Control logic for landing-abort autopilot mode

,

•

CONTROL LOGIC FOR LANDING-ABORT AUTOPILOT MODE

BY

BERNARD ETKIN AND SHANGXIANG ZHU

February, 1982

TECHNISCHE HOGESCHOOL OElFT LUCHTVAART- EN RUIMTEVAARTTECHNIEK

BIBLIOTHEEK

Kluyverweg 1 - DELFT

983

'"

6 JAN. 1

UTIAS Report No. 258

CN ISSN 0082-5255

CONTROL LOGIC FOR LANDING-ABORT AUTOPILOT MODE

BY

BERNARD ETKIN AND SHANGXIANG ZHU

SUBMITTED OCTOBER, 1981

UTIAS REPORT NO. 258

CN ISSN 0082-5255

Acknowledgement

This work was financially supported by the National Science and Engineering Research Council of Canada through Grant No. A0339.

Abstract

This report describes the results of an investigation of an automatic control for an aborted landing.

Emphasis was on the use of a body-mounted accelerometer, which is assumed to be both available and reliable, to provide a surrogate for an angle-of-attack signal. The control logic was developed for a typical large commercial jet transport and tested by simulation on a digital computer.

The objectives were to achieve a safe aborted landing and climb-out, such as might be required as a result of missing the landing window at Cat. 11 decision height, in the presence of severe wind shear.

The automatic control system developed here in met the objectives, and the performance demonstrated showed the logic to be effective and safe for initiating a go-around maneuver.

I. 11. III. IV. V. Contents Acknow1edgement Abstract

Notation and Reference Frames INTRODUCTION

SYSTEM MODEL

2.1 Aircraft Dynamic Model 2.2 Aircraft with Autopilot CONTROL LOGIC

3.1 Consideration of the Control Logic for Landing-Abort Autopilot

3.2 The Control Law

3.3 Determination of the Gain Set SYSTEM PERFORMANCE i i iii v 1 1 1 6 9 9 11 12 12

4.1 Response to Wind Shear 13

4.2 Engine-Fai1ure Test and Sensitivity to Engine Time Constant 14

4.3 Effect of Configuration on Performance 15

4.4 Response to Initia1 Condition Errors and Discussion of

Category 11 Wind ow 15

SUMMARY AND CONCLUSIONS REFERENCES

TABLES FIGURES

APPENDIX I: PHYSICAL AND AERODYNAMIC CHARACTERISTICS OF THE AIRCRAFT USED IN THIS STUDY

APPENDIX 11: THE LOAD-FACTOR SIMULATION

APPENDIX 111: DEFINITION OF THE PERFORMANCE MEASURE INDEX

17

~, _{~l' ~2} B f F FRL g 'w

K

liK

h h hd lIh min I (lB' iB' ~B) (ls' is' ~s) J

~l

' K'J - L . K E K -g Kd K-d K· d K n ~ KU K· U K-U

Notation and Reference Frames

system matrices control matrix

parameter, command signal intensity external force applied to the aircraft fuselage reference line

acceleration due to gravity gravity vector

wind matrix

height above ground

aircraft angular momentum about mass centre decision height

height loss fr om initiation of abort to minimum height above ground

identity matrix unit vectors along x

B YB zB

unit vectors along _{Xs yS Zs} pay-off function

feedback gain matrices

elevator-actuator time constant diag {KTK

E}, time constant matrix

glide path deviation proportional feedback ga in glide path deviation integral feedback gain glide path deviation rate feedback gain load factor proportional feedback gain airspeed proportional feedback gain airspeed rate feedback gain

Ke K'

_e

KT ~BS ~SE L th Ón z Ón zc n qe Q. -1 Reu SCt) SK tI' t₂, t₃ Tt Cu

~

~U V V _s W

~

W e c v w) E wE) v

pitch angle proportional feedback ga in pitch angle rate feedback gain

throttle actuator time constant rotation matrix from F

S to FB rotation matrix from FE to F

S

perpendicular distance fr om CG to thrust line normal load factor perturbation

normal load factor command load factor Cn = L/W) dynamic pressure Cl PV e 2 ) weighting matrix ratio of Ke to Ku switching function

gain set, SK = _{{CLc/CLmax ' Kn' Ku' Kû' Ke' Kë}} switch times Csee Fig. 8)

engine time constant components of ~ in F

B

components of VE in F

B

airspeed command signal

velocity vector of vehicle MC relative to local air mass Cairspeed vector)

reference equilibrium value of airspeed velocity vector of vehicle MC relative to FE

AE E nondimensional ground speed,V = V

IV

_e stalling speed

wind speed with respect to FE

mean value of ~, velocity of frame FA reference equilibrium wind speed

(W l W2 W3) A W (XE YE zE) (X y Z) 6x X a A 6~ 6~ af Y YG f l f3 ET ME MT M -c oE

o

(6h . ) ml.n 0-(w w W ) x x z ( .) c (

.

) e (

.

) f l(t-T) '

..

wind speed components in FE

A

nondimensional wind speed, W W;V

e

spatial coordinates in FE

components of aerodynamic force in F S matrix of state variables

distance of accelerometer away from CG desired augmented state vector

state vector error from desired state vector, (6! - 6~) angle of attack of FRL

the angle ~ makes with the horizontal

glide slope angle with respect to the horizontal shear of horizontal wind

shear of vertical wind

angle between thrust line and FRL elevator deflection

throttle setting measured as a fraction of full throttle cornmand signal matrix

elevator angle 6h. dispersion

ml.n

performance measure index

angular velocity of aircraft relative to FE cornmanded value

reference equilibrium, landing state final state

positive unit step at time T

Reference Frames Earth-fixed frame - OX

E points in direct ion of mean wind

FA: (x

A, YA' zA) frame convected with the mean wind at velocity !A F

B: (xB, YB' zB) vehicle-fixed frame F

S: (xS' YS' zS) stability reference frame (vehicle-fixed)

Notation for aerodynamic coefficients and derivatives is standard, as for example in Ref. 2.

'"

I. INTRODUCTION

Landing of commercial airplanes remains the most dangerous element of air travel. As such, all aspects of landing are under continuing study by investigators in universities, aircraft manufacturers, and government agencies. Poor visibility and wind are the twin hazards that beset landings, and are responsible for most of the bad accidents. The wind characteristic th at has been identified as most troublesome is severe shear - the vertical gradient of either horizontal or vertical air motion that can exist in severe storms - particularly when downbursts are present. When a landing in progress reaches a point where the pilot (human or automatic) determines that safe completion to touchdown is not assured, as for example when the landing window is missed at CAT 11 decision height, then an abort must be initiated. If there is severe wind shear, as is not at all unlikely since shear might be the reason for missing the window in the first place, then the subsequent optimal control of the vehicle is not a simple matter, and indeed one can only expect rather imperfect performance from a human pilot. There are too many variables to monitor, everything is happening too fast, and the control actions needed are unusual. For such a maneuver it is not obvious how to construct a useful quantitative criterion for optimality, since any maneuver that misses the ground and achieves a safe climb-out is a success. In the following we have taken the position that there are two main regimes in this maneuver. During the first it is imperative to check the descent at the maximum safe rate to avoid ground contact. Af ter

bottoming out, it is then necessary to control speed and pitch attitude

50 as to achieve a normal climb. We have therefore constructed a control

logic that contains switching functions to implement these two stages. The entire maneuver is supposed to be initiated at CAT 11 decision height.

The system as developed for a 8-747 class airplane was tested in a variety of wind-shear conditions, including the shear that caused a crash of a DC-9 airplane at Philadelphia in 1976. It was successful in all cases.

A significant issue in our view is th at of the landing window (Ref. 11). We have examined the effect of wind shear and of errors in descent rate on the ability of the airplane to abort safely, and find that the "abort window" we have inq:'oduced might intersect the "landing window" in some cases. Wh en this happens the landing window must be reduced correspondingly.

11. SYSTEM MODEL

2.1 Aircraft Dynamic Model

To carry out the required analysis, it is necessary to formuiate an appropriate set of equations of mot ion for the aircraft flying in the presence of wind shear. The aircraft used for this investigation is a large jet transport, with characteristics summarized in Appendix I. This data is primarily taken from Ref. 1, but some that was not otherwise avail-able is 'based on our own estimates.

The equations of mot ion tions, as derived in Ref. 2. axis form of Fig. 5.7 of th at accommodate the wind shear.

th at were employed are the usual linear equa-They are used here in essentially in the body-reference with some modifications required to

Reference Equilibrium

The exact equations can be written as

m(~ +

!)

=

F (2.1)

h

₌

M (2.2)

VE

₌

V + W (2.3)

The maneuver to be studied is one in which the changes of state are not

so large as to invalidate a linear analysis, 50 we have adopted that

approach herein. 1t is important when dealing with transients as small perturbations to choose an appropriate reference state from which to define the perturbations so that they remain small. To that end we have chosen a reference state as follows:

(i) the reference flight condition corresponds to equilibrium at a

const~nt _{airspeed Ve in the presence of a constant horizontal}

wind;

(ii) the reference flight path is the glide slope, i.e., it is

recti-linear at an angle YG below the horizon (see Fig. 1) . (For the

present investigation this angle was chosen to be 3°,

representa-tive of current commercial aviation.);

(iii) the reference horizontal wind is represented by a mean wind that occurs at some point along the approach; in this study the wind at decision height was selected as the reference wind;

(iv) the stability-axis frame was chosen as the reference frame for the equations of motion.

As a consequence of the above, the kinematics of the reference equi-librium state is characterized by

Pe

=

0 (2.4) qe

=

0 (2.5) r 0 _(2.6) e u .- _{V (2.7)} e e v

₌

0 _(2.8) e w

₌

0 _(2.9) e J

,. .

From the reference equilibrium geometry, as seen in Fig. 2, it may be shown that V E =

~(V cosy cos1jJ

+ W 1e)2 + (V cosy sin1jJ + W2e)2 e e e e e e e V E . ee sin

[

e sln_YG

1

=

Y_e

=

-arc V e <Pe

=

0

[

-w

_J

1jJe

=

arc sin _{(cosy V )} 2e e e XE

=

(V cosy cos1jJ +

w

1 )t + xE e e e e e 0 ZE = -V siny t e e e YE _e

=

0 + (V siny )2 e e (2.10) (2.11) (2.14) (2.15) (2.16) (2.17) (2.18)

A1so, the reference equilibrium is dynamica11y characterized by

x

=

mg sine e e (2.19) y

₌

₀ e (2.20) Z _e

₌

-mg cose e (2.21) L

₌

e 0 (2.22) M

₌

e 0 (2.23) N

₌

0 (2.24) e

Equations (2.19), (2.21) and (2.23) can be expanded and put into nondimen-siona1 form as fo11ows:

CT cos (af + ET) - CD - _{Cw sine}

₌

0 (2.25)

e e e e e

CT sin (af + ET) + _{CL - Cw cose}

=

0 (2.26)

e e e e e

LC

=

0 (2.27)

m

Here the subscript 'el denotes a value at the reference equilibrium state, af is the angle of Xs with respect to the FRL, ~ is the angle that the thrust line makes with respect to the FRL, CT is the total thrust coeffic-cient, CD is the drag coefficoeffic-cient, CWe is the weight coefficient and LCm is the sum of the aerodynamic and thrust pitching moments about the CG. (p, q, r) are the angular velocities of the aircraft with respect to FE written as components in FS. (u, v, w). are the airspeed components of the aircraft written as cQmponents in FS. (~, e, ~) are the Euler angles and

(xE~ YE' zE) are the inertial position coordinates, with the altitude (2.28)

Longitudinal Equations of Motion

Perturbations in the aircraft's state vector away from the reference equilibrium are treated as arising from initial conditions, wind shear effects, turbulence and control inputs. Because the equations are linear, the response to a combination of the above effects can be found by computing the response to each in isolation and then summing the results.

The longitudinal perturbation equations are obtained in the usual way (e.g. Refs. 2-6). Af ter linearization about the reference equilibrium described above and with ee « 1, the perturbation equations referred to the body-fixed stability axes FS are as follows:

~lt-.~

=

~-l'! + B t-.o + -1 -T-t-.g + - 1 . -T t-.g + P (2.29) where t-.XT

₌

(tm t-.w t-.q

t:.e

t:.x_E t-.h) (2.30) MT _{(t-.0T ME)} (2.31)

t:.K

T

=

(t-.W_I t:.W 3) (2.32) pT

₌

_{(PI P2 P3 0 0 0) (2.33)}

where PIP2P3 are perturbation forces and moments other than those due to wind shear and control action. These are included to permit configuration

changes to take place during the maneuver, e.g. retracting

u/e

or changing

flap angles. m 0 0 0 0 0 0 m-Z. _w 0 0 0 0 0 -M. I 0 0 0 ~1 = w y 0 0 0 1 0 0 (2.34)

l

0 0 0 0 0 0 0 0 0 1 0 1 X _u X _w 0 -mg 0 0 Z _u Z _w MV +Z -mg8 0 0 e q e M M M 0 0 0 ~2 = u w q 0 0 1 0 0 0 (2.35) 1 8 _e 0

-v

8 0 0 e e 8 _e -1 0

-v

0 0 e XOT XO E ZOT ZOE B = MOT MOE _(2.36) 0 0 0 0 0 0 0 0 0 0 0 0 Tl = 0 0 (2.37) 1 0 0 -1

-m mB e -mB _e -m 0 0

1:.

2 = (2.38) 0 0 0 0 0 0

Here 60 are control inputs (elevator

oE

and throttle

oT

respectively) and 6g are-wind shear and/or turbulence inputs. In the present case, ~l, ~2 B, Tl, T2 are constant matrices. Since only the response to wind shear is sought,-WI and W3 are taken to represent the x and z components of the

local wind in FE'

Once the initial state, wind condltl0ns ana control inputs are given, the equation (2.29) can then be solved for the state vector 6x.

2.2 Aircraft with Autopilot

A general feedback system suitable for this investigation can be described as follows.

If the actuator time lags are taken into account using a first order lag model for the engine and elevator, the controller equations are given by Mi = K 60 - KM -g -c -g - (2.39) where A A M = _{!l~ +}

!i.

-c (2.40)

Kl and !2 are gain matrices

E: = _{6y - 6x.}

:-..c (2.41)

6x.T = (6!T KT) _(2.42a)

6 T _{= (6X}T _.Q)

Y..c -c (2.42b)

The g element in (2.42a) is present because in this investigation, we

intro-duce -the load factor as a controlled variabIe . 6nZB relates to the aircraft ~' state variables and wind vector through the expression (see Appendix 11)

I

[dW

dW3 . ]

We rewrite (2.43) as

where

Thus (2.44) can be expressed as

1 h = -1 g x h 2 a = g V E h3

- -

e _g

.

.

6n zB = ~16~ + ~26K where (2.44) (2.45) (2.46) (2.4 7) (2.48) (2.49) (2.50) In order to include 6nzB as a controlled variabIe, we construct the control command as

where

Thus the gain matrices in

H3 = K H 2 - -n-KT = [0 K ] -n n (2.40) are "-!1 = [!1

Q]

!2 = [!3 ~3]

Combining (2.51), (2.40) and (2.39) yields

or -K K₁6x - K 60 - K H 36g + K K16X + K K36X -g- - -g - -g- - -g- -c -g- ~ (2.51) (2.54)

Now we construct a set of augmented matrix equations by combining (2.54) and (2.29) as follows:

[

~I

:]

_[:~l

[

~2

_{-~] [:~]}

+

[!I]

6.8.

[ !2]

6i = -K K + K K -K H -g-3 -g-l -g-3 +

[~~J [~~l

+

[~~J [~~l

₊

r~]

lQ

(2.55)

In order to accommodate switching functions in command and feedback signaIs, we need to modify the associated elements in (2.55). By defining

f l = -!g!l~(t) (2.56) F = -2 !g!3~(t) (2.57) f3 = _-g-K Set) (2.58) H = -K H -g-3 (2.59) (2.55) becomes (2.60) where (2.61)

~(t) is an NxN diagonal signal switching function matrix, i.e.

Set) = diag{S. (t)}

- 1 (i = 1,2, ... N) (2.62)

Si(t) is a switching function corresponding to the feedback signal to be controlled or to the command signal . . It may be a switch-on function, such as

Sn (t) = 1 (t-T) (2.62)

The system of equations derived above does not include the load-factor explicitly in the state vector 6X. This is appropriate when deriving the system matrices, as in (2.60), for the purpose of calculating eigenvalues and eigenvectors. However for calculating time-histories, we have used a slightly different structure of the equations, in which the load-factor appears explicitly.

I I I .

3 . 1

CONTROL LOGIC

Consideration of the Control Logic for Landing-Abort Autopilot

Figures 5 and 6 show the initial (A) and final (B) equilibrium states thatare presumed to bound the landing-abort maneuver for our example airplane.

(A) represents descent on a 30

glide slope at airspeed Ve , and (B) a climb at 150 and speed Vf. Te and Tf are the thrust curves corresponding to the

landing and climbing throttle positions. It is assumed that at initiation of the abort at t = 0, the throttle is suddenly opened, and th at the engines begin to speed up to generate the thrust Tf. A first-order lag is assumed for thrust build-up. The single drag curve implies that there is no change of configuration during the maneuver.

The requirements for control of the transient that takes the vehicle fr om (A) to (B) can be stated quite simply - (1) minimize the height loss following the decision to abort; (2) keep the angle of attack below the stall-ing angle; and (3) effect a smooth transition to the climb-out state. These requirements are to be met in the presence of strong wind shear and turbulence.

The first requirement calls for maximizing the lift, or normal accel-eration, to generate the shortest possible pull-up. Now for a large jet transport the minimim altitude is reached a few seconds af ter initiation of the maneuver. During this short time, the speed cannot change very much, so the first requirement comes down essentially to maximizing a within the con-straint of (2). This portion of the maneuver would be most effectively con-trolled, therefore, by simply commanding a value of a safely below the stall, and holding it whatever the airspeed, even if the latter should drop below the stall speed. (It is a, not V, that controls the stall in a transient dynamic state.)

Following the pull-up - more precisely af ter the point of minimum height has been passed - attention must be redirected to requirement (3), and from this point on, pitch attitude, speed, and angle of climb are all variables of interest, to be controlled so as to lead to a smooth transition to climb-out while meeting requirement (2).

The above outlines the logic we have pursued in developing the control. We have however considered the question of how the information on a could be obtained. The most direct method of course would be to use an a sensor, which would have to give reliable performance in the landing configuration (flaps and U/C extended). This may be difficult to accomplish in practise. An alternative we have thought to be attractive is to infer a fr om a combination of normal acceleration and airspeed. Since the speed changes but little during the critical first few seconds, this amounts essentially to knowing the normal (or z-axis) acceleration, a quantity that may be preferabIe to a

as a primary source. Thus the command can be stated in terms of a safe normal acceleration instead of a safe angle of attack. Actually, there is no need to assume the speed to be constant, since its variation can readily be allowed for. This might weIl be mandatory for airplanes of lower wing loading than the large jet transport considered herein.

Figure 7 shows the assumed lift curve of the airplane, with key values of CL and a noted: _{CLe is the lift coefficient in the reference equilibrium} (landing) state, corresponding to (A) on Fig. 5, and CLf is the final value corresponding to (B). _{The lift margin (CLmax - CLe) limits the load factor}

th at can be generated in the initial stage of the pull-up. We assume th at a constant lift coefficient CLc is commanded, chosen with some margin below CLmax, say 80 - 90% CLmax. We want to command the normal load factor ~nzc that corresponds to this CLc. Since the speed will change, albeit little fOT

the subject large airplane, so will the commanded load factor. We ignore the small difference between lift and Z force and write

1 PV2S 1 V 2S CL - _{- CLe}

2"

_{P e} ~nz = c 2 (3.1) c W But W = CL 1 V 2S

2"

P e e 50

(

CL

_J

(~

r

~nz = c - 1 (3.2)

CL

c e e We write CL c 1 + f (3.3) CL _e =

where f measures the "strength" of the pull-up. To choose f we note that the approach speed Ve is 1.3Vs . It follows th at CLmax/CLe = (1.3)2 = 1.69. Thus there is a substantial margin in lift coefficient between CLe and CLmax. Equation (3.3) can be restated as follows:

1 + f = _(3.4)

We arbitrarily choose CLc/CLmax to be 0.9 to get a nominal value of f, i.e., f

=

0.521. The sensitivity of the pull-up to f is explored in the examples that follow. Equation (3.2) can now be rewritten as

~nzc

= (1 + f) (V e :

~V

J

2 - 1

e

'"

On linearizing for small lIV, this becomes

'"

lm z = f + 2l1V(l + f)

c (3.6)

The actual lIn_{Z '} which is compares with lInzc to generate an error signal, is presumed to come from a z-axis accelerometer, as detailed in Appendix 11.

Although (3.6) shows that the commanded load factor should vary with speed if the commanded lift coefficient and angle of attack are to be con-stant, the digital simulations we have carried out show that, for a large jet transport at any rate, lInzc

= constant

= f provides a satisfactory

con-trol law. This represents a desirabie simplification in the realization of the system.

Although the successful outcome of the transient is dominated by the height 1055 af ter initiation, lIh, nevertheless we have considered th at some

weight in judging the success of the maneuver should be given to the manner in which the aircraft approaches the climb-out af ter reaching its minimum height. To this end a quadratic performance index cr has been constructed that includes the air speed at two points along the path as weIl as the height 1055. Both lIh and cr are considered as performance measures (see Appendix lIl).

3.2 The Control Law

Based on the preceding analysis and some preliminary trial computation, it was found that the control system shown in Fig. 9 would yield satisfactory results. The control law for the throttle is of course simple - open the throttle fully at t = O. The control law for the elevator is, following

(2.51)

which we can write conveniently in terms of measured variables in view of

(2.44) as

= K [S (t)lIn~ - lIn ] + S (t)[K (llu

n n c z u u c - lIu) - K·lI~] u

(3.7)

The commanded va lues of lIec and lIuc are 14° and 0 mis respectively. The switching functions included in the elevator control are crucial to its correct operation (see Fig. 8). At the beginning, the maneuver is dominated by the requirement to pull-up as rapidly as possible. Thus the only command at first is lInzc, 50 Sn(t) switches on at t

=

0 while the lIe and lIU switches

remain open. Later, when the minimum height has been achieved at t = tI both

e

and U commands are activated by closing Su and Se. Thus

At time t = t3, when the climb-out pitch attitude has been reached, the load factor command is switched off (but the 6n z feedback is kept on), 50

S _n let) 1(t

3 - t) (3.9)

The values of the speed and pitch angle commanded are those corresponding to the climb state (B) of Fig. S. The abort mode would be switched off and climb mode selected by the human pilot sometime af ter t3'

3.3 Determination of the Gain Set We de fine the gain set to be

Figure 10 shows the effects of CLc/CLmax and Kn on performance. As CLc/CLmaxand Kn increase, the aircraft pulls up more rapidly, as evidenced by the monotonically decreasing height 1055 6h. This figure also shows that the performance measure cr, that includes speed errors at times t2 and t3, leads to a choice of larger values of Kn and CLc/CLmax than would be selected on the basis of height 1055 alone. This choice in the final analysis must be made arbitrarily by the designer. We found that still larger values of Kn

(the load factor feedback gain) led to violent oscillations of OE and n z with a very short period.

Investigation showed that results for 6h and cr are not very sensitive to Ke, but that there is a critical value of Ku that should not be exceeded if stalling is to be avoided. Figures 11 and 12 show that the time histories of speed and angle of attack when flying in severe wind shear are in fact sensitive to the ratio Reu = Ke/Ku, and that a value greater than 50 is indicated for the exa~ple airplane. The effect of Keu in still air is shown in Fig. 13. No tendency to stall is evident for Reu as low as 50, but the airspeed time history shows that a large value of Reu (200) corresponding to a small Ku leads to larger oscillation of the speed. The rate terms Kë and Kü were also investigated with the results shown on Figs. 14, 15 and Table 1. Kü is not sufficiently helpful to merit its inclusion, but Kë helps suppress pitch oscillation, and is retained, with the value K'

=

-2.5. Finally, we have examined the effect of the fore-and-aft location of

t~e

accelerometer on the p'erformance. When not at the CG, Xa

F

0, there is a signal proportional to

q

=

ë

generated by.the accelerometer. (More generally, the accelerometer will also respond to p if it is not in the y = 0 plane of the airplane.) This signal can be beneficial for the short period mode, as shown on Figs. 16, 17 and Table 2, in reducing cr without much effect on 6h.

IV. SYSTEM PERFORMANCE

functions given by (3.8) and (3.9). Figure~18 and Table 3 s~ow ~he.s~a~e­ vector time history for this case. The nom1nal aborted land1ng 15 1n1t1ated _(t

= _{0) at a height of 30m, tI = 1.75 sec, t2 =}

3.35 sec, t3 = _{3.60 sec and}

the height 1055 is only 6h = 5.22m. _{The air speed increases rapidly fr om the} approach speed af ter t

=

_{0, maintaining a satisfactory margin for coping with}

wind shear, and both 8 _{and u approach their climb-out values in areasonabIe}

manner. _{The angle of attack remains below the stall angle by a comfortable} margin throughout the maneuver. In short, the system works very weIl in the absence of initial state errors and in the absence of wind.

The time constant assumed for thrust build-up, Tt = 4 sec, is realistic

but conservative for a large airplane. Maximum up-elevator of 25° is required about 1/2 sec aft er initiation. The commanded 6nz of about 1/2 (acceleration 1/2 g) is reasonably weIl followed.

4.1 _{Response to Wind Shear}

Various wind-shear models of the same genera 1 structure (see Fig. 19) were used. _{All these models have a linear or piecewise linear variation of}

horizontal wind velocity and vertical wind velocity with altitude. Both head-to-tail and tail-to-head wind shears with the initial wind velocity being 2/3 of the total wind-velocity change were modeled. The test cases are shown in Table 4. _{The wind shears were introduced at decision height to} represent a more critical situation. Ground effects were neglected and no crosswind components were considered.

(i) Head-to-Tail Wind Shear

Figure 20 shows the performance measures 6h and cr _{for different wind} shears. The height 1055 remains under lOm for all cases and is insensitive to rl, and the cr values are similar to those for zero shear. The initial mot ion of the aircraft in the head-to-tail wind shear encounter is character-ized by an increase in airspeed and angle of attack. The aircraft climbs out with relatively high climb rate, which leads to a steep flight path as shown _{in Fig. 21.}

(ii) Tail-to-Head Wind Shear

Figure 20 (right) shows the response of the aircraft to tail-to-head wind shear. _{In this case, as the aircraft penetrates the shear the airspeed} initially increases, because the vehicle cannot slow down as rapidly as the wind changes. _{The effect of tail-to-head shear on 6h}

min is consistent with head-to-tail shear in that ahmin/arl is of the same sign.

(iii) Shear of Vertical Wind

Figures 22 and 23 give the results for landing through a downburst. The height 1055 and cr values are much larger than for shear of the horizontal wind, and increase more sharply with r3. Nevertheless, the automatic control produces successful aborted landings for 30m decision height for the most severe case considered, a vertical wind of 6 mis at 30m with a shear of .2 m/s/m. _{The detailed calculations showed that 60max during the pull-up} increases with r3.

Clearly, the presence of a down dra ft generates the critical case for executing a safe aborted landing. The "worst case" would include a combina-tion of downdraft, horizontal wind shear, and initial error.

High Severity Wind Shear

The reconstruction of the wind profile from a real accident was used to test the control system (see Fig. 24 and Ref. 7). The aircraft commenced an ILS landing under the guidance of an automatic landing system. The control law for the approach phase is

(4.1 )

(4.2)

(see Fig. 25). Figure 26 shows that, initially, the aircraft was trimmed in the headwind of -20.3 mis. The trim airspeed was 73.06 mis and the ground

speed was then 52.81 mis. Glide slope and airspeed errors were moderate as the aircraft descended, and the height error was not significant. The maximum airspeed error was less than 2 mis. The glide path tracking was good until

the aircraft neared the decision height. At this point, since the weather at the airport surface had deteriorated and was not suitable for landing, an aborted landing was called for, and the automatic abort was activated. The subsequent minimum ground clearance was 27m, and af ter 3 seconds the aircraft returned to its decision height successfully and climbed out at a rate of

6 mis. Figure 26 shows that the abort maneuver is a violent one. The elevator

was deflected to its limits 5 times - twice down and 3 times up; and the load factor reached positive peaks of about 0.9 twice, 0.7 once, and a negative 0.5 once. Toward the end of the pull-up the angle of climb rose to about 300

!

But the angle of attack remained safely below as throughout, and the airspeed did not fall below the approach value of 1.3 Vs. Following the period dis-played on the figure, there is a relatively smooth approach to a 15° climb-out. The maneuver should certainly be considered a successful one.

4.2 Engine-Failure Test and Sensitivity to Engine Time Constant Figure 27 and Table 5 show the performance with failure of one or two engines during a pull-up in calm air. The effects of engine time constant are presented in Figure 28 and Table 6. It is clear that the failure of one engine had little effect on height loss. Comparing with the nomina 1 state vector there was only 0.15m difference of 6hmin. However, the final trimmed climb angle was reduced to 7° (4.5° difference compared to the nomina 1 case). With two engines out, the height loss almost does not change. The aircraft was able to sustain its airspeed but the flight path angle remained small through the pull-up. Finally, the aircraft was able to climb out at a rate of 2 ~ 3 mis. Table 6 shows that for engine time constants of 1, 4 and 8 sec, the difference of height loss is not large. But the response related to the 8 sec time constant is slow.

4.3 Effect of Configuration on Performance

Table 7 shows th at the landing gear position has insignificant effect on 6hmin (when climb rate was equal to or greater than 0, the gear was assumed gradually retracted within 3 sec), but retracting the gear increases the

equilibrium climb rate by about 2 mis and the corresponding airspeed by about

2 mis. Retraction of the flaps during pull-up might be expected to result in

a large height 10ss because of the concomitant loss of lift. However, if the flaps are retracted af ter bottoming out, the performance change occurs only during the end phase of the pull-up (see Figs. 29 and 30). In this case, the aircraft will gain a litt1e airspeed but reduce the climb rate by about 3.5

mis.

A recommended go-around procedure would therefore be to leave the flaps in the landing position, and af ter a positive climb rate has been established, to retract the landing ge ar in order to reduce the total drag. When the

climb-out phase has been achieved, th en the f1aps can be retracted.

4.4 Response to Initial Condition Errors and Discussion of Category 11 Window

Figure 31 presents the resu1ts obtained for airp1ane response to initial condition errors. By fitting the results computed, it was found th at the

initial state variabie errors and wind shears contributed to _6hmin almost independently. Empirically, we have found the following expressions:

(6h . ) d

=

6h d

ml.n (4.3)

(oh . _ml.n

)h

₌

-(-1. 7957 oh ₀ + 0.11104 oh ₀ 2) _{(for oh 0} < 0) (4.4a)

(oh . _ml.n

)h

₌

1.6783 oh - 0.08605 oh 2 _{(for oh > 0) (4.4b)}

0 0 0

(oh . ) _{ml.n u}

=

-(-0.1875 ou ₀ + 0.03125 ou ₀ 2 ) (for ou < 0) (4.5a) 0 (ohmin)u

=

0.1717 ou ₀ (for ou ₀ > 0) (4.5b) (ohmin)w

=

1.8 w₃ (4.6) 3 (oh . )

=

0.083 w 1 (4.7) ml.n w 1

where o ( )

₌

_{the dispersion from nomina 1 state,} n

₌

nomina1 state,

hd

=

dec:j.sion height,

The total dispersion of 6hmin due to initial state variabIe errors and winds can then be expressed by

oh. = oh

d + (oh . ) h· + ( oh . )

mln mln mln u + ( oh . ) mln W + ( oh . )

l mln W3

(4.8)

Investigation revealed that among the initial errors that in sink rate (I'::f uo6yo) was most important (Fig. 31) and th at airspeed was also significant. In the presence of wind, the horizontal shear can almost be neglected for predicting 6hmin, but vertical wind is very important. It is pertinent in the context of initial errors to consider the conditions that lead to an aborted landing. The current FAA definition of a successful ILS Cat. 11 approach is given in Refs. 8 and 9 in terms of maximum acceptable aircraft dispersions at an altitude of 30.5m (100 ft) above the runway. Actually, the FAA has defined a 'window' that an aircraft must be within at the 30.5m decision height. If the state vector is outside the window at that height the pilot may not descend in the absence of adequate visual references to land. Without these the pilot or autopilot must initiate a go-around at the decision height. The permissible height deviation 6d = ± 3.66m and lateral deviation, 6y = ± 2l.95m, are limits recommended by some airlines for Cat. 11 operations, while the permissible airspeed deviation, 6AS

=

2.58 mis, is an estimate by several airline pilots

as to an acceptable number for Cat. 11 operations (see Ref. 10 and Fig. 32). Other limits, such as the choice of what constitute 'excessive' attitude angle or control deflections, were not made quantitative. They were finally and fuzzily set on the basis of rough judgment. In Ref. 11 Walter and Rogers pointed out th at such a 'window' is inappropriate for some airplane/control-system combinations, and recommended a method for determining the appropriate longitudinal and lateral decision height dispersion limits for any airplane/ control-system combination. The basis of that method was to de fine the limits of acceptable touchdown conditions for aircraft of interest, and th en to

determine the decision height conditions that correspond to the touchdown limits. They proposed a definition to predict the touchdown location error with

-XTD = X(d lOO ' u lOO ' hlOO ) (4.9)

-where the subscript 100 denotes the 100 ft (30.5m) decision height. hlOO is a filtered vêlue of instantaneous sink rate. The results given in Ref. 11 showed that 11100 has a much smaller effect on the touchdown locatio~ than the other variables. Thus, the modified window suggested was based on nlOO = 0

(Fig. 33). The concept of a window is clear. If the state vector lies within i t at the decision point, a safe landing can be made. Tt is implici t that i f

the airplane misses the window a safe go-around can still be affected. But clearly this is not the case for all possible initial states outside the window. Hence one can conceive of two windows, one within the other. The smaller is the landing window (as in Fig. 34) and the larger is the abort window. The latter should be large enough to accommodate all reasonably achievable states at the decision height. A second very difficult question arises in definipg a safe window, whether landing or abort, and that is the selection of state variables to use. Additional variables such as descent rate (h), attitude angles (8, ~, ~), angular rates (p, q, r) are all possible

candidates. Each added variabIe can in principle increase the preclslon of the decision to be made, but at the expense of more complication, and hence of increased probability of system failure. If the decision is to be made by a human pilot, the fewer variables the better, and the current FAA window meets this requirement in a practical way. If an automatic system is used to make the decision, more variables can be included. Our results suggest that

h

has sufficient influence on the go-around to include it, at least for the abort window.

Figure 34 shows an abort window based on a height loss of 30.5m (100 ft) with initial descent rate as a parameter. So long as the abort window does not intersect the landing window, a missed landing can be followed by a safe abort. As can be seen from Fig. 34, the margin between the windows disappears at an initial descent rate error of 7.9 mis (without winds). For larger errors than this, safe landings could not be affected from the lower-left corner of the landing window. This descent error corresponds to a flight path angle error of 6.1°, a value large enough that it would not be expected to occur during normal airline operations, even in severe wind shear.

Figure 35 shows th at the head-to-tail wind and downdraft reduce the size of the abort window from th at of calm air. The descent-rate limitation becomes 5.5 mis which corresponds to a flight path angle error of 4.3°.

v.

SUMMARY AND CONCLUSIONS

An analytical study has been made of an automatic landing-abort control system for a large jet transport. The response of the aircraft to vertical gradients of the horizontal and vertical wind, as weIl as to a real-case thunderstorm profile, were tested. Also, the sensitivity of the system to engine time constant, engine failure, undercarriage and flap retract ion and errors in initial state variabIe at Cat. 11 decision height were examined.

The FAA Cat. 11 window has been discussed in light of the go-around requirement. Based on the results of this investigation, the following conclusions are arrived at:

(i) A successful go-around control can be achieved using normal acceleration as a primary command signal combined with airspeed and attitude control and signal switching. The attitude and airspeed commands and feedback signals to the elevator are required to improve phugoid damping and to guide the aircraft to the climb-out state.

(ii) The primary concerns in determining the gains are to choose a suitable ratio Ke/Ku, and appropriate times for switching the signals on and off.

(iii) Positive wind shear (head-to-tail) reduces the height loss, while the negative wind shear (tail-to-head) increases it; in both cases, however, the difference in height loss attributable to wind is small. Positive vertical winds (downdraft), on the other hand, increase the height loss significantly.

(iv) The aircraft is sensitive to initial state errors at decision height. In particular, an initial error in descent rate can cause significant height loss. An initial negative airspeed error can also cause a notice-able increase in height loss.

(v) Ouring pull-up, it is not necessary to retract the undercarriage and flaps for a conventional large jet transport. Nor does a moderate variation of engine time constant affect the performance very much. (vi) With one-engine failure on a 4 engine airplane the aircraft is able to

execute a successful pull-up; with two engines out, the aircraft can still execute a safe abort but the response is relatively slower and more height is lost.

(vii) The abort window contains the landing window (in zero wind) for initial errors in descent rate less than 7.9 mis. The allowable error in descent

1. Heffley, Robert K. Jewell, Wayne H. 2. Etkin, B. 3. Etkin, B. Reid, L. D. Teunissen, H. W. Hughes, P. C. 4. Etkin, B. 5. Reid, L. D. Markov, A. B. Graf, W. O. 6. McRuer, D. Ashkenas, I. Graham, Q. 7. Ellis, D. W. Keenan, M. G. 8. 9. 10. Walter, A. J. McRuer, D. T. Ilo Walter, A. J. Roger, H. H. REFERENCES

"Aircraft Handling Qualities Data", NASA CR-214t1, 1972 .

"Dynamics of Atmospheric Flight", J. Wiley

&

Sons, New York, 1972.

"A Laboratory Investigation into Flight Path Perturbations During Steep Descents of V/STOL Aircraft", AFFDL-TR-76-84.

"The Turbulent Wind and i ts Effect on Flight", University of Toronto, UTIAS Review No. 44, 1980.

"The App1ication of Techniques for Predicting STOL Aircraft Response to Wind Shear and Tur-bulence During the Landing Approach", University of Toronto, UTIAS Report No. 215, 1977.

"Aircraft Dynamics and Automatic Control" , Princeton University Press, New Jersey, 1973.

"Development of Wind Shear Models and Deter-mination of Wind Shear Hazards", Report No. FAA-RD-79-119, Washington, D.C., Jan. 1978.

"Criteria for Approval of Category 11 Landing

Weather Minima", FAAAC No. 120-20, June 1966. "Automatic Landing Systems", FM AC No. 20-57, Jan. 1968.

"Development of a Category II Approach System

Model", NASA CR 2022, Oct. 1970.

"Determination of ILS Category II Decision

Height Window Requirements", NASA-CR-2024, May 1972.

Case (Uni t) 1 2 3 Tab1e 1

Effects of K. and Ke· on Performance

u -K· _u t.h . _mln a 1 t.o. _max 1 * (rad/mis) (m) (deg) 0.1 -5.21 0.01547 12.17 0.2 -5.19 0.01534 12.00 0.4 -5.16 0.01512 11. 71 Sk = {0.9, -0.8, 0.02, Kü' -2.0, -2.5} *During interval (0, t 3) -Case K· t.h min a 1 t.o. 1 *

e

max

(Uni t) (sec) (m) (deg)

1 0 -5.13 0.01508 14.91 2 -1.5 -5.17 0.01534 13.27 3 -2.5 -5.22 0.01559 12.35 4 -3.0 -5.26 0.01588 11.96 _. -_. -- -Sk

=

{0.9, -0.8, 0.02, 0, -2.0, Kë} *During interval (0, t 3) Tab1e 2 Effects of X on Performance a -Case X t.h min a a (Unit) (m) (m) 1 -5 -5.22 0.0156 2 0 -5.13 0.0151 3 10 -5.47 0.0171

It.v

_max 1* (m/sec) 1.653 1.581 1.439

It.v

_max 1* (m/sec) 1.426 1.277 1.268 1.200

THé: 1 1'·1(' Hl STU:~'Y Uf 1 'J .J. () () • 'J (). S~) 1 . 0:) I.SC :? O:) 2.50 :J • IJ r} 3.50 4.00 4.50 ~;. 00 :).5".> 6.00 6. :,1') 7.00 7.50 ~. C:) U .5:) 9.01 9.5,) 10.0') 10.50 1 1.00 l l . j ü 12.00 12. ~.J 1 3.00 13. S') 14.00 14.<")1.1 o • :::. 4 ':J Be, - ~) I C. 1 (' 2 1 l. .. ,) J o • ;.: 0 1 JI: - ;) 1 - 0 • 1 j ,) 1 D+ :) ()

-

o.

'f :J '"j)O i" ') J - ) . ' 1':'<'4-,)+ ')1)

-

c.

':1 1\;:>1) • ').) - 0 • 1 2 ( 8D ... IJ 1 - 0.1 '-'1 2D+ UI - O.1C4.::n+Ol - 0 .1 ·:" ~OL) .. ()l - 0.1 I OJ'..i"+ Ol - 0 • 1 7 c) 3f) .. :} 1 - 0 • 1 I:'.' 'J 41 j + ~) 1 - 0 . I C 7 t0+01 -(:.,.l c..l~':>OU+ ')1 - c • 1 ( 1 a:) + ,) 1 - ü.1 Jrj-3J+ 01 - C . l ~4t:)~H' .)1 - 0 • 1 c,.j ';I/.) t ;, 1 -O.I4-73Li+ül - 0 • 1 4 J dD .. IJ 1 - 'J • 1 l. ,/ ól). ) i -o. 1 3 7 d,-H 0 1 - 0.1.:S'.:>.J'H Jl - o. ! 3:3 _jfH ')1 - ;) • 1 ~~ 1 "70 + ;) 1 - o. 1 :~ 0 51) + J 1 - û • I ? ~ (3u .. 01 Table 3

Nominal State-Vector Time History

STATt-~ VAr' IAHLcS

AL~A T~US ;). ':)nl 20+01 .) • C :j 4 1 [) + J 1 .) • (" SI-; 21)+ I) 1 J . 1 tB tfH O~ ") • 1 <:: J 51:) +L~ :~

o

•

1 1 H HL) + () ? :) • 1 12 60 .. 0 2 .) • 1 C 7 7rH :.>:,' () • 1 (I i'.. 30 + 0 2 J . E:.J9 6lHO 1 0.70480+01 ") • (, (.ij 1 t) + J 1 . ) • '-> 7? eD + () 1 ·) . f 76:.Jl>+O 1 ') • (. 7:5 0 U + U I !) . t f,ó 20+i) 1 ~: • ó '5 ç, 3 L> + () 1 O.t.5:31D+-01 :> .6412D+') 1 ].64150+-01 O) .(,J60D+Ol :J .630 óCH 01

o

•

f ;:c.) 4D +-() 1 ') • '" ~~() 4L>+-:) 1 0.(1550+01

i

'

. 6 11 00 +(' 1 ) • ü (" 6 60 +-0 1 ··) .f:(;2 5D+O l ) . ")<)1.3 6,)+() 1 o .:" )4-9P+û 1 I) .~~?':I.lD + 'E) Û • .1 :.1 J <)f) +- J J O. J 1J2D+JC.i 1).4.41D+v~ C-.4u_{o JJ+-O:j} (l • ".) 4 /f. 3u ~ () '::; (j.~iJ/O)+J~j o . f,24 6ü +;) Ij <) • 6 ~ 'ti!) +-ü ~ O.6f,71U+') .:, 0.71 30[;" ,) 5 (;."7.~ JU;) + ij::> (l • 7 ':.,5 -:1:) + () S \) • 17.3 7") + v ~ c' • 7 f· 9 <4 D + !) :; O.CLl.1~;)+J~ ; • f, 1 .) 4 [j + J 5 () • 8~ 6,» .. 0 S (I.n:'::;10 +J5

()

•

e

,~ <+ 1 ) + J 'j (J • b ~ 1 ~..iJ +-J IJ CJ • H ~_, ·l 1 L) + U::> :.) • b (,'.3 8') + IJ 5 l.' • ti t.;.j 'Ju + 0 :5 (' • fJ ., 1 4) + JI.)

c

.

ó

,

, ....

J +)~ 11 • r1.ie1 J '-J,) + v ~) \J • ö ol 4 I.U + ):5 () . ,')'-·.D 7D +.J'J :j.8c,)I:)"J~:> TliFT -,~ • :3 () ,) 0 D t r, 1 -v • I d:.1 10 .. Ij 1 :; • 1 .) 4-1 D t ::' 1 ,l • r.j Dl 9D. Cl O.7512ntü l \) • :'j "I t} 2 LH ( I v. :Jt 4-'" '") .. (j 1 ·.l.1!.)4 /fJ+O? ·j.l1210+0;" ,j • 1 :) .. 10+ r;~ J • ~ .::)" .;>f) + Co I I) • <) 1 ó t;.f) + C 1 o. ')4 IJ C!..H C 1 u.<}101i)+1J1 ;) • ,~,.,) :" 0 D + (. 1 O. l() IID+O? IJ .1;")(:'>30t·!';> .) . 1014 (lol) +-:_~2 () • 1 Ü (; 0 D + ü 2 0.107(0+02 v.l û'-:iOD+02 D.I10 4û+02

o

•

l i l Hl) + () 2 l).11 ·110+02 Ü • 1 1 4 "]ü + 02 O.11:j5L>+1J2 Ü • 1 ! (~ (. [) +-02 0.1177;)+0,-' ) . t I37D+-C2

o

•

1 1 :; 7D t 02 XI I

o.()

().:!! .. ~ .)[) +-02 J • 7 .~ ,) 1 G t 02 o. t O·:)t:;i)+')J o • 1 4 'j t D +-!) .1 ei .1 te. ,'" ( D +0 J r;. • 2 1 ':'W [; .. IJ J () .2t~})D+03 " .?(; t'jD+-O_~ ': ."3:-' ,6D +0 J ~) • J f ~ -TI) + ().~ (' • .1 ':.1 <)7') -+ o_~ c .(~ .-; ,7U +0 :3 Co . 4-7 t ?[I +-0 3 o .5 C -,-,;) +0:1 ',".. ~)4_i7i) +-OJ ti .~; 7 Hlrl +1J.1 O. t }<jCmHJ] t} • {~~J,~'

or.

+ O:J 1") . (, ti'.! 1 f) +03 C.7242D+-0:3 f) .7 tI <.I 4 0 +0 1 Cl. 7':'(J6D t-l):3 ,:'. b .Y>9!1 +0]

o

.

Ri.·..)1 D tOl C.90::".D+OJ -.) • ç 4 1 ',0 + () 3 ::: • <) -, '79D +-0 1 J • 1 G t 40 +0 4 i:' • 1 L' "l I I) +:) 4 HIT o .'3 ,V) J[) t J;:> () • ?i.:::! J D +-0? 'J • ;;>(.1 :"3D t ')2 î .:~,' •. ~_: ')0 + 0;:> ;) • .:> 4-7 Sr., .. () ' ::-'.l • :."':ïd ~,r~ t.J 2 :) • '-' 1');,)(:, + '1::' \) . 30 J4t: t-(J2 ) • . 51+ / Ar;, .... );> :) .3':,:~~;l.>-i \)? o • 4'~:'17f) + J2 J . 4~l~-)lû .... :'l;'l ;) • ~-> 4-7 ( r;. t ~) ? () • h l) 11:, D + "12 I) • (,'ï-' 3D + 0 2-') • 7 1/~ 7 [l +:."' ~~ :) .7735[1+,):' () • <3 ~>. ~ ';10 + i'" :;: -:) • 'i 'Y;.t'..Ji.' .. r) .~~ (' • ':I':;~~ 7L', + f) ~ ü . 1 :):-' ](.1 +-{':'\ 0.1 ().>39G +')3 q • tir. f'l.l .. ") ~~ .) • 1 ;;>o 4f~ +-·T~

"

.1

2._'" 30 + i):;: 0.1 30JDt0:l () • t i .. '?, 4i·'.,· O.~ tJ . J ~)(,6r~+03 I) • 1 :; 7 9rl +-~J 1 () • I V-; 3[' +,) ~ :) [ L T ~r.: - :") • ')? :14 !.lt-O 1 - 0 • ) L:, \) iJ 1) .. 'J '" - () •. ~ 'c'"7 ,-'n·t-') -, - -l.1 :.11):',)+-:, 1 - .) . l <)4.):'./+') 1 - 0.7 UW f)+-)'1 - 0 • ,} .1 ! f~ !") +-() 1 - :) .'"i·1B91_)-+-O l ').1 7?6 [H-O ") - 1). 1 ;., '3f;iH /) l - o. :.J4·!t DH) 1 - o. ';<} 7',"11) Fl t -() .;)f.f~ lD~n 1. - ,) • 1 .'11 :11)+ '.) 1 _.) . \ 2:'"l J r)+v t - ,).131.-)')+01 - ). 1 2

I.

~) n... '1 1 - ') .1 () ,r;!)+-., 1 - 'Î . -J,)r,7~)+OI) - 0 • 7 ".i ':-) ~,,~) H) ,') - f) •. ',."} ()4 iH'"l ") - 'J .:.~ 121 r) ... o<) - ') • .11 () 1 <) [HO ,) - :) .:! 'M 1 f) .... , .) - I) .:~ ,) 1 7 rHO -.) - O • .l1211J+O") - Cl • ::".3 77 'Ç) - 0 t :) . .... .:. ." r_{j - { ) 1} ) • 1 2:) t.F) ~ () "1 i) • 1 ". 7 "J' l+ ,) " j 1\ r·iC - 0 . J 000rHn] - J . j 16()D· ... 'J ~ - J . 2.0 1 ,)1)+-') 1 - u • 1 1 21', n + i) 1 J. rl 7(": 1)+') (' O • .! j 1 h ~ H .l 1 v.J'.I'-;4':~')+P l J. ~ _~ 1 '}I '+0 t 0. y.)~\4 H f) 1 o. ' u."i,.,ç.+") 1 J . I :J '~t·.I)+:) 1 .J . j;] » '-:, I) +-'J t O.d~~()c.)+·.) t J.J;;)/~r\Î)+-(~ 1-0.dó1 2PHI I 0).') J ':';~: )'h' 1 ;:; • :J .l-,.j ,~i ,''':' 1 0.'j::J2..1,)+-::' 1 ;je )7/~ 1 I) t-:) 1 O. J 'J Lj .:> r.H t) 1 ij • 1 ;].1 ~~.; U ... i) 2 J.lv·F)~)+0? J • .1 J ~')4 ') .. ) ,) V. l 'J ' ;>[1+-1);' J. 1 t) "1 '.i i"l +-!) : . J . 1 1 ')':\ Cl t ': :~ J . l L:> 1 ,~)+O.;> Û • 1 1 3 () i 1 t ") .) v.l i c-~') )t. ".l:~ u. 1 1 r:, ~ () ... , :.~

T 0.0 0 . :'.>0 1.00 1.~O 2.00 2.t>O .1 • ,) () 3.~-)O 1~.!)O 4.';=;ü ~). 00 5.:"0 t.00 f). 50 7.00 , • ~j ,) 1::.. 00 û.sa '-~t.('O SI.:.JO

I

O

.oa

1 ü. '.) 0 11.00 1 1 • ':)') 12..00 12.:)1) lJ .00 1:3 .'.:;; 0 14.:>0 1/~. ~o \)~,:7C o. ~.)2 100 o. 'j232'~ 0.S2525 0.5?184 0.51312

o.

~.;i022~ o. 1+9104 o • .r~-'977 O. d 0.0 1).0

o •

."i O.Cl

o.

,

)

0.0 0.0 o • .) o. (1

o.

()

o.a

o.

,

)

0.1)

o.()

o.u

0.0 0.0 i) • ()

o.

,

}

0.0 0.,') l),'fL J .'J -j.Jo::':l':l -J.2.:!U35 I j . :'309:) O.j.<::öd2 v. 1+2 7U 6 J.3564b 0 • .12..310 v .'H>ÓJU \).ljjO~ \i.vvu~4 \..1.02.012. 0.00117 ;) • ,) 71 :'j":: 0.'J6d':'0 v.00313 ,J. u:,,>·.,/i.>ó v.>jS7~0 U. 05':>u0 -). 0~)J6;5 J . J . .>luJ 0.0'.'-101 Ioi.Jl."O\J U.04tibQ J .û".3ól v.()~loJ .) • \J.J <)6 0 ,,).J3/59 U.O.;o:)') (s .0 J..5::;'j Table 3 - Continued

Nominal State-Vector Time History

Hf-4D~) - 1.~ '~:1~.) 7 .. I • • 0.2 '.~:,,\ f) - ) . 3 P 1 3 - f~-,LF~.f f 0.9 ·'./64':; '.2?:>J 1 5 . 1 2.C;~! '7 é . 0 r)9! ' j 'J. 4 46 ~ r, ·1.1·.#~):j '~ 1 ). 1 '-FJ5 '1 1 o • .3.iiûe 7 10. G ·41)Q 1 10. <) !;;91L ,:) 11. ]05.! f. , I . f) ~ '>3 <) l).';}.~}?i 1 2 .? f) 7} ') 1 2 • '1 \ i ?i'; t 12. 74Fi37 I :3. Cl 'l /kJ ,) 1.1 •. ~,)0 31 1 :3 • I~ 'J6 7 :) 1 '1.7' :n 7 } ... 9.~()1 -, i I~. 1 37 _{7 ?} 1 4. ] ,'j~ '.~ ; '4.. ~ :r~", ) 14.7')~12 1. I • • H 7 /.1n '1 NOTE: T U ALFA TRUS THET XII HII DELTAE GAMC DNZC HHDD time Csec)

airspeed perturbation (mis)

angle of attack (deg) thrust (Kg)

pitch angle (deg) distance Cm) height Cm)

elevator angle (deg) path angle (deg)

commanded normal load factor

Table 4

Table 5

Thrust Effect on Performance*

/), ** .**

Case /)'h . 6a u

f cr hf tI t2 t3

mln max

(Unit) (m) (deg) (mis) (mis) (sec) (sec) (sec)

Full _{-5.22 12.35 -1. 296} 0.01559 14.87 1. 75 3.35 3.60 Thrust One Engine -5.30 12.32 -6.141 0.01793 9.429 1.83 3.43 4.28 Failure Two Engine 5.38 12.30 -11.35 0.0231 2.60 2.0 3.50 5.53 Failure S = k {0.9, -0.8, 0.02, 0, -2.0, -2.5}

*In calm air, without initia1 errors **At 14.5 sec

Table 6

Engine Time Constant Effect on Performance*

Case /)'h . 6a /), **

mln max uf

(Unit) (m) (deg) (mis)

T -1 t sec -4.93 12.48 0.285 T =4 t sec -5.22 12.35 -1. 296 I I T =8 sec -5.33 12.31 -4.378

I

t L Sk = {0.9, -0.8, 0.02, 0, -2.0, -2.5} *In calm air, without initial errors **At 14.5 sec

cr h** _tI

t2~

f

(mis) (sec) (sec) (sec)

0.01416 19.17 1.60 3.08 3.00 ,

!

0.01559 14.87 1. 75 3.35 3.60

Tab1e 7

F1aps and/or Gear Retraction Effect on Performance*

6U** .**

Case 6h

min 6a _{max f} h_f 0

(Unit) (m) (deg) (mis) (mis)

Gear down

(oF=300) -5.22 12.35 -1. 296 14.87 0.01559 Gear retract ion

-5.22 12.35

( °F=300) 0.7804 16.40 0.01559

Gear and flaps

05.22 12.35 1.467 11.24 0.01559 retract ion

S =

k {0.9, -0.8, 0.02, 0, -2.0, -2.5}

*In calm air, without initial errors

Gear retracting time: _{3 sec; flap retracting time: 6 sec} **At 14.5 sec

W(h)

Frame

n

.

/Frame

F.

s

~

B

Xe

....

, h

/Glide Slope

)(;

f---Decision

Height

o

PUII-UP\

~ _"-

-" -"

"-"-

"-"

_"

FE

XE

ZE

'ZA

FIG. 1. TYPICAL AIRCRAFT DESCENT THROUGH THE PLANETARY BOUNDARY LAYER.

V

_e

sin

re

---

-

....

---Wie

--

....

_-Ys

Zs

Horizontal

Reference

Plane

FIG. 2. REFERENCE EQUILIBRIUM GEOMETRY (NO VERTICAL WIND)

1.0

Sn

(t)

o

2

T

4

6

8

10

t(sec)

FIG. 3. SWITCH-ON FUNCTION.

Sf

(U"

1.0

---=-~~--___,

o

2

4

6

_T

10

t{sec)

>

:>

11 LO <t:

.

~

--

c..!) ... u..

~o~__________________

___

~o

~hmin

hd

hd

Ground Plane

CLI

aST= 15.97°

afe = 5.61°

ae= 13.4°

ao = -9.86°

CL

_max

~.,---

...

I '

Ve = 73.06

mIs

VST = 56.20

mIs

CLc~---~

Vf

= 73.06 mIs

I

CLf= CL

er---7f'"

I

I

I I

I

I

I

I

I

_I

I

_I

I

_I

I

I

I

I

I

I

I

I

_I

I

_I

I

_I

I

_I

I

_I

I

_I

I

I

ao

0

_{af=ae ac}

_aST

_a

8~---~---~ o en _ 0 o~ - 0 XN · X

_...

~o ::z::o L.:) • _ 0 LLJ ::z::

~.OO B.OO 12.00 16.00 20.00 2Y.00

T IHE (SEC) 8.--r--~---_ ë

,.,

o o ë3~ LLJ-Cl LLJ -J ~8

ti

~cb

00 ~

~

-

,

/ t18c

8.00 12.00 16.00

TIME (SEC) 20.00 2Y.00

~~~~~---L.:) LLJ Cl I;) ~

.

40

~+-~~~~---+----~---+---;---~~

FO.OO 11.00 B.OO 12.00 16.00 20.00 2Y.00

(W,W2 W

3)

Pi

68

_T

_max

KT

~8T

~nz Sr(t)

TTS+l

~8

àn

_ze

_AIRCRAFT

Sn(1)

!l8c

+

+8E

_~

!l8E

!lU

+

_TESt1

~hmin

CT{

xiO-

2)

(m)

-10 2.0

----

,.

...

J

_

...

~e • • __ ~ ...

Llnze

=

Constant

Lln Ze = Va rio bie

CLc/CLmax

=

0.9

Ku=.02

Ke=-2.0

Kë=-2.5

~~=t

Llh

•••••••

- 5

1.0=ru~-=iOr::_-====X)caG=_

~

4 J

=-0

:

---:---

~

0

-0.5

-1.0

-1.5

-2.0

Ku=.02

CT(,dO-

2 )

Kn=-.S

~hmin

Ke=-2.0

(m)

-10

1.6

-5

1.5

o

1.4

0.70

Kë=-2.5

•

_•

- 0 ₀

Llh\

0 ₀

0.75

QSO

0.85

Q90

Kn

..

0

C) C

r---,

~ C) c :r Cl o o C\I ('I') c o c =' C\I Wo 0 0 :::::> • I--g

...

I---l a:: C) c Cl CD c C) Cl

--0.00 (1) Reu

=

100 (2) Reu

=

20 (3)

RBU

= 10 (KB

= -

2.0)

-

---110.00 80.00

--

_--

_'

_-

---

---120.00 160.00 200.00 2ijO.00 280.00

DISTANCE (Ml (Xl0

1

₁

FIG.

ll(a).

COMPARISON OF RESPONSE WITH DIFFERENT R

e

u RATlOS

(WITH SEVERE WIND SHEAR) - FLIGHT PATH.

/

(1)

gr---~ CD I ' o o ~CD (f)1' "'-:E: Cl

t::::g

a.. . (f)j! Cl: a: o o N+_----_+---+_----_+---+_----~---~~ 1'0.00 3.00 6.00 9.00 12.00 15.00 18.00 TI HE (SEC) 0 0 è C") 0

aST

~ In

-t::) lJ...I Cl 15.00 18.00 0 0 In

-

I

g.---,

o :r o o ~o t::)N lJ...I Cl lJ...I ~ t::)o z~+--~~+_----_+---+_----_+---+_----~--~ a : ' ~ ~ l -a: a..g 6.00 9.00 TIHE (SEC) 12.00 15.00 18.00 o ~~---~

2

I 11

-2

I I I I I I I I I

I \

I

ö

en l

ö '

"'I

_I

I

I

I

I

I I

I

I

8

C\J

o

o

O l 10

o

·

...-.... 0:::: ex: LLI ::c V') LLI 0:::: LLI :> LLI V') :z: ... ~ <D 0:::: o I- >- I-... :> ... I-... V') :z: LLI V')

·

N

·

~ ... lL.

~ o o o o C\J o o o f.D o o o C\J W D o :::::>0 t-c:::i - C D t --1 cr: o o o ::::1'

R8u

=

200

R8u = 100

R8u = 50

K8=-2

o I GROUND FLRNE o o 0.00 15.00 30.00 Ij 5. 00 60.00 75.00 90.00

OISTANCE (M) (Xl0

l ₎ (3)~ /~I"J # # / y'" 105.00 120.00 135.00 150.00

a::: c CD ('\J

"

~~1-____

-+ ____

~~=;~=+======+==/~(~1~)~ ______ r-~

"0.00 3.00 6.00 9.00 12.00 15.00 18.00 TIME (SEC) 8~---, (\j

-o c Q) 0 : 0 :z::c IL..cö ...I a: o

c+-____

-+ ______ +_----_+---+---~~----~~ "'b.00 3.00 6.00 9.00 12.00 15.00 18.00 TI ME (SEC) 8~---, CD

-LLJ ...I <.:Ic (2)

zc+-__

~_+---+_----_+---+_----~~--~~~ CJ:c::h 00 3.00 6.00 9.00 12.00 15.00 18.00 ~ TIME(SEC) a: IL.._c o ~L---~

FIG. 13(b). COMPARISON OF RESPONSE WITH DIFFERENT Reu RATlOS

(IN CALM AIR) - TIME HISTORIES.

-10- 1.6

- 5 t-1

.

5

o

al

I

02

I

Q3

I

₀₄

I

_0.5

I

.-Kü

,~

-2

L\hmin

CT(

x 10 )

(m)

10 2.0

5 1.5

/~h

o

-1.0

I

_-2.0

I

_-3.0

I

x: o o o o N o o o ( 0 o o o N W D o ::Jo ~o -co ~ --.J a: o o o :::7 o '0 o 0.00 15.00 30.00 ij5.00 Ké=-3.0 Kë=o 60.00 75.00 90.00

DISTANCE (Ml (Xl0

t

₁

105.00 120.00

FIG. 15(a). COMPARISON OF RESPONSE WITH DIFFERENT Kë - FLIGHT PATH.

o CD N ... o ClO u.J • lL.J~ 0.... <f) a: ~~ +---+--~--+-~~-+---+---+---+-~ ... 0. 00 3. 00 6. 00 9. 00 12 . 00 15. 00 18. 00 TIME (SEC) g.---~ ( 0 -o o N o

o+-____

_+---+_---r---~----~~--~~~ =rO• 00 3. 00 6. 00 9. 00 12 . 00 15. 00 18 . 00 TIME (SEC)

g.---,

( 0 L.I.J ---J t : ) o

zo+-__

~_+----~+_----_+---~----~~--~~~ Cl:

eb

00 6. 00 9. 00 12 . 00 1 5 . 00 18. 00 ~ TIME (SEC) Cl: 0....₀ o ~~---~