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METNODOLOGYFORDESIGNOFACTIVECONTROLS FOR V/STOL AIRCRAFT George Meyer and Luigi Cicolani NASA Ames Research Center ABSTRACT .An e f f o r t is underway a t t h e Ames Research Center t o develop techniques fo'r t h e , d e s i g n of i n t e g r a t e d , f u l l y automatic f l i g h t c o n t r o l systems f o r powered l i f t STOL and VTOL a i r c r a f t . The paper d e s c r i b e s t h e s t r u c t u r e of t h e c o n t r o l system which has been developed t o d e a l w i t h t h e s t r o n g non- l i n e a r i t i e s inherent i n t h i s class of a i r c r a f t ; t o admit automatic coupling with t h e advanced ATC r e q u i r i n g a c c u r a t e execution of complex t r a j e c t o r i e s ; and t o admit a v a r i e t y of a c t i v e c o n t r o l tasks. The s p e c i f i c case being con- sidered is t h e Augmentor Wing Research A i r c r a f t .
INTRODUCTION N A S A through its STOL and VTOL research programs i s i n v e s t i n g s u b s t a n t i a l resources i n developing powered l i f t technology. I n a l l cases, t h e wide range of l i f t c o e f f i c i e n t required t o cover a l l f l i g h t conditions between c r u i s e and landing is achieved by i n - f l i g h t modification of a i r c r a f t configuration.
These modifications r e s u l t i n d r a s t i c changes i n c o n t r o l c h a r a c t e r i s t i c s of t h e a i r c r a f t , and, p a r t i c u l a r l y i n t h e h i g h - l i f t t r a n s i t i o n and landing con- f i g u r a t i o n s , t h e a i r c r a f t response t o c o n t r o l i n p u t s is very nonlinear. More- over, t h e presence of powered and d i r e c t l i f t generators i n c r e a s e s t h e t o t a l number of c o n t r o l s a v a i l a b l e t o t h e p i l o t who must c o n t i n u a l l y make d e c i s i o n s on c o n t r o l techniques. F i n a l l y , t h e coming short-haul t r a n s p o r t a t i o n system w i l l be required t o s a t i s f y s t r i n g e n t environmental c o n s t r a i n t s which w i l l n e c e s s i t a t e a c c u r a t e execution of complex t r a j e c t o r i e s . Accurate, unaided manual tracking of complex t r a j e c t o r i e s by manipulating a l a r g e set of i n t e r - a c t i n g c o n t r o l s of an a i r c r a f t whose c o n t r o l c h a r a c t e r i s t i c s are non-linear and r a p i d l y changing r e p r e s e n t s a n unacceptably high p i l o t work load. Active c o n t r o l technology has t h e p o t e n t i a l t o provide a means f o r reducing t h e p i l o t work load t o a n acceptable level by i n t e g r a t i n g c o n t r o l f u n c t i o n s i n such a way as t o generate d e s i r a b l e handling q u a l i t i e s without reduction i n t h e per- formance of t h e a i r c r a f t as an element of t h e advanced c i v i l air t r a n s p o r t a t i o n system.
The advantages of a c t i v e c o n t r o l technology are p o t e n t i a l l y even more s u b s t a n t i a l i n m i l i t a r y a p p l i c a t i o n s of STOL and VTOL a i r c r a f t . Both t h e Advanced M i l i t a r y STOL and t h e S e a Control F i g h t e r VTOL must u t i l i z e t h e maneuvering c a p a c i t y of t h e b a s i c a i r c r a f t t o t h e f u l l e s t . The tracking of complex p e n e t r a t i o n t r a j e c t o r i e s must be s u f f i c i e n t l y a c c u r a t e f o r proper exe- c u t i o n of mission, and t h e p i l o t work load associated with f l y i n g must not adversely a f f e c t h i s a b i l i t y t o perform other t a s k s . Again, t h e maneuverability, accuracy, and level of p i l o t work load can be improved by means of a c t i v e P c o n t r o l technology. A t t h e present time, however, t h e p r a c t i c a l problems of I n applying t h e technology t o powered l i f t a i r c r a f t are n o t w e l l understood.
order t o provide t h e required d a t a base, an applications-oriented program has been i n i t i a t e d a t t h e Ames Research Center. The o b j e c t i v e s of t h i s program are t o generate design guide l i n e s and t o provide f l i g h t test confirmation re- quired f o r incorporation of a c t i v e c o n t r o l technology i n t o t h i s class of air- c r a f t . The present paper d e s c r i b e s t h e progress made i n one segment of t h i s program, namely, t h e development of a methodology f o r t h e design of automatic t r a j e c t o r y c o n t r o l systems f o r powered l i f t a i r c r a f t .
THE A U G M E N T O R WING RESEARCH AIRCRAFT The s p e c i f i c case being used i n t h e development and tests of t h e design methodology is t h e Augmentor Wing Research A i r c r a f t . The a i r c r a f t i s a d e Havilland C-8A "Buffalo" modified according t o t h e general arrangement shown i n f i g u r e 1. The a i r c r a f t is powered by two turbofan engines. The r e l a t i v e l y cold flow from t h e f r o n t f a n s is ducted through t h e wing and fuse- l a g e t o t h e augmented jet f l a p , blown a i l e r o n s , and f u s e l a g e boundary l a y e r c o n t r o l systems. The hot gas flows through two p a i r s of nozzles which can be r o t a t e d i n f l i g h t t o provide vectoring of t h e hot t h r u s t through a 9 8 ' range.
The hot and cold t h r u s t s are nonlinear functions of t h e t h r o t t l e s e t t i n g . The nozzle servos move t h e nozzles i n unison i n response t o a s i n g l e nozzle angle command. The system is q u i t e f a s t , being l i m i t e d t o 90 ("/set.). The t h r o t t l e - t o - t h r u s t c o n t r o l system is r e l a t i v e l y slow with a bandwidth of approximately 1 (rad. /sec. ) .
The cold flow has a pronounced e f f e c t on t h e l i f t and drag p o l a r s of t h e a i r c r a f t . For example, f i g u r e 2 shows t h e wing-body p o l a r s f o r two f l a p s e t t i n g s . The independent v a r i a b l e s i n t h e p l o t s are t h e a i r c r a f t angle of a t t a c k , a, and t h e cold t h r u s t c o e f f i c i e n t CJ = Tc/QSw, where t h e cold t h r u s t Tc is a nonlinear f u n c t i o n of t h r o t t l e , and d e n s i t y and temperature of t h e air; Q i s t h e dynamic pressure, and S w i s t h e wing area. Of p a r t i c u l a r s i g n i - f i c a n c e f o r t h e design of f l i g h t path c o n t r o l systems is t h e l a r g e v a r i a t i o n i n t h e b a s i c aerodynamic characteristics of t h e a i r c r a f t .
C e r t a i n l y , t h e r e is a l a r g e change between t h e c r u i s e configuration ( f l a p = 4 . 5 " ) and t h e landing configuration ( f l a p = 6 5 " ) . But present indica- t i o n s are t h a t t h e n o n l i n e a r i t y is s i g n i f i c a n t even over a much smaller region.
For example, f i g u r e 3 shows t h e t o t a l l i f t and drag c o e f f i c i e n t s , including t h e e f f e c t s of t h e hot t h r u s t f o r t h e case of constant f l a p , t h r o t t l e and speed yhich corresponds t o a t y p i c a l landing configuration with angle of a t t a c k and nozzle angle V i n t h e active c o n t r o l mode. Point A 1 i n t h e f i g u r e repre- s e n t s equilibrium f l i g h t along t h e -7.5" g l i d e slope. Point A 2 r e p r e s e n t s level f l i g h t . Also shown are t h e d e r i v a t i v e s of t h e t o t a l f o r c e c o e f f i c i e n t a t t h e s e two p o i n t s . A s t h e a i r c r a f t is maneuvered from p o i n t A 1 t o p o i n t A2 t h e changes i n t h e s e d e r i v a t i v e s may adversely a f f e c t closed loop dynamics.
But of g r e a t e r concern is t h a t i f t h e maneuver is performed by means of a feed-forward comand based on t h e l i n e a r model a t p o i n t AI, then t h e aircraft w i l l be out of trim a t A2 by ACL /CL Because of bandwidth l i m i t a t i o n s = 4.7%.
0.5 rad./sec.) by unsteady aero- imposed on t h e a l t i t u d e c o n t r o l loop (% dynamics, t h e e r r o r i n t r i m r e s u l t s i n an a l t i t u d e e r r o r A h > 6 f t . Similarly, t r a n s i t i o n from A2 t o A 1 w i l l end up a t A21; t h e corresponding e r r o r A h > 16 f t .
Of course t h i s hangoff e r r o r can b e removed by means of an i n t e g r a t o r , b u t t h e removal w i l l be too slow f o r many maneuvers. Consequently, t h e t r a n s i t i o n be- tween A 1 and A2 must b e considered t o be nonlinear.
The design problem is f u r t h e r complicated by t h e presence of redundant c o n t r o l s . Thus, t h e two-dimensional t o t a l f o r c e c o e f f i c i e n t C = (CD,CL)~ is a function, say C(F,T,a,V), of four v a r i a b l e s , namely f l a p , t h r o t t l e , angle of attack, and nozzle angle. For example, f i g u r e 4 shows t h e p l o t of C(F,T,a,V) = Co, where Co corresponds t o steady f l i g h t along -7.5O g l i d e slope. It may be noted t h a t t h e p l o t i s r a t h e r nonlinear. The problem is t o be a b l e t o generate o n l i n e optimum t r i m v a l u e s of t h e c o n t r o l s (F,T,a,V) f o r any admis- s i b l e trim values of (CD,CL).
DESIGN APPROACH The approach i s motivated by t h e following l i n e of reasoning. L e t equation (1) be t h e system state equation.
j, = f(x,u) (1) The c o n t r o l u i s r e s t r i c t e d t o a set U which may depend on t h e state x. A t r a j e c t o r y (xo(t), t E T) is f l y a b l e i f f o r a l l t E T, t h e r e i s a c o n t r o l u o ( t ) such t h a t The t r i m problem is t o f i n d a c o n t r o l uo s a t i s f y i n g (2), given t h a t t h e t r i m t r a j e c t o r y i s f l y a b l e . The s o l u t i o n w i l l be a n i n v e r s e of (l), namely a func- t i o n (g,F), which we c a l l t h e trimmap, such t h a t f o r a l l (k,x) E F, E f(x,g(A,x)) = i (3) The corresponding t r i m c o n t r o l i s given by Usually, t r i m r e f e r s t o cases with constant u0. H e r e uo may vary with t i m e .
Note t h a t when t h e c o n t r o l s are redundant, state equation (1) alone is n o t (g,F), and a d d i t i o n a l conditions must be i d t r o - enough t o d e f i n e t h e trimmap duced t o r e s o l v e t h e redundancy.
The t r i m problem may be d i f f i c u l t t o solve; b u t , e v i d e n t l y , its s o l u t i o n t o required accuracy is t h e e s s e n t i a l f i r s t s t e p i n t h e design of automatic f l i g h t p a t h c o n t r o l systems. The next s t e p u s u a l l y taken is t o design a con- a f l y a b l e nominal tra- t r o l system based on p e r t u r b a t i o n models. Thus, given j e c t o r y (ko,Xo) E F trimmed by uo according t o equation ( 4 ) , t h e l i n e a r model (5) is obtained f o r t h e p e r t u r b a t i o n s 6x = x - xo and 6u = u - u0.
6% = f 6x + f U 6u
(5) X 0 0 Then, t h e a p p l i c a t i o n of t h e methods of l i n e a r c o n t r o l theory y i e l d s t h e p e r t u r b a t i o n c o n t r o l l a w (6).
6u = K6x (6) Since t h e c o e f f i c i e n t s i n (5) depend on t h e nominal t r a j e c t o r y , t h e process must be repeated f o r s u f f i c i e n t l y l a r g e number of nominal t r a j e c t o r i e s The r e s u l t is a scheduled gain (k0,%) E F u n t i l F is adequately covered.
matrix K(&o,xo), and t h e complete c o n t r o l l a w is The major drawback of t h i s approach is that when t h e state equation (1) is highly nonlinear, t h e procedure f o r choosing t h e proper set of nominal tra- j e c t o r i e s t o cover t h e f l i g h t envelope F is, a t p r e s e n t , r a t h e r unclear. For w e a t A m e s have decided t o i n v e s t i g a t e a d i f f e r e n t approach.
t h i s reason Then i n Consider t h e t r i m equation ( 4 ) . Suppose t h a t i n i t i a l l y x = xo.
t h e absence of modeling e r r o r s t h e c o n t r o l uo w i l l maintain x = xo. The tracking w i l l be p e r f e c t even i f a t some p o i n t t h e a c c e l e r a t i o n of t h e nominal t r a j e c t o r y is perturbed from ko t o k0 + &go, provided t h a t (ko + &ko, X)E F.
The corresponding c o n t r o l i s
u = g(ko + 6ko,x) (8)
Now, suppose t h a t i n i t i a l l y x - xo = 6x # 0, but t h a t t h e e r r o r can be removed by means of a f l y a b l e t r a j e c t o r y . Then t h e r e is a perturbed nominal acceler- a t i o n ko + 6%o which w i l l t a k e x i n t o xo by means of t h e c o n t r o l l a w (8).
That is, t h e feedback f o r t h e c o n t r o l of process u n c e r t a i n t i e s can be closed through t h e trimmap as i n equation (8), r a t h e r than a f t e r t h e trimmap as i n equation (7). Such c o n t r o l by means of c o n t i n u a l adjustments i n commanded a c c e l e r a t i o n forms t h e b a s i s of t h e Ames approach. The emphasis is s h i f t e d from p e r t u r b a t i o n models on F t o f l y a b l e p e r t u r b a t i o n s i n commanded accelera- t i o n . The next s e c t i o n d e s c r i b e s t h e r e s u l t i n g s t r u c t u r e of t h e c o n t r o l system.
FULL FLIGHT ENVELOPE AUTOPILOT The proposed s t r u c t u r e of t h e a u t o p i l o t is shown i n f i g u r e 5. The p l a n t r e p r e s e n t s t h e b a s i c a i r c r a f t together with a t t i t u d e and t h r o t t l e servosystems, and sensors. Everything t o t h e l e f t i s t h e a u t o p i l o t . It c o n s i s t s of four
blocks - trimmap, wind f i l t e r , compensator, and command generator - which
c a r r y out t h e following functions.
Trimmap computFs t h e active c o n t r o l uc t o generate a c c e l e r a t i o n with in- e r t i a l coordinates Vsi. For t h e case shown, t h e a c t i v e c o n t r o l s are t h e com- manded a t t i t u d e and nozzle angle; while t h e redundant c o n t r o l s are t h e t h r o t t l e and f l a p . Any o t h e r p a r t i t i o n of t h e c o n t r o l s i s t r e a t e d s i m i l a r l y . The t o t a l commanded aerodynamic f o r c e Fsc is transformed i n t o estimated s t a b i l i t y coor- d i n a t e s Fvc from which commanded r o l l (d, angle of a t t a c k a,, s i d e s l i p angle Bcs and nozzle angle Vc are computed o n l i n e using t h e nonlinear inverse function g, The commanded a t t i t u d e d i r e c t i o n cosine matrix is given by The a t t i t u d e c o n t r o l system (servo) may operate d i r e c t l y on Acs. I n c a s e I n any Euler angles are required, they are given by Acs = E l ( 4 ~ ) E 2 ( 0 ~ ) E 3 ( $ ~ ) .
case, commanded a t t i t u d e and nozzle are defined.
Wind f i l t e r computes smoothed i n e r t i a l coordinates v$ of a i r c r a f t velo- c i t y relative t o t h e airmass from body mounted a i r v e l o c i t y sensors, and i n e r - t i a l v e l o c i t y and a t t i t u d e of t h e aircraft. The relative v e l o c i t y is needed i n t h e trimmap t o l o c a t e s t a b i l i t y axes and t o convert f o r c e s i n t o c o e f f i c i e n t s .
Note t h a t only i n e r t i a l coordinates of wind are f i l t e r e d . The a i r c r a f t v e l o c i t y i s unaffected. Hence, i n t h e absence-of sensor e r r o r s and wind, 4 = Vs.
Trimmap, wind f i l t e r , and a t t i t u d e and t h r o t t l e c o n t r o l systems form an a c c e l e r a t i o n c o n t r o l l e r . The input is t h e output is t h e a c t u a l accelera- t i o n O s of the a i r c r a f t . Moreover, Vs = V s i 3- e where t h e e r r o r e depends on t h e inaccuracies of i n v e r s i o n g and wind esti- mates, t h e presence of unsteady aerodynamics i n f such as alpha dot e f f e c t s , t h e purpose of t h e and on t h e a t t i t u d e and t h r o t t l e servo dynamics. It i s compensator t o generate c o r r e c t i v e a c c e l e r a t i o n s C s m t o compensate f o r t h e I n e r t i a l coordinates of p o s i t i o n , e r r o r e of t h e a c c e l e r a t i o n c o n t r o l l e r .
v e l o c i t y , and a c c e l e r a t i o n are transformed i n t o approximately l o n g i t u d i n a l , lateral, and normal e r r o r s by means of t h e d i r e c t i o n cosine matrix A , , compu- ted from t h e commanded i n e r t i a l v e l o c i t y Vsc; t h e e r r o r s are weighted by con- s t a n t g a i n matrices Kl, K2, and K3 commensurate with t h e a c c e l e r a t i o n capa- cities of t h e a i r c r a f t i n t h e s e d i r e c t i o n s , and t h e r e s u l t is f i l t e r e d t o in- s u r e c o m p a t i b i l i t y with a t t i t u d e and t h r o t t l e servo dynamics. The c o r r e c t i v e ? c c e l e r a t i o n is transfqrmed back i n t o i n e r t i a l space and added t o t h e command I n t h i s way, t h e feedback i s closed around t h e VSC t o g i v e t h e input V s i .
process u n c e r t a i n t i e s e so t h a t t h e r e p r e s e n t a t i o n i s s u f f i c i e n t l y a c c u r a t e provlded t h a t eSc is admissible, namely (fJsc,Vs) is f l y a b l e and t h e bandwidth of Vsc is s u i t a b l e r e s t r i c t e d .
The last major block of t h e a u t o p i l o t is t h e command generator. Its purpose i s t o porvide only admissible commands t o t h e a c c e l e r a t i o n c o n t r o l l e r .
One of t h e subblocks d e f i n e s t h e a u t o p i l o t mode. For t h e c a s e shown i n t h e diagram, 27 modes are a v a i l a b l e . Every mode d e f i n e s whether p o s i t i o n , velo- c i t y o r a c c e l e r a t i o n is t o be tracked i n each of t h e t h r e e axes. Thus, mode (O,O,O) r e q u e s t s t h r e e a x i s a c c e l e r a t i o n tracking; mode (l,l,l) r e q u e s t s t h r e e axis v e l o c i t y tracking; etc. A s a n example of t h e use of modes suppose t h a t t h e a u t o p i l o t is i n mode (2,2,2) t r a c k i n g p o s i t i o n of a 4-D t r a j e c t o r y com- manded by t h e air t r a f f i c c o n t r o l (ATC) as t h e a i r c r a f t penetrates a heavy, l o c a l i z e d turbulence. The mode may have t o be changed t o , say, (l,l,l) o r possibly even (O,O,O). On e x i t i n g t h e turbulence, t h e mode may be returned back t o (2,2,2). The command generator must generate an admissible t r a j e c t o r y f o r bringing t h e a i r c r a f t back a n t h e t r a j e c t o r y commanded by t h e ATC.
The ATC t r a j e c t o r y may be transmitted continuously t o t h e a i r c r a f t , o r more l i k e l y , it may be generated onboard from a given set of t r a j e c t o r y para- meters. The latter may be transmitted by t h e ATG o r s e l e c t e d by t h e p i l o t .
* * e *
I n any case, i f t h e commanded t r a j e c t o r y (Rsc,Vsc,Vsc) is discontinuous i n any of t h e v a r i a b l e s (e.g. "step down a l t i t u d e by 500 f e e t " o r "change g l i d e p a t h from - 7 . 5 O t o -2"",), t h e command generator must generate the required f l a r e maneuver.
Such f l a r e maneuvers are generated by means of t r a n s i t i o n dynamics. This subblock c o n s i s t s of a s t a b l e state equation, i n i t i a l conditions, and an out- put map. A t t h e t i m e of t h e i n i t i a t i o n of t h e t r a n s i t i o n dynamics, A t t h e end of t h e t r a n s i e n t , (Rsc,VSC,QSC) = (Rsc,VSC,QSC) = (Rs,Vs,QS).
t h e t r a n s i e n t are made compatible w i t h t h e (R$c,V$c,fl$c). The dynamics of a c c e l e r a t i o n c o n t r o l l e r by a proper s e l e c t i o n of t h e state equation. To en- state equation s u r e c o n t i n u i t y i n p o s i t i o n , v e l o c i t y , and a c c e l e r a t i o n , t h e must be a t least three-dimensional (and three-axis). I n t h e diagram, a l i n e a r state equation is shown. Nonlinear t r a n s i t i o n dynamics are c u r r e n t l y being designed t o permit a r b i t r a r i l y l a r g e i n i t i a l d e v i a t i o n s from t h e ATC command.
The f e a s i b i l i t y of t h e a u t o p i l o t has been t e s t e d by a p p l i c a t i o n t o t h e unmodified C8A and t h e Augmentor Wing Research A i r c r a f t f o r which d e t a i l e d simulations are a v a i l a b l e a t Ames. Eresent i n d i c a t i o n s are t h a t t h e proposed s t r u c t u r e is f e a s i b l e , although f i n a l evaluation must a w a i t f l i g h t tests which are scheduled i n 1976.
The p r e s e n t paper presented an overview of t h e proposed design methodo- logy. Several r e p o r t s , c u r r e n t l y i n preparation and soon t o appear, d i s c u s s t h e methodology in g r e a t e r d e t a i l .
CONCLUSION The proposed design approach has s e v e r a l advantages, among which are t h e following.
The approach i s a p p l i c a b l e t o a l a r g e class of a i r c r a f t w i t h (1) nonlinear dynamics.
The approach i s n e a r l y algorithmic.
(2) The approach is i n v a r i a n t f o r a wide spectrum of t r a c k i n g accuracy (3) requirements.
There is an e f f e c t i v e trade-off between t r a c k i n g accuracy require- (4) ments and computer requirements and a p r i o r i knowledge of system dynamics.
Present i n d i c a t i o n s are t h a t the proposed design methodology is f e a s i b l e , but d e f i n i t e evaluation must a w a i t f l i g h t tests.
Figure 1. Modified C-8A, General Arrangement 5.5 r CL I -I :4.5 -u u - 1 2 -I 0 1 2 3 CD Figure 2. Typical Wing-Body Polars of the Augmentor Wing Air speed = 65 knots - 3 . 5 - 3.4 - 3 3 - -
t
0 ‘ 3 0 - c u l - .2 2 9 - r r c l ” c 2 0 - *c - - f 2 7 - - - 2 5 - - 2 3 1 1 I I I 2 2 - 4 2 0 2 4 .6 Figure 3 . Total Force Coefficient Angle o f attack a I05
Nozzle Y -
Figure 4. Controls f o r One Value of Total Force Coefficient