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NASA TECHNICAL NASA TM X• 73,154MEMORANDUM

SIMULATION OF AN AUTOMATICALLY CONTROLLED STOL AIRCRAFT

IN A MICROWAVE LANDING SYSTEM MULTIPATII ENVIRONMENT

Mitsuhiko Toda, Stuart C. Brown, and Clifford N. Burrous

Ames Research CenterMoffett Field, Calif. 94035

rI

(NASA—TN- •7t-73154) SIMULATION OF AN N77-11063

AUTOMATICALLY— CONTROLLED STOL AIRCRAFT IN AMICROWAVE LANDING SYSTEM MULTIPATHENVIRONMENT (NASA) 42 p HC A03/MF A01 Umclas

t CSCL 17G G3/08 54508

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NOY 1976CO

RECEIVED a ^c NASA STI FACILITY `^' (

!{July 1976 ^ INPUT BRANCH ^tg

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1, Report No. - 2. Government Acau_hm No. - 3. Recipient's Catalog No.NASA TM X-73,154

1. Title and Subtitle S. Report DateSIMULATION OF AN AUTOMATICALLY-CONTROLLED STOL AIR-CRAFT IN A MICROWAVE LANDING. SYSTEM MULTIPATH 6. Performing Organisation CodeENVIRONMENT

7. Authorial 6. Performing Organlrallon Report No,Mitsuhiko Toda, Stuart C. Brown, and Clifford N. A-6693Burrous - 10, Work unit No,

513-53-029. Performing organization Name and Address

Ames Research Center, NASA 11, Contract or Grant No.Moffett Field, California 94035

- 13. Type of Report and Period Covered

-)Technical Memorandum12, Sponsoring Agency N.ml and Address

Nations].' Aeri nautics °and Space_ Administration 14. sponwring Agency CodeWashington, D.-C. 20546

15. Supplementary Notes

16. AbWact

This report describes the simulated response of a STOL aircraft toMicrowave Landing System (MLS) multipath errors during final approachand touchdocin. The MLS azimuth, elevation, and DME multipath errors werecomputed for a relatively severe multipath environment at Crissy Field,California, utilizing an MLS multipath simulation at MIT 1incoln Laboratory.A NASA/Ames six-degree-of-freedom simulation of an automatically-controlleddeHavilland,C-8A STOL aircraft was used to determine the response to theseerrors.

The results show that the aircraft response to all of the Crissy FieldMLS multipath errors was small. The small MLS azimuth and elevation multi-path errors did not result in any discernible aircraft motion, and the air-craft response to the relatively large (200-ft (61-m) peak) DME multipathwas noticeable but small.

4.i

17. Key Words ISuggnted by Amhor(t)) 16. Distribution statementMicrowave landingsystemMultipath effects)

aircraftAutopilot

STAR Category - 08

19. Security Claalf. (of thisreport) 20. Security Gesif. (of if.:; pap) No, of Pages "s2. prtelUnclassified Unclassified

T.- 42 X3:75

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1

SIMULATION OF AN AUTOMATICALLY-CONTROLLED STOL AIRCRAFT IN

A MICROWAVE LANDING SYSTEPi,MULTI°ATH ENVIRONMENT

MitsuhLko Toda, Stuart C. Brown,and Clifford N. 'Burnous

Ames Research Center

SUMMARY

od

This report describes the simulated response of a STOL aircraft to Micro-wave Landing System (MLS) multipath errors during final approach and touchdown.

o The MLS azimuth, elevation, and DME multipath errors were computed for a rely-tively severe multipath environment at Crissy Field, California, utilizing anMLS multipath simulation at MIT Lincoln Laboratory. A NASA/Ames six-degree-of freedom simulation of an automatically-controlled deHavilland C-8A STOLaircraft was used to determine the response to these errors.

The results show that the aircraft response to all of the Crissy FieldMLS multipatherrors was small. The small MLS azimuth and elevation multipatherrors did not result in any discernible aircraft moition, and the aircraftresponse to the relatively large (200-ft (61-m) peak) DME multipath was,notice-able but small. -

INTRODUCTION':,

An investigation was conducted at the NASA-Ames Research Center to deter-mine STOL aircraft performance ina Microwave Landing System (MLS) multipath

j environment. The site simulated, Crissy Field, California, was selected by the

as a potentially difficult STOL gort multipath environment due to the proximit yof

International` Civil Aviation Organization (ICAO) All Weather Operations Panel

buildings to the a

MIT andoDMEositingvateCrissylField

(ref.) 1). The NASA Ames six-degree-of-freedom simulation of a deHavilland ; <g^^ \\ C-BP_^STOL aircraft and Automatic Flight Control System (AFCS), designed to

utilize the MLS DME aswell as angular infrrmati-in, was used. to determine theaircraft response to these multipath errors. The effects of'iridividual"andcombinations of MLS multipath errors were evaluated in the automatic control

` mode from 500 ft (152 m) altitude on the final approach to touchdown. The

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sensitivity of several AFCS variations to multipath errors was also determined.

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SYSTEM DESCRIPTION

This section contains a brief description of the simulated ST-OL aircraftand pertinent portions of its flight control system, the MLS and Crissy Fieldsiting, and the simulation conditions.

'J

Aircraft-. 7

The STOL aircraft simulated in this study is a prototype version of thedeHavilland DHC-5 (C-8A) twin-turboprop STOL transport (ref. 2) illustrated

- in ,figure 1. The simulation program used in this study is a"representationof the automatic control portion of the STOLAND-piloted simulation facilityon an IBM 360 computer (ref. 3). The simulation model includes the six-degree- =r

_ of-freedom nonlinear aerodynamic equations of the aircraft; the kinematic andnonlinear aerodynamic equations of the aircraft; the kinematic and nonlinearaerodynamic equations of motion (ref. 4) and a General-Electric T64-10 turbo-prop engine model. Further descriptioa;s of the systems represented by theSTOLAND facility are included in references 5 and 6."

MLS Multipath Errors and Siting

The MLS multipath errors were computed through the use of a simulation- developed by MIT Lincoln Laboratory (ref. 1). This simulation represents a

Time Reference Scanning Beam (TRSB) MLS with a conical coordinate system,C-band azimuth (AZ), primary elevation (EL-1) and flare elevation (EL-2), andL-band DME signals. Multipath errors are de%ermined at the actual transmittedsampling rates (40 Hz for DME, EL-1 and EL-2, and 13.5 Hz for AZ). The datawas proces-ed by a model of the MLS airborne receiver which includes motionaveraging of the signals over each output sampling period. The receiver outputdata rate was 5 Hz for all MLS functions. The errors were calculated at dis-crete points along the nominal undisturbed flight path. The STOLport MLSsiting and multipath environment used for this study are shown in figures 2and 3. The simulated buildings are based on actual Crissy Field locations andrepresent a"potentially severe multipath environment due to the closeness ofthese structures to the runway and MLS antrnnas. Some of these structures are

r located above the transitional surface specified by the STOLport design cri-teria - (ref. 7) as shown in figure 2(b), j

Control and Navigation Systems

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The aircraft control system functions are simulated on ar.-In M 360 root-puter in a manner similar to that programmed in the airbornedigital computerso that the fixed-point computational accuracies in the airborne computer are

-reserved.day advanced

The'sensing and frequency ranges used are comparable with present-y autopilots; however, this AFCS is designed to use all of the MLS

information including DME. Although the simulation is capable of representingvarious modes of automatic flight in the terminal area (refs. 5 and 6), the j

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{simulation results in this report are limited to the final portion of theglidepath, flare and touchdown.

Only those portions of the AFCS system which interact with the multipathdisturbances and result in aircraft motions will be described.

The pertinent STOLAND navigation and longitudinal control systems are_illustrated in figure 4. The details of each subsystem are described inappendix A. In addition to the basic AFCS described in figure 4, an alternateglide-slopo tracking system, which is intended to-v ie less sensitive to DMEnoise, was simulated (see fig. 20, appendix A).-^The separate glide-slopetracking filter obtains filtered glide-slope error and rate directly from thecalcu'ated error relative to the nominal glide slope. In the basic system,these errors are computed from thq 1orgigdinal and vertical runway-orientedposition/rate estimates (RR , 2R, kR, and ZR in fig. 4). Details of the dif-ferences between the two systems are described in appendix A (fig. 20), and ananalysis of their sensitivity to DME,noises is shown in appendix B.

Since aircraft lateral motion due to the very small azimuth multipatherrors is negligible, the lateral control, localizer tracking, and roll/yawstability augmentation systems are not shown. Similarly, since the multipath -.disturbances do not affect airspeed or throttle motion, , the description of the

autothrottle system is not included.

Simulation Conditions

All runs were made with the following conditions: a six-degree glideslope, 71-knot airspeed, aircraft in the landing configuration, and initial-ization of multipath errors at 500-ft (152-m) altitude,

The MLS multipath errors were calculated at discrete points along thenominal unperturbed flight path for the C-8A/STOLAND simulation to investigatetheir effects on aircraft motion. Note that this procedure neglects any changein the received multipath signals due to perturbations of the aircraft fromthe nominal path. However, this can be justified since the excursions of the'aircraft due to these errors were small as shown in the following section. Inorder to isolate the effects of the multipath errors, no atmospheric distur-bance or MLS errors other than multipath errors were simulated.

SIMULATION RESULTS

The - glide-slope tracking and flare results are discussed separately.

Glide-Slope Tracking

Simulation with the Basic C=8A/STOLAND- System- The Crissy Field multipatherrors, supplied by the Lincoln Laboratory, are ,shown in figure 5. A detailedanalysis of these errors is included in reference 1. Note that the MLS

3

azimuth multipath errors are negligible (<0.001° peak-to-peak), and the onlysignificant elevation multipath error is negative 0.02° spike at 2!43 sec whichis caused by Building B-5 (fig. 2). The DME errors are initially small butgradually increase. A small positive DME bias and several cyclic negativespikes of 25200 ft (61 m) maximum amplitude occur near the threshold. Thesespikes are apparently caused by Building B-1 (fig. 2). Multipath errors duringthe flare will be discussed in the section on Flare and Touchdown.'

The response of the aircraft is shown in figures 6 through 9 for the fol-lowing sets of multipath errors:

figure 6 (run 1): No MLS errorsfigure 7 (run 2): MLS Elevation (EL-1) multipath errors onlyfigure 8 (run 3): MLS DME multipath errors onlyfigure 9 (run 4): MLS EL-1 and DME multipath errors

Generally, the plotted results are shown with expanded scales so that therelatively small aircraft mot'nns are apparent. For the data with doublelines, the right scales correspond to solid data lines and left scales co2re-spond to the dashed data. (This is true for both systems of units shown.)The lateral response of the aircraft to the very small azimuth errors(<0.0006 deg) was negligible, and hence the aircraft's lateral response resultsare not shown. -

Time stati stics and-maximum values of selected aircraft parameters, whichrepresent the incremental effect of the multipath disturbances are summarizedin table 1. The incremental data for a particular run were computed as thedifference between the response with (run 2, 3, or 4) and without (run 1) themultipath disturbance. The statistical averages were computed for the flight-time interval for which multipath errors were determined (t = 10.8 sec tot = 46.9 sec).

The response of the aircraft to angular multipath errors was negligible.As was previously noted, the very small MLS azimuth errors do not cause anynoticeable aircraft lateral motions. Figure 7 and run 2 of table 1 show thatthe MLS elevation multipath also does not cause any noticeable motion. Eventhe effects of the small elevation multipath spikes near the CAT I decisionheight (t 43 sec) are filtered out by the airborne system.

The response of the aircraft to the DME multipath is noticeable but small(fig. 8 and run 3 of table 1). The maximum perturbations (table 1, run 3) showthat the maximum deviation from the glide slope due to the DME multipath is0.6 ft (0.2 m)., This value is small compared to the CAT II decision heightindicated vertical window of ±12 ft (3.7 m), 2a (ref. 4). The peak verticalacceleration 0A ft/sec 2 ,(0.11 m/sect = 0.012 , g), with a frequency of approxi-mately 1/3 Hz, is below any of the passenger comfort- criteria tested or pro-posed-in ref. 8. For instance, it is below the 0.1 g (rms) objectional accel-eration level and roughly the same as the 0.015 g (peak) perceptible levelreported for large transport aircraft in reference 9.

The DME multipath errors affect the vertical aircraft motions because theSTOLAND autopilot utilizes DME to augment glide-slope angle tracking error

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REPRO))UCIBILITY OF THEORIGMA.L PAGE IS POOR.

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during the final apprarh phase as shown in figure 17. 1(See appendix A-for" the explanation of fig. 17), That is, a gain scheduling function, slant range

(atd), and a vertical velocity damping term (20 are used. Although not shown jin detail, the DME errors propagate into the aircraft vertical motions mainlythrough the calculation of estimated 2g, then inertia;: flight path angle (YI),iand hence pitch command ( B c) as shown in the glide-slope tracking` nontrol lawof figure 17. An examination of the DME multipath errors of fig. 5 indicates,:two forms of disturbance: (1) a slowly increasing positive bias which ispresent for most of the approachpath, and (2) a series of spikes which 'occur

' during the latter portion of the path, An examination of the aircraft responseindicates that the aircraft is equally sensitive to both forms of disturbance.

Simulation with densitized guidance systems- In order to _examine the sen-sitivity of the basic airborne system to the DME errors, two runs were madewith gain changes in the navigation filters and the glide -slope tracking poor-tion of the autopilot, respectively.

,rIn the first change the cut-off frequencies of the navigation filters

I

s ^!erea lowered by a factor of 0.7. The damping ratios were also slightly changed.

p appendix for the comparisonfrequency

fresponses of the (-y

ori ginal and desensitized filters. Figure withshows the aircraft responsegsure 10 this navi gation filter modification

'

and time statistics for this run (run 5)b

-

are included in table 1. Comparison of figure 10 to figure 8 (run ,3 and run 3of table 1) shows a reduction in the aircraft accelerations 'rat, and ele-vator deflection; however, the position deviations are approximaely doubled. i

The second simulation modification involved desensitizing " the autopilot(with the nominal navigation filters). The proportional gain Kp and thederivative gain KDin figure 17 were reduced by a factor of 0.75 and 0.5,respectively, while the integral gain KI remained the same. The results of

g this modification are shown in figure 11 and run 6 of table % 1. This data showsthat some improvement is obtained relative to the basic system of run 3; how-ever, the amount. of improvement is not significant considering the smallP g g jres onse of run 3.

s Simulation with alternate Aide-slope tracking system- Although the effectof DME multipath errors on the aircraft performance was small, the alternateglide-slope tracking scheme was investigated in order to see what further 1'improvements in performance could be made. This scheme which utilized aglide-slope tracking filter (fig. 20) is intended to reduce effects of DMEnoise resulting from any source. The filter has also been tested with other - +.

q types of DME errors, and has resulted in a better tracking performance than

iithe basic system.

The simulated results of figure 12 and run 7 of table 1 show the reduc-tion in aircraft perturbations due to the DME errors compared to the basicAFCS of figure 8 and run 3 of table 1. The superior performance of this Sys- -tem is primarily due to the reduction of DME propagation into the

s^&., 1Present- day autopilots utilize signals other than the DME to augment the

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f glide--slope tracking error signal; hence, these systems would not be affected jby DME multipath.

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estimated vertical velocity and hence into the glide-slope tracking command(appendix B).^ o

Flare and Touchdown

The multipath errors during flare are shown in figure 5. The azimuthmultipath errors during flare are larger than those on the glide slope. Theseerrors are due to the reflection of sidelobes from the structure B7 (train,fig. 2). The magnitude of'tha errors, however, is still small (maximum 0.0024°),and since the larger errors occur just before touchdown (duration less than2 sec), the automatically controlled aircraft does not respond to these errors.The flare (EL-2) multipath errors are small on the 'glide slope (maximum magni-tude 0.0076 0). The EL-2 errors monotonically increase near touchdown to amaximum of 0.09°. This increase, however, occurs during the last second, andhence does not cause any noticeable aircraft perturbation. The large multi-path errors during the last second are mainly caused by the ground reflection,_since the EL-2 antenna (bore center height = 15 ft_ (4.6 m), fig. 2) is lookingdown toward the aircraft (height 10 ft (3 m)).

The response of the aircraft without MLS multipath errors (run 8) andwith DME multipath errors (run 7) is shown in figures 13 and 14, and summar-ized in table 2. The alternate glide-slope tracking system was used during -glide-slope tracking for these simulations. The effects of the azimuth, ele-vation (EL-1) and flare (EL-2) multipath errors are negligible, and hence thedata for the runs with these errors are not included.

An examination of the results shows that;,the relative importance of themultipath errors during flare is the same as was observed during glide-slopetracking; that is, the effects of MLS azimuth and 'elevation (both EL-1 andEL-2) ,angle multipath on aircraft motion are negligible, whereas the DME errors'result in noticeable but small motions. The DME errors can affect touchdownaccuracy both by altering conditions at flare initiation (end - of glide-slopetracking), and by further modifying motion during the flarr `I because of estima-tion errors. However, while not separately shown, the DME errors during flaredid not alter the aircraft motion significantly so that changes at touchdownare due primarily to changes at flare initiation height. As shown in table 2,,the DME multipath errors cause the longitudinal touchdown to vary by 23 ft(7 m ), which is a ;p711 percentage of 700 ft (213 m), 2a total allowable STOLlongitudinal dis erg p ;ion suggested in reference 6.

CONCLUSIONS

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The simulation results show that, during the final approach and flare, theresponse of an automatically controlled C-8A STOL aircraft to the MLS multipathat Crissy Field, California is as follows:

Neither the azimuth nor elevation (EL-1/EL-2) multipath affects the air-craft response. The response of the aircraft to the relatively large DMEmultipath [200 ft (61 m) peak] is noticeable but small. For instance, during

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glide-slope tracking, the maximum aircraft deviation from the glide slope isonly 0.7 ft (0.2 m), the maximum vertical acceleration is 0.012 g, and themaximum pitch angle-change is 0.34°.

ACKNOWLEDGMENT

The authors would like to express their gratitude to Dr. Tsuyoshi Goka,Ifo:; his valuable suggestions and Flora Watson for her help in computer-, ?;programming.

APPENDIX Ar^ I

DESCRIPTION OF CONTROL AND NAVIGATION SYSTEMS ?°

The pertinent STOLAND navigation and longitudinal control subsystemsillustrated in figure ,4 are described in this section.

` a ^I.

Navigation Filteringi

Thefilters used, in this study are fixed parameter complemen- -at are intended for use with a variety of navigation aids andtar. filte rs that

control system modes. The filters combine resolved accelerometer information 3with MLS derived position information given in a runway-referenced rectangular {coordinate system (XR, Y', and ZR in fig. 4). In the basic system, the calcu-lated altitude (derived Prom DME and EL-1 signals) processed by a second_is Sorder filter to obtain estimated altitude and rate ` ior glide-slope tracking.A separate altitude calS:ulation using the EL-2 signal is blended into a secondvertical filter between ' 400 and 200 ft (122 and 61 m) altitude to provideestimates during flare.

The filter black diagrams are given in figure 15. The transfer functionsfor position estimates are given by

1

horizontal Filter i

!R(S) XR(S) 0.4(52 + 2^,a 3S + a3)11 (S)_ Xi(S) Yn(S)

7(S 2 (1).'7(S + „ a l )(S + 24 2a2S + a2 ) si

- al = 0.2,- a2 = 01, 14, a3 = 0.1

52 = 0.7, C3 = 0.75

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2R(S) _ 0.65(S + as) ^''a

HV(8) = 2R(S^^)

) S2 ,+ 244a4S + a2

a4 = 0.42, as = 0.27, K4 = 0.787

XR, YR, ZR : Position derivedfrom MLS measurements

XR, !R, 2R° Position estimates

Note that the horizontal channel consists of three integrators whereas thevertical channel involves two. The gains for the filters are based on flighttest experience with the STOLAND system.

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-^frequencies- p g quencis are reduced so that-Results- Glide-SlopeiTracking), the cutoff8freqtheir transfer, functions are expressed by

3aHS 2 + 3a 2S + aHH (S) - (Horizontal Filters)H,i (S + a ) 3H

o 1,2aVS + av

H p S) _ (Vertical Filters)

(

33

where the cut-off frequencies - are _aR = 0,l, aV = 0.3. Figure 16 shows the-original and desensitized navigation filter frequency responses (HH(S) andHV(S)). Figure 16 also gives the response of the correspondig transfer func-tions between derivatives of MLS measurements and rate estimates(Xg(s)/sXg(s), etc.).

I^^i

Glide-Slope Tracking Control. _

The glide-slope tracking law illustrated in figure 17 is expressed by the1

following equations.

Pitch Command

C (Y IY)TD GS D REF - 3)B KP n 6 +KJ`J

IXP 3

322

", KD = 1 s YREF 6 0- ,

Pitch Integral Command'

0CI = KI J nTDSGS ' KI _ 960(4)

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TITD xR + fR + 2R : Slat range to touehdown 2 (5)

f zR

dGS = YREF - tan- 1 ^X.) : Planar glide-slope dcviation 2 (6)

`Y1 = tan- 1 Lk : Inertial flight-path angle2 (7)XR + YR

The vertical position error from the nominal glide slope (nTDSGS) is com-puted from position estimates (4, ^R and LR) and used to provide propor ionalQnd integral terms of the glide-slope tracking law. The rate estimates XR,YR and $R) are used to calculate the vertical flight pain angle YT and pro-vide a derivative term in the control law.

r

Flare Control

Filtered altitude and altitude rate derived from the flare (EL-2) antennasignals are used to initiate flare and determine flare control during theflare.' Altitude rate feedback is usrai used on a calculated rate command. Apredictive command-is also added sing feedback control alone is not sufficientto generate the required change from the six-degree glide slope to the desiredsink rate at touchdown: --

The flare laws re illustrated in figure 18 and summarized by the follow-ing equations.

Flare 'Initia'tion Law

Z Tp$R < ZF

-Tj, = 2.0 sec , ZF = 19.0 ft 0.8 m) -

2Although the data presented in this reportare expressed, in the coordi -nate system given in figure 2, the rectangular coordinate system implementedin the airborne computer is.;as follows (ref. 4). Its origin. and polaritiesare defined by the following sketch.

Ay

EL-2 X EL-1 X

ORIGIN R AIRCRAFT

Az° X -^- X X EL•2 X t- lX EL ,.` Z DME/AZ

Zl

1 ORIGINAZ (ARROWS INDICATE POSITIVE DIRECTIONS)

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Flare Control Law

Pitch Command (Closed Loop Command)

6^'= KPFZe t KIF J Ze + KDFZK

KPF 5/4 , KIF - 1/4 , KDF ° -3/4

Ze = ZCMD - (ZR k ZTp)

C rr t to)

ZCMD ^ZR(to) ZTD] exp f- T

I Exponential flare\\ e / sink rate command-

ZTD = 1.5 ft/sec (0.46 m/sec) , Te = 1.8 see'

to : Time of flare initiation

r Predicted Pitch Command (Open Loop Command)

t -oop = (YKEF + YF) r1 - exp( T

L \ oYr = 3.9 0 , To = 2.0 sec

A-slight amount of throttle retard was used during the exponential flaremaneuver to reduce the probability of long floating touchdowns.

Pitch Stability Augmentation System

The pitch commands (8 c , Bcl , 0 ) of the glide-slope tracking and flarecontrol laws are augmented by pitch angle and angular rate feedback signals tostabilize pitch attitude., The augmentation system is illustrated in figure 19.The pitch rate measurement

is fed through a washout filter to suppress steady-

state rates during turns.

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Glide-Slope Tracking Filter

For the alternate glide-slope tracking system, a glide-slope trackingfilter was implemented to reduce the effect of DME errors during glide-slopetracking. Figure 20 illustrates the difference between the two systems inestimating the altitude error, Ah, from the nominal glide slope.

The glide-slope tracking filter has th- same structure and gains as the-,'vertical filter in figure 15. However, its MS position input is the measuredaltitude error from the nominal glide slope calculated by

4

dh' Z''- (tan YREF)xR ZEL (8)

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where ZEL is the height of EL-1 antenna. Its outputs, estimated altitudeerror (®h) and error rate (®h), are utilized in the modified glide-slope track-ing :aw:

®C KpAh + KDDAh (9)

32 1KP = 360 ' KDD 120

OCI KI I Ah (10)

1RI = 360

Note that this law is equivalen t to the basic glide-slope tracking law ofequations (3) and (4). Ali and eh in equations (9) and (10) are equivalent to

"TDdGS and (YREF - YI) in equations (3) and (4). The difference in thederivative gain KDD in equation (9) versus KD in equation (3) is due tothe difference in dimensions between A and ( YREF - YI)-

APPENDIX E

ANALYSIS OF DME V ;;- R REDUCTION IN THE GLTDE-SLOPE TRACKING FILTER1

The improvement of the glide-slope tracking performance in the presenceof DME errors with the glide-slope tracking filter (see Simulation Results) isprimarily due to the reduction of DME noise propagation into the damping termof the glide-slope tracking law. This section contains an analysis of theimprovement.

The equations for the conical to rectangular coordinate conversion in theairborne computer are (fig. 4)

YR = -R' sin AZ'

XR = (E- 1i^y/A

ZR = ZEL XR2 + (YR - YEL) tan EL'

where

A = 1 + tan g EL'

B = XDME

C = XDME2 + YR2 + (YR - YEL)tan2 EL' - R' 2 cos t AZ'

11

REPRODUC1i31L1TY UI,' THE

ORIGMAL PAQR J5 I'k? R

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-^XDME: X position of the DME antenna

P YEL: Y position oi'the EL-1 antenna

ZEL: Z position of the EL-1 antenna

During glide-slope tracking, the lateral motions and azimuth errors aresmall so that

( 1 I

AZ' 0 , YR R 0 and IYELI << IXRI

Furthermore, since EL' yRE^; = 60

tang EL' °° 0.01 °° 0

Therefore, XR and ZR are - approximated by

XRR -

°

XDME - (R + AR)

Z'-' (tan EL') (R -f+ AR -XDME) - ZEL

where AR is the DME measurement noise. With the above approximations, equa-tion--(8) becomes

Ali' y- (tan EL' - tan YREF) (R + AR - XDME) (12)

Differentiating equations (11) and (12), and rearranging with the approximationtan EL' =-EL'

ZR- EL' AR + EL' • R + EL''(R + AR - XDME) (13)

Ah' e AR + e R + EL'(R + AR - XDME) (14)

where e = EL' - YREV

A comparison of equations (13) and (14) explains the reduced sensitivityto DME noise for the alternate glide-slope tracking system with the glideslope tracking filter. The error due to higher frequency DME noise, AR, atthe input of the. glide-slope tracking filter is significantly smaller thanthat at the basic vertical filter. This;is because the DR multiplicationfactor in equation (14) (e) is much smaller than the factor in equation (13)(EL'). Since the same vertical filter is used for each system, the same_rela-tive magnitudes of DME errors propagate into the rate estimates, 2p and Ah,and hence, into the glide-slope tracking laws (eqs. (3) and (9)).

I^i

i

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7

3

REFERENCES t °

1. Shnidman, D. A.: .MLS Multipath Errors for Four Representative Airport .-

K

Environments, MIT Lincoln Laboratory ATC Working Paper 44WP-5022,September 1975. i

McGraw-2. Taylor, J. W. R. (ad): Jane's All the World's .Aircraft 1968-1969, % pyHill, New York, 1969. 93

3. Karmakar, J. S. and Kareemi, M. N.: Organization and Use of a Software/Hardware Avionics Research Program (SHARP), NASA CR-137576, July 1975. j

4. McFarland, R. E.: A Standard Kinematic Model for Flight Simulation atf

;NASA-Ames, NASA CR-2497, 1975.- i

5. Young, L. S.; Hansen, Q. M.; Rouse[, W. E. and Osder, S. S.: Developmentof Control System, NASAof STOLAND, a Versatile Navigat+'on, Guidance andTM X-62,183, 1972.

6. Burrous, C. N.; Brown, S. C.; Goka, T. and Park, K. E.: Microwave LandingSystem Requirements for STOL Operations, AIAA J. Aircraft, vol. 13,

l1976, pp. 140-148. r;

7. Anon.: Planning and Design Criteria for Metropolitan STOLports, FAA } = -" Advisory Circular 150/5300-8, November 5, 1970.

I

8. Proceedings of Symposium on Vehicle Ride Quality, NASA TM X-.2620, ,a1972. —__ "° r

9. Holloway, R. B.; Brumaghin, S. H.: Tests,and Analyses Applicable toPassenger Ride Quality of Large Transport Aircraft, NASA TM X-2620,1972, pp. 91-113.

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