o • --1

_ I

I I I I I

30 35 40 45 50 TE c.g. _% mac DOWN -8 TE UP -6 _, -4 I.-- -r" -2

0 _ I I I I I

25 30 35 40 45 TE c.g. "-'% mac DOWN Figure 48. - Stabilizer deflection trim range for various flight conditions.

ORIGINAL PAGE IS OF POOR QUALITY -12 -8 ,- ,_ .>.=.

g, i- ,,r 1.15 in 4 m t I I 1 I I I I -4 -3 -2 -1 0 1 2 3 X S_in Figure 49. - Modified trim stabilizer position versus trim servo displacement characteristics.

80 - t,,IJ u.i ,,-a lalJ ZOO C_OO NO.

MACH I - .860 OR MORE .= .780 B • _ 40 .700 .605 2O -- .500 i • 423 ORI LESS I I I I I I I I 2 0 -2 -4 -6 -8 -10 -12 6HT _deg Figure 50. - Modified pitch feel spring rate schedule.

6. PILOTED FLIGHT SIMULATION TEST The flight simulation test was performed to identify pilot/control inter- face problems and evaluate flying qualities of the advanced PACS.

The test was performed at the NASA Langley Flight Simulation Facilities.

Setup of the simulator included a check-out of the computer program, motion system interface, cockpit controls, and instrumentation. Two Lockheed and three NASA pilots performed the flight simulation tests.

6.1 NASA Flight Simulator Center The Langley simulator is a general purpose visual motion simulator con- sisting of a two-man cockpit on a six-degree-of-freedom synergistic motion base. A collimated visual display provides a 60 degree out-the-window color display which was activated during the landing approach task. A programmable hydraulic control loading system is provided for the column, wheel, and rudder. Instruments and displays are typical of transport aircraft. Photo- graphs of the motion base, cockpit interior, and visual display are presented in Figures 51 through 53 respectively.

6.2 Simulation Math Model The simulation mathematical model represented the L-1011 S/N i001 air- craft. This L-1011 is a unique aircraft that has the Dash i version long fuselage, and the extended wing tips and AACS of the shorter fuselage Dash 500 derivative. Inertia characteristics of this configuration are given in Figure 54, and the weight/center-of-gravity envelope is presented in Figure 55.

The aerodynamic data model for the L-1011 S/N i001 aircraft possesses a high-speed nonlinear pitch instability at high lift coefficients which is typical of swept wing designs. This characteristic defines the control system authority and aerodynamic control power requirements for the horizontal stabi- lizer and elevator. Figure 56 shows the aerodynamic longitudinal stability characteristics which were used in the simulation.

Engine characteristics were represented by the installed thrust for three Rolls Royce RB.211-22B high-bypass-ratio turbofan engines.

Control functions were represented by a complete dynamic model of the longitudinal system and a simplified model of the lateral-directional system.

The advanced PACS block diagram is shown in Figure 26.

Longitudinal control forces in the simulator are supplied by a hydraulic column-loader which is a closed-loop servo system with position feedback and a high forward loop gain. The math model consisted of a second order system having position and rate feedback as follows: FC s 2 - + K d X C K + s(K v + Kc) + K s

ORIGINAL PAGE 1 8

OF PObR QUAL!l"f

ORIGINAL PAGE 1 9

OF POOR QUALlTV

.

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I

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F i g u r e 53. - NASAILangley transport visual display.

ORIGINAL PAGE' !_' OF POOR qUALITY

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== PRINCIPAL AXISPOINTSBELOW FRLAT THE NOSE

0 I I I I I I I I

261 280 300 320 340 360 380 400 420 WEIGHT X 10 -3t''lbs Figure 54. - L-1011 S/N I001 weight/inertia characteristics.

OF poOR QUALITY %--- NEAR-TERM CONTROL _ SYSTEMAFT LIMIT %.

ADVANCED CONTROL SYSTEM AFT LIMI/ _ / \': X I-- ::= 360

- / i

I.JLJ 32q I I / I , I I 28O [" : ,

i I

241 I

1 i

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12 16 20 24 28 32 36 40 44 48 52 CENTEROF GRAVITY - % mac Figure 55. - L-1011 S/N i001 weight/center-of-gravity envelope.

where K = spring rate S Kd = detent spring rate K = viscous friction v K = coulomb friction C = system mass X C = column position F = column force C s = laplace operator The spring rate is varied as a function of trim stabilizer position and Mach number as shown in Figure 50. Figure 57 presents a block diagram of the model which was used to generate the longitudinal column forces.

8O ORIGINAL PAGE _S POOR QUALITY _J -H 4..I .r,,I OJ _J r.J 4,..I _6"0 e 06"0 88"0 98"0 13) £9"0 r/l I 08"0 ,H iJ.i ,"-t Z -I-, Z r.3 <C =E 0L'0 I C) I I ,g u_ 0_'0 n.

ORIGINAL PAGE I_1 OF poOR QUALITY "I- (,o "[3 X "T, i I,- _ X IJ.P _ "_ re'Z a., o • 1 -r- i.i.

o _J ee- u.

N ÷

I

X U .H ÷ k co I m I..4 X Q.

.S I..- 0 -JO N Z *X _ A block diagram of the lateral-directional control system is shown in Figure 58.

6.3 Flight Conditions Specific flight conditions (Table 12) were selected for the simulation test. Simulation concentrated on regions of the flight envelope designated by the shaded areas in Figure 59. Stability characteristics of each flight con- dition are discussed in the following paragraphs.

Flight condition i0 is an average (W/6 = 1.4 x 106 Ibs)cruise condition for commercial airline service. The L-1011W/6 value of 1.4 x 106 ibs and Mach number of .83 represents a C L value of .4. Since a constant C L value is required to evaluate control characteristics, each flight condition i0 test was initiated at the same W/_ and Mach number values. Maneuver stability about trim is essentially linear at this flight condition. A region of reduced maneuver stability can be reached at high load factors. This condition can be considered a region of linear stability for small maneuvers with a region of nonlinear stability at high load factors.

Flight condition 15 is the maximum range cruise W/6 for the simulated aircraft. Stability characteristics at this flight condition are essentially the same as at the intermediate W/_ condition except that the region of non- linear stability is encountered at a lower load factor.

Flight condition 7 is the highest W/8 at which the simulated aircraft can operate with a 1.3 g maneuver capability to buffet onset. The 1.3 g cri- terion is a typical aircraft operating restriction. This is a condition of non-linear stability caused by the wing aerodynamic flow separation which is perceived as buffet. The nonlinear region begins about 0.i g from trim and is well into the unstable region of buffet onset which is 0.3 g.

Flight condition 16 is near the knee of the simulated aircraft maximum operational speed boundary (Figure 59). Because of the high dynamic pressure, the load factor to buffet onset is beyond the 2.5 g aircraft load factor limit.

This condition can be considered a region of linear stability at high dynamic pressure.

Flight condition 17 is a typical intermediate-speed, flaps-up, holding pattern condition which is often encountered when approaching airports with heavy traffic. The condition provides linear stability at low dynamic pressure.

Flight condition 18 represents a typical landing configuration at normal approach speeds. The condition is characterized by linear stability characteristics.

Flight condition 19 represents the takeoff configuration for the second segment climb speed (1.2 V ). Stability characteristics are linear at this s condition.

oRIGi_ OF, pOOR QUALi'gV "o

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z o ORIGINAL PAGE _E_ OE POOR QUALITY FLIGHT CONDITIONS IDENTIFIED

F

BY NUMBERS: SEE TABLE 12 40 - 4: FLIGHT CONDITIONS 4f_ 30- o1 !

C) x MJ -- £3 20 - _9_" 16__16 10 - [ ] I I r I I II I |1 , 120 160 200 240 280 320. 360 400 440 V e "-- Kt Figure 59. - Flight simulation test conditions.

The range of c.g. positions from 25% (positive 15% static stability margin) to 50% mac (negative 10% static stability margin) were covered for flying qualities evaluation of each flight condition. Also, c.g. positions to 60% mac were covered for flying qualities evaluation of some of the flight conditions.

The atmospheric conditions for each test condition were calm air and moderate turbulence (o = 4 ft/sec rms at high speed and o = 6 ft/sec rms at low speed).

6.4 Evaluation Tasks The tasks performed in each flight regime were as follows: Cruise Wind-up Turns: Wind-up turns were performed to evaluate maneuvering force and stability characteristics by stabilizing at increasing load factors.

S-Pattern Turns: The aircraft was banked to a 4-minute turn attitude and flown through a 90 degree heading change while descending 500 feet.

Then, the bank angle was reversed and the aircraft was turned back and rolled out on the initial heading while climbing 500 feet.

Trimmability: The workload to initially trim the aircraft and to recapture trim from a disturbed condition was used as another measure of performance. The trim recapture was evaluated by advancing power to upset the aircraft altitude and flying back to the initial altitude without retrimming.

• Airline Operational Turns: 20 degree and 30 degree banked turns were performed while maintaining constant speed and using column force to control attitude and altitude. Turn entry and exit characteristics were also evaluated. This maneuver was limited to a 20 degree bank angle at a W/_ of 1.9 x 106 ibs because of the high angle-of-attack pitch divergence characteristics of the aircraft.

• Pitch Attitude Change: Attitude stability was evaluated by changing and holding a new pitch attitude with column force inputs.

Power Effects: Power was advanced and retarded to restabilize the aircraft on a new pitch attitude while maintaining speed by holding column control force.

Emergency Descent: Power was pulled back to idle and the nose was pushed over to start the aircraft descent. The aircraft was maneu- vered into a banked turn after start of descent to increase drag.

Short-Period Dynamic Stability: Short-period characteristics were evaluated by using quick forward and aft control column inputs and releasing the column to upset the aircraft from 1 g flight. Pitch attitude and load factor were observed while the aircraft returned to 1 g trim.

Phugoid Dynamic Stability: The aircraft was displaced slightly from trim, and the phugoid damping and period were evaluated by observing excursions in rate of climb and pitch attitude.

Static Stability: Longitudinal static stability, sometimes referred to as speed stability, was evaluated by determining the variation of column force with deviation from trim speed.

Maximum Operating Speed Tasks performed at maximum operational speeds included wind-up turns, operational turns, and trimmability. Descriptions of these tasks are similar to those for the cruise conditions.

Land in g • Wind-up Turns: Wind-up turns were conducted to evaluate maneuvering force characteristics by stabilizing at load factors up to 1.2 g.

ILS Approach: The approach task was initialized 8 miles from the airport at 2000 feet above ground level with a 1000 foot lateral offset. The task entailed flying the airplane to the localizer, capturing the glide slope, and tracking the glide slope down to 50 feet. A few flares and touchdowns were attempted, but the pilots felt that this added nothing to the evaluation. The approaches were made on raw data displays.

Holding • Airline Operational Turns: 30 degree banked turns were flown while maintaining speed and using column force to control attitude and altitude.

Takeoff 30 degree Heading Change: The takeoff condition was initialized with the aircraft climbing in the second segment configuration. Con- trollability was evaluated during 30 degree banked turns through 30 degree heading changes.

6.5 Evaluation Guidelines Flying qualities of the aircraft were evaluated in terms of the Cooper- Harper pilot rating scale defined in Figure 60. In this report ratings 1 to 3.5 are designated as satisfactory, ratings 3.6 to 6.5 are unsatisfactory, and ratings 6.5 to i0 are unacceptable. Satisfactory/unsatisfactory and unsatisfactory/unacceptable divisions are shown on each of the rating charts at 3.5 and 6.5 respectively. Any rating higher than 3.5 indicates that improve- ments in the flying qualities are desired.

Basic flight parameters were recorded on analog strip charts with the PACS on and off and compared to show benefits achieved by engaging the PACS.

6.6 Simulation Test Results Results of the simulation test show that the PACS fulfills the function for which it was designed. Pilot ratings indicate that flying qualities of the PACS configured aircraft with the c.g. at 50% mac are as good as the baseline aircraft with c.g. at 25% mac. The results are most impressive at high-speed conditions where handling qualities of the baseline aircraft quickly degrade to unacceptable levels (pilot ratings >6-1/2) for c.g. positions aft of 40% mac.

Data for the PACS configured aircraft show satisfactory ratings (pilot ratings _3-i/2) for c.g. position to 50% mac and very little degradation occurs when tile c.g. is moved from 50 to 60% mac.

Q

Z(n (.0 _z _u.J ;i_ r,-

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c= I.IJ C2 Results of the simulation are presented for each flight condition in the following sections.

6.6.1 Flight Condition i0: Mid Altitude Cruise. - Flight condition i0 was evaluated by five pilots. However, all c.g. positions, which covered the range from 25 percent to 60 percent mac, were not tested by all of the pilots.

Pilot ratings for the c.g. positions tested by each pilot in calm air and moderate turbulence condi£ions are presented in Figures 61 and 62 respectively.

The solid symbols show ratings for the baseline aircraft (PACS off) and the open symbols show ratings for the PACS configured aircraft (PACS on).

The baseline aircraft ratings for the calm air and turbulence conditions showed unacceptable flying qualities for c.g. positions of 40 percent and aft.

The wide scatter in ratings at 39% is due to the sensitivity of the pilot in judging the onset of unacceptable flying qualities. Engagement of the PACS in calm air showed satisfactory flying over the entire c.g. range of 25 percent to 60 percent mac. Flying qualities in moderate turbulence were not as good as in calm air but were considered to be satisfactory for c.g. positions to 55 percent mac. At a c.g. position of 60 percent mac, the ratings showed the flying quali- ties to be unsatisfactory.

Pilot comments were evaluated to determine specific flying quality charac- teristics for each c.g. position. An example of the pilot comments for Flight Condition i0 in calm air is given in Table 13.

6.6.2 Flight Condition 15: Maximum Range Cruise. - Flight condition 15 was evaluated by Pilot 5. The Cooper-Harper ratings for calm air and moderate turbulence are presented in Figures 63 and 64 respectively.

The baseline aircraft flying qualities degrade rapidly aft of 40 percent mac. Engagement of the PACS in calm air provides a rating that is near the satisfactory/unsatisfactory boundary for the entire c.g. range. In turbulence with the PACS on, ratings are about the same over the c.g. range but are not as good as for the calm air ratings.

6.6.3 Flight Condition 7: High W/6 Cruise. - Flight condition 7 was evaluated by three pilots. The Cooper-Harper ratings for calm air and moderate turbu- lence are presented in Figures 65 and 66 respectively.

Flight condition 7 was the least stable of the three cruise conditions due to the close proximity of the nonlinear static stability flight region.

This reduced stability is reflected in the rapid degrading of the baseline aircraft flying qualities. Engaging the PACS in calm air provided satisfactory flying qualities to 50 percent mac and near satisfactory flying qualities at OR]G|NAL PP,_ _ OF POOR QUALITY O PILOT 1 Z_ PILOT 2 l [] PILOT 3 <> PILOT 4 _7 PILOT5 • • PACSOFF (BASELINE AIRCRAFT) [-] PACS ON O- UNACCEPTABLE Z l-- ,,,,e.

Lu Q.

5 -- • • =:, re- a.

O (.3 O O _7 D 3 [] • ZX [] 2 -- ZX SATISFACTO RY

I I I I

20 30 40 50 60 c.g. "_ % mac Figure 61. - Cooper-Harper rating for Flight Condition i0, calm air.

9O ORIGINAL PAGE _S OE POOR QUALITY O PILOT 1 /% PILOT2 10- [] PILOT3 <> PILOT 4 V PILOT 5 • AIRCRAFT) • PACSOFF (BASELINE I-1 PACSON ,& -- • UNACCEPTAB LE

• v O

UNS CTORY

=_ ..... 0----0-, --

¢JJ_ Z_ SATISFACTORY

I I I I

20 30 40 50 60 e.g. _" % mac Figure 62. - Cooper-Harper rating for flight condition i0, moderate turbulence.

TABLE 13. PILOT COMMENTS, FLIGHT CONDITION i0, CALM AIR PACS Off PACS On c.g. Position • Trimmability was good.

e Altitude hold was -+20 feet in 20 degree banked turns, e Stability about trim was good and column • PACS improved attitude control but forces to maneuver around trim were heavier.

forces were acceptable.

25% e High column forces during large maneuvers • Column forces were objectionably high during made control difficult.

large maneuvers.

• Short period mode was more heavily damped.

e Short-period mode was well damped.

e Pitch attitude response was crisp and there was no bobble around the new attitude.

e Trimmability was degraded.

e Altitude hold was -+40 feet in 20 degree e Altitude hold was -+30 feet in 20 degree banked turns. banked turns.

e Force lightening was apparent at about • Forces were higher but the airplane was much easier to control since it appeared more 1.8 g.

34.5% stable.

e Short-period mode damping was good.

e Phugoid mode was divergent.

e Airplane appeared looser and precise control was more difficult.

• Trimmability was difficult. • Trimmability was significantly improved.

e Altitude hold was -+50 feet in 20 degree banked turns.

• Significant force lightening was observed at high load factors.

e Forceswere heavier and maneuvering • Forceswere too light.

39% characteristics were improved.

• Short-period mode was reasonably damped.

e Phugoid mode was rapidly divergent.

e Pitch attitude oscillations were observed.

• Attitude control was improved.

• Considerable pilot attention was required.

e Controllability was marginal.

• Trimmability was very difficult.

e Trimmability was excellent.

• Altitude hold was -+150 feet in 20 degree banked turns.

43% e -+0.5 g oscillations occurred during 20 degree • Forces and controllability in turns and banked turns.

high-g maneuvers were good.

e Largemaneuvers were no longer considered possible.

ORIGINAL P._GE _8 OF POOR QUALITY, TABLE 13. PILOT COMMENTS, FLIGHT CONDITION i0, CALM AIR (Continued) c.g. Position PACS Off PACS On 50% • Same comments as PACS On at 43% mac.

• Airplane was no longer considered flyable.

55% • Not flyable • Altitude control was slightly looser than at 50% mac.

• Not flyable • Altitude control noticeably looser.

• Nose wandering occurred during S turns.

6O% • Aware of reduced forces around 1.8 g.

• Control sensitivity was increased because of reduced stability and lighter forces.

10- • • PACS OFF (BASELINE AIRCRAFT) V PACS ON m UNACCEPTABLE Z q rv- m r,- ¢X: -r" r_- &.u (=3 UNSATISFACT0 RY f-3 - • _7 V V • V - • SATISFACTORY

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2O 40 50 6O 3O c.g. _ % mac Pilot 5 Cooper-Harper rating for Figure 63. - flight condition 15, calm air.

OF POOr', _,"-_ .... " '_ • PACS OFF (BASELINE AIRCRAFT) '_ PACS ON V UNACCEPTABLE z 6 I- t,=.- B ,-,- 5 UNSATISFACT0 RY "-r V V V i..¢J c= 4 -- • • V _7 V V SATISFACT0 RY

I I I I

20 30 40 50 60 c.g. _% mac Figure 64. - Pilot 5 Cooper-Harper rating for flight condition 15, moderate turbulence.

rp_ OF POOR QUALITY .10 O PILOT 1

O

PILOT 4 _7 PILOT5 • PACS OFF (BASELINE AIRCRAFT) [] PACS ON

I

UNACCEPTABLE Z n- n- n,- ,5 n,- UNSATISFACTORY I,.I.I a.

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20 30 40 50 6O c.g._% mac Figure 65. - Cooper-Harper rating for flight condition 7, calm air.

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20 30 4O 50 6O c.g. "_ % mac Figure 66. - Cooper-Harper rating for flight condition 7, moderate turbulence.

55 percent and 60 percent mac. The turbulence ratings indicate a trend toward degraded flying qualities at the 55 percent and 60 percent mac c.g. positions.

Pilot 4 ratings were satisfactory in calm air and turbulence to the 50 percent mac c.g. position which he evaluated.

Pertinent parameters were recorded on strip charts during the pilot evaluations. Three strip chart segments have been selected to illustrate the difference between the baseline and PACS configured aircraft for the Pilot 1 evaluation of flying condition 7. Figures 67 through 69 compare the flight characteristics at c.g. positions of 39%, 43%, and 50% mac respectively.

ORIGINAl PA_ _I

OF POOR QUALITY INU) '6_F PACS0FF I PACSON ANG.OF ATTACK ....

({leg) 6 (N PITCH ANGLE (deg) (ND) -25 L PITCH RATE (deg/sec)

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(TED) F STAB.POS. 0 i 8 (deg) (TEV) Figure 67. - Flight condition 7 comparison of damping response character- istics with PACS on and off, c.g. at 39 percent mac.

16 PACS OFF I PACS ON !

(NU) [ ANG.OF ATTACK (deg) (NO)_ (NU) PITCH ANGLE (deg) (NU)r

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(FWD)

..,, ,,. .k Ll

COLUMN POS.

0 ' (in) (TED) STAB. POS.

(deg) (TEV) [ _ I I I I I J _1011 I I I I I I I I I I I I I I I I I I J I I I [ I I I I 11 11 I I I I I I I Figure 68. - Flight condition 7 comparison of damping response characteristics with PACS on and off, c.g. at 43 percent mac.

ORIGINAL P_G_' _ OF POOR QUALI'i_ PACS OFF PACS 0 N ANG. OF ATTACK (deg) (NO O) PITCH ANGLE (deg) (NO) -25 &,l- .

PITCH RATE oL.-/h ^._,_ .__ _,,_L,,.-.,.,.

(deg/sec) I ...... , I! _ ' I_ .....

___' L

co, /'l__^ .A.__ _w, ,,.__. __,/!_. A _, ........ A

c.g. VERT. ACCEL 1 (g) _.__--u- -_,_- _-_ zz,_qp v.1,_/ -v,_--- v W--V-_V_..qr .-y_--V --- , (RT)

A

BANK ANGLE 6 _@ v

L

(FWD) COLUMNPOS. 0 (in) (AFsT-

F

STAB. POS. 0i ...... ,8 _.

_]_l,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,, I ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Figure 69. - Flight condition 7 comparison of damping response characteristics with PACS on and off, c.g. at 50 percent mac.

The 39 percent mac condition (Figure 67) was flown in moderate (4 fps RMS) turbulence only for shallow banked turns. In each instance the airplane was first evaluated with PACS off, afterwhich the PACS was engaged and the evalua- tion was repeated. The pilot workload shown by the control force was high and excursions in c°g. normal acceleration were approaching +0.5 g with the PACS disengaged. After engaging the PACS, the c.g. vertical acceleration excursion and the control column input forces were less than half.

Figure 68 shows the evaluation at a c.g. of 43 percent mac in calm air.

With PACS disengaged the workload was about the same as the c.g. of 39 percent mac in turbulence. Again only shallow banked turns were attempted. With the PACA engaged the pilot workload was dramatically reduced and the pilot com- fortably rolled into a 30 degree banked turn.

Figure 69 shows the evaluation in calm air with the c.g. at 50% mac.

With PACS disengaged the aircraft was difficult to control and large, rapid, cyclic, control column inputs were required to fly level. The PACS was engaged and the airplane could be comfortably rolled into a 30 degree banked turn.

6.6.4 Flight Condition 16: High Speed Flight condition 16 was evaluated by three pilots in calm air and by one pilot in moderate turbulence (4 ft/sec rms). The Cooper-Harper ratings for calm air and moderate turbulence are presented in Figures 70 and 71 respec- tively. The PACS on ratings showed satisfactory flying qualities for the calm air condition and near satisfactory for the turbulence condition.

6.6.5 Flight Condition 18: Landing Flight condition 18 was evaluated by three pilots in calm air and moderate turbulence (6 ft/sec rms) for the c.g. range of 25 percent to 50 percent mac. The aft c.g. position was limited to 50 percent by the nose- down authority of the trim system. The ratings are presented in Figures 72 and 73.

The baseline aircraft flying qualities in calm air were near the satisfactory/unsatisfactory rating line over the entire c.g. range. Engage- ment of the PACS did not show significant improvements in the flying qualities.

The baseline aircraft Cooper-Harper ratings for turbulence conditions were scattered throughout the unsatisfactory rating band. Engagement of the PACS reduced the scatter and indicated some improvement of the flying qualities.

6.6.6 Flight Condition 17: Holding Flight condition 17 was evaluated by pilot 5. Ratings in calm air and moderate turbulence (4 ft/sec rms) are presented in Figures 74 and 75 respec- tively.

ORIGINAL PAGE Ig OF POOR QUALIW 0 PILOT 1 A PILOT 2 _' PILOT5 l PACSOFF (BASELINE AIRCRAFT) [] PACS ON UNACCE_ABLE z !1 !1 ! ! ! _ ! lll_ I-- ,.=.

t-e,- W.

UNSATISFACTORY

-----_--_-_

m W Z_ V _7 V Z_ Z_ 1-- SATISFACTO RY

I I I I

2O 30 40 50 60 c.g. '" % mac Cooper-Harper rating for flight Figure 70.

condition 16, calm air.

ORIGINAL P;':_-_ _._ OF POOR QUALITY 0 PILOT 1 I0,_ • PACSOFF (BASELINE AIRCRAFT) O PACSON 8- 7- UNACCEPTABLE r..o m m m rw- 6- ee- I.M ,,'-,e- ,,.¢,.

5- ,.=, ft UNSATISFACTORY 4-- 0 0 __.__ 0__0_ 0 3- 2- I- SATISFACTORY

I I I I

20 30 40 50 60 c.g. "% mac Figure 71. - Cooper-Harper rating for flight condition 16, moderate turbulence.

ORK_INAL_ _ OF. POOR QUALITY 0 PILOT 1 A PILOT2 10- i _7 PILOT5 • PACS OFF (BASELINE AIRCRAFT) m I":1 PACS ON 8- -- UNACCEPTABLE 6-- =¢ I-,- e'e" I,M 5"- O. UNSATISFACTO RY IZ EL= m !1 ! ! lm

--

3 - =z SATISFACTORY

I I I

r 30 40 50 80 c.g. " % mac Figure 72. - Cooper-Harper rating for flight condition 18, calm air.

, :,_ _._ I.I_L/,.'J_'_ _ OF PO0*, _-- O PILOT 1 A' PILOT 2 V PILOT 5 • PACS OFF (BASELINE AIRCRAFT) Áº-Á PACS ON UNACCEPTABLE t-."

,.=, • A • • ,=., _L _ UNSATISFACTORY

8 o o

...... ..,_,- -.-- _, .....

SATIS FACTO RY

I I I I

2o 30 40 50 60 c.g. _' % mac Figure 73. - Cooper-Harper rating for flight condition 18, moderate turbulence.

ORIGINAL PAGE _g OF POOR QUALITY PILOT 5 • PACSOFF (BASELINE AIRCRAFT) V PACSON -- UNACCEPTABLE II elll_ll_Dlln mllalllallli iI Ull _ IIi I m 141B !I ! _ l• I m z_ 6 I-- PP e,,- 4.1 " 5 m ee.- z ,,--,, = 4 -- UNSATISFACTORY CJr ==,1 ! ! em=l !=_=, I Ill Iq_=l 1 i lain _ le_D 1 • • V V V SATISFACTORY

I I I I

2o 3O 40 5O 60 e.g.'"% mac Figure 74. - Cooper-Harper rating for flight condition 17, calm alr.

OF po0_. _UA_-_TI

10 -- V' PILOT 5 • PACSOFF (BASELINE AIRCRAFT) V PACSON UNACCEPTABLE r._ UNSATISFACTORY Q.

,,,,r- • v

v v v

v v

C_ SATISFACTORY

I I I I

20 3O 4O 5O 6O c.g. "" % mac Figure 75. - Cooper-Harper rating for flight condition 17, moderate turbulence.

The baseline aircraft had reasonably good flying qualities (satisfactory to mid unsatisfactory ratings) to c.g. positions of 50 percent mac. The flying qualities became unacceptable at approximately 55 percent. Engagement of the PACS resulted in unsatisfactory flying qualities over the entire C.go range for calm air conditions. Turbulence conditions resulted in unsatisfactory flying qualities with Cooper-Harper ratings between 4 and 5 over the entire c.g. range.

6.6.7 Flight Condition 19: Takeoff

Flight condition 19 was rated by pilot 5 for calm air and moderate turbulence (6 ft/sec rms) over a c.g. range from 25 percent to 50 percent mac.

The ratings are presented in Figures 76 and 77.

The baseline aircraft had good flying qualities for the calm air flight condition and engagement of the PACS did not show a significant improvement.

Flight in turbulence degraded the flying qualities and resulted in baseline aircraft Cooper-Harper ratings between 4 and 5. Engagement of the PACS enhanced the flying qualities slightly.

6.6.8 Summary of Simulation Test Results The solid lines in Figure 78 show the spread in Cooper-Harper ratings of the baseline aircraft for the cruise and high speed flight conditions (7, I0, 15 and 16). Engagement of the PACS results in a rating spread shown by the dashed lines. The rating spreads include calm air and turbulence conditions ratings. The holding condition (18) is not included in Figure 78 but the rating trend is similar. The PACS did not provide a significant benefit for the landing and takeoff conditions (18 and 19) although some improvement of fly- ing qualities in turbulent flight were shown.

A summary of the Cooper-Harper ratings for the PACS configured aircraft are given in Table 14 for all of the flight conditions. The Cooper-Harper ratings shown are the typical best estimate for each test point. In general the turbulence Cooper-Harper ratings have a value of one greater than the ratings for the calm air conditions. The most unsatisfactory rating in the table is 5.

OF POOR QUALITY 10 - _7 PILOT 5 m • PACSOFF (BASELINE AIRCRAFT) V PACSON 8 - 7 -- UNACCEPTABLE E 6 - l.-- rY- e,,-.

5 -- r,-.

UNSATISFACTORY a.

4 -- m m 3 -- V 2 -- 1 -- SATISFACTORY

I I I I

2o 3O 4O 50 60 c.g. _ % mac Figure 76. - Cooper-Harper rating for flight condition 19, calm air.

V PILOT 5 10-- • PACSOFF (BASELINEAIRCRAFT) V PACS ON 8- -- UNACCEPTABLE z GE 6-- M.I 0.

e_ UNSATISFACTO RY w- GE 5- MJ Q.

(:3 V (::3 V 4 V V Imm m mmm m mww mm _mmm m mm imm)_'_mm _ mm _m ,ram _ im 3- SATISFACTO RY

1 I I I

20 30 40 50 60 c.g. _% mac Figure 77. - Cooper-Harper rating for flight condition 19, moderate turbulence.

OF PC, OR _-_Li_Y lO t-P I= iJU Q.

"E PACS CONFIGURED / AIRCRAFT

.I

./

l .L

2o

3o J

6O c.g. _ % mac F_gure 78. - Summary of Cooper-Harper ratings for cruise and h_gh speed flight conditions.

11o OF POOR QUALITY TABLE 14. - SUMMARY OF COOPER-HARPER RATINGS WITH PACS ON c.g. Position _% mac Atm.

Flight 25 34.5 Condition Cond. 39 43 5O 55 6O 30 3.0 2.5 30 C.A. 2.5 3.5 3.5 3.0 3.5 3.5 35 40 4.0 4.5 C.A. 35 3.0 30 2.5 25 3.5 3,0 35 3.5 3.5 3.5 3.0 3.5 5.0 C.A. 3.5 3.5 3.5 3.5 3,5 3.5 4.0 4.5 4.5 40 4.0 3.5 4.0 4.5 C.A, 3.5 3.5 30 30 30 3.5 3.5 35 3.5 3.5 4.0 35 3.5 3.5 C.A, 30 30 3.0 3.0 4.0 4.0 45 4,5 4.5 5.0 C.A. 3.0 3.0 3.5 3.5 3.5 T 4.0 4.0 4.0 4.0 4.0 C.A. 3.0 3.0 2.5 3.0 3°0 T 4.0 4.5 5.0 5.0 5.0 7. PACS ARCHITECTURE This section shows the control law mechanization for an advanced PACS which would be suitable for a Lockheed L-1011 (S/N i001) flight test program.

Although the advanced PACS control law was developed to provide good flying qualities to a 50 percent mac aft c.g. position and shown by simulation test to provide good cruise and high speed flying qualities to a 60 percent mac aft c.g. position, the PACS architecture that is suitable for an L-1011 flight test program was based on an aft 43 percent mac c.g. limit. This represents a negative 3 percent static stability margin and is the maximum aft c.g. limit that the Lockheed L-1011 (S/N I001) can operate without significant structural modifications.

The advanced PACS interface block diagram is shown in Figure 79. The controller input signals from each component are shown on the diagram. Output signals were provided to the series servo channels and failure signals were provided to the Flight Control Electronic System (FCES) panel.

Tasks performed by the controller (digital computer) are analog-to- digital conversion, signal monitoring and voting, automatic configuration switching after failures, digital-to-analog, gain scheduling, and filtering operations. Redundancy of the advanced PACS components are shown in Figure 80. The architecture design was based on the following rationale.

Single failures are bound to occur and it is impossible to predict exactly when they will happen. Therefore, the design aim is to incorporate safety provisions to protect the system against critical effects of any single fail- ure. Also, the flight crew needs to be warned of any failure, critical or not, so that exposure time for the build up of a possible hazardous multiple fail- ures is limited. The design aim is accomplished when there are no critical single failures and the probability of potential hazardous single failures is acceptably remote.

The advanced PACS equipment specification document was completed in August, 1981. Its contents covered a normal Lockheed specification format for submittal to vendors. The section specifying system requirements included functional requirements, performance (including safety), interface (including sensors and servos), environment, operational utility (including reliability), monitoring, and software procedures. Several appendices were included to expand the specification with background.

PRECEDING PAGE BLANK NOT FILMED ORIGINAL F_C;_ |g OF POOR Qb_LITY -_W-- C_C_oz: I.IJ C2 =w zz_ =p (.._ c=_z r---z ._n.- -r-I cn C ¢ ..r- C/) ¢ LJ.I LIJ .._C_ U n,- c# a. Q. i_ L O.-m c_ ¢ P_ I-C:) U C ,_[ r,- L ..r- c.3 I-- U C _z U L z_ C A -r-I U _S "ql _> I ¢_1'-- C_ :=" Q-C.3 ,H i) I : l) I) _1 1) ;

"

._, C.3 , | C.3UJ I LLJ I.L.I !

I ORIGINAL PAGt i_ OF. POOR QUALITY ,=1 ,c a: _ E,

°° I*1

--'E-- I I ;a oH '-o 0J o m m

g

!

= I CONCLUSIONS The piloted flight simulation test showed that addition of the advanced PACS to the L-1011 longitudinal control system provided flying qualities to a 20% negative static stability margin which were comparable with the best base- line aircraft flying qualities (15% positive stability margin). The PACS sen- sor inputs required for flight in the linear stability region are normal accel- eration, pitch rate, and pitch attitude. Additional sensor inputs required for nonlinear stability flight conditions are angle of attack, bank angle, and Mach number.

Analyses and piloted flight simulation tests also showed that handling qualities for the flight test L-lOll (S/N i001), which was the baseline air- craft used for the study, become unsatisfactory at about a negative 3% static stability margin. Consequently, a commercial transport equipped with a PACS that has the capability to fly at i0% negative static stability margin should have a longitudinal control system that has a reliability equivalent to the structure reliability. Thus, a major step toward implementation of a PACS for commercial airline service is to determine that it satisfies the reliability requirement. The advanced PACS architecture shown in this report was designed for a flight test program with static stability margins to negative 3%.

The advanced PACS program provides strong evidence that technology is available to develop PACS control laws which provide good handling qualities for commercial transports for the c.g. range from +15% to -10% static stabil- ity margins. Further validation of the advanced PACS control laws developed during the current program requires hardware development and flight testing.

However, indications are that the analytical methods developed during the program can be applied to reduce the number of sensor inputs required by the PACS.

PRECEDING PAGE BLANK NOT FH;_D"

APPENDIX A Aero Data Table 15 is a computer output sheet of the aircraft trim conditions and dimensionless stability derivatives for flight case 7b (Table 2). The nomen- clature for this table is given below: DLC - Direct lift control DAC - Aileron active control DARIG - (6aright + 6alert)/2 , aileron deflection due to aileron active control system _ deg FLAP - Flap setting _ degrees W - Gross weight _ ibs C.G. - Center of gravity location _ % mac ALT - Altitude above sea level _ ft.

VE - Ve, Equivalent air speed _ knots M - Mach number UO - True airspeed, ft/sec RHO - , air density _ slugs/ft 3 Pitch axis inertia _ slugs/ft 2 IY - Iy, ALPHA - _, trim angle of attack _ degrees TIIETA - 0, climb angle _ degrees GAMMA - y, yaw angle _ degrees WLCG - center-of-gravity position on the water line DH - _H' horizontal stabilizer trim angle _ degrees i I TI - Thrust of engine i _ ibs T2 - Thrust of engine 2 _ ibs T3 - Thrust of engine 3 _ ibs PRECEDING FACE Ta_ ,\','_ )_u_T ORIGINAL PAGE iS OF POOR QUALITY TABLE!I5. LONGITUDINAL AERO DATA, CASE 7b TRIM CONDITIONS, AEROELASTIC EFFECTS INCLUDED GEAR UP DLC OFF OUT OF GROUND EFFECT OAC ON, DARIG = 0.0 FLAP = 0 'W = 408000. CG = 25.0 ALT -- 37000.

VE -- 254.3 M = 0.830 UO = 803.5 RHO = 0.000678 IY = 1.49500E07 ALFA = 4,37 THETA = 4.37 GAMMA = 0.0 WLCG = 186.5 DH = -3.15 T1 = 9773. T2 = 9773. T3 = 9773.

MBT1 = 6.33 MBT2 = -12.77 MBT3 = 6.33 LONGITUDINAL STABILITY DERIVATIVES (LINEARIZED) CD = 0.03845 "CL = 0.535 CM = -0.00171 CDA = 0.01'685 CLA = 0.1243 CMA = -0.0151 CLQ = 9.88 CMQ = -20.45 CLADT = 4.16 CMADT = -10.16 CLDH = 0.0297 CMDH = -0.0671 CDDAC = -0.00014 CLDAC = 0.00182 CMDAC = -0.00427 CDU = 0.1859 CLU = 0.4942 CMU = -0.1019 DTDM = 6739. DTDU = 6.96 DTDH = -0.53 DTDTHR = 303.1 MBTI - Perpendicular distance from center of gravity to thrust line of left engine (positive for nose-up pitching moment) _ ft.

MBT2 - Perpendicular distance from center of gravity to thrust line of center engine _ ft.

MBT3 - Perpendicular distance from center of gravity to thrust line of right engine _ ft.

CD - CD, Drag coefficient CL - CL, Lift coefficient CM - Cm, Pitching moment coefficient _C D CDA _ , change in drag coefficient due to angle of attack _ i/deg _C L CLA _ , change in left coefficient due to angle of attack _ i/deg ORIGINAL PAGE lg OF POOR QUALITY _C m CH__ _, change in pitching moment coefficient due to angle of attack _ 1/deg 2U _CL change in lift coefficient due to pitch CLQ - CL_ - mac _q ' rate _ i/rad _C 2U m CMQ -C - change in pitching moment coefficient due to m_ mac _ q' pitch rate _ i/rad _C 2U m CLADT - CL& = ma--'_-' change in lift coefficient due to rate of change of angle of attack _ 1/rad _C 2U m CMADT - C change in lift coefficient due to rate of change m.

mac _& ' of angle of attack _ I/rad (_ _C L _H change in lift coefficient due to stabilizer deflection _ i/deg m _H change in pitching moment coefficient due to stabilizer deflection _ 1/deg _C D , change in drag coefficient due to AACS CDDAC - CmdAC - _6AC deflection _ i/deg _C L CLDAC , change in lift coefficient due to AACS - CL_Ac _6AC deflection _ i/deg _C D CMDAC change in drag coefficient due to AACS - Cm_AC 86AC' deflection _ i/deg U 3CD CDU - CDu = 2 @U' change in drag coefficient due to speed U @CL CLU - CLu = -_-, change in lift coefficient due to speed _C U m CMU change in pitching moment due to speed Cmu - 2 3m '

_T

DTDM --_, change in thrust due to Machnumber _ ibs.

DTDU- change in thrust due to speed change _ lbs.

_T

DTDH -_, change in thrust due to height _ ibs/ft.

_T

DTDTHR -

• change in thrust due to throttle position _ ibs/in.

_XTHROTTLE

ORIGINAL PAGE 19 OF POOR QUALITY APPENDIX B Baseline Aircraft Math Model The baseline aircraft math model is a state-space equation (Reference 4) for open loop condition of the PACS control model shown in Figure 9. In matrix notation the state-space equation is: {x} = [A]{x} + [B]{u} (Eq. B.I) The matrices are defined as follows: x - state vector - derivative of the state vector u = input vector A = dynamic matrix B = input distribution matrix The expanded form of equation B-I is given below:

All AI2 AI3 AI4 AI5 AI6 AI7 AI8 °l BII BI2

A21 A22 A23 A24 A25 A26 A27 A28 B21 B22 I A31 A32 A33 A34 A35 A36 A37 A38 B31 B32

ul

A41 A42 A43 A44 A45 A46 A47 A48 B41 B42

I+

6Hc] A51 A52 A53 A54 A55 A56 A57 A58 B51 B52 NZ F

_Ac]

"z I

8F A61 A62 A63 A64 A65 A66 A67 A68 8 F B61 B62 _H A71 A72 A73 A74 A75 A76 A77 A78 6H B71 B72 6 H A81 A82 A83 A84 A85 A86 A87 A88 B81 B82

L

1'23 ORLG,_._;;,-', _ ' - ......

Elements of the state vector (x) and the input matrix (u) are defined as follows: angle of attack increment pitch rate pitch attitude increment u normalized airspeed increment (Au/U) o {x} = filtered normal acceleration increment NZ F filtered pitch rate 8F horizontal stabilizer angular velocity

au

horizontal stabilizer angular increment 6H .

-_ ° n horizontal stabilizer command signal {u} = Outboard aileron symmetric command signal Elements of the dynamic matrix (A) and the input distrubution matrix (B) are derived from the aerodynamic data trim conditions and stability derivatives of Appendix A. The elements of these matrices are defined in Table 16. The symbols in the table are defined below.

m - Mass of Aircraft (slugs) V - True Air Speed (ft/sec) o q - Dynamic Pressure (i/2p V 2) (ibs/ft 2) o S - Wing Area (ft 2) w C - Coefficient of Drag Change due to Speed Change x u C - Coefficient of Drag Change due to Angle-of-Attack Change (deg -1) x CL - Coefficient of Lift Change due to Gravity as Pitch Attitude o Changes (deg -1) C - Coefficient of Lift Change due to Speed Change z u - Coefficient of Lift Change due to Angle-of-Attack Rate (rad -I)

C

Z.

- Coefficient of Lift Change due to Angle-of-Attack (deg -I) C Z C - Coefficient of Lift Change due to Pitch Rate (rad -I) z q g - Constant Acceleration due to Gravity (ft/sec) - Time Constant of Accelerometer Filter (sec) Z C Coefficient of Lift Change due to Horizontal Stabilizer Change (deg -I) z6 H C m Coefficient of Lift Change due to Horizontal Symmetrical z 6 Aileron Change (deg -I) a C i Coefficient of Pitching Moment Change due to Speed Change m u C Coefficient of Pitching Moment Change due to Angle-of-Attack m" c_ Rate (rad -i) C Coefficient of Pitching Moment Change due to Angle-of-Attack m Change (deg -I) SW - Wing Area (ft 2) - Mean Aerodynamic Chord of Wing (ft) Coefficient of Pitching Moment Change due to Pitch rate (rad -I) C m q C Coefficient of Pitching Moment Change due to Horizontal Stabilizer Change (deg -I) m6 H C Coefficient of Pitching Moment Change due to Horizontal m_ Stabilizer Change (deg -I) a T_ - Time Constant of Pitch Rate Sensor Filter (sec) C Coefficient of Drag Change due to Symmetrical Aileron Change x_ (deg -I) a - Distance of Accelerometer Forward of c.g. (ft) T - Time Constant of Series Servo (sec) s Time Constant of Horizontal Stabilizer Servo (sec) P ORiG=NAL PAGE |g OF POOR QUALITY TABLE 16. DEFINITION OF ELEMENTS FOR MATRICES A AND B G/F H/F 0 ElF 0 0 0 J/F 0 K/F GN,P__

H._N+R 0 EN+M 0 0 0 J._NN +S o KN +T__

FQ Q FQ Q. FQ Q FQ Q FQ Q 0 1 0 0 0 0 0 0 0 0 [A] = C/A 0 -D/A B/A 0 0 0 0 [B] = 0 V/A -(GW+YP) - (HW+RY-I) 0 -(EW+MY)-L 0 0 -(JW+SY) 0 -(KW+TY) U 0 0 0 -U .I) 0 o '0 0 10 0 0 0 -(Zl+Z2) -ZIZ 2 Z1Z 2 0 0 0 0 0 0 1 0 0 0 where:

A

B = C = E = CZu C Xu CX_ ' D = CLo q Sw

i=Vo

F = A - XCz , G = CZ_r H = A+XCZq g 'rz J = CZ'_ H N = XC L =- r-'_- M = Cmu K = CZ6 a p = Cm_ m& u=-L T = Cm8 R = XCmq S = Cm_ H _-o a N_ + OV o W= X- E" z I =J-- V = CX_ y = g Tz-'--'-'_" 7" S a g ,r z FQ 2 V o

ORtGBNAL PAGE [9 OF POOR QUALITY APPENDIX C Modal Control Method The eigenvalue/eigenvector assignment problem is generalized for both the output feedback and full state cases. Therefore, the C-matrix referenced throughout this report is assumed to be a general matrix of dimensions r x n.

If all C-matrices are set equal to an n th order identity matrix, this will convert the generalized eigenvalue/eigenvector assignment problem into a full state feedback problem.

The development of the eigenvalue/eigenvector assignment problem will include the following three major areas: • Eigenvalue assignment • Eigenvector assignment • Feedback gain calculation C.I Eigenvalue Assisnment.- We consider the standard multivariable lin- ear time-invariant feedback control system.

x = Ax + Bu, x(t o) = Xo (Eq C.I) y = Cx (Eq C.2) u = Fy (Eq C.3) By substituting the feedback equation (C.3) into the system equation (C.I), we obtain the closed loop state equation x = (A + BFC)x (Eq C. 4) The closed loop system has the eigenvector equation: (A + BFC)_ i = %i v._ (Eq C.5)

where

%. (i = i, ".-, n): Set of distinct closed loop eigenvalues

i v. (i = i, "'" n): corresponding set of closed loop eigenvectors i We can rearrange equation (C.5) to obtain the following expression [%.1 - A]v. = BFCv. (Eq C 6) 1 1 1 Since the B matrix has full rank of m, it is always possible to partition the B matrix to form B' = [Bi B2] by reordering the state variables in equa- tion (C.I). B1 is an m x m nonsingular submatrix.

With no loss of generality, we can assume that the B matrix has the following partition form BI] (Eq C.7) B = B2 where BI: m x m nonsingular matrix B2: (n - m) x m matrix Consequently, we can express equation (C.6) in the following partitioned form (Eq C. 8) -A21 %1"In-m - A22 B 2 w

[ilmAll Al2 ILl [i] FC EzJ

where m n-m _All__ AI2 ] m A _ (Eq C. 9) ORIGINAL PA_ ;_ OF POOR QUALITY m B _.

(Eq C. I0) n-m V. = ZI___. I m (Eq C.ll) 1 [wil n-m N and where th I. = the j order identity matrix Considering the first matrix equation of (C.8), we readily obtain (Eq C.12) kll m - All -AI2] [_.i] = BIFC [w_. i] or equivalently (Eq C. 13) [%i[Imi0] - [AlllAl2]l[wZ_] = BIFC [wZ_] Letting I (Eq C.14) = ii AI then (C.13) can be expressed as: (Eq C.15) %i[Im! O] OF POOR QUi-i.-_

Rearranging (C.15) we obtain

= l.z. (Eq C.16) or using (C.ll) we get (Eq C. 17) (AI + BIFC) _i = lizi With the rank of C equal to r, one can assign r closed loop eigenvalues using output feedback (Reference 5). It should be noted that one can assign n closed loop eigenvalues in the full state feedback case where the C matrix is an n th order identity matrix.

Rewriting equation (C.17) to include the complete set of eigenvectors and eigenvalues: (Eq C. 18) (A I + BIFC) V = ZA where A =, 2 (Eq C.19) (Eq C. 20) Z = [z I z 2 --- Zr] (Eq C.21) V = [_i v2 --- _r ] Rearranging (C.18) we have (Eq C.22) FCV = Bll/ZA- AIV )

C and V each have full rank of r; therefore [CV] is nonsingular. From equation

(C.22), we can solve for F directly

(Eq C.23)

F = BII(ZA - AIV)(CV)-I

The inverse of UV will always exist in physical systems with a meaningful

sensor implementation.

C.2 Eigenvector Assignment. - In the previous section we have mentioned

that the number of assignable closed loop eigenvalues equals the rank of the C matrix. In this section, the significance of closed loop eigenvector assign- ment in modern flight control theory are discussed.

Consider the time-invariant, closed loop system (Eq C.24) = (A + BFC)x, X(to) = x ° Suppose the matrix [A + BFC] has distinct eigenvalues and eigenvectors denoted by (XI, %2, "'" %n) and (_I, _2, "'- _n), respectively. It can be shown that the solution of (C.24) can be written as n _.t (Eq C.25) x(t) = e _i i (liXo) i=l where .th row vector of T -I I. -- 1 and T = [_i _2 "'" _n ] (i.e., T is the modal matrix of (A + BFC)).

This shows that the response of the closed loop system (C.24) is a compo- sition of motions along the closed loop eigenvectors vi (i = i, 2, ... n). It is important to know that the i th mode X i is excited by the component of the initial state, Xo, along its corresponding closed loop eigenvector vi. There- fore, in flight control system design it is desirable to decouple the motions

by proper choice of the closed loop eigenvectors to improve aircraft handling

qualities. For example, in an aircraft lateral axis design problem, we want

the roll subsidence modeto show up dominantly on roll rate, but not on yaw

rate or sideslip. Similarly, we want the dutch roll modeto showup dominantly

on sideslip and yaw rate respectively for the real part and imaginary part of

closed loop eigenvectors, but not on the roll rate. In this simplified example, we show a desire to decouple the roll subsidence modeand the du$ch roll mode.

In the sense that the roll subsidence modeonly affects the roll rate while

the dutch roll modeonly affects the yaw rate and sideslip.

It is well known that (RefereNce 4,5) we can not completely specify a set

of closed loop eigenvectors for our feedback system. But we do have someflexi-

bility in obtaining a set of closed loop eigenvectors such that they will best

approximate the set of predescribed or desirable eigenvectors (Reference 6).

Wewill discuss the eigenvector assignment problem for the following two

situations:

(i) Completespecification of desired eigenvectors

(2) Incomplete specification of desired eigenvectors

C.2.1 Complete specification of desired eigenvector case: The closed

loop eigenvalue and eigenvector are defined by the following equation:

(A + BFC)_. = %._. (Eq C.26)

i 11

where %i and vi are the closed loop eigenvalue and eigenvector, respectively.

The above equation can be rewritten in a different form.

(%.1 - A)-IBm. = _. (Eq C.27)

l 1 l

where

A m. = FC_. (j = i, 2, -.. r) (Eq C.28) J 3 A closer look at equation (C.27) reveals that the designer has the free- dom to arbitrarily select a set of r independent m-vectors (r = rank [C], m = rank [B]) such that the closed loop control system will have the desired performance characteristics. The only restriction on mr is that m i = m* • J j whenever %i = %j" The asterisk indicates the complete conjugate. This condi- tion must be satisfied in order to obtain a realizable feedback matrix.

J OF POOR QUALITY In order to capitalize on the freedom in m-vector assignment, it is beneficial to select a set of m-vectors {mi} such that they will best approxi- mate the desired eigenvector, _, with _i" Therefore, we define a cost function (Eq C. 29) J(mi ) A__(d. v0T (di- _i)= (d- Limi)T (d. Limi ) where (Eq C. 30) Li _ (%i I - A) -I B and proceed to minimize the cost function with respect to m i.

(Eq C. 31) d d d T _i - _

( .)'(,0 dm--_ J(mi) = dm. vi - Limi - Lira = 2Li imi

i Setting equation (C.31) to zero yields the following = tLTL_-I T d m.1 _ i i_ L.v.l i (Eq C.32) Therefore, the least squares method (described by equation (C.32) is an opti- mum way for selecting the set of m-vectors of (C.28). The closed loop eigen- vector (_i) obtained from equation (C.27) will best approximate the desired eigenvector (v_) in the least squares sense.

i C.2.2 Incomplete specification of desired eigenvector case: In the previous section, we have described an optimum way in selecting the m-vectors for the case where all components of the desired eigenvector are specified.

However, it will generally be true that only few components in the desired eigenvector are actually specified; while the rest can be arbitrary. In this case, we will formulate our problem as follows: Given: (i) closed loop eigenvalue/eigenvector equation (lil - A)-iBmi = _'i (Eq C.33) and (2) desired closed loop eigenvectors d (Eq C. 34)

L x ]

ni where v.. = designer specified components x = unspecified components Problem: Find m i such that the actual closed loop eigenvector (i.e., _i in equation (C.33) will best approximate the desired eigenvector (_d) in the least squares sense.

R.

To solve this problem, we will introduce a row reordering operator,|, _ m matrix The operation involves simultaneous reordering of the I(lil - A)-IB| e d co d o and th _i vet r until v i is partitioned into two subvect rs. One contains the specified components and the other contains the unspecified components.

After the row reordering operation, we have the following matrix representation.

ORI@INAK PACE _ OE POOR QUALITY (Eq C. 35) (Eq C. 36) where d i I = contains the specified components of 9.

i d d i = contains the unspecified components of 9i then

t

(Eq C.37) imi = i i Using the same minimization procedure described in paragraph (C.2.1), we obtain the following results.

(i) row.dimension of _i Z,m

, t -i

_T _T m. = L.I.

(Eq C. 38) i _lil Ii (2) row dimension of _i = 0 If the row dimension of _i is zero, it corresponds to the situation that the designer does not care about the mode distribution among output components. Hence, this design procedure is similar to out- put feedback designs using only pole placement. In this case, the designer must arbitrarily select a set of m-vectors (mi). The closed loop eigenvectors are computed using equation (C.38); i.e., _i = (_.I - A)-IBm. (Eq C.39) 1 l C.2.3 Feedback gain calculation: Once we have obtained r closed loop eigenvectors, the feedback gain matrix can be calculated from equation (C.23).

OF POOR QU_L_'_ APPENDIX D Pitch Attitude Loop Lag-Lead Circuit The pitch attitude sensor channel includes a lag-lead circuit to produce a signal component of derived incremental speed. Consequently, the speed increment feedback signal used for phugoid mode control is no longer required.

A block diagram of the lag-lead circuit used in the pitch attitude loop is given in Figure 81. The symbols K I and K 2 represent the static parts of the velocity and pitch attitude transfer functions, respectively. The symbols G I and G 2 represent the frequency variant parts of the velocity and pitch attitude transfer functions.

The speed and pitch attitude transfer functions can be expressed in the following forms by taking the Laplace transform of the open loop state-space equation (Equation B.I of Appendix B) and applying Cramers rule.

u ]Nul 1KIG l Kl(YuilS+l)(_uS+l)...(_uTS+l)

(Eq. D.I)

6Hc = _ = _ = (YD_S+l)(YD2S+l)...(YD8S+l)

_= ..N@__ _ K2G 2 = K2(Y@iS+l)(y0 s+l)...(Yo7s+l) (Eq. D. 2) 6Hc [Dl D (YDlS+l)(YD2S+l)...(YD8S+l) Where:y denotes a root reciprocal (real or complex).

The yu i (i = 1,2...7), yo_(i = 1,2,... 7), and YD= (i = 1,2,...8) represent the root reciprocals of t_e polynomial equations _or the velocity, pitch, attitude, and dynamic determinants respectively. The lag-lead circuit (Fig- ure 82) transfer function is:

l

Figure 81. - PACS lag-lead circuit block diagram.

ORIGINAL. PA_ ._I OF POOR QUALITY, 8 KIGI (Eq° D.3) = Ku K2G 2 + K 0 Substitution of Equations D.I and D.2 numerators into Equation D.3 provides: s+l) KI(YUl s+l) (Yu2 s+l) " " " (Yu 7 (Eq. D.4) 8 = K s+l) + KO 8 u K2 (`(81s+l ) (`(02 s+l)... (,(87 Writing of Equation D.4 in terms of index notation provides: (`(uiS+l) KI i=l (Eq. D. 5) _=K m + KO u K 2 7 (Yej s+l) j=l The effect of the higher order powers of s are negligible in the phugoid range of frequencies. Thus 8/0 can be written as: (YuPA + YuPB ) s + I = KuKI (Eq. D. 6) G K 2 (YOPA + ¥GPB ) s + I+Ko where the PA and PB subscripts designate the complex or real pair of root reciprocals corresponding to the phugoid mode frequencies. To facilitate writing, the following notation will be adopted.

al = YuPA I bl = _uPB a2 = Y@PA b2 = YOPB Equation D.6 can now be written in the following form: = KuK I (aI + b I) s + i (Eq. D.7) + K e e K 2 (a2 + b2) s + 1 OF POOR QUAL_":_ By mathematical manipulation Equation D.7 can be put in the following form: B KuKI + KoK2 [( 1 ] [KuKl(al + bl) + K@K2(a2 + b2) I] = K 2 a 2 + b 2) s + I KuKI + KoK2 s + Let: KuK I + K0K 2 = K 3 K 2 KuKl(a I + b I) + KoK2(a 2 + b 2) KuK I + K@K 2 = T I a 2 + b 2 = T 2 Then:

--_ : K3 _22 s-_-J = _ 3T21 + - --i/ 21 (Eq. D.8)

1 +-7-]

This equation is now in the form for gain scheduling. The polynomial coefficients for each of the gain-scheduled terms are given in Table 6.

OF POOR QL_AL_F_/ APPENDIX E Feed-Forward Loop Control Law The block diagram used for development of the feed-forward control law is shown in Figure 82.

The input to the summing point from the feed-forward loop is: (Eq. E. i) X I = (i + CFKFFGFF) X C The transfer function for the aircraft with feedback loop closed is: N Z J, KAG A (Eq. E.2) X I i + J 'KAGAKFBGFB Substitution of Equation E.I into Equation E.2 and setting X C = Fc/C F gives: N Z J'KAG A (Eq. E. 3) i + J'KAGAKFBGFB (i + CFKFFGFF) Fc/C F __ KFFGFF I FEEL FEED.FORWARD | AIRCRAFT I SPRING TRANSFERFUNCTION.[ J CURVE TRANSFER FUNCTION 6H C NZ j, FEEDBACK TRANSFERFUNCTION Figure 82. - PACS feed-forward loop block diagram.

Equation E.3 can be solved to Obtain the force gradient:

FC C F (i + J'KAGAKFBGFB )

(Eq. E. 4) N Z KAJ'G A (I + CFKFFGFF) A value for the force gradient that is desired can now be picked from the design criteria of Figure 6 (e.g., a line that is half way between the upper and lower limits). This value is defined as (FC/Nz) D to designate that it is the desired column force gradient.

The problem is to determine the feed-forward gains that will provide the desired column force gradient. Thus Equation E.4 is solved for KFFGFF to give: 1 (i + J'KAGAKFBGFB) - (Eq. E°5) KFFGFF CF + J,KAGA (Fc/Nz) D The symbols in Equation E.5 are defined as follows: Pitch feel spring rate C F = jl = J curve derivative Aircraft open loop transfer function KAG A = Feedback transfer function based on N Z signal KFBGFB = (Fc/Nz) D = Desired column force gradient The pitch feel spring rate is a function of stabilizer trim position and Mach number. Figure 50 shows the spring rates for the L-1011 S/N i001 aircraft.

J' is the derivative of the J curve which is shown in Figure 4.

The method for computing the KAG A and KFBG _ transfer functions is Fm illustrated by the block diagram in Figure 83. the value of the KAG A transfer function is obtained by solving the baseline aircraft state-space equation B.I by using Cramer's rule. This gives: NZ I (s)l NN Z (Eq. E.6) KAG A -- =

= 6Hc ID(s) I

OF. POOR qUALITY (_ r./) o • j

I"

I oo _J o ,.Q oo "o _J u,..i 4J :> QJ rJ_ I oo oo The values of the determinants are determined as discussed in Appendix D (e.g.,

Eq. D.I). Cramer's rule is used to obtain the transfer functions U/_H_ and

• " "d P e/_H_. These transfer functlons are then dlvm ed by the NN_IdHc transfer func- tionUto express the respective signal values in terms of th_ N Z signal. The KFBGFB transfer function is: E KNzNNz (s) + KuNu(S) + KoNo(s) + K_N_(s) KFBGFB = _-_Z = NNz(S) (Eq. E. 7) It can be noted that the transfer function I/_Hc is the same, regardless of_ which signal is fed back. Now, since the desired column force gradient (Fc/NZ)D was picked, all terms of Equation E.5 are known, and the feed-forward transfer function KFFGFF can be computed.

The PACS is not sensitive to the frequency variant part (GFF) of the transfer function. Thus mechafiization was achieved by making the following assumptions.

j / • Only the short-period mode frequency is important.

• The frequency is an average value.

• The damping ratio is equal to one.

• One of the duplicate poles is dropped.

These assumptions allow GFF to be written as: = (Eq. E.8) GFF (-_SP + i) If i/msp = TC, G__ defines the low pass filter in the feed-forward loop shown in Figure IS.

The static part (KFF) of the feed forward control is: (Eq. E.9) KFF = _ i + C (Fc/Nz) D KL = total loop gain of closed-loop system The resulting feed-forward gains are scheduled and plotted in Figure 13.

OF poOR QUALITY, APPENDIX F Primary Gain Scheduling Plots of the compensated feedback gains (e.g., the pitch rate gains in Figure 12) for each flight condition indicate that gain scheduling can be expressed as polynomial functions of dynamic pressure (q) and of horizontal stabilizer trim position (6HT).

The feedback gains to be scheduled were: K_ _ degrees 6Hc/degree per second KNZ _ degrees _Hc/g AN Z -i I/T 2 _ sec (_--21 - _ _ dimensionless T I K 3 T2 % degrees _Hc/degree The feed-forward gain to be scheduled was: KFF _ in/ibs A comparison of the least-mean-square values determined the order of the polynomial to be used. The second order polynomial given in Equation F.I was found to provide a satisfactory curve fit.

(Eq. F. i) K = a + bq + cq 2 + d6HT + e62T Pseudo-inverse matrix operations were used to determine the coefficients of the least-square fit for the complete flight envelope gain values. Thus, a set of simultaneous equations relating the set of points {p} to the set of coefficients {c} can be written in terms of a matrix equation.

[P] {c} = {p} (Eq. F.2) If the polynomial matrix [P] is not a square matrix, it has no inverse matrix with which to solve the coefficient vector {c}. However, if its dimensions are m x n with n > m, then by premultiplying both sides of the equation by the P matrix transpose [p]T as shown in Equation F.3, the pTp matrix is a square matrix with m x m dimensions.

EP] T [P]{c} = [p]T {p) (Eq. F. 3) Thus, the equation can not be solved explicitly for a coefficient vector.

--1 {c} = [prp] [p]r {p} (Eq. F.4) [pTp] -i [piT is the pseudo-inverse matrix of P. Equation F.4 yields a set of numbers {c} which represent the least-square fit for the set {p}.

An expression of a set of equations such as Equation F.I in the matrix form of Equation F.2 provides Equation F.5.

m a 1 ql ql Pl 6HT I HT I i q2 q2 b P2 6HT 2 HT 2 C _- (Eq. F.5)

d

2 2 e i qn qn 6HT 6HT PH n n By using the values of required gains that have been computed (e.g., K_ of Table 4) for the column-matrix elements (pl_ p2..Tp n) and the corresponding 6HT and q values of Table 5, the values of _ne polynom_ml coefficients (a, b, ... e) can be computed. The results of the computation are given in Table 6.

APPENDIX G SecondaryGain Scheduling Secondary gain scheduling is used to compensatefor: • Pitch-up at high-Mach/high-g flight conditions • Outboard aileron symmetric effects when the AACSis activated The pitch-up phenomena is caused by stalling of the wing tips at high-Mach/ high-g flight conditions. Thus, the lift aerodynamic center is shifted forward relative to a fixed c.g. location and the static stability margin is reduced.

The AACSoperates the outboard ailerons in a symmetric modein response to normal acceleration of the aircraft c.g. and wing tips. For high speed flight conditions (flaps-up), the outboard ailerons are up biased approxi- mately 2 degrees and for the low speed flight conditions (flaps-down) the ailerons are up biased approximately I0 degrees. The response of the ailerons to normal acceleration provides a pitching momentthat is equivalent to reducing the static stability margin by about 5 percent.

The reduced static stability due to pitch up and active AACS are similar to reducing the stability margin by moving the e.g. _ft= Therefore, the scheduled feed-forward and feedback primary gain schedules (such as Figures 15 and 14) can be used to provide the required pitch control for pitch-up and AACS operation conditions by modifying the value of _HTby an increment A_HT.

This modified value has been designated * _HT" A block diagram of the secondary gain controller is given in Figure 84.

Inputs to the controller are: • Angle of attack (_) • Bank angle (_) • Machnumber • AACS/Flapconditions The equation for _HT can be written from the diagram to be (Eq. G.i) _HT = _HT+ Km + C_6HT (i - cos _) + _AACS This is the _HT value shown for secondary gain scheduling in Figure 16.

ORIGINAL PAGE I_1 O_ POOR QUALITY "1= _.

-I- 3i ._ ..% ,,=, u. _..._ I-H r--t .I-J

_L_._

v C.3 C3 ee.

Z "0 C_ Z C.D .< I

T

el)

l"

T

APPENDIX H Pitch Attitude Loop Synchronizer Circuit The pitch synchronizer has two modes of operation: fixed or controlled.

These operational modes are shown in Figure 85. The fixed mode provides a reference attitude (OR) equal to the aircraft trim attitude (@T). Thus, if a control column force changes the attitude of the aircraft, the sensed attitude (0S) will be compared with OR to provide an error signal (OE). Thus, when the control force is reduced to zero the aircraft attitude will return to 0 T.

The controlled mode causes the reference attitude signal to track the sensed attitude signal during a maneuver. Then, at the instant when the control column force is reduced to zero, the reference attitude is set equal to the aircraft controlled attitude (0C). Any sensed attitude changes will result in an error signal which will cause the aircraft to return to the controlled attitude.

Figure 86 represents a schematic diagram of the pitch synchronizer circuit. Symbols used in the figure are defined as follows.

C - Pilot optional control switch state (0 or i) F - Applied column force switch state (0 or I) K C - Controlled reference integrator gain K T - Trim reference integrator gain S I - Trim switch S 2 - Pilot-optional-control switch S 3 - Controlled reference tracking switch S 4 - Integrator-closed-feedback switch S 5 - Trim reference tracking switch T - Horizontal stabilizer trim button switch state (0 or i) The circuit logic operation is determined by Boolean Algebra methods.

The switches in the circuit are controlled by one or more of the following three inputs.

• Pilot optional control _ C • Trim setting _ T • Column force _ F ORIGINAL PAGE IS OF POOR QUALITY / ATTITUDE f SIGNAL

/

/ TIME _ SEC a. FIXEDMODE ee_.o ATTITUDE SIGNAL CONTROLCOLUMNFORCE REDUCED TO ZERO TIME "_ SEC b. CONTROLLED MODE Figure 85. - PACS pitch synchronizer operation modes.

ORIGINAL PAGE tS OF POOR QUALITY ; 0 s s2 I' .,

I

(_) + _ l'-eC KC 0c _T - +

/ -/ I,-, .^ I

| - +

$5 -IF---_-_C SI - T Figure 86. - PACS pitch attitude loop synchronizer circuit.

Each input has two conditions (on or off). Thus, logic theory requires that a system with three inputs which are controlled by two conditions have 8 dif- ferent input states (2 ° ) as shown in Table 16. A 1 in the table indicates the signal is applied and a 0 indicates that a signal is not applied.

The switches in Figure 86 are norma]ly open (O) or closed in the direction of the arrow (C) as determined by the Boolean Algebra equations shown for each switch. The Boolean terminology used is: x = signal is applied = signal is not applied x + y = signal x or signal y is applied x + y = neither signal x nor signal y is applied xy = signal x and signal y are applied xy = signal x is applied and signal y is not applied _y = signal x is not applied and signal y is applied.

oR=G|NAL pAGE. IS OF pOOR QUALITY, The last two columns of Table 17 show that for circuit conditions I and 2 the reference attitude is equal to the trim attitude, for circuit condition 3 the reference attitude is equal to the controlled attitude, and for the other conditions the reference attitude is tracking the sensed attitude signal.

TABLE 17. - PACS PITCH SYNCHRONIZER INPUT STATES CIRCUIT CONDITION NUMBER F T .C TABLE 18. - PACS PITCH SYNCHRONIZER SWITCH POSITIONS AND ATTITUDE REFERENCE PITCH ATTITUDE CIRCUIT CONTROL CONDITION REF. (0 R) CONDITION NUMBER S1 S 2 S 3 S 4 S5 1 0 0 0 O 0 HOLD 6 T 2 0 0 C C 0 3 0 C 0 0 C e C 4 C 0 C C 0 5 C C C 0 0 TRACKING 6 0 C C 0 0 8 S 7 C 0 C C 0 8 C C C 0 0 REFERENCES lo Guinn, W.A., "Development.and Flight Evaluation of an Augmented Stability Active Controls Concept," NASA CR 165951, September I, 1982.

o Urie, D.M., "Accelerated Development and Flight Evaluation of Active Controls Concepts for Subsonic Transport Aircraft - Volume II - Aft C.G.

Simulation and Analysis," NASA CR 159098, September 1979.

o Rising, J.J., "Development of a Reduced Area Horizontal Tail for a Wide Body Jet Aircraft," NASA CR-172278, February i, 1984.

, Moore, B.C., "On the Flexibility Offered by State Feedback in Multivariable Systems Beyond Closed Loop Eigenvalue Assignment," IEEE Transactions on Automatic Control, October 1976, pp. 689-692.

Srinathkumar, S."Eigenvalue/Eigenvector Assignment Using Output Feedback," 5.

IEEE Transactions on Automatic Control, Vol. AC-23, No. I, February 1978, pp. 79-81.

6. Harvey, C.A. and Stein G., "Quadratic Weights for Asymptotic Regulator Propertles_r IEEE Transactions on Automatic Control, Vol. AC-23, No. 3, June 1978, pp. 378-387.

1. Report No. 2. G_nmemAccession No.

3. Recipient's Catalog No.

NASA CR-172277 4. Title and Su_itle 5. Report Date Development of an Advanced Pitch Active February i_ 1984.

6. Performing Organization Code Control System for a Wide Body Jet Aircraft 7. Author(s) 8. Performing Organization Report No.

LR 30644 Wiley A. Guinn, Jerry J. Rising, and Walt J. Davis 10. Work Unit No.

9. _rforming Organization Name and Address Lockheed California Company 11. Contract or Grant N'o.

Burbank, California 91520 NA51-15326 13. Type of Report and Period Covered 12. Sponsoring Agancy Nameand Address Contractor Report National Aeronautics 14. Sponsoring Agency Code and Space Administration Washington_ DC 20546 15. _pplementary Notes Langley technical monitor: Dennis W. Bartlett, Final Report 16. Abstract An advanced PACS control law was developed for a commercial wide-body transport (Lockheed L-iOll) by using modern control theory. Validity of the control law was demonstrated by piloted flight simulation tests on the NASA Langley visual motion simulator. The PACS design objective was to develop a PACS that would provide good flying qualities to negative i0 percent static stability margins that were equivalent to those of the baseline aircraft at a 15 percent static stability margin which is normal for the L-lOll. Also, the PACS was to compensate for high-Mach/ high-g instabilities that degrade flying qualities during upset recoveries and maneuvers. The piloted flight simulation tests showed that the PACS met the design objectives. The simulation demonstrated good flying qualities to negative 20 per- cent static stability margins for hold, cruise and high-speed flight conditions.

Analysis and wind tunnel tests performed on other Lockheed programs indicate that the PACS could be used on an advanced transport configuration to provide a 4 percent fuel savings which results from reduced trim drag by flying at negative static stability margins.

., 17. Key Words (Suggested by Author(s)) 18. Disfribution Statement Active Control System, Control System, Pitch Control, Longitudinal Control, Aircraft Fuel Savings 22. Price" 19. Security Oa=if.(ofthis_port) 20. Security Classif. (of this page) 21. No. of Pages Unclassified 172 Unclassified