Prediction of aircraft handling qualities using analytical models of the human pilot

, 4 /' / _.-_ 7- /- _- 3,_2,33

' NASATechnical Memorandum 84233

N AS A- TM -84233 1 98200 16 332

Prediction of Aircraft Handling

Qualities UsingAnalytical Models

o f the HumanPilot

R ona ldA. He ss

Ap ri l 1982 _" ''_''' ":_"""

" LANGLEYRESEAR;: R LIBRARY,NASA H.A...,TON, VIR G Ir'I!A

,N / A

Na t ional Aeronautics and

SpaceAdministration

NASATechnical Memorandum 84233

Prediction of Aircraf t Handling

Qualities Using Analytical Models

of the Human Pilot

i

Ronald A . Hess, AmesResearch Center,Moffett Field,California•

N AS A

Na t ional Aeronauticsand

SpaceAdminis t ration .

Ame s R es earch Center

MoffettF i eld , Cal if orn i a 94035

25- 1 P RE DICTIO N O F A I R C RA F T HA N D L I N G Q U AL ITI ES U S I N G A N A LYTI CA L MO D ELS O F THE H U MAN PI LOT , b y Ronald A . Hess R e s earc h S c i en ti st NASA Am es Research Ce nt er , M off ett F i eld, Cal i forn i a 94035 SUMMARY The opt i m al c ontr o l m odel (OC M ) of t h e hu m an p i l o t i s appl i ed t o th e s tudy of a ir - craf t h and ling qua lit l e s. A t t e ntion i s fo cused pr i m arily o n l on g i t udina l t asks. T h e m od e l lng t e chnique di f fe r s fr o m prev io us app l ica t ions o f t he OC M in t ha t c o nsiderab l e eff o rt is expended in si m plifying t he pi l o t / ve h lc l e ana ly sis. Aft e r b r i e fl y r e v i ewing t he OC M , a t e chniqu e f or m ode l lng the pi lot c o n t r o lling highe r o r d e r syst e ms is in tro - duced. Following t h i s, a si m pl e cri t e rion f o r de t e rm ining t h e suscep t ib i li ty o f an a ir cra ft t o pi lot - i nduced o sci ll a t ions (PIO) is f o rmu l a t ed. Fina l ly, a mo de l -based m et ri c for pilo t ra t in g p r edic t ion is discussed. The resulti n g m od e ling p ro c e dur e provid e s a r e la t iv e ly si m p l e , y et u nifi e d approach t o th e s t udy of a va r i e t y o f handling q ua l i ti e s p roble m s.

1 . I N T R ODUC T IO N The a dvent o f mode r n digit a l s t ab ility a nd cont r ol a ugment a ti o n systems h a s c r e a te d a rene w ed inte r e s t i n the s t ud y of a irc raf t l o n g i tud i nal h a ndli ng qua li t ies . This renewed interest i s a ttri b ut a ble to two fac to rs: Firs t , the hi g her order n at ure of the d y namics typ icall y a s so cia t ed wi t h di gi t a l con t r o! systems makes an a ly t ical predic t i o n of h a n d li n g qu a li t ies d iffi c ul t . Con t emp o r a r y h a n d lin g qu a litie s spe c i f i ca t io n s (R ef . I ) a re wr i tt en a ssumin g "cl a ssic a l" a ircr af t c h a r ac t eris t i c s , e. g ., in the lo ng itudi na l m o de, the existen c e of dis t in c t a n d domin a n t short-pe T iod d y n a m i c s is a ssume d . With moder n sys t e m s, the sho r t -perlod c h ara c t er i s t i c s m ay be dr a m a tic a ll y a l t e r ed by f eedb ac k a nd t he hi g her o r der control s y s t em d y n a m i c s ma y domin a t e the vehicle h a ndlin g qu a li t ies.

Second, shor t c omin g s in predi c t i ve t e c h ni ques a r e m a de even more cri t ic a l b y the f ac t t h at severe h a ndling qu a li t ies defi c iencies of t en a r i se in pr ac t ice w hich a re directl y a tt ribu t a ble to the hi g he r orde r n a t u r e of the d ig i t a l con t rol l aw implement a tion. An ex a mple of t h i s is the a bilit y o f high frequen cy ph a se l ag s o r t ime del ay s i n the control s ystem t o sh arply d e g r a de ai r craf t h andlin g quali ties a nd t o be a co n t r ibu t i n g fac t or t o pi lo t -l n duc e d o s ci ll a t io n s ( Re f _ 2 ).

I n th e r esea r ch t o b e d e sc ri b e d , a p i lo t - m od e l ing t echniqu e fo r h and l i n g q ua l i t les r es e arc h, di s cus s e d i n Ref . 3 , i s u ti liz e d a n d e x t e nd e d t o c o v e r hi ghe r or d e r s ys t em s.

The c h ara cteristi c s o f o ver t hir ty a ircr aft c onfi gu r a t i o ns ar e ana lyzed, p rim a r ily i n the lon g itud i nal mode. Par t i cul a r emphasis is p l a ced u p on t h o se con f i g ura t ions where c o ntrol sy s tem dynam i cs and t ime del ay s h a ve b een reco gn ized as con t r i bu t in g fac to rs to handl i n g qu a li t ies de f icienc i es . The c o ntribution o f vehicle / contr o l system d y n a mics t o PI O te n dencies is o u t l ined, an d a me t ric f or pilot ratin g p redict i on is d i scu s sed.

2 . BA C K G R O UND The pilot-modeling te ch nique a s dis c ussed in Ref. 3 forms the fr a m ework f or t he rese a rch des c ribe d here. This t e c hniq u e u t ilizes the o p timal con t rol model of the huma n pilo t and a novel me t hod for the a priori sele c tion of d om i nant OCM parameters ( i n d ex of performance weighting c oef f i c ients and observa t ion noise / slgnal ratios). A brie f tutorial review o f the pro c edure for sele c t in g in dex o f per f orma n c e weigh t ing coefficients is now prese n t ed. Co n sider t he longitud i nal t racki n g t ask o f Fig. I in w h ich the pilo t is attempti n g to min i m i ze p i t ch a tti t ude devi a t ions e(t) i n the presen c e of a t mospheri c d i sturba n ces. I gnore the d a shed " i nternal attit u de c om m a nd " for the presen t . An ac c ep t - a ble i nde x of per f orma n ce for t his t ask would be (Ref. 3 ) lim I ee(t) / e_ + &2(t) / & d t J = E X _ _ 2 X

{ !: I

. × w here _(t ) is c ontrol rate.

As discussed in Re'f . 3, w e assign an arbitrary maximum allo w able deviation to the t ime rate of change of the error, _(t ), and denote it eM. Now an effective time constant T ca n be i n t r o d uce d to def ine m a x i m u m a ll owab le dev ia tions o f t h e i n te g r al a nd deri va tives of _(t ) as : 2 5 -2 0 K - 6.T ; 8M TM spe ci f ied bu t a rbi t r a r y ; 8M = eM / T ; ( 1 ) a nd T he j us ti f ic a tio n fo r us i ng a s i ng l e ti m e co nstant to re p rese nt t he rat io o f th e max i m u m value o f a va ri a bl e t o that o f it s nex t hi ghest de ri va ti v e r ests upon th e sy s te m b andw i d t h i mpl ica tio ns which fo l l ow whe n E q . ( 1 ) is us e d in i mpl e me nti n g t he OC M . We w i ll a l s o assign a m ax i m u m all o wabl e devia t i on to t h e t i me r a t e of change of th e pil ot 's contr o l, _ ( t ) , a n d deno t e i t _M " Si m i l ar t o E q . ( 1) we wri t e 6M = 6 M T ; 6 M = to b e s el ec t e d ; 6M = 6 M / T ; T h e v a l u e of 6M i s not a rb i tr ary , h o w e v e r , but i s f o und us ing Eqs . ( 1) a n d ( 2 ) a nd t h e v e h icle dy n a m i c s a s fo l l o ws: Let t h e p itch at titu d e dyna mic s o f the a i r cr aft be give n b y sn-1 + an_2sn-2 + + als + a e " " o (3) (s) = K s n + b n_l s n_ l + . . . + b lS + bo Th en , as exp l a ine d i n R ef. 3 , we wri te ( 4 )

I / T n- I . I b n_ l i / T n-2 * . . . Is ll * IbolT _=

• +la n * l a ll + f a ol T)

Th us , on c e T i s k n ow n, _M a n d 8M (a n d , i f n eed e d , 8M, e t c.) c a n be dete r m ine d i m m e di - a t e ly . C hoo s i n g T i nv olv es se l e c tl n g a do main o f l / T: I / 4_ < I / T < 4 / T a n d t h e n pl o tti n g J , t he value o f t h e OC M ind e x of p e r fo r m a n ce , vs I / T. The o p e r a t ing p oin t o r " kn e e " of t h i s curve d et e rm i n e s T. The k n e e is d e f i ned as t h e po in t w h e re _ J JIT =_ / 4 - JIT=4T _log(l l T ) = n6 iog( 4 1 _ ) - log(l 1 4_) ( 5) H e r e n 6 is a c ons t ant , n o m i na lly u nit y, wh ich c a n b e used t o re f le c t m an i p u lat or c h arac ter is t ics , m uc h li ke an e ffic ie ncy fac t or; T is th e p i lot 's t i m e delay (no m inal ly 0. 2 s e c). J IT =T / 4 is th e va l u e o f t he i n d e x of p erfor m ance which r e su l t s wh e n T = T / 4.

Th e a b ili ty of the OC M p ara m e t e r s e l e c t i o n t e c h ni q ue t o p rovid e a p ilo t m od e l w hi c h m a t c h es me asured p i lot d e scri bing f unc t io n s , r e m n an t p o w e r s p e c t ra l d e n si t i e s and root me a n squa re ( RMS ) pe r fo rmanc e me as u r es wa s d em o ns t ra t ed i n Re f . 3 . I n a ddi t i o n, the 25-3 m ode li n g t echn i que was shown capabl e of pr o viding qualita t i v e and quan t i t a ti ve handling q ua l i t i e s as se s sment s. T h e m e tho d f or se l e ctin g o b s e rva tio n n o ls e / sl g nal ra t i o s fo r t he OC M i s discuss e d in R e f. 3 and wi ll not b e d e a lt wl t h h e r e .

A l th o u g h E q . ( 3 ) sh o ws d y nam i cs o f ar b i t rary o rd er , all t h e p it ch at t i t ud e dyn am ics o f Re f. 3 w e r e of t h e f o r m : e K e (s+ 1 / TL) - s ( s2 + 2 ¢ n _ nS + _ ) ( 6) Wh e n high e r o r der d y na m ics are e nc o untered, t h e me thod f o r se l e cting t he o pera t in g p o in t needs to h e m odifi e d s l ight l y. Th e l a rg e phase l ags typ l ca ll y ass o cia t ed with th e dyn am ics of vehicles wlth highe r o rd e r dyn am ics n e ed t o be ref l ected in ch oo sing t he d o m ain o f 1 / T t o be us e d i n Eq. ( 5 ). To acco m p ll sh this, a de l ay T D i s defined as t he d e lay which accrues wh e n t he v e hic l e d ynam ics o f Eq. (3) are r e present e d as e K e (s + I / TL)e- r Ds 2 (_ ) - s(s 2 + 2 _ n _n S + _ n ) T h e p aram e t e r s o n th e r i g ht ha nd side o f E q. ( 7 ) ar e fo u n d usi ng a pr o gr a m t o fit a lln_ar t ransfer fun ct ion mod e l t o t h e a c tual v ehic l e d ynami c s (R ef . 4) . Equation (5 ) i s mo difi e d by s i mply repla c ing z w it h z + YD. Th e r e sult i ng equa ti on i s in te rpr et e d grap hic al l y i n F ig . 2. Ca l c ul a t in g z D an d i n c l udi ng it i n Eq. ( 5) c on s t i t u tes th e e x t e nsio n o f t h e m ethods o f R e f. 3 to hi g he r or der s y st em s. I t i s i m po r tant to e m ph a size that t he ac t u al hi g he r o r d e r veh i c le dy nam ics are us e d i n the mod e lin g pro cedu r e; E q. ( 7 ) is empl o y e d o n ly t o se l e ct TD w hich, in tu r n , det e rm i ne s t he do ma in of I / T us e d i n fi n di n g th e inde x of p e r f o r m ance w e l g h _ in g co e fficie nt s.

3. APP L I CAT IO N TO AIRCR AFT H AN DLI NG QU A L I TI E S 3 .1 P il o t - In d uc ed O s ci llations T a b l e I l is ts t h e a ircr a f t confi g uration s w hich ha v e been a n al yz e d in thi s s t udy .

Th e d e s ignat io n s in th e c o lumn l ab e l e d " Co nf i g u ra t ion" use n o ta t i o n fou n d i n t he co rr e- s p o n d ing r e f e r e nces. T h e f i r st six t e en de al w i t h h i gh p e rf o rma nc e f i ght e r - t y pe a irc raft in tr ack i n g o r lan d ing appro ac h co n di t ions a nd ar e t a ke n fr om R e f s. 2 , 5 , a n d 6. Th e s e co nfig ur at ions co n s t i t ut e t he t e s t c a ses for t h e m a j o r i t y o f t h e assess m e nt s. Th e n e xt f ou r c onf i g u r a t io n s are t a k e n f r o m R e f . 7 a nd repre s en t p i l o t -ln- t h e -lo op si m ul at io n s of a h ov e r in g h e lico pt e r . Co nfig ur a tio n s 21 - 25 a re f li g h t t e s t r e sul t s fr o m R e f. 9 in w h i c h t h e P ri nc et on U ni v e r si t y Var iable Re s po ns e A i r c r a ft (V RA ) w a s us e d t o de t e rm i n e t h e e ffe c t o f di g i t al-sam p li ng r a t es an d t i m e d e lay s on l ong i t udin a l ha n d l in g q uali t ies.

T h e v eh ic l e d y n am ics appropr i at e fo r 1 0 5 k t s ai r s pe ed w er e used in th e m o del i n g pr oc e dure.

T h e p ilo t ra t ing s us e d w e re av e rag e v a lues o b tai n e d f rom al t i t ud e tra c king an d approa ch a nd l andi ng t as ks ( F i g . 3 of R e f . 9). Finally , co n f ig u rati ons 2 6-3 2 ar e t aken fr o m Ref . 1 0 w he re a m o v i n g - b as e s i m ul at o r e xper i men t on th e NASA A m es Fl i ght S i m ul a t or for A dva n c e d Air c raft ( F S AA ) wa s d e scri b e d whi ch i n v e sti ga t e d a w in g s l e ve l - t u r n co n t ro l m od e f o r ai r - t o- gr ou n d w e ap o n s deliv e r y. N o t e t h at u nl i k e th e pr ev i ous twe n t y- f lv e co nf i g u r a t i o ns , th es e in vo l v e la t e ral -dir e c t lo n al a irc raf t ha nd l i ng q ua lit i e s. Th e e f fe c t ive v e h i cl e d ynami cs fo r t h e lat e ra l g unsl g h t a i m i ng t a sk we r e param e ter iz e d b y a da m p i ng rati o _n, an u n dam p ed n a t ur al freq u e n cy _ n a n d a p u r e t i me d e lay T D ( R e f . 1 0). Th e d ata f o r th e so-c a l l e d " fin e " t as k w e re u sed. T h is t a s k is ex p la i n e d i n R e f . I0.

A s a n e x amp le of th e m od e lin g r esul t s , F ig . 3 s ho ws t he l ongit ud in a l o p en-l o o p p il ot / v e hlc l e ch ara c teris t i cs ( Yp Yc) fo r t hr e e o f t h e co nf i g u rat i on s used i n R e f . 2.

H er e, t he NA S A Dryd en F - 8 d ig it al fl y -b y -wlre ai r c raft is con si d ered w i th a rudi m entary augmen t a t i on s y s t em (" Pi t ch D i rect") and t hree tran s p o r t t i me del ay s o f 0 .13 sec, 0. 23 sec, and 0.33 sec , respec ti vel y . The p red i c t ed effect o f t he t i me dela y s is a p p arent in t h e reduced o pen-loop cr o ss o ver frequenc i es mc. This o pen-l o op charac t eristic o b v i o u s l y has a d ele t eri ous e f fec t o n t he c l o sed l oop 8 / e c t ran s f e r f u n ct i o ns a s s h o wn in Fig. 4 [e / e c = Y p Y c / ( l + Y pY c ) ] . T hi s t ransf e r func tio n i s i mportan t i n a sses s ing P I O s u scep t ibili ty . Altho u gh t he t ask has bee n def i ned as p l t c h-attitu d e dis t urbance regul a tion, a tt i t ude com m a nds e c i n t ernall y gener at ed b y t he p i lo t would be emplo y ed in p r e c ise aZtit u d e regulation (d a shed llne i n Fig. i). N o t e in Fig. 4, t hat as rD incre a ses, le / e c l and L e / ec de c re a se at all f requencies. Perfe c t comma n d fol l owing, of course, i mpl i es e / e c = 1.0 a t a ll frequen c ies. I n Fig. 4, (e / e c l < 1 .0 for all configurations wh e n _ < 3 .0 rad / se c , a nd i s par t i cul a rly poor for t he co n figuration wi t h T D = 0. 3 3 sec. I t ca n be readil y shown t ha t open-loop crossover frequencies less t han 3 -4 r ad / se c will invari a bl y resul t in poor closed-loop a tt i t ude c om m an d -followlng ch a r ac t eris t i cs. The simples t a nd mos t direct wa y for t he pilo t to a tt emp t t o improve this closed loop com m a nd-follow i ng perform a nce is to in c rease _c b y increasing h i s 2 5 -4 static ga i n . I f t h e p il ot at temp t s t h i s f or th e F- 8 c on fig u ration w ith _ D TM 0.33 s ec, a v e r y lightly da m ped c l o se d -lo o p o s cill a tion o ccur s at _ = 3 .3 rad / se c (see Fi g . 4) .

Th i s i s i d enti ca l to th e PIn f r e q u e ncy shown i n R e f . 2 f o r t h i s con fi gu r a ti on.

Simila r r e sul t s a r e a l so obta in e d for c onf i g u r at io n s fr o m R e f. 5. F i g u r e 5 co mp a re s a p ai r of op e n- loo p t r ans f e r func t ions o bt ained usin g co n f i gu r a tio ns "11" a n d " 12 " f r o m R e f . 5 a nd a p plying t h e p i l o t - mo d el lng t e chn iq ue discuss e d abo ve . Onc e a gai n , t h e d r a m a t ic d iff e r en ce i n th e cross o ve r f r e q u e nci e s _ c is a pp a r en t . Th e e f f e c t s o f t he p il ot' s a ttempti n g to i m pro v e t h e p e rfo r m a n ce o f c o n f i g u r a ti on " 12" by i nc r e a sing his s t a t ic g ai n b y 1 0 dB are shown in F ig. 6. O n ce aga i n , a li gh t ly da m pe d osci llator y m od e is s e e n t o appe a r . Th e simulations of R e f . 5 w ere i n t e n d e d t o pro vid e p e rform ance c o m pa r is o ns for c o n f igu r a tio ns w h ich w ere f li g h t te s te d and discuss e d in R e f . 8. The l a tt e r r ep ort in c l ud e d Pllot -Induc e d-Osci llation - R a t i n gs ( PIO R ) ob t ain e d usi n g th e sc al e of F i g. 7 . I t i s in t e r e s t ing to n o t e t hat con f i g u r a ti on "I I " r eceived an ave r a g e PIO R of 1 i n d i ca t in g a v er y sa t is f ac tor y v e hicl e wh e r e a s c on f i gu r a t ion "1 2 " r eceiv e d a ma r g ina l av e r age r a t ing o f 2.7 indic at ing a vehlc le wi t h defini t e PIn t end e nci e s. Thes e e xp e rim e n tal r e su lt s ar e se e n t o co rro b or a t e t he an alyti ca l f ind i ngs d us t discussed.

Next, c o ns i de r t wo conf ig u r a t i o ns f ro m R e f . 6 d e no te d a s "4 - 1" a nd "6 - 1 . " F i gu re 8 s h ows t he YDYc pl o t s f o r th es e c o nfigu rat io n s. Con fig ura ti o n " 4- 1 " r e ceived a v er y sa ti s f ac tor y.PIO R o f 1 whe r eas c o nf i gu r a t i o n " 6- 1" re ceiv e d a v e r y p o o r P IO R o f 4.

Ind e e d; co n figu r a t io n "6-1" p rod u ced a PIn in fli gh t t es t wi t h a fr e q ue n cy o f a pp ro x i- m ate ly 3. 75 r ad / s e c. A n a l yt i c al ly inc r e a sin g t h e p ilo t 's s tat ic g a in by 4 . 75 dB ( t h e li m i t f o r clos e d- l oo p s t abi l i t y) in th e m ode li n g - re su lt s for t h i s co nf igu rati o n pr oduced a clos e d- l oo p osci ll a ti o n at a p p r o x i mat e ly 3. 5 ra d / s e c. Th i s 4 . 75 dB i n c r e a s e wo u l d i n c r e as e _ c f r o m ar ou n d 1 .5 r ad / s e c t o o n l y a r ou n d 2.5 r ad / s e c as co mp a r ed t o a va l u e o f 4 . 5 r ad / sec f o r co nf igu r a t io n " 4- 1 ."

Figu re 9 shows t h e p r e d i c t ed Yp Yc's f o r a pair o f c onf igu rati o n s f r o m Re f. 9 .

The t ask was longi t u d i nal c o n t r ol in a pp r o ach a n d l a n di n g us i n g t he P r i n c et on VRA.

The va r ia bl e of in t er e s t h er e was t he am oun t of e ff e c t iv e de l ay i n t h e co n t r ol s ys te m .

In t he firs t, an e ffec t ive delay of 0.055 s e c was em p lo ye d , while i n th e s e co n d , 0.3 55 s e c wa s us e d. A g a in , no t e t he s tr ik i ng di ffe r en ce in c r ossove r fr e qu e n ci e s in th e p re dic te d p i l o t / vehl c le dynam ic s. I n the f ir st c ase, _ c = 3 .4 r a d / se c , w h ile i n t he lat t e r , _c TM 0.5 5 r a d / se c . Fli g ht tes t of the f i r st c onfi g u r at i on showed no PIn tenden c ies, while those fo r the l a t t er p r odu c ed P i n's (Ref. 9).

Fin a ll y , Fi g . i0 sho w s the p r edicted YpY c 's fo r a p a i r of confi g u ra tions f r om Ref. i0. I n the fi r s t , the cont r ol s y stem pa ra m e t ers w e r e _n = 1.4, wn = 2 .0 r a d / se c a nd T D = 0.0 se c , while i n t he second, _n TM 1 .4, _n TM 15.0 ra d / sec a nd T D = 0.49 sec.

The _c diffe r ence is a g ain eviden t . Simul at ion r esults indicated that t he confi g ura- tion w ith del ay wa s definitel y P i n p r one a nd t h e one w ithout del ay w a s not. I t is inte r estin g to point out th a t the c onfigu ra tion without del ay still r e c eived an a ver ag e C o ope r -H ar per pilot r atin g of 6 . 5 , eve n t hou g h it w a s no t P i n p r one. Thus, poor pilo t r a tings, pe r se, a re not a ne c ess a r y c onditio n for P i n suscep t ibilit y .

I n e a ch of the cases abo v e , we h a ve m a de di r ect c omp ar isons of vehi c les which we r e found t o be PIn p r one w i t h t hose which we r e not. This w a s done to emphasize the f ac t th a t the m ethod p r oposed he r e is c le ar l y d i s cr i m in a to ry in predicting PI n suscep t ibility.

The simple c r ite r ion for exoneratin g a vehicle f r om P I n tenden cl es r equi r es th a t the p r edicted pilot / vehicle c r ossove r f r equen c ies a ssoci a ted w ith inne r at t itude-loops be g re a te r than 3 -4 r a d / sec.

3.2 C oo per -H arpe r R a tings F igur e Ii i s a pl o t of the C oo per- Harp e r ra ti ng s w hi c h the thl r t y - o ne co nfig ura ti o ns f r om T a ble I r eceived in simul a t i o n o r fl ig h t t es t vs the v a lue o f a p r oposed h a ndling qu a lities me t r ic defi n ed a s K_[( T + T D) / T3 _.J. No ra t i ng s w e r e r epo r t ed in Ref. I0 fo r c onfi g u ra t ion 3 2 of T a ble I. h e nc e , onl y t hl r t y -one da t a poin t s ar e sho w n in Fi g . Ii, The K i c a n be in t erp r e t ed a s a "c a lib rat ion p ara me t e r " w hich, w hen mul t iplied by [(T + T D) / T ]_.J, _llo w s the r epo r ted pilo t ra t in g s f r om di f fe r en t t a sks a nd d a t a sou rc es t o c o a lesce a s sho w n in Fi g . ii. No t e th a t w e do n o t a llo w Ki t o v ar y w i t hi n the a n a l y sis o f a ny p ar t icul ar t a sk, r e gar dless of c onfig ura t ion ch a n g es. Thus, the a n a l y sis of t he si x configu ra t ions f r om Re f . 2 used a s i n g le v a lue of K i (c a ll i t K I ). The a n a l y sis of the seven conf i gu ra t ions f r om Refs. 5 a nd 8 used a single v a lue of Ki ( ca ll i t K 2 ) , etc. I n a ll, six different K i v a lues (e a ch one co rr espo nd in g to t he six diffe r en t s y mbols in Fi g . ii) w e r e used to g ene ra t e Fi g . Ii. Wi t h t he excep t ion of Ki, a ll the p ara me t e r s of t he me t ric ar e a n in t ri nsi c p art of t he modelin g p r ocedu r e, a nd, a s su c h , involve no g uess w o r k on the p a r t of the a n a l y s t . I n o r de r to de t e r mine Ki, the ana l y s t mus t h a ve a n a c t u a l p ilo t ra t in g fo r one of t he confi g u ra t ions t es t ed for the t a sk unde r study. If t he ana lys t does not h a ve su c h a ra t in g a v a il a ble, Fig. ii is s t ill useful, since the c u r ve i s ne ar l y line ar f r om a pilo t r a t in g of a b o u t 2 .0 to i0.0 , a ra nge w hi c h c ove r s 80% of t he Coope r - Har pe r sc a le. Thus, reZ u t£ u e ra tin g ch a n g es m a y be a ble to be p r edi ct ed usin g t he line ar po r t ion of t he cu r ve. No t e t h a t , w i t h the excep t ion of one d a t a poin t (Conflg. 1 9 f r om Ref. 7), t he sc a tt e r in the ra t i n g s in Fi g . Ii is onl y a bou t ±½ a pilo t ra t i n g .

The inclusion o f t he f a cto r [(T + T D) / T ]_ in t he me t r i c dese r ves a b r ief discussion.

I n p r evious r ese ar ch w i t h the OCM, the v a lue of J, a lone, h a s been found to co rr el a t e w ell w i t h pilot op i nion ra t ing (Ref. II). I n m a ny of the confi g u ra t ions s t udied he r e, ho w eve r ( t hose w i t h TD > 0), the v a lue o f J wa s no t ac cep t a ble a s a met r ic. I n 2 5 -5 g e n e r al , the " predicted " opin io n rat i n g in cre m en t s were s m all e r than t hose repor t ed i n e x pe r i m e n t . T he r e a pp ea rs t o b e a r ea son f or thi s b a se d upon p il ot t r ac k i ng p e r f orm a n ce .

Na me ly , w h e n t h e task i s dis t u rb a n c e r egu l at ion i n v o lvi ng re l at l ve ly low- b a n dw l dth t u rb u l e nc e , lar g e tim e d e lays a r e no t n ec e ssa r ily a har b i n ge r o f drama t ic d et e r i o ra t io n in tr ackin g p e r f o r m anc e . This is ana l y ti ca l l y ve r ified by c d nslderi ng th e RM S t r ackin g sco r es fo r c o nfi g uration s 1 a n d 3 f r o m Ta bl e I. H e re, a 15 4 % i n cr e ase in t i m e de l a y b e t w ee n c o nfi g u r a t i o ns 1 and 3 i n v o lves a l og _ c regression o f nearly a d e cad e .

How e v e r, t h e pr e dic te d RM S p itch a tt i t ude sc o re increas e s by o n ly 36% and t h e p re dic t e d • RM S cont r ol-rate sc o re actuall y dec r eases. As w e have atte m pted t o p o int o ut here , h o wever , t he sa m e cann o t b e said fo r discrete c on_n andf o llo w ing or a b r u pt m aneuv e rs.

In this cas e , _ c r e gressi o n can have a si g nif i can t i mp ac t on the ability o f t h e c l osed- l oo p p il o t / vehicle sys t em t o f ol l o w abrupt, int e r nally g e nerated co m m ands. I t c e rtain ly i s n o t u n reas on a b l e to p ost u lat e t h at suc h s ho r t- te rm res pon se c h aract er istics ( in add i - t ion to RM S c h arac t eris ti cs) a r e r e f l ec t e d i n pilot op ini o n ra ti n g . Ind e ed , r e corded p i l o t c om me nts su ppo r t this n ot i o n ( e .g., R e fs. 2 and 6 ). Th e inc l usion of E (T + TD) / T ]_ i n t h e m e tri c a pp e ars to acc o un t f or t he influenc e of th es e dela y s o n p i lot op ini o n in a s tr a ight f or wa r d m ann e r, e m p lo y ing an e asi ly i de n t i f i a b l e pa r am e t e r ( TD).

4. CO N C L USIO N S Th e re s e arch sum m ariz e d in t h i s paper pr o v i des a unif i e d app r oach to pil o t / v e h i c l e analysis , and in p ar ti cu l a r f o r: 1 ) M od el in g t h e pil o t con t ro l l i n g h i gh er o r der sys t e m s .

2 ) Predic t in g t h e s usc ept ibili t y o f airc r af t t o l o n g i t ud i nal PIO 's .

3) Pr e d i ctin g pi l ot r a ti ngs fo r t asks wh en on e c o nf ig ura t ion ra t in g is known , or p r e dicti n g rela t iv e r a ti n g chan g e s be t w e en confi g u r a tion s.

A lt h ou gh t he ma j ori t y of t asks s t udi e d deal t w ith l on gi tud i nal c o n tr ol, five la te ra l - di re c ti onal c o nf i gu r a tion s w e r e s u cc e ssfully analyz e d wi t h n o cha ng es i n t h e m od e l in g t e chniqu e .

5. REFER E N C E S I. Anon. : Military Spe c ifi c ation, Flying Qualities o f Pil o te d Airplane s : M IL- F -8 7 8 5B ( ASG ) , A u g us t 196 9.

2. Be rr y, D . T., Powe r s, Bruce G. , Szala i , K .J ., a n d Wi ls on , R.J. : A S u m m a r y o f a n I n -Fl i ght Evalua t io n o f Co n t r ol System Pur e Ti m e D e lays Du r ing Land in g Using t he F - 8 D F B W Airpl a n e , A I AA Pape r N o. 80- 1626 . 1 980 A I AA At m os p he ri c F l i g h t M echanics Co n f e r e n c e , Da n v e r s, M ass.

3 . H e s s , R . A .: A Pilot M ode l in g Techn iq u e fo r Hand ll n g Q ua l i t i e s R esea r c h , A I AA P a p e r N o. 80- 162 4. 1980 A I A A A t m o s ph e r ic Fli gh t M echan i cs Co n f e r e n ce , Danv er s , M ass.

4. S e i d e l, R. C . : Transfer- F un c tlon- P ar a met e r Estimat i on F rom Fr e q u e n cy R e spon s e Data--A FORTRAN P rogr a m. NASA TM X-3 2 8 6 , 1 9 7 5 .

5 . Arnold , J . D.: An I mprov e d M e tho d o f P redi c t i ng A i r c raft Longitudina l Ha nd li ng Qual l ties Ba sed on t he M i n i mum Pi lot Rating C on c ept. A i r F or c e I n s titute o f Te c hn o logy , GG C / MA I 73- 122, 1 9 73.

6. Smith, Rog e r s, E. : Eff ec t s of C ontrol Sys t e m Dyna m i c s o n F ig h t e r Ap p r o a c h an d L a _ding Long i tu di na l F lying Qua li ti e s, Vo l. 1 . A i r For ce Fl i ght D y n a m ic s Laboratory, A F FDL-TR-7 3 -1 2 2, 1 978.

7. M i ll e r, D. P .; and Vlnj e , E.W. : Fix e d-B a s e Flight Simulator S tud ie s of VTOL Air c raft H a n d lin g Qu al itie s in H o ve ring a n d Lo w - Spe e d Fligh t. Air F Or ce Flight D ynami cs L a bor at ory, A F FDL-TR -6 7 - 152, 1 968 .

8 . N e al , Peter T .; a n d Smi t h , Rogers E .: An I n-Fllght I nvestig a tion to Develop C ontrol System Design Cri t eri a f or Fighter Airpl a nes. Air For c e Flight Dyn a mi c s L a bor a tor y, A F FDL-TR-70-7 4 , 1 970.

9 . Stenge l , R . F. ; a nd Miller , G . E.: F li g ht T ests o f a Mi c r o pr oc ess o r C ontrol System .

Journ a l o f G u id a nce a nd C on t ro l , Vol. 3, No. 6, Nov.-De c. 1 980, pp . 494-5 00.

I0. Sammonds, R .I .; a nd Bunnel l , J.W. , Jr. : F l yin g Qu a l i ties C ri t eria f or Wings-Lev e l- Turn M a neuvering Durin g an Air- t o-Ground W ea pon Deliver y T a s k. A I AA P a per No.

80- 1 6 2 8. 1 980 A I AA A t m o s phe r ic Fl i g h t M ec h a ni c s Co n fe r e n ce , A u g . 11-13 , 1 98 0.

11 . He s s , R.A . : Pred icti on o f Pilo t Op i nion Ra t ings U sing an Op t lmal P il o t Mod e l.

H uman Fa ct or s , V ol. 19 , No. 5 , O ct . 1977 , pp. 459-475 .

Tabl e I. Aircraft Co n f ig urati on s Anal y zed N o . Con f ig u r a t i on R e feren c e 1 F-8 " Pit c hD ire ct "0 . 1 3 sec d e lay 2 2 .23 2 3 .33 2 4 " I SA S " 0. 1 3 s ec d e l a y 2 5 . 2 3 2 6 .33 2 7 " 2D " 5,8 8 " 5 A " 5 , 8 9 " R A " 5 , 8 l O "9" 5,8 11 " 1 0" 5, 8 1 2 " 11 " 5, 8 13 " 1 2" 5,8 14 " 3 -1" 6 1 5 " 4-i " 6 1 6 "6- 1" 6 1 7 "P H- 2 8 " 7 18 " PH -29 " 7 19 "P H -32" 7 20 "PH -35 " 7 2 1 P rin c et o n V R A 0.055 s ec d el a y 9 22 . 135 9 23 . 2 5 5 9 24 . 355 9 25 . 455 9 FSAA Wi n gs - Level T u rn _ n _n r D I 0 (lateral-direction a l) (rad /seo) (sec) 2 6 1.4 15.0 0 I0 27 1 .4 2.0 O 1 0 28 2.0 8 .0 "0 1 0 29 0.7 6 .0 0 1 0 30 0. 5 4. 5 0 1 0 31 0. 3 4 . 5 0 I0 32 1 . 4 4.5 0.49 1 0 / PARALLEL

// I L , NE S

JI _ /' ( ' _8 " t o) T - (f+ 'r o) / 4 OPERATING / / _ /" POINT / //" r " -- -- _ -- _ - _ DISTURBANCE J CO M MAND I I _v , , _ # PITCH -- INTERNAL _ ATTITUDE COM M AND . _ j ATTITUDE I ERROR I """ TR " L ] i

_T U OE o J_ '- 4( " +' o ) " " i /

f f I • log( ¼ ( _ ' + 'r D)) log(4 / ( 'r' P r D)) log(l i T) Fig ur e i. A pi t c h a ttitu d e r egul a tion Figu r e 2. Sele c t ing an "ef f ec t ive tim e t a sk. co ns t a n t " T.

2 5 - 7 @ F O R r D - 0,33le¢AND 5 d8 INCREMENT IN Yp O © m r D - 0.13 _ 20 -- _ _ , _ { ' CL" 0.1 -20 r D B - 20 - r D " -100 ; o: _ .: - 100 r

- 3 oo . , o -o.=, =_/ " - = o "o '"=- ',\\\

-400 i f I I It ''I , , , , , ,l,t,_,| , -400 ........ t .... A. tt I i .1 1 10 .I 1 lO r ad / m c _ ru d / _ Figure3. Pllo t / vehlcle dynamicsf or F ig ure4. Closed - lo o p c hara c t e ri s t ics t h r ee con f i g u r a t ion s f r o m f o r t h r ee c o nf ig u ratio ns Re f . 2. fro m R e f . 2 .

20 _ ' CL< 0.1 / ,* "" ' " /_ =_ ,., o ......................

_o . _ y _ € 1 T _ , _ -20 "'' _ c F O R " 12 " AND 10 dB,N C REMEN 0 0 '100 , , • o -1 0 0 °. ® 1 _ x _w % %, v \ -300 -300 \ -40 0 , -40 0 .1 1 10 .1 1 10 red / m = _ rad / _ Figu re5. Pilot / v e h l c le d y na m i cs f or Fig u r e 6. C l o s ed-loop ch a r ac t e ri st ic s tw o con fig u ra t io ns f r om fo r a con f i g u ra t ion f ro m R e f. 5. R ef. 5.

2 5 -8

NU M Em C AL 9 _ -

DESCRIPTION RATING _ NOTENDENCYFOR PILOTTO INDUCE 1 " r d - 0.3E6 m ¢ UNOESI RABLEMOTIONS.

UNDESIRABLE MOTIONSTEND T O OCCUR 2 0 WHENPILOT INITIATES ABRUPT MANEUVERSORATTEM PT STIGHT CONTROL THESEMOTIONSCAN BE - 100 PREVENTEDOR ELIMINATED BY PIL O T ° u TECHNIQUE . >' _ >- -2oo UNDE S IRABLE MOTION S EASILY 3 V INDUCEDWHENPILOT INITIATES ABRU PT MANEUVER S OR A TT EM PT STIGHT -300 CONTROL THESEMOTIONSCAN BE PREVENTEDOR ELIMINATED BUTONLY AT S ACRIFICETO TA S K PERFORMANCE - 400 OR THROUGHCONSIDERABLE PILOT .1 1 10 ATTENTION AN D EFFORT. _ rad /,= c O SC ILLATION S TEND TO DEVELOP 4 WHENPILOTINITIATES ABRUPT Fi gure 9 . Pi l o t/ ve h lc le d y n a m ic s for MANEUVERSORATTEM PT S TI GHT tw o config u rations from CONTROL . PILOTMUST REDUCEGAIN OR Ref . 9 .

ABANDONTASK TO RECOVER .

DIVERGENTOSCIL LA TION S TEND TO 5 DEVELOPWHENPILOT INITIATES ABRUPTM AN E UV ERSOR ATTEM PT S TIGHT CONTROL. PILOT MU ST OPEN 40 LOOPBY RELEASINGOR FREE Z IN G T H E _ ' n " 1.4 DI S TURBANCE OR NORMALPILOT 6 _ + " 0 sac CONTROLMAY CAUSEDIVERGENT " >" -A I STICK. 9 20 _ _ nD = /\ = 2.0/rad / sec OS C IL LA TION. PILOTMU ST OPEN / FREEZINGTHE ST ICK .

CONTR O L LOOPBY RELE AS INGOR 0 '_ _ cc _W_

, o

Fig u r e 7. T he p il o t-lnduced-os c illation _- _ n" 0rad / l ec ra t ing scale. R / _ T D = 0.49sac ( _ 'n 0 : 1 . 4 --'--'- - -- - . ... _ I. _ n 2. 0 rad / _ c

o - l oo _ - 0,.c

> __ _ 1 8oo _ rn " 1 .4 _

v -2 oo ,.. , ,. - _ o. _ / _ \ \

% , "D + o.49,,_ \ . \ - 300 , , , , ,,,,I ' ' , '\',,'I % , .1 1 10 rad / m c t w o configurations from Ref . z o .

20I ___ Figure I 0. Pil o t / vehl c le d yna m icsf o r -- o ¢ _% .

:, ... 0 >. __ 4.1 ' '_ -20 " 1 " CONFIGURATION ° u 0 Z 7 >_ _ 0 1 4 z l O _ ....

'_ 4 -100 _" 4 , . 1 " _ 789 _i ] _ 1 _ 7-13 ---- - 300 _ 3 - " RATING -200 --- " 6-_ _ _ : 6 , . * 4 00; , , , ,,,,,I r , j ,,l,,,l I I I . 1 I 10 1 1" 10 1" 1 02 1" 10 3 1" 10 4 , , .,, ; , rad l z e c Fig u re 8 . Pil o t/ vehicle d ynamics f o r t wo configurations from Ref. 6 . Figure II. Cooper-Harper pilo t ratings vs a proposed model-based me t ric.

1. R e por t N o. 2. GovernmentAccessio n No. 3. Rec i p l en t ' s Cata l og No.

NASA TM-84233 4 . Title end S ubtitle 5 . Report Date PREDICTION OF AIRCRAFT HANDLING QUALITIES USING April 1982 ANALYTICAL MODELS OF THE HUMAN PILOT 6. Perfor m ing Or ga ni za tion Cod e 7 . Au t h o r( s ) 8. Perfo r rning OrganizationReport No.

• Ronald A. Hess A-8884 10. Work Uni t No.

9. Performing O r ga nization Name and Address T - 3608Y Ames Research Center, Moffett Field, C A 94035 11 . Cont ra ctor Gran t No.

13. Ty_ of R e po_ a nd P _ i _ _ v _ 12. S po ns _ ing A _ ncy Name a n d Addr _ s Technical Memorandum National Aeronautics and Space Administration 14. S _ n _ ring A _ ncyCode Washington, DC 20546 505-44-21 15. _ pple m en t a r y No t e s Point of contact : Ronald A. Hess. Ames Research Center , MS 210 - 9 , Moffett Field, CA 94035. (415)965-5443 or FTS 448-5443.

16. Abstract The optimal control model (OCM) of the human pilot is applied to the study of aircraft handling qualities. Attention is focused primarily on longitudinal tasks. The modeling technique differs from previous appli- cations of the OCM in that considerable effort is expended in simplifying the pilot / vehicle analysis. After briefly reviewing the OCM, a technique for modeling the pilot controlling higher order systems is introduced. Fol- lowing this, a simple criterion for determining the susceptibility of an aircraft to pilot-induced oscillations (PIO) is formulated. Finally, a model-based metric for pilot rating prediction is discussed. The resulting modeling procedure provides a relatively simple, yet unified approach to the study of a variety of handling qualities problems.

17. Key Wo r_ (Suggest _ by Auth . (s)) 18. Distrib _ ion S ta t e m en t Pilot Models U nlimite d Handling Qualities Pilot-Induced-Oscillations Subject Category-08 t 19 . Security Oa_ if . (of thi s re _r t} 2 0 . SecurityCla _ if . (of this _ga ) 21 . No. of Page s 22. D ice " Unclassified Unclassified II A02 " For w le by the NationalT _ hnic a l Information _ i _. Spri ng field , Vi _ ini a 22161

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