Dynamics and Adaptive Control for Stability Recovery of Damaged Aircraft

Source of Acquisition NASA Ames Research Center M a n Nguyen" Kalmanje Krishnakumart John Kaneshigez

NASA Ames Research Cente7; Moffett Field, CA 94035

Pascal Nespecas University o f California, Davis, CA 95616 This paper presents a recent study of a damaged generic transport model as part of a NASA research project to investigate adaptive control methods for stabiIity recovery of damagA aircraft operating in off- nominal Bight conditions under damage and or failures. Aerodynamicmodeling of damage effects is performed using an aerodynamic code to assess changes in the stability and control derivatives of a generic transport aircrafk Certain types of damage such as damage to one of the wings or horizontal stabilizers can cause the aircraft to become asymmetric, thus resulting in a coupling between the longitudinaland lateral motions.

Flight dynamics for a general asymmetricaircraft i s derived to account for changes in the center of gravity that can compromise the stability of the damaged aircraft. An iterative trim analysis for the translational motion is developed to refine the trim procedure by accounting for the effects of the control surface deflection. A hybrid direct-indirectneural network, adaptive flight control is proposed as an adaptive law for stabilizingthe rotational motion of the damaged aircraft. The indirect adaptation is designed to estimatethe plant dynamics of the damaged aircraft in conjunction with the direct adaptation that computes the control augmentation.

Two approaches are presented 1) an adaptive law derived from the Lyapunov stabfity theory to ensure that the signals are bounded, and 2) a recursive least-squaremethod for parameter identification. A kardware-in- the-loop simulation is conducted and demonstrates the effectiveness of the direct neural network adaptive ftight control in the stabfity recovery of the damaged aircraft. A preliminary simulation of the hybrid adaptive flight control has been performed and i n i t i a l data have shown the effectiveness of the proposed hybrid approach.

Future work will include further investigations and high-fidelity simulations of the proposed hybrid adaptive Bight control approach.

E . ~ ~ ~ ~ ~ d ~ ~ t i ~

Aviation safety research concerns with many aspects of safe, reliable fiight perfornanc modern aircraft to maintain safe air transportation for the traveling public. While air travel r transportation, accidents do occur in rare occasions that serve to remind that much work is still remained to be done in aviation safety research. American Airlines Flight 587 illustrates the reality of hazards due to structural failures of airkame components that can cause a catastrophic loss of control.' Not a l l structural damages result in a loss of control. The World War I I aviation history filled with m y stories of aircraft coming back home safely despite suffering major structural damage to their airfi-ames. Recently, the DflL incident involving an Airbus A300-B4 cargo aircraft in 2003 further illustrates the ability to maintain a controlled flight in the presence of structural damage and hydraulic loss?

In damage events, sigdicant portions of the aircraft's aerodynamic Lifting surfaces may become separated and as a result this may cause the aircraft's carefully designed center of gravity (C.G.) to shift unexpectedly. The combined *Computer Scientist, Intelligent Systems Division, Mail Stop 269-1 iComputer Scienbt, Intelligent Systems Division, Mail Stop 269-1 iComputer Engineer Intelligent Systems Dimion, Mail Stop 269-1 §Ph.D. Student, Mechanical Enginwring Department 1 of 23 Ameiican Institute of Aeronautics and ASEOMU~~CS loss of lift, mass change, and C.G. shift can manifest in an unstable, off-nominal flight condition resulting from the aircraft being out of t r i m that can adversely affect the ability for an existing flight control system to maintain the aircraft stability. In some other instances, aircraft's damaged smcmes may suffer losses in structural rigidity and may develop elastic motions that can potentially interfere with an existing fkght control system in an unpredictable manner.

Moreover, the load carrying capacity of damaged structures may also become impaired and therefore can potentially in excessive structural loading on critical Lifting surfaces due to flight control inputs by the unaware pilot Thus, result in a highly dynamic and difficult off-nominal flight environment with many uncertainties caused by damages to the aircraft, the inner-loop flight control must be able to cope with complex and uncertain aircraft responses that can greatly challenge an existing flight control system.

Flight control of damaged aircraft in off-nominal flight conditions poses signrficant technical challenges in many areas of discipbi=esincluding aerodjzamics, struct~al dynamics, flight dynmics and control, as well as h 1 m fix- tors. Thus, a comprehensive investigation from the aircraft integrated system perspective is needed to research and develop adaptive flight control technologies that can be used to retrofit conventional flight control systems in order to enable aircraft to achieve safe flight objectives. This comprehensive investigation would provide an integrated approach to damage effect physics-based modeling and simulation, safety-of-flight assessment, flight control and re- covery, and adaptive system verification and validation. Damage effect physics-basedmodeling generates a knowledge base for understanding the behavior of damaged aircraft performance in the areas of flight mechanics, aerodynamics, and strucmal dynamics to address system interactions among various sub-systems such as aircraft dynamics, airframe structures, engines, and Sight control actuators. Using this knowledge base, flight mechanics of the damaged vehicle can be evaluated by flight simulation to assess classes of d at can be recovered with different types of flight control effectors. On-board modeling provides state assessments of damaged aircraft in-flight that can be used to aide pilot's decisions and control. Adaptive flight control is a critical technology that enables damaged aircraft to recover post-damage flight stability. Research in neural network adaptive flight control provides a possibility for developing an effective damage adaptive control strategy that can adapt the damaged aircraft to changes in the vehicle stability characteristic^.^ Emergency flight planning and post-damage landing technologies are also investigated and control to aide pilots with an intelligent decision support system to identify a suitable landing site, flight path planning under a reduced flight envelope, and ultimately a safe landing execution strategy? While adaptive flight control has been much researched, it has not been universally adopted in the aviation industry due to a number of software and stability issues that are inherent with any adaptive flight control system. Certification of these adaptive flight control systems is a major hurdle that needs to be overcome. Thus, research in adaptive system verification and validation is needed in order to develop stability and certiiication requirements for new adaptive Sight control methods.'

This paper focuses on the flight mechanics and the adaptive flight control of damaged aircraft. The damage nature is primarily due to changes in the aerodynamic corQuration of the vehicle brought about by various modes of damage that include airframe and flight control surfaces. Some of these types-of damage can cause a rapid loss of vehicle loss of control power. A Aight dynamics stability and control resulting from a si-cant loss of lift capability andlor a model for a damaged aircraft is developed to account for various damage effects including changes in aerodynamics, mass, inertias, and C.G. A trim andysis is presented to entable a rapid estimatiotl of new trb.n sates 'cs r n a i m b the aircraft flight conditions. Damage adaptive fight control methods are developed to enable stability recovery of the damaged aircraft. Research in the adaptive reconfigursble flight control provides a method of risk mitigation for certain types of damage. Recent advances in neural network, direct adaptive flight control provide a foundation for much of this research?, ''9 l2 A hybrid direct-indirectadaptive control method is proposed to extend the cmeu? capability of the neural network adaptive Sight control. The hybrid adaptive control includes an indirect adaptive lzw that perfom an on-line estimation of plant dynamics of the damaged aircraft.The stability of this indirect adaptive law is established by the Lyapunov stability theory. An alternative approachis also presented whereby a recursive least-square method is used for the parameter identification process.

][I. Damage Effect Modeling A twin-en,gine transport-class generic aircraft is chosen as a platform for the damage effect modeling. We will refer to this notational aircraft as a Generic Transport Model (GT-M). Fig. 1 is an illustration of the GTM. Damage to an aircraft airframe and/or control surfaces can cause the aircraft to be out of trim, which consequently can lead to dynamic upsets of the aircraft flight states. Understanding the aircraft aerodynamic characteristics during a damage event is critical to developingflight control strategies for the stability recovery of a damaged aircraft. In order to assess the damage effects on the GTM, aerodynamic modeling is performed to estimate the aerodynamic coefficients, and the 2 Of 23 American Lnsdtute of Aeronautics and Asnoi~autics stability and control derivatives of the damaged GTM for various damage confi,prations under consideration. Damage aerodynamictharacteristics will then be incorporated into a flight dynamic model of the damaged aircraft that will be used to develop adaptive fligbt control strategies. A ControUability study can be performed using the flight dynamic model to determine which damage configurations are controllable and those that cannot be controlled.

The damage effect aerodynamic modeling is performed using a vortex-lattice code developed at NASA Ames Research Center! This computational fluid dynamics modeling is capable of rapidly computing the aerodynamic characteristics and control sensitivity of the damaged GTM due to various flight control surface inputs. The damage the left wing, left horizontal stabilizer, and vertical stabilizer, as shown in Fig.

effects are modeled as partial losses of 1. Wing loss represents one of the critical modes of damage that is a current focus of the research.

Fig. 1 - Generic Transport Model 1 1 0- 0 9 0 8 0 O f 0 2 03 04 0 5 Fraction of Left Wing Loss 0 0 2 0 3 0 4 0 5 ' L o o n of Left Wing ~ o s s

Fig. 2 - Aerodynamic Coefficients Due to Wmg Loss at a = 12' and p = Oo

Fig. 2 shows the damage effect due to wing loss for the damaged GTM. The effect of wing loss can be seen as a si,dcant source of loss of Lift capability of a damaged aircraft as the lift coefficient can be reduced by as rnuch as 25% for up to a 50% span loss of one of the wings. Changes in the pitching moment coefficient are also a result of the wing loss. Changing lift and pitch moment causes the aircraft to be out of trim that leads to the inability for the 3 of 23 American Insutute of Aeronautics and ASEOMU~~CS &ght control system to hold altiade and flight path angle. Moreover, the aircraft lateral motion becomes a factor as a sieficant side force and yawkg moment develop without any aileron or rudder input. This lateral motion causes the lon&l&al and lateral motions of the damaged aircraft to couple, resulting in changes in the angular rates. The stabifity of the damaged aircraft can be regained if sufficient control powers are still available to overcome the rolling and yawing moments as well as to retrim the aircraft in the pitch axis.

(at Fraction o f Left Wing Loss x lo" (d)

;' 0 1 0 0 1 0 2 03 0 4 0 5

Fraction oi Left Wing Loss Fig. 3 - Control Derivatives Due to Wing Loss at Q = 1 2 O and ,8 = 0" For an ideal symmetric aircraft, the aileron deflection effects the roll control with insignilkant contribution to the Lift and pitching moment coefficients. The effect of Wing loss causes the aileron deflection to induce a change in the l i f t coefficient as well as a change in the pitching moment coefficients as seen in Fig. 3(a}-(b). The abrupt changes in the lift control and pitch control derivatives are due to the complete loss of one of the ailerons for a wing loss that extends beyond 25% span. The consequence of this that the damaged aircraft would exhibit a pitch-roll coupling when the A e i G i i s a s p ~ e t & 2 1 ~ . TC = a % + & 2 w i sate, the Bight xnt;.o! mrrg compemBIe for &e mwanred pitch motion ~ 7 i f i the elevators. The situation is sknilai' for the elevator control as the effect of wing loss introduces a change in the side force coefficient and a change i n the yawing moment coefficient as seen in Fig. 3(c)-(d). Thus, a deflection of &e elevators would result in a pitch-yaw coupling that must be compensated within the flight control system by adjusting the rudder control accordingly. Because of the asymmeu-y, the general motion of a damaged aircraft is coupled in dl the three axes. As a result, any adapuve flight control strategy must be able to effectively handIe this cross-coupled effect.

p r l [ . Flight Dynamics of Asymmetric Aircraft The 1ongiadina.I motion of a symmetric aircraft is typically symmetric with respect to the aircraft fuselage ref- erence line. The lateral motion is uncoupled from the 1ongitudina.I motion owing to rhe aircraft symmetry. For a damaged &cr& fie Symmetr-Ymay no longer be preserved depending on the nature of the damage such as wlng damage. The asymmetry of the damaged aircraft thus causes the longitudinal motion and lateral motion to couple together. Furthermore, the C.G. is shifted away from the 5 - z plane. The motion of an asymmekic damaged aircraft?

therefore, must be understood in order to evaluate any flight control design. To this end, we consider an asynmetric aircraft with a C.G. offset from some reference location as shown i n Fig. 4 . The reference location is a fixed point located at the coordinate (IC@, yo, 20) on the aircraft which ma~7 be taken as the original C.G. of the undamaged aircraft 4 of 23 American Institute of ASOMU~~CS and Asnonautics in order to maintain the same coordinate reference frame. The C.G. of the damaged aircraft can move relative to this fixed reference point.

Fig. 4 - C.G. S h i f t Relative to Reference Point 0 The damage effect resulting from a wing loss creates a larger C.G. shift in the pitch axis y than in the other two axes as shown in Fig. 5. This results in an additional rolling moment that the fiight control must be able to compensate for using the available control surfaces in order to maintain the damaged aircraft in a t r i m state.

Fig. 5 - C.G. Shift due to Wmg Loss .

A. Linear Acceleration To understand the effect of the C.G. shift, the standard equations of motion’for fiight dynamics of a symmemc aircraft must be modified to allow for the asymmetry. Assuming a flat-earth model for a rigid body aircraft, the force vector in the body-ked reference frame of the aircraft is 5 of 23 American Institule of Aeronautics and ASEOMU~~CS T where W = mg [ -sin8 cosBsin4 COSOCOSQ, is the gravitational force vector, w = [ p q r ] isthe

I T

aircraft angular rate vector, r = F f Ar is the position vector of the reference location such that ? is the position vector C.G. and Llr = AX Ay is the displacement vector from the C.G. to the reference location.

of the

i I '

The aircraft mass is assumed to undergo a change so that m=m*+Am (7-1 where m* is the oria$rtal mass of the aircraft and Am < 0 is the mass change due to damages.

Assuming that the change in the mass of the aircraft is instantaneous, the force vector then becomes dv dw dAr FB =m- +m- x Ar +mw x __ - W dt d t dt where % is the speed of the C.G. relative to the reference location which is assumed to be small relative to v and therefore may be neglected.

Transforming from the body-fixed reference frame to the inertial reference frame yields F = F ~ + ~ w x v (4) Expanding Eq. (4) gives

X = m(G+ ~ A z - f 4 y - TW + qw fgsin6')

(5)

Y = m (8 - pAz + ?Ax +- ru - pw - gcos8sin~P)

(6)

Z = m (w + pAy - 6Llx - qu + pv - gcos8cos+)

(7) The an,dar acceleration terms appearing in Eqs. (5)-(7) are a result of the C.G. shift. Thus, the Linear acceleration of an asymmetric aircraft is coupled with its angular acceleration.

B. Angular Acceleration We consider the angular momentum vector in the body-fixed reference frame

H g = / [ r x (w x r)]dm + (r x v) dm

s

Expanding this expression yields

HB = I w + mAr x v

(9) where I is the mass moment of inertia matrix with respect to the reference frame at the reference location.

The time rate of change in the angu€armomentum gives rise to the moment equation in the inertial reference frame 7 - 7 dv - dw

&f=- + W x Rg =I- +mar x - + w x iw+mw x (ar X V )

dt d t dt Expanding Eq. (10) results in the following inoment equations L =

- ~,,q - I,:,,+ + Izypr - Ix,pq + (I,, - I,,) qr + I ~ , (r - q 2 )

+ m(qv + rw) Ax + m(2i) - qu) Ay - m (8 + ru) Az

(11)

M = --I~,$ + ~,,q - ~,,i + Iyzpq - Izyqr + ( I ~ ~ - I z , ) p r -+ I,, (p2 - r')

- m (zb i p v ) Ax + m(pu + T W ) Ay+ m(iL - T U ) Az (12)

i V = - ~ , : , , p - I,,@ + I Z , ? + IzZqr - Ivzpr + (I,, - I,,)pq + I , , (q2 - p 2 )

+ m ( i ' - p w ) Ax - m ( f ~ + qw) Ay + m (pu + qv) Ar ( 1 3 )

Equations (11)-(13) indicate that the C.G. offset effectively creates additional moments on the aircraft. Cross coupling in both the linear and angular accelerations are present. Thus, the longitudinal and lateral motions of the aircraft are generally coupled and the aileron or elevator commanded input therefore will affect the aircraft motion in both stability axes.

6 of 23 American Institute of Aeronautics and ASEOMU~~CS C. Aerodynamic and Propulsive Forces and Moments Assuming that the engine thrust vector is aligned with the z-axis of the aircraft, then the forces and moments due ‘to aerodynamics and the propulsion are

X = &-Tmaa: + (C; + ACL) Q S s i n a - (Cz + ACD) QScosacosp

(14

u’ = (C; + ACy) QS - (C; + 4 c D ) QS sin p

(1.5)

= - ( c ; + A C L ) QScosa - (c& 4- A c D ) Qssin a c o s p

(16)

L = (C; + 4 s ) Q S E

(17) M = (C; i ACm) QSE+ STTmax (Ze - ZO) (18)

N = (C: + ACn) Q S C + 6 A T T m a x y e + 6TTrnazYo (19)

where (ze, fy,, 2 , ) are the centers of thrust and the subscript * denotes the force and moment coefficients for the undamaged aircraft evaluated at the reference location.

We assume that the left and right engines produce the same amount of thrust with a combined maximum thrust equal to T,, and are symmetrically positioned with respect to the aircraft fuselage reference line. Then 6~ where 0 5 6~ 5 1 is the throttle position corresponding to a desired total engine thrust, and 6 & ~ where --+ 5 AT 5 is the throttle differential position difference that results in a desired engine differential thrust equal to the left engine thrust minus the right engine thrust. The incremental changes in these coefficients due to damages are defined as

A C = ACo i AC,a + 4Cop + ACs6

(20) T T

where A C = [ CL - Cz CD -CY, Cy - C$ CZ -C,* Cm - C7T, Cn - C; ] , 6 = [ 6a he & ]

is the flight control surface deflection vector, the subscripts a, 8, and 6 denote the derivatives, and the subscript 0 denotes the coefficients at a = 0 and p = 0.

IV. Trim Analysis The aerodynamic forces on asymmetric aircraft include a non-zero side force component that is generally not experienced on Symmetric aircraft. For a steady fiight, the side force equation becomes

mgcosOsind, + (C$ + 4Cy) QS - (Cz + 4 c D ) QSsinP = 0

(21) The side force trkx for the asymetric aircraft can therefore be accoEplished by trimming the &xraft at a non-zero bank angle d, with zero sideslip angle p. Xowever, this wo-dd result in a knittiion in the ba& angk in coordkated turn maneuvers. Another side force trim approach is to trim the aircraft level with zero bank angle q5 but at a non-zero sideslip angle /3. In either case, the aircraft would have to be tcimmed in both the longitudinal and lateral directions simultaneously by searching for the steady state solution of Eqs. (14) to (16) with d, = 0 or /3 = 0. The t r i m analysis thus computes the trim values for the kgle of attack a, bank angle d, or sideslip angle p, and engine throttle position 6~ as functions of the aileron deflection da, elevator deflection S , , and rudder deflection 6 , for a @en aircraft Mach = 0.

number and altitude. We assume that the engine thrusts will be symmetric at aIl times so that If an undamaged symmetric aircraft has a mass m* and is flying wing-level, i.e., fl = 0, with zero control surface deflection at the ori,@nal trim angle of attack a*, sideslip angle p* = 0, and trimthrottle position 6 ; correspondingto a l i f t coefficient CE, drag coefficient Cz, and side force coefficient C G = 0. Then for small changes in the aircraft mass and aerodynamic coefficients, we can determine the incremental trim angle of attack, bank angle, and throttle position to maintain approximately the same trim airspeed V and flight path angle y* by taking small but finite differences of Eqs. (14) to (16) and setting them to zero, thus resulting in 7 of23 American Instime of Aeronautics and ASGOMU~~CS - (ACL + C L , , A ~ + c ~ , p A p + C L , ~ QScosa* + (CL i C L & ~ -k C~,p4/3 + CL,& QSsin a*Aa - (ACD + CD,,AQ + C ~ , p a p + C D , ~ S ) QSsina" - (CD + C D , , A ~ + C D , ~ A @ + C D , ~ & ) QScoscr'Aa

- mg sin (T* + a*) Aa + A ~ ~ C O S (y* -I- a*) = 0 (24)

To lind the trim bank angle at zero sideslip angle, we set = 0 in the equations above. Equation (24) then is a quadratic equation in terms of Aor whose solution can easily be computed as 2a U with u = ( C L . ~ sina* - CD,, cosa*) Q S (26)

b = [(CL + C L , ~ - CD,,) sin a* - (CD + C D , ~ + CL;,) COS ax] Q S - mg sin (y* + CY*)

(27)

c = - [(ACL + CLJS) cos a5 + (ACD i CD,SS) sin@*] QS + Amgcos (y* - + a*)

(28) From Eq. (23), we now find the trim bank angle Finally, the incremental t r i m throttle position can be solved directly from Eq. (22).

Trimming the damaged aircraft with bank angle will result in a reduced bank angle limitation. This would poten- tially affect the aircraft's turn capability. Moreover, the aircraft will not fly wing-level which would not be acceptable for a landing approach. Therefore, the damaged aircraft can be trimmed alternatively with the sideslip angle. This will enabIe the aircraft to m a i n t a i n a level flight but the control authority of the rudder control surface will be reduced since it has to compensate for the non-zero sideslip angle. To obtain the trim sideslip angle, we set A4 = 0 in the Eq. (23) and solve Eqs. (22) to (24) simultaneously.

In examining Eq. (23) with A4 = 0, it is noted that if the undamaged aircraft is in a cruise phase at a minimum drag, then the trim sideslip angle for the damaged aircraft could be large if the damage develops a significant side force. Typically, it is not advisable to fly the aircraft at a high sideslip angle because of the stability issue. Depending on the extent of damages, an effective trim approach may be one that uses a combination of the trim bank angle and sideslip mge.

in cases where the rudder conrrol power is insugcient due to damages, then the engine ditterential a h s t -&-oiiIe position ~ L \ T could be used to provide an additional control effector to trim the aircraft in yaw. Using engine differen- tial t h r u s t for yaw control requires examining the issue associated with a slow en,gine response relative to the responses of typical flight control surfaces. While in theory the en,@e thrust can be used to nim the aircraft i n yaw, offen by the time the engine thnist is adjusted Merentially to the correct t r i m value, the aircraft may have reached a different if the damage condition is severe enough to cause the aircraft dynamic state due to the loss in airspeed and or altitude performance to rapidly deterioratein its flight envelope. Because of the time scale difference between traditional flight control surfaces and engines, engine actuator dynamics must be accounted for in the overall flight control strategy.

In addition to using the en,&ie differential thrust as a control effector, other flight control surfaces can be used in an overaLz control redundancy design strategy. This investigation would examine the control effectiveness of a various combinations of flight control surfaces. For example, wing spoilers can be used for roll control and the wing flap extension or deflection can be used for pitch control. Some of these control surfaces may have different time latency characteristics such as wing flaps versus spoilers. In the control and srability analysis, actuator dynamic model of slow in the overall flight dynamic modeling.

systems should be included The trim analysis shows that upon damage, the damaged aircraft would have to be retrimmed with a new trim angle of attack a = a* 4- Aa, new bank angle 4 = 4 4 or new sideslip angle /3 = Ap, and new throttle position 6~ = 6 $ + A & . The t r i m a, 4 or p. and 6~ are a l l functions of the Eght control surface deflection S as well as the aircraft damage confi,p-ation. In general, the stability and control derivatives needed to retrim the damaged aircraft 8 of 23 Amencan Insmute of Aeronautics and Astronautics are not known. Thus, it is necessary that these parameters be identified in flight by a parameter identification process.

Assuming that the effect of damage on the aerodynamics can be estimated, then a trim strategy is to initially retrim the damaged aircraft with zero control surface deflection by setting 6 = 0 in Eqs. (22) to (24). Then, using the inner-loop rate-command-attitude-hold (RcAK) control, the control surface deflection for the damaged aircraft can be obtained.

This .allows the trim values to be refined. Depending on the nature of damage, the t r i m refinement may be repeated until the damaged ahcraft becomes completely trimmed.

V. Damage Adaptive Fright Control Most conventional fight control systems utilize extensive gain-scheduling in order to achieve desired handling qualities. While this approach has proved to be very successful, the development process can be expensive and often results in aircraft specilic implementations. Over the past several years, various adaptive control techniques have been investigated? Damaged aircraft presents a challenge to the conventional flight control systems because the aircraft dynamics may deviate from its known dynamics substantially due to a significant degradation in the flight performance of the damaged aircraft. This makes it difficult for the conventional flight control systems to cope with changes in the stability and control of the damaged aircraft. Adaptive fight control provides a possibility for maintaining the stability of a damage aircraft by means of being able to quickly adapt to uncertain system dynamics. Research in adaptive control has spanned several decades, but challenges in obtaining robustness in the presence of unmodeled dynamics, parameter uncertainties, or disturbances as well as the issues with certification, verification and validation of adaptive flight control s o h a r e prevent it from being implemented in fight control systems.* Adaptive control laws may be divided into direct and indirect approaches. Indirect adaptive control methods provide the ability to compute control parameters from on-line neural networks that estimate plant parameter^.^ Parameter identilication techniques such as recursive least squares and neural networks have been used in indirect adaptive control methods." In recent years, model-reference direct adaptive control using neural networks has been a topic of great research interest^."-^^ Lyapunov stability theory has been used to establish robustness of neural network adaptive control to ensure that adaption laws for ne>ural network weight updates are asymptotically stable.

In the current research, we adopt the work by Rysdyk and Calise" to develop a neural network adaptive con- trol with dynamic inversion for damaged aircraft. The adaptive flight control is able to provide consistent handling qualities without requiring extensive gain-scheduling or explicit system identilication for a damaged aircraft. This particular architecture uses both pre-trained and on-line learning neural networks, and reference models to specify desired handling qualities. Pre-trained neural networks are used to provide estimates of aerodynamic stability and control characteristics required for model inversion. On-line learning neural networks are used to compensate for errors and adapt to changes in aircraft dynamics. As a result, consistent handling qualiries may be achieved across flight conditions and for different damage co&prations. An architecture of the neural network adaptive fight control in Fig. 6. Furthermore, we will extend this architecture to include an indirect adaptive control element that is shown pioyides an o n - h e estimation of the t x e p l a t &pullics. The estimtion approach is provided by an d q t i v e 1z.u based on the Lyapunov stability analysis. In addition, we also consider a recursive least square method for the on-line estimation.

uad W . G, 6 / Fig. 6 - Direct Xeural Network Adaptive Flight Control Architecture 9 of 23 American Institute of Aeronautics and Astronautics A. Linearized Plant Dynamics First, we need to arrive at a linear dynamics of the damaged aircraft for the feedback bearization control. To maintain airspeed and altitude, the damaged aircraft has to be retrimmed using the trim method above. The damaged aircraft stability must be recovered by the RCAH controller. This results in control surface deflections necessary to maintain a desired an,dar rate command. To design a b e a r RCAH controller, we want to eliminate the linear acceleration terms in Eqs. ( 1 1) to (13) corresponding to the uncompensated damaged aircraft dynamics of linear motion resulting from damages. Combining Eqs. (5) to (7) with Eqs. (I 1) to (13) yields

Tzz+ - Lye - Tz2+ 4- Ixypr - Izzpq 4 - (Izz - I j , ) qr + I j Z (r2 - 4”)

+ m (qv + rw) A x - m p v A y - mpwAz = (C; + bel) QSF (39)

- L,@ + G Y 4 - G z + 4- Iyzpq - 1zyqr + (1m - 1 2 2 ) pr -I- Iz, (p2 - 7-2)

- m q u A x + m @u + rw) Ay - mqwAz = (Ck + ACm) QSF + &-Tmar ( z , - ZO) (31)

where A2

AY

A(?i=ACl+C,-=- cosOcos&=- - c o s 8 s i n c b ~ (33) c c c A X cos8sin$~+sinO--=- c c where C,, Cy, and C2 are X, Y, and Z force coefficients normalized to the dynamic pressure force QS.

The linear dynamics of the damaged aircraft is computed by linearizing Eqs. (30) to (32) - dG

(fx + AI) = (f: + Afi) c;l+ (f; t- A f i ) CT + (g” + Ag) 6

(3 6 ) T T

where G = 1 A p A q A r ] is the angular rate vector, m = 1 Lla

A& ] is the b h parameter

vector, m n d 10 of 23 American Institute of Aeronautics and Assonautics

m , a , AG,& AG,&

& = QSC ACrn,,,

AC'm,,= A C ~ J ~

~. A&,,, AG,,, AZl,,,,.

Equation (36) is the angular acceleration equation of the asymmetric aircraft which can be written in a state-space form as

b = (Fi + A F l ) G + (F2 + A F z ) a + (G j AG) E

(37) where F1 = f*-lf;, F2 = z*-If;, G = I*-lg*, AF1 = f-l (f; + Afi) - Fl, AF2 = f-l (fz $- Af2) - Fz, and A G = 1-l (g* + Ag) - G.

Under ideal situations, the plant dynamics of an undamaged aircraft i s assumed to be known. However, for a damaged aircraft, the plant dynamics become uncertain as the stability and control derivative matices AFl ,4F2, and AG are usually unknown. Consequently, the flight control needs to be able to adapt to the uncertain plant dynamics of the damaged aircraft. The angular acceleration vector 2 of the damaged aircraft may be written as the sum of an ideal angular acceleration vector bz of the undamaged aircraft and a differential an,dar acceleration vector A W due as to damage G = W z + A W (38) The ideal, undamaged aircraft plant dynamics can be written as

bz = F I G + F~CT + G6

(39) where the stability and control matrices for the undamaged aircraft F1, F2, and G are assumed to be known.

B. Direct Neural Network Adaptive Control The goal of the adaptive flight control is to be able to fly the damaged aircraft whose handling characteristics i s specified by a reference model. The control adaptatiun must be able to accommodate damages using the available flight control surfaces. A reference model is used to filter a rate command vector w , into a reference angular rate vector w, and a reference anplar acceleration vector wm via a first-order model Wm + W,W, = wnw, (40) where ~rr, = dbg (wp, wq, ur) is the frequency matrix.

The reference freqGency parciiaeters must be chosen appropriately in order to ob& 2 good transieat response that satisfies position and rate limits on the control surface deflection. For transport a i r c r a typical values of the reference model frequencies wp, wQ, and w, are 3.5,2.5, and 2.0, respecti~ely.~ Lrr cases when the reference mode1 is over- or under-specified, the parameters of the reference model must be adjusted. The tuning of the reference model parameters can be performed using an adaptive-critic approach to ensure that the flight control can track the reference model in order to achieve desired handling qualities.16 The reference model anplar rate vector wm are compared with the actual angular rate output G to form a tracking error signal w e = w , - G. A pseudo-feed back control vector u, is constructed using a proportional-integral ( P I ) feedback scheme to better handle errors detected from the roll rate, pitch rate, and yaw rate feedback. The error dynamics, defined by proportional and integral gai~~s, must be fast enough to track the reference model, yet slow enough to not inkrfere with actuator dynamics. The issue with the integrator windup during a control saturation is addressed by a windup protection which l i m i t s the integrator at its current value when a controI surface is commanded beyond its limit. The pseudo-control vector u , is computed as wedr u, = K p w , i- KJ

l

American htitute of Aeronautics and Astronautics In order to ensure low-gain error handling performance, the error dynamics is designed with natural frequencies that match the reference model frequencies in the roll, pitch, and yaw axes. A damping ratio is chosen with rp = CS = C , . = l/a. These frequencies and damping ratio are incorporated into the proportional and integral gains as A dynamic inversion is performed to obtain an estimated control surface deflection command 8 to achieve a desired angular acceleration vector w d using the known plant dynamics of the undamaged aircraft from Eq. (39) as

6 = G-I (iL'd - F I G - F2E)

(44) assuming that B is invertible.

In order for the dynamic inversion control to track the reference model angular acceleration rate vector Gm, the desired angular acceleration vector &d is set to be equal to = w m t u e - u a d (45) where u a d is an adaptive control augmentation designed to cancel out the dynamic inversion error, so that in an ideal setting, the desired angular acceleration rate b d is equal to the reference model angular acceleration rate w , as the traclcing error goes to zero asymptotically.

Because the true plant dynamics of the damaged aircraft is unknown and is different from the undamaged aircraft plant dynamics as can be seen from Eq. (37), a dynamic inversion will result from the control surface deflection b.

This error is equal to A E = ij - L j d = ij - F I G - F ~ o - Gb (45) Comparing with Eq. (371, we see that the dynamic inversion error can also be expressed in terms of the unknown plant dynamics due to the damage effects

E = AW = A F l G -!- AF2a + AGB

(47) Substituting Eq. (45) into Q. (46) results in

E = -We - ue +- u a d

(48) Combining Eq. (41) with Eq. (48) yields

e = Ae + B ( u a d - E )

(49)

wheree = 1 Jl W , ~ T W , ] aad

The adaptive controI augmentation vector u a d is based on a neural network adaptation law by Rysdyk and CaJise' that guarantees boundedness of the tracking error and of the network weights using a single-hidden-layer sigma-pi neural network u a d W ~ P ( ~ 1 , ~ 2 , ~ 3 ) (50) where p is a vector of basis functions computed using a nested Kronecker product with C1, C2, C3 as inputs into the neural network consisting of conuol commands, sensor feedback, and bias term.

The network weights W are computed by an adaption law, which incorporates an adaptation gain J ? > 0 and an 1-1 > O I 4 according to the update law e-moacation tern W = - I ' (peTPB t 1-1 /leTPBII W) (5 1) where the mattix P solves the Lyapunov equation ATP f PTA = -Q for some positive-definite matrix Q and the norm is a Frobenius R O ~ .

12 of 23 America0 institute o f Aeronautics and Astronautics The e-modtkation term provides a robustness in the adaptation law.14 The update law in Eq. (23) guarantees the stability of the network weights and the tracking error. The proof o f this update law using the Lyapunov method is provided by Rysdyk and Calise." Solving for the matrix P with Q = I, the update law can be rewritten as

w = -r (pv -+ llvll w) (52)

where t

V = IwFK;' 2 (f + K,') + f Jd wFd.rKT'

(53) While the direct neural network adaptive law has been extensively research and has been used with good successes in a number of applications, the possibility of high gain control due to aggressive learning can be an issue. Aggressive learning is characterizedby setting the learning rate I ? high enough so as to reduce the dynamic inversion error rapidly.

This can potentially lead to a control au,mentation command that may saturate the control authority. Moreover, high gain control may also excite unmodeled dynamics of the plant that can adversely affect the stability of the adaptive law. To address this issue, we are considering a modification to the present direct adaptive law to include an indirect adaptive law that provides an opportunity to perform an on-line estimation of the plant dynamics of the damaged aircraft explicitly. We call this approach as a hybrid direct-indirect adaptive controI concept. The indirect adaptive law will provide an estimated plant dynamics that will be used in the dynamic inversion. If successful, the control command will result in a smaller dynamic inversion error so that the learning of the direct adaptation neural network can be reduced. An architecture of the proposed hybrid adaptive control concept is shown in Fig. 7. In the current study, we are developing some initial indirect adaptive laws for the on-line estimation of plant dynamics based on the Lyapunov stability theory and also the well-known recursive least-square method. Future research still remains ahead to rigorously investigate this proposed concept followed by high-fidelity simulations.

Fig. 7 - Hybrid Direct-Indirect Neural Network Adaptive Flight Control Architecture A. Indirect Neural Network Adaptive Control We would like to estimate the unknown plant matrices using a linear-in-parameter neural nstwork approach as A@, = Wzp, (54) A@'z = w:pc (55) A& = W$pS (5 6) where the hat symboI denotes the estimated plant m a ~ c e s and pU, Dm, ps are some neural network architectures that may not be necessarily the same as , f . ? for the direct adaptation neural network.

The error dynamics now can be expressed as

e = Ae -k 3WTP - SW-3,G - 3MTZP,a - BWTp,8 - B A e

(57) 13 of 23 American Institute of Aeronautics and Astronautics where AE < E is the residual error ftom the estimation of the plant matrices.

We now propose the following adaptive laws for the estimation of W,, W,, and Wa W w = r,p,GeTPB (58) W, = Tu&ueTPB (59)

? ? , = rsps&eTPB (60)

where I?,, I ? , , rs > 0 are the adaptation gains.

proof is as follows: The

We let W = W' + *, W, = Wz 4- a,, Wu = VJ: + S@,, md SV,- = SVi -+ TgTa where the zsterisk

symbol denotes the ideal weight matrices to cancel out the resi&ualerror AE and the tilde symbol denotes the weight deviations.

The ideal weight matrices are unknown but they may be assumed constant and bounded to stay within a A- neighborhood of the residual error AE so that We define the foIlowing Lyapunov function where P 2 0 and tr (A) denotes the trace of a matrix A.

The time derivative of the Lyapunov function is computed as Substituting Eqs. (57) and (5 1) into the above equation yields We n5te that tr (AB) = tr fS-4) , so that eTPBWTp = tr (eTPBWT&) = tr (WTpeTFB) ( 6 5 )

eTPBWzpwG = tr ( eTPBWZP,G) = tr (WzP,ISeTPB)

(66) eTPBW:p,cr = tr (eTPBW:pPcr) = tr (W:,B,eeTPB (67) eTPBWF,B6& = tr (eTPBWF/3sd) = tr (WF@sdeTPB) (68) Also, by completing the square, we have I 4 of 23 American Instime of Aeronautics and Aslronautics

Since W, = W w , W, = TfVu, and W s = W s , Eq. (64) then becomes

where p (Q) and p (P) are the spectral radii of Q and P.

In order to guarantee that V 5 0, we require that the trace operator be equal to zero, thus resulting in the adaptive laws in Eqs. (58) to (60). In addition, we also require that The time rate of change of the Lyapunov function is then strictly negative and therefore it would guarantee that the

signals are bounded. We note that e, G , u, 8 E C, but e E L2 since

Utilizing Eq. (74), we have Thus, the value of V as t -+ 03 is bounded. Therefore, we establish that ll$Vii --+ 0, IlW, 1 1 -+ 0, liW,il -+ 0, and W b i 0 imply ]/e11 -+ 0 as t 4 03. This means that the adaptive laws win result i n a convergence of the

ll . i t

estimated AF1, AF2, and A G to their steady state values. In practice, the inputs # = [ .iT 6T f ] must be swfficiently rich that contain enough frequencies to capture all the plant d y n d c s . In order for the on-line estimation to converge the their correct values, the inputs need to be a persistent excitation (PE) class of signals such that if t h e r e exist ao, ( ~ 1 , To > O theng (77) J t We can also "robustif"' the adaptive laws similar to Fq. (52) to better handle unmodeled dynamics and distur- bances by adding an e-modification term'4 to Eqs. (58) to (60) as Wu = I ' , (P,GeTPB - pw IleTPBII W w ) (78) W, = Tu (P,aeTPB - p, lleTPBll W,) (79) (80) W s = Tb (P68eTPB - p8 lleTPBII Wa) 15 of 23 American Institute of A ~ M U ~ ~ C S and ASUOMUI~CS in which case the time rate of change of the Lyapunov function becomes The effect of the e-modification is to increase the negative time rate of change of the Lyapunov function SO that as long as the effects of unmodeled dynamics and or disturbances do not exceed the value of V , the adaptive s i p a h should remain bounded. The e-modification thus makes the adaptive law robust to unrnodeled dynamics so that the€% condition may not be needed.15 B. Recursive Least-Square Parameter Identification While the indirect adaptive laws above provide a computational method for on-line estimation of the plant d p d c s , it would be incomplete to not consider the well-known least-square method which is equally robust in parmeter identification process. If the dynamic inversion error is somehow can be estimated, then we should be able to apply a to determine the weight matrices W,, W,, and WS. Suppose the estimated d p ~ c recursive least-square method inversion error can be written as E = + T B + A E (W where eT = [ Wz Wz WF 1, e = [ p,G P u r p6$ ] *, and A E is the computational error in the estimated dynamic inversion error E, which may contain noise resulting from the on-line derivative computation of since

E = & - F ~ G - F~~ - G$

(83) where & is the estimated angular acceleration which may be subject to computational errors.

One method of computing & is to use a backward finite-difference method to estimate & at the i-th time step, but this method can result in a significanterror if At is either too small or too h%e.

Another approach is to collect n number of data points which wiU be used to generate an at least C1 smooth CUme in time using a cubic or B-spke method. This curve is then differentiatedat their knots to find the estimated derivative - -1- - In eitter case, ihe derivztive computatioi~ will intmhce an exor source A€. If the ezxx is ~&jased, Le., it cm vauea.

be characterized as a white noise about the mean value, then the least-square method can be applied to estimate the plant dynamics.

We consider a minimization of the following cost function Our objective is to find recursive least-square adaptive laws for W,, W,, and Wg. To minimize the cost function, we compute the gradients with respects to the weight mabkes, thus resulting in The recursive least-square formula using the gradient method is

& = RB (ZT - B T @ ) (87)

where R = -RBBTR 16 of 23 American Institute o f Aeronautics and A S ~ ~ O M U ~ ~ C S To show this, we see that fromEq. (86) t

6eTd7@ = i 6dTd7

Let t

R-l= i BBTd.r > 0

Then, differentiatingEqs. (89) and (90) results in Substituting Eq. (92) into Eqs. (91) and (92) and solving for & and R yield the recursive least-square adaptive law. The matrix R is called the covariance matrix and the recursive least-square formula has a very similar form to the Kalman filter where Eq. (88) is a differential Riccati equation for a zero-order plant dynamics. We will show that the recursive weight update law is stable and results in bounded signals as follows: We let @ = Q* + & with the hat and tilde symbols denoting ideal weights and weight deviations, respectively.

Then, the error dynamics can be written as e 5 A e + BWTp - BGT8 + B A (94) We choose the following Lyapunov function

L = V + tr ( 6TR-16)

(95) where V is the Lyapunov function for the direct neural network adaptive control and we have established that V 5 0.

The time rate of change of the Lyapunov hnction is computed as

L = V + @ (2&TR-1$ + &TR-l&)

(96) The weights Qj can be shown to converge to the ideal weights so that Substituting Eq. (97) into Eq. (96) results in Thus, the recursive least square weight update law is stable.

In practice, the recursive least-square method can be used to estimate the plant dynamics either continuously or discretely at every n d a t a samples. Continuous time estimation requires solving the differential equations (87) and (88) at each time step. On the other hands, the discrete-time sampling estimation provides more flexibility in that the estimation can be executed after a specified number of data points have been collected. This would ensure that the signals contained in the sampled data are sufficiently rich to enable an accurate coovergence. Another advantage of the it provides an optimal noise fittering to minimize noise effects in the estimation recursive least-square method is that of the plant dynamics. The discrete-timerecursive least square formula is American Institute of Aeronautics and ASWOMU~~CS where k denotes the update cycle that repeats every n data samples, @ : = [ W : , , W:Jk W6,k is the weight matrix at k-th update cycle, X is a forgetting factor that can be used to discount past data, and The neural network adaptive flight control for damaged aircraft is evaluated in a medium-fidelity simulation test environment. The Eght simulator is a fixed-motion simulator equipped with a pilot station, progammable displays, and a 1 2 0 ' field-of-view visual system as shown in Fig. 8. Pilot commaftd inputs are received through a control stick, a rudder pedal, and a throttle quadrant. Flight control software includes a Eght dynamics model of damaged aircraft as developed herein. Simulations are performed at a 30 Hz frequency.

Fig. 8 - Flight Simulation Test Environment The damaged GTh4 is evaluated with various wing loss configurations. Fig. 9 shows the angular rates of the damaged GTM with and without the neural network adaptive flight control. The neural network control azgmentation can be seen to quickly adapt to the changjng dynamics of the damaged GTM. The roil, pitch, and yaw raEes zre quickly brought to zero to stabilize the damaged aircraft. In contrast, without a neural network control aumentation, the aircraft rates are chan,@ng rapidly, particularly in the roll axis. A rapid increase in the pitch attitude can result in the damaged GTM reaching its stall angle of attack that would render the aircraft in a dangerous situation.

18 of 23 American Institute of Aeronautics and Astronautics 0 a , with NN control - without NN control 0-, E Li 0 0 1 E

-with NN control - without NN control

G = I I I < I 1 , I

0 -

with N N control - without NN control W 0 o-.-\ L - r I J Fig. 9 - Rate Control with and without Neural Network Adaptation t, sec Fig. 10 - Control Surface Deflection Fig. 10 shows the control surface deflections corresponding to the neural network control aumentaiion. The right aileron is commanded to move substantially to correct for a left turning rolling moment resulting from a left wing damage. A maximum aileron limit of 3 5 O is nearly reached. Thus, it is possible that for certain damage scei.arios, the 19 0: 23 American Institute of Aeronautics and AS~IOMU~~CS control augmentation will not be able to stabilize the damaged aircraft due to the control power limitation. In such situations, other types of control snrfaces must be considered to provide additional control authorities for stabilization.

contro1 docation approach must be incorporated i n t o the neural network adaptive flight con&ol to maximize Optimal the control effectiveness of all the available control authorities.

To evaluate the hybrid adaptive flight control with the indirect adaptive law and the recursive least square method, a simulation was performed in MATLAB environment. A damage confi,o;urtion corresponding to a 30% loss of the left wing is selected. A step input pitch doublet is simulated. The tracking performance of the three control laws is compared in Fig. 11.

- --

a , Direct N N Q -0 0 -

s

---- - _ -

a , HybridNN , Q 0-f

-a s

0' , I I . , 0.05 I

_ - - R e - , LS + Direct NN

I n

D= I , J

-0.05 '

0 5 10 15 20 t, sec Fig. 11 - Pitch Doublet Tracking Performance t, sec Fig. 12 - Tracking Error N o m 20 of 23 American Institute of Aeronautics and AS~TOMU~~CS As can be seen, the hybrid adaptive control with the indirect adaptive law is able to improve the tracking perfor- mance of the direct neural network adaptive control. The combined direct adaptive control with the recursive least square parameter identification actually outperforms both the direct and hybrid adaptive control approaches as the tracking error is sigmficantly reduced as seen in Fig. 12. The control surface deflections to achieve this pitch maneu- ver are shown in Fig. 13. The elevator deflection for this pitch maneuver is nearly saturated. The direct neural network adaptive control produces more overshoot than the hybrid adaptive control and the recursive least square approach.

The left rolling moment is compensated by the right aileron input and the adverse yaw is compensated by a small rudder input. For this simulation, the actuator dynamics is not included in the study.

0)

s- 20

rn 0 I 2 3 4 5 t, sec (bl 0) a , -20 rn -40 0 1 2 3 4 5 t, sec (c) Direct NN - - - Hybrid NN - - RLS + Direct NN

-1 I I

0 1 2 3 4 5 t, sec Fig. 13 - Control Surface Deflection The current research in the damage effect aerodynamic modeling has focused on single damage sites. Multiple damage sites can also exist in a d m g e event. The next step in damage effect aerodj~namic modeling is to generate a predictive capability for multiple damage sites. An approach would be to conduct eFD modeling for representative multiple damage patterns. These modeling results are compared to single damage site models and a learning system to establish a surface response snapping between multiple and single damage sites. Using this can be developed damage surface response mapping, damage effects for any arbitrary damage pattern can be rapidly estimated.

In the current adaptive fiight control research, only traditional control effectors that include ailerons, elevators, and rudder are used. In severe damage situations, these control effectors may not be suf5cient to stabilize and maintain good handling qualities of the damaged aircraft. Therefore, any adaptive flight control method must include a control allocation strategy that utilizes other potential control effectors that are otherwise not used in a conventional fiight control system. These control effectors can include engine differential thrust for yaw control, wing spoilers for roll control, and wing flap extension or deflectionfor pitch control. Research in the areas of control redundancy design and reconfi,prable control will be conducted to investigate optimal control allocation strategies for these control effectors.

are important for systems with different time latency The issues of time-scale separation due to actuator dynamics such as en,~es and flaps and thus will be an area of adaptive flight control re~earch.'~ Damage effects can presat a serious chatienge to conventional flight control system because the aircraft flight dynamics may deviate from its nominal flight dynamics substantially as result o f the degradation in the flight per- formance of the damaged aircraft. This makes it difficult for the conventional flight control systems to cope with 21 of 23 .American Institute of Aeronautics and Astronautics changes in the stability and control of the damaged aircraft. While neural network adaptive control offers a promise of being able to adapt to changes in flight dynamics of damaged aircraft, rigorous validation by simulations and flight testing will be pursued to explore areas of concern in the neural network adaptive flight control. One of the mesolved concerns is the learning characteristics of a neural network. If the dynamic inversion error is Iarge due to a large dis- crepancy between the true and nominal plant dynamics used in the dynamic inversion control, the learning rate must be set sufficiently high in order for the neural network to reduce the error rapidly. As a consequence of the aggressive This learning, the neural network tends to generate high gain control signals that may not be dynamically achievable.

potentially can cause a number of problems including control saturation, load constraints during flight being exceeded, excitation of unmodeled dynamics, and others. One potential solution is to introduce the proposed hybrid adaptive control that incorporates an explicit parameter identification based on an adaptive law derived from @e Lyqunov stability method or a recursive least-square method to estimate the true piant dynamics, which would be used for the dynamic inversion control rather than the nominal plant dynamics. This approach potentially offers a way to reduce the dynamic inversion error that the neural network has to compensate for.

Integrated flight dynamics modehg is another area research &at addresses interactions among many types of physics problems during flight. An integrated flight dynamics model will be developed to include an aeroservoelas- ticity interaction model of a flexible-body vehicle dynamics with a propulsion model and its actuator dynamics. This integrated mode1 will capture the combined effects of the 6-dof rigid body dynamics, structural dynamics of airframe, in the aerodynamic coefficients and derivatives which and propulsion model. Post-stall aerodynamics can be included can influence the flutter margin and the aerodynamic damping of the airframe.

Structural interaction with a flight control system is critical to any flight control development.18-20 Elastic de- flection and mode shapes can adversely contribute to the vehicle stability and control, resulting in problems such as flutter, control reversal, structural frequency interaction within the flight control bandwidth, and others. Research in the area of aeroservoelasticity is very important for advancing the knowledge of damage adaptive flight control.

Recent advances in fluid-structure interaction modeling using coupled computational fluid dynamics-finite element method provide a predictive capability for aeroservoelastic effects on the stability and control of damaged aircraft?'

will need to observe and obey structural load constraints imposed on a damaged New adaptive fight control methods airframe. The resulting adaptive Bight control methods therefore would be more dynamically achievable. Aeroser- voelastic frequency interaction with a safety-critical flight control system will be investigated in order to develop an integrated approach for dealing with potential issues with high frequency signals from elastic modes injecting into the frequency bandwidth of the rigid-body aircraft dynamics. Research in aeroservoelastic filtering and structural iden- tification for flight control will provide methods for assessing the elastic contribunon of the airframe and developing adaptive Bight control methods that can effectively filter out unwanted structural resonant modes within the flight control bandwidth.

This paper has presented recent results on the modeling, control, and simulation of damaged aircraft as part of the aviation safety research at NASA. The damage effect aerodynamic modeling has been performed to provide an understanding of the control and stabaty of an asymmetric damaged aircraft. The effects of aerodynamic and control coupling in all the three stability axes are revealed from the modeling results. A tj-dofE&t dynamics of asymmetric is derived in order to account for the effect of the center of gravity shift resulting from the damage. An aircraft approach for trimming the damaged aircraft for the translational motion is presented. The trim procedure provides iIlitial estimates of the t r i m values for the angle of attack, angle of sideslip, and en-gine thrust. The influence of the control surfaces on these trimmed values is then accounted for by adjusting the initial trim values with the control surface deflections obtained from the flight control. A hybrid direct-indirect neural network adaptive flight control concept has been proposed to provide an opportunity to estimate plant dynamics in conjunction with the current direct adaptive control au,Omentation strategy. The on-line estimation of the plant dynamics is provided by an adaptive law derived from the Lyapunov stability theory and the recursive least-square method. The adaptive flight control is designed to track a reference model that specifies desired handling characteristics for a class of transport aircraft. The feedback control augmentation uses a proportional and integral scheme to handle errors in the roll, pitch, and y2w rates.

A control simulation of the direct adaptive control law is performed in a flight simulator to assess the stability recovery of a damaged generic transport model using d e neural network adaptive flight control. The results cf the simulation show that the direct neural network control au,mentation scheme is able to stabilize a damaged aircraft. I n the near future, a control simulation of the hybrid adaptive control law will be conducted to investigate the potential benefits 22 o f 23 American Institute of Aeronautics and ASUOMU~~CS offered by this proposed scheme in reducing the possibility of high gain control in the present direct adaptive control strategy. Moreover, adaptive flight control research will advance the knowledge in the area of integrated flight control with propulsion and airframe effects in order to address interactions between vehicle dynamics, propulsion dynamics, and structural dynamics that may be present. The assumption of rigid-body aircraft flight dynamics no longer holds true as the aircraft will have to be treated as an elastic body. This will give rise to challenges in developing adaptive fight control that can handle aeroservoelastic effects of damaged aircraft.

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23 of 23 Amencan Institute of Aeronautics and Astronautics