Aircraft landing control system

United States Patent [19] [111 4,357,661

Lambregts et al.

1451 Nov. 2,1982

[54] AIRCRAFF LANDING CONTROL SYSTEM 3,523,664 8/1970 Doniger et al. ..................... 244,487 3,545,703 12/I970 MontvaIe ........................ 364/430 X [75] Inventors: Antonius A. Lambregts, Renton; Rolf 3,578,269 5/1971 Kramer et al. ...................... 244/187 Hansen, Bellevue, both of Wash.

3,665,465 5/1972 Miller .............................. 244/188 X 3,666,929 5/I972 Menn ................................... 364/428 [73] Assignee: The Boeing Company, Seattle, Wash.

al. ....................... 364/430 3,705,306 12/1972 Lydon et 4,141,522 2/1979 Lambregts ...................... 364/429 X 1211 Appl. No.: 123,529 Primary Examiner-Felix D. Gruber 1221 Filed: Feb. 22, 1980 Attorney, Agent, or Firm-James P. Hamley; Bernard A.

[51] Int. c1.3 ......................... G05D l/Q G06G 7/70; Donahue

B64C 13/18 A B S T R A a [52] U . S . CI. .................................... 364/430; 244/183; 244/ 1 87 Upon aircraft landing approach, flare path command [ S S ] Field of Search ....................... 364/428, 429, 430; signals of altitude, vertical velocity and vertical acceler- 244/183, 185, 186, 187 ation are generated as functions of aircraft position and velocity with respect to the ground. The command [561 References Cited signals are compared with corresponding actual values U.S. PATENT DOCUMENTS to generate error signals which are used to control the flight path.

3,169,730 2/1965 Gaylor et al. ....................... 244/187 3,309,707 3/1967 Tatz et al. ....................... 244/187 X 3,523,663 VI970 Doniger et al. ..................... 244/187 8 Claims, 7 Drawing Figures

---

I

I

FLARE

U.S. Patent NO^. 2, 1982 Sheet 1 of 4 4,357,661

I

FLARE

-

, -- ? 1

L

U.S. Patent NOV. 2, 1982 Sheet 2 of 4 4,357,661

-7-

U.S. Patent NOV. 2, 1982 Sheet 3 of 4 4,357,661

U.S. Patent ~ o v . 2, 1982

Sheet 4 of 4 4,357,66 1

4,357,661

tion. The second is a vertical velocity command signal AIRCRAFT LANDING CONTROL SYSTEM

Kc The final comma?! signal is a vertical acceleration

signal, h,. The h, and h, command signals are defined as BACKGROUND OF THE INVENTION a function of both ground position and ground speed in The invention described herein was made in the per- 5 proper relationship to the altitude command ::lgnal.

Preferably, the command signals ha b a n d hcmaY be formance of work under a NASA contract No. NASI- generated via either disctosed differentiating Or inte- 14880 and is subject to the provisions of Section 305 of grating methods Or using exponential functions.

the National Aeronautics and Space Act of 1948, Public Law 85-568 (72 Stat. 435; 42 USC 2457).

BRIEF DESCRIPTION OF THE DRAWINGS The present invention pertains to the aircraft guid- lo ance art and, more particularly, to a system for control- FIG. 1 is a generalized block diagram illustrating the preferred embodiment of the flare out command sys- ling aircraft flight during landing flare.

tem; A critical portion of aircraft landing trajectory is FIG. 2 is a graph illustrating aircraft landing trajec- commonly known as flare out or flare. Flare is that portion of the landing trajectory between the fixed l 5 tory; angle glide slope and aircraft runway touchdown. Thus, FIG. 3 is a block diagram illustrating the preferred it is desirable, particularly for commercial aircraft, that embodiment of the flare path command signa! generat- the flare profile depart smoothly from the fixed angle ing apparatus utilizing integration techniques; glide slope approach providing a smooth transition to FIG. 4 1s a block diagram illustrating the preferred runway taxiing.

2o embodiment of the flare path command signal generat- In COmmercial aircraft, attempts have been made at ing apparatus using exponental function techniques in a generating landing flare commands to be used either as digital implementation; a director to the pilot or for automatic, i.e. autopilot FIG. 5 is a block diagram illustrating the preferred landing. One such system commands a linear decrease embodiment of the flare path command signal generat- of sink rate as a function of altitude above the runway. 25 ing apparatus using an analog implementation; Thus, the sink rate is of the form: hC(hh)=khh+kBL4S FIG. 6 is a graph illustrating the response characteris- where h(h) is aircraft sink rate, and and kBIAS are tics of the system shown in FIGS. 4 and 5 for a given set defined constants.

of constants; and The problem with this system, however* FIG. 7 is a graph illustrating the vertical acceleration is that ground speed affects touchdown dispersion. That 30 commands for two different flare paths.

is, since aircraft ground speed is not taken into account, OF THE the actual touchdown point of the aircraft on the run- DETAILED DESCRIPTION way can vary considerably depending on the ground PREFERRED EMBODIMENTS OF THE speed. This is undesirable both for safety reasons and INVENTION because reduced touchdown dispersion is essential to 35 is a diagram the Of effective runway utilization and continued aircraft op- eration under adverse weather conditions. the instant flare path control system. Operation of the is better understood with reference to FIG. 2 system system is subject to large touch- addition, the down dispersion due to its sensitivity to sink rate signal which illustrates an airplane 10 on its landing descent to 40 a runway 12. During the landing maneuver, the aircraft errors.

Further, the prior art flare command system had normally approaches the runway on a glide slope 14 narrow control flexibility, e.g. bandwidth and gain se- which is defined by a fixed angle, commonly three de- lection, thereby limiting its accuracy and adaptability. grees, with respect to the runway. At an altitude hothe airplane begins its flare-out, indicated by reference nu- SUMMARY OF T H E INVENTION 45 meral 1 6 . The purpose of the flare is to provide a It is an object of this invention, therefore, to provide smooth controlled landing. The airplane position rela- an improved aircraft flare command system which may tive to the runway at which flare is initiated is defined as be used to reduce touchdown dispersion. xg. For the example of FIG. 2, the commanded flare It is a further object of the invention to provide the Path intersects the runway 1460 feet from the Xo ]oca- above described improved aircraft flare command SYS- 50 tion. Deviations from this 1460 foot touchdown point tern which is not dependent on a single sensed aircraft are referred to as dispersion. In the prior art automatic flare-out control systems, the dispersion was quite large paramater.

It is an additional object of the invention to provide due to the effect of variation in ground speed, from one the above described aircraft flare command system, approach to another.

which is flexible in design, allowing extreme accuracy 55 Thus, to minimize dispersion, the present automatic flare-out control system, as shown in FIG. 1, utilizes and adaptability.

Briefly, according to the invention, apparatus for both ground position and ground speed as a basis for generating flare path control signals for an aircraft in- generating its control signals.

cludes a means which produces a ground position sig- In many cases, aircraft distance relative to a point on nal, x, corresponding to the position of the aircraft with 60 the runway can be obtained from distance measuring respect to a reference point on the runway. A signal, equipment (DME) which produces a signal xDMEcorre- is produced corresponding to aircraft ground sponding to the position of the aircraft with respect to a VG, speed. A command generating means monitors the fixed point on the ground. Where the XDME signal is ground position signal and the ground speed signal and available, it is received at the instant system at an input produces in response thereto, and as a predetermined 65 line 20 and routed both to a flare detect box 22 and to the negative input 24a of a summer 24.

function of said signals, a sequence of three command signals. The first signal, hc, is the altitude command Block 22 monitors the aircraft’s position signal and, signal, defined uniquely as a function of ground posi- when it is less than a signal xo corresponding to the

4,357,661

3 4

desired distance to initiate flare, an output is provided tion, integration and exponential function, for generat- ing the command signals.

on its output line 22u. When a standard aircraft system, not shown, determines that the distance measuring DIFFERENTIATION TECHNIQUE eauiument is oDerating DroDerlv. a switch 26 is acti- . . - . . I .

vated to its position 26a thereby routing the flare detect 5 In this approach, the function h,=h(Ax) is selected in output signal to operate a second switch 28. During the accordance with the constraints of a given condition.

landing approach maneuver, switch 28 is in its position Thus, the function may be selected such that the flare 28a whereby it routes an elevator command signal path slope is continuous with the glide slope at the start ( 6 & to the aircraft's elevators. The signal (a& repre- of flare and then smoothly reduces to the desired slope sents the elevator command signal for glide slope con- 10 at the touchdown point, yielding a desired sink rate as, trol and is provided by circuitry (not shown) commonly for example 2.5 feet per second as shown in FIG. 2.

Once the function h,=h(Ax) is defined, the flare path found in modern aircraft.

When the aircraft has reached the flare initiation command computer may use either approximating func- position x,, the flare detect block 22 flips switch 28 to its tions or a look-up table to generate the altitude com- second state 286. In this state, the output command 15 mand signal h, for a given ground position signal Ax.

signal to the aircraft's elevators is provided by the flare Now, the sink rate command signal may be deter- mined from the equation path command circuitry.

In some caes, a distance measuring equipment signal XDME is not available. However, a valid ground speed 20 h, = signal VG may be available, as provided, for example, by an inertial reference system. In this event, the ground But since h(Ax) is solely a function of AX, this expres-

speed signal vG is input On a line 40. This signal is

sion becomes: routed bv a switch 42 in its Dosition 42u as one inDut to the flare path command computer 50. Also, the signal is 25 h,=(d/dx)h(Ax)(dx/df) integrated in an integrator 44, which has an initial con- But, by definition dx/dt = VG. This, ground speed dition of zero at flare initiation, thereby producing a vG enters into the sink rate command computation: relative ground distance signal Ax which is Dassed via a

- -

switch 46, in its position 460, also to an input'of the flare hc= Vp(d/dx)h(Ax) path command computer. Switch 46 assumes its posi- 3o tion 46b in the event that the distance measuring equip- The commanded vertical velocity h, may be calcu- ment signal is valid.

lated by taking the derivative of h(Ax) with respect to Finally, if neither a distance measuring equipment ground distance and multiplying this by the input value signal XDMEnor a ground speed signal Vcis available, a of ground speed VG. This is done by the flare path ground speed signal can be determined by the circuitry 35 command computer 50 using modern computer tech- indicated generally at 48. Here, the vertical velocity niques. As such, a detailed analysis of the computation signal hCF, which has been complementary filtered, and will not be given here.

the Output signal from a horizontal accelerometer X are Finally, the vertical acceleration command signal K, both input to a filter and hold circuit 52 to produce a is given by vertical sink rate signal h,. At flare initiation, the caicu- ..

lated value of sink rate h, is held by the circuit 52 and hc=(dz/dt2) h(Ax).

multiplied, in block 54, by the inverse tangent of the aircraft's flight path angle y. This results in a calculated But, from the above relationship for vertical velocity value of ground speed VG appearing at the output line this becomes 56 of block 54. Thus, when the aircraft i s not provided 45 with a valid ground speed signal VG as from an inertial

reference system, the switch 42 is in its position 42b .. d

hc = z( V G F h ( W

whereby the calculated value of ground speed is routed

" 1

both directly to the flare path command computer and through the integrator, thereby producing the relative 50 and, finally, ground position signal Ax, which is also routed to the ..

hc= V&d2/dxz)h(Ax)+( pg/Vg)kc flare path computer.

In addition, for the condition wherein the distance measuring equipment signal XDME is not available, or is The term V G N G hc is negligibly small and may be detected as not being valid, switch 26 switches to its 55 ienored. Therefore, the longitudinal acceleration signal position 266. Here, the initiation of flare is sensed by VG is not-Jequired to compute vertical acceleration determining that instant at which the aircraft's actual command he Thus, given that h , = h ( b ) is defined, the altitude h, as determined by an altimeter, is less than the corresponding vertical velocity h,and vertical accelera- flare initiation altitude h,. This is done by a block 56 tion hc can be computed by the flare path command which then produces an output signal on its line 560 60 computer 50 using standard differentiati?? techniques.

which is routed to switch 28 thereby switching the The flare path command signals h , h, and h, are system from its glide slope command to the flare-out routed via flare path command computer output lines command. 61-63, respectively to the negative input of summer The flare path command computer 50 processes the circuits 71-73 respectively. Applied to the positive in- position signal Ax and ground speed signal VG, thereby 65 puts of summer circuit 71-73 are sensor signals h, h and producing commanded altitude,. vertic?] velocity, and h corresponding to the aircraft's actual altitude, vertical vertical acceleration signals h , hc and h,, respectively. velocity and vertical acceleration, respectively. Thus, Described below are three methods, namely differentia- the summer circuits 71-73 produce at their outputs

4,357,661

5 6

error signals hc, fie and Kc corresponding to the error With the dzh(Ax)/dxz function defined, the various difference between the actual aircraft state and their commands may be determined as is explained below.

CorresPOndiW c0mmanded states. These si.i@s are FIG. 3 is a detailed block diagram illustrating the multiplied by suitable gain factors kh, k h and k h in gain preferred construction of the flare path command com- blocks 81-83, respectively. They are then all combined 5 puter 50 shown in FIG. 1 wherein integration tech- reducing a composite error The in a Summer 90 niques are used to generate the command signals. As

E hand ‘ h do not determine the flare Path

gain factors kh, before, the system receives an input as to relative posi- but, rather, the magnitude of the elevator control with tion of the aircraft, Ax, on an input line 200 and aircraft which the aircraft is directed to the desired path. Thus, ground speed VG on input line 202. These parameters the instant system allows a convenient means for opti- 10 FIG. 1.

are determined as is discussed with respect t o mizing gains for the sole purpose of providing optimum The relative position signal Ax is fed to a block 204 path tracking and therefrom minimum touch down which produces an output signal F(Ax). In this case, dispersion.

The summer 100 combines the composite error signal e & ) = (d*/dx*)h(Ax).

with a damping signal. Damping signals are ordinarily 15 provided in aircraft avionics, normally as a function of pitc., rate, and not be fully described here. The functional relationship between the second de- This damping signal is routed Over a line 110 to a gain rivative of relative position and the relative position is itself may be Provided via a standard memory Iook-uP

block 112 having a gain factor b. The gain factor

selected in accordance with the constraints and require- 20 table Or Via computation O f an analytical function. For ments of a given system. The resulting damping signal is one application of the invention, the following approxi- passed to the summer 100 where it is summed with the mating functions were used: composite error signal thereby producing the control ~Ax)=l+~os(0.0062&-~) forO<&x<844 ft.

signal, (6,,)jwhich, as described above, is routed to the aircraft’s elevator controls during a flare maneuver. 25 = 1 +cos [0.00165(&-844)+1.92] for 844 ft.

Thus, once flare begins,..the ajTcraft’s path begins to <Axx<1583 ft curve, and as a result of h,, an h, is moduced and thus a corresponding elevator comrfland: The aircraft will the preselected Of d2h(Ax)’dx2 is passed then rotate before a significant h, and h, error develop 206. Ap- and will therefore track the command flare path closely. 30 to the first input 206a Of a multiplying plied to the second input of 2066 of the multiplying INTEGRATION TECHNIQUE block 206 is a signal corresponding to ground speed As described above, the flare path command corn- squared, VG2- This signal is generated by taking the puter 50 of FIG. 1 may utilize differentiation to derive input ground speed signal VGon line 202 and passing it 35 to both inputs 2080 and 2086 of a multiplier 208. Thus, the vertical velocity and vertical acceleration corn- mands given the functional relationship between com- the output from multiplier block 206 is the first term of mand altitude and relative ground position. Alterna- the equation for commanded vertical acceleration x, tively, integration techniques may be utilized to derive given above. The second term is generated by passing the same command signals. This may be understood as the ground speed signal vG on line 202 to a divider follows.

40 circuit 210. Divider circuit 210 has, as its numerator As derived above, the desired vertical acceleration input the output of 212. Multiplier 212 has at command signal is expressed its first. input 212a the commanded vertical velocity ..

signal h , which is produced in a manner discussed h,= Vd(d2/dx2)h(Ax)+( ~ G G / V G ) ~ ~ , 45 below. At the remaining input 212b of multiplier 212 is Thus, rather than preselecting the function h,=h(Ax) VG, the first derivative with respect to time of ground as with a differentiation technique, it is possible to pre- speed which is obtained by Passing the ground speed VG through the differentiating block 214. Thus, select the function d2h(Ax)/dx2. A requirement for this signal function is that it equal zero at Ax=O in order to realize the output from multiplier 212 is of the form \jGh,.

a smooth transition from a linear glide slope to a curved 50 When this is divided by ground sqeed VG, the output flare path. A further requirement may be to limit the from divider block 210 is, thus (VGhJVG). As men- magnitude of this function at touchdown. The higher tioned above, although this term is small and is not this magnitude at touchdown, the more the curvature of important compared to the main term of the h, defini- the flare trajectory occurs at 10W altitudes and therefore tion, it cannot be neglected in this system. The reason the higher the risk of landing with a high sink rate due 55 for this is that omission of this term a seri- to deviations from the commanded flare trajectory.

ous in the computation of h, as a result of the

Also, the more the flare trajectory curvature occurs at integration process with time. Likewise, the resulting low altitude, the lower the final sink rate must be to in the hCcomputation becomes even greater due to touchdown at a preselected point on the runway. This, bo the dual integrations if this term is omitted. The result of then, adversely effects the touchdown dispersion.

The pitch attitude at touchdown is roughly propor- omitting this term is that commanded flare trajectory would no longer intercept the runway at a fixed point tional to the vertical acceleration, It is desirable that pitch attitude increase steadily during flare. This can be thus resulting in increased touchdown dispersion.

Hence, a Summer 218 is used to sum .the first and done by shaping the d2h(Ax)/dx2 function such that it UP smoothly and then maintains a relatively 65 second terms O f the Vertical acceleration he equation.

builds Given the vertical acceleration signal, the sink rate steady value until touchdown. The aircraft speed bleed- off also helps to provide an increasing pitch attitude as command, or vertical velocity command is then simply flare progresses. given as

4,357,661

where kl, k2 and k4 are all constants related to the de-

sired flare path.

I . .

The matching sink rate command then follows: h, = hr=o + 1 hcdt.

dhc d h --=- In this formula, ht=,= VG tan YGS, where YGS is the E - dt dx hc* glide slope guidance flight path angle, is the initial con- dition for the integration. Referring then to FIG. 3, the ground speed signal on line 202 is multiplied by tangent = & l V ~ [ d kz yGsin block 220 the output of which provides the initial 10 condition (IC) to an integrator 222. The input to inte- Similarly, the matching vertical acceleration com- grator 222 is the commanded vertical acceleration sig- mand becomes: nal h,. Thus, the output from the integrator 222 is scen to be the desired vertical velocity command signal h, Finally, the altitude command becomes 15 & = d 2 h c dt2 VG .

where hct=ois either the aircraft’s altitude at flare initia-

= V$ kl [e-kB - e - k 3 q + -

tion when flare initiation is triggered by altitude or it is VG the glide slope altitude at the flare initiation point when flare initiation is triggered by the DME signal. Thus, From. this it follows that &=O at flare initiation the command altitude h, is determined by integrating 25 (x=O, VG=O). However, this flare path definition al- the vertical velocity command signal h, in integrator lows no direct control over the vertical acceleration 224 which has the aforementioned initial condition rise time, since the four constants k1-b are deteryined by the four path constraints hx=o, hx=o, xh=oand hh=o.

h,,,o applied at input 2242.

A certain difficulty arises with the requirements of The vertical acceleration rise time is controlled by achieving both the desired sink rate and distance at 30 the relative values of k2 and k3 and the maximum verti- cal acceleration occurs for touchdown. To obtain the desired touchdown sink rate, given a certain ground speed, requires that the function dzh(Ax)/dxz have a certain area under the curve. This area is a function of both the magnitude of d2h(Ax)/dx2 i h m a x = ( - ) I 1 n h . k3 and the total flare distance. If the flare distance is to be 35 increased without affecting the sink rate at touchdown, If, therefore, the relative values of k2 and k3 can be the d2h(Ax)/dx2 term curve must be reshaped to pro- selected, the acceleration can be controlled to the de- vide a higher level of vertical acceleration early in the sired rise time. This turns out to be possible by adding a flare and a lower level during the later part of flare. ln 40 term proportional to x to the flare path definition. Such this way, the flare path starts to curve upward a term does not contribute to the definition of the accel- but the final slope stays the same, resulting in an in- eration. The path definition then becomes: creased distance but an unchanged sink rate at touch- down.

h c = ( k l / k 2 2 ) [ e - b - ( e - k R e x ] +kyr+ k4 In summary, integration techniques may be used to 45 generate the flare path command signals, starting with a and predefined function dZh(Ax)/dxz and using the input signal variables Ax and VG.

i,= V d k l / k ~ ) [ - e - ’ C L ” + ( e - ~ R q + k j

e-function Technique 50 and FIGS. 4 and 5 illustrate detailed block diagrams of ..

hc= Vc?kl[e- kx+.-e- kRkL7 + ( ~ G / V G ) ~ , preferred embodiments of the flare path command com- puter 50 of FIG. 1 wherein e-functions are used to de- In these equations the constants kt-hare determined termine the command signals. The use of e-functions is attractive since their derivatives are identical to the 5 5 by the four flare path constraints given above, whereas original function and the sink rate and vertical accelera- the constant kR is selected to yield the desired vertical rise time.

tion commands may thus be formed readily without FIG. is a detailed block diagram illustrating the imposing a significant additional computational burden.

preferred digital implementation of the flare path corn- The system described is especially suitable for digital computers, as shown in FIG. 4, but may also be em- @ mand computer utilizing the e-function technique. As played in analog flight control computer system, as before, the inputs to the computer are the relative posi- tion x of the aircraft with respect to the runway, pro- shown in FIG. 5.

vided on line 300 and the aircraft ground speed VG Referring to FIG. 2, the desired altitude command provided on line 302.

signal as a function of distance x along the runway as The altitude command signal h, is generated as fol- measured from the flare initiation point may be given as: 65 lows. The aircraft position signal x on line 300 is routed to blocks 304, 306 and 308. The block 306 receives the h c = k i [ ( e - b / k 2 2 ) - ( e - k - / k 2 2 ) ] + k4, signal x and computes the function e-&. The output

4,357,661

9 10

from block 306 is applied to the positive input of the correspond to the following condition kl=0.0001816455 summer 310. The block 308 produces the signal k2=0.00204795 e-kRkD. This is passed to a block 312 which multiplies k3= -0.0079918 its input by l/k$. The output from block 312 is coupled 5 k4=9.51766 310. The output of to the negative input of summer k ~ = 2 summer 310, when passed through the block 314 having The curves labeled B correspond to the transfer kl/k2* thus becomes the first term of h, as kl=O.O001645 given above. This is passed to one input of a summer k2=0.00095 316.

10 k3 =0.0342 The second term of the altitude command signal h, is b=94.68 x with a fac- easily computed by multiplying the signal k ~ = 2 tor k3 in block 304 before it is passed to the summer 316.

These examples illustrate the variability of the flare Finally, the only remaining term is the added constant trajectory and thereby the flare dynamics. The flare k4 produced in block 320, and also passed to summer 15 trajectory can thus be defined to obtain not only the 316. Thus the output from 316 is the desired altitude desired touchdown conditions (sink rate and distance), command signal h,.

but also to a large extent the time history of elevator and

The vertical velocity command signal h, is generated

thereby pitch attitude and vertical acceleration. For by passing the output from block 308 through block example, the flare trajectory with a high vertical accel- 322, to apply the gain factor I/kR, before it is passed to 20 eration level at touchdown results in a higher pitch the positive input of a summer 324. Applied to the nega- attitude at touchdown.

tive input of summer 324 is the output from block 306.

Thus, a system has been described for generating The resulting signal output from summer 324 is multi- flare commands h , h, and h, utilizing e-functions.

plied by the constant kl/k2 in block 326 and then by the In summary, an aircraft landing control system has ground speed VG in multiplying block 328 to produce 25 been described which utilizes either a differentiation or the principal term of commanded vertical velocity. The integration function of position on the ground. The resulting signal out of block 328 may be added in sum- instant system may be employed to reduce landing dis- mer 330 with the constant k3 provided in block 332 to persion while allowing the designer broad control over thereb produce the desired vertical velocity command system parameters.

signal h ,.

While preferred embodiments of the invention have 3 0 Finally, the commanded vertical acceleration signal been described in detail, it should be apparent that many

i, is generated by passing the output from block 306 to

modifications and variations thereto are possible, all of the positive input, and the output from block 308 to the which fall within the true spirit and scope of the inven- negative input of a summer 340. This signal is multiplied tion.

in block 342 by the constant k l and multiplied by 35 Weclaim: ground speed squared V$ in multiplier 346. The VI$ 1. Apparatus for generating flare path control signals signal is produced at the output of multiplier 344. The for an aircraft comprising: resulting output from multiplier 346 is. the vertical ac- ground position means for producing a ground posi-

celeration signal, wherein the term VG/VG h, is ne-

tion signal, Ax, representative of the position of the glected. aircraft relative to a fixed reference point on the ground; FIG. 5 illustrates the preferred analog implementa- tion of the flare path command computer 50 of FIG. 1 ground speed means for producing a ground speed signal representative of the ground speed of the for the e-function technique. Here, the e-functions are aircraft; obtained using lag circuits in which the variable time command means for processing said ground position 45 constants are determined as follows: signal and said ground speed signal in a predeter- x= VGI mined manner to produce: (a) an altitude command signal, h,; k2x = kz V G I = I/T 1

(b) a vertical velocity command signal, 3 , ; and

..

50 (c) a vertical acceleration command signal, h,, k ~ k 2 x = k ~ k 2 V @ = I / r 2 whereby said h, command signal defines the c ! c - sired flare path of the aircraft and said h, and h, The time constants command signals represent desired sink rate and vertical acceleration respectively, corresponding T I = I/k2 VG 5 5 to said desired flare path;

repre- sensor means for producing signals h, h and

si= I/k~kzVc sentative of the aircraft’s actual altitude relative to the runway, vertical velocity and vertical accelera- are seen to be functions of VG and are implemented tion, respectively; using multiplier circuits. Given the discussion above, subtracting ?leans f?: subtracting each actual aircraft one of ordinary skill in the art would have no trouble

signal h, h and 5 from.$he corresponding com-

understanding the arrangement, or hardware implemen- manded value h , h,and h, to produce error signals tation of the circuit topology given in FIG. 5. Thus, a he, h, and h,, respectively; and detailed discussion of its operation will not be given aircraft co?trol means for processing said error sig- here.

nals hc, h, and h, and control the aircraft to the 65 Sample flare trajectories and corresponding accelera- command flight path.

tion commands for a ground speed of 120 knots are 2. The apparatus o f claim 1 wherein the command illustrated in FIGS. 6 and 7. Here, the curves labeled A means includes means for determining the altitute com-

4,357,661

mand signal b a s a predetermined function, hc= h(Ax), (d) producing signals h, h and corresponding to of said ground position signal and wherein the com- aircraft actual altitude, vertical velocity and verti- mand means further includes means to determine the cal acceleration, respectively; vertical velocity and vertical acceleration command

(e) subtracting each actual aircraft signal h, h and-g

signals according to the relationships:

from.>he corresponding commanded va!ue h,, .hc

and h, and producing error signals he, h, and he,

i,= Vdd/dx)h(Ax)

respectively, in response thereto; and (0 processing said error signals in a predetermined and manner to control the aircraft to the commanded .- flare path.

%= Vo(d2/dx2)h(Ax) + ( ~ ~ G / V G ) & .

6. The method of claim 5 wherein step (c) further comprises the steps of: 3. The apparatus of claim 1 wherein the command (i) producing said altitude command signal h, in ac- means includes means for generating a signal corre- cordance. with a predetermined function sponding to dzh(x)/dxz where h(x) is the altitude of the l 5 h,=h(hx); aircraft as a function of aircraft position x, the command (ii). producing said vertical velocity command signal means further comprising means to determine the verti- h, in accordance with a predetermined function cal acceleration command according to the relation- &=VG dh(Ax)/dx; ship: and (iii) producing said vertical acceleration command signal hc in accordance with a predetermined func- tion the command means further comprising means to deter- 25 mine the altitude and vertical velocity signals according to the relationships: 7 . The method of claim 5 wherein step (c) comprises 30 the further stem of: (i) producing a signal corresponding to dZh(Ax)/dxz where h(Ax) is the commanded altitude of the air- where b t = o is the desired vertical velocity rate at flare craft as a function of aircraft position; initiation and (ii) proclvcing said vertical acceleration command signal h, in accordance with a predetermined func- tion

h, = hcl,O + h C d t

where hct,o is the altitude at flare initiation.

4. The apparatus of claim 1 wherein the command means includes means for determining the command (iii) producing said vertical velocity command signal signals according to the relationships: h, in accordance with a predetermined function h,=(k1/k2~)[e-k2J-e- kRK*/k22] f k y r f k 4 I A,= Vdkl/kz)[e-kt’+e-kRk2J/k~]+k~ hc = hcl=o + j hcdf.

..

he= V d k l [ e - k 2 J - e - k R q + ( fiG/vG)h, where where the constants kl-k4 are selected in accordance hct,O represents with the constraints of the desired flare path and kR is the commanded vertical velocity rate at flare initia- selected to yield the desired acceleration rise time.

tion; and 5. A method for generating aircraft flare path control (iv) producing said altitude command signal h, in signals comprising the steps of: accordance with a predetermined function (a) producing a ground position signal, x, having a 5 5 value representative of the position of the aircraft with respect to a predetermined ground location; (b) producing a ground speed signal, VG, having a value representative of the ground speed of the 60 where hcr=Ois the altitude at command flare initia- aircraft; (c) producing an altitude command signal, hc, a verti- tion.

cal velocity command signal, h-,, and a vertical 8. The method of claim 5 wherein step (c) comprises

acceleration command signal, Kc, said h, signal

steps of: the further being functionally related to said position signal x (i) producing said altitude command signal h, in ac- and said hc and hc signals being functionally related 65 cordance with a predetermined function to said position signal x as well as said ground speed signal VG, said command signals h,,-lic and hc=kl[e-kt’-(e-kAk2J/k~2)]+kp+kq; h defining the desired flare path of the aircraft;

4,357,661

13 14

signal in accordance with a predetermined func- (ii) producing said vertical velocity command signal tion; h, in accordance with a predetermined function: ..

h , = V d k i [ e - ~ - e - k R ~ + ( r V ~ ) ~ ~ i,= V d k i / k z ) [ - e - k - L ’ + ( e - k R k Z x / k ~ ) ] + k x 5 where the constants kl-k4 are selected in accordance with the constraints of the flare path and k~ is selected and to yield the desired acceleration rise time.

* * * * *

(iii) producing said vertical acceleration command