Dynamic Characteristics Analysis and Flight Control Design for Oblique Wing Air- Craft

Accepted Manuscript

Dynamic characteristics analysis and flight control design for oblique wing aircraft

Wang Lixin, Xu Zijian, Yue Ting

PII: S1000-9361(16)30182-0 DOI: http://dx.doi.org/10.1016/j.cja.2016.10.010 Reference: CJA 711

To appear in: Chinese Journal of Aeronautics

Received Date: 15 December 2015 Revised Date: 15 June 2016 Accepted Date: 17 August 2016

Please cite this article as: W. Lixin, X. Zijian, Y. Ting, Dynamic characteristics analysis and flight control design for oblique wing aircraft, Chinese Journal of Aeronautics (2016), doi: http://dx.doi.org/10.1016/j.cja.2016.10.010

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Chinese Journal of Aeronautics 28 (2015) xx-xx

Contents lists available at ScienceDirect

Chinese Journal of Aeronautics

journal homepage: www.elsevier.com/locate/cja

Dynamic characteristics analysis and flight control design for oblique wing aircraft

Wang Lixin, Xu Zijian, Yue Ting*

School of Aeronautics Science and Engineering, Beihang University, Beijing 100083, China

Received 15 December 2015; revised 15 June 2016; accepted 17 August 2016

Abstract

The movement characteristics and control response of oblique wing aircraft (OWA) are highly coupled between the longitudinal and lateral-directional axes and present obvious nonlinearity. Only with the implementation of flight control systems can flying qualities be satisfied. This article investigates the dynamic modeling of an OWA and analyzes its dynamic characteristics. Furthermore, a flight control law based on model-reference dynamic inversion is designed and verified. Calculations and simulations show that OWA can be trimmed by rolling a bank angle and deflecting the triaxial control surfaces in a coordinated way. The oblique wing greatly affects longitudinal motion. The short-period mode is highly coupled between longitudinal and lateral motion, and the bank angle also occurs in phugoid mode. However, the effects of an oblique wing on lateral mode shape are relatively small. For inherent control characteristics, symmetric deflection of the horizontal tail will generate not only longitudinal motion but also a large rolling rate. Rolling moment and pitching moment caused by aileron deflection will rein- force motion coupling, but rudder deflection has relatively little effect on longitudinal motion. Closed-loop simulations demonstrate that the flight control law can achieve decoupling control for OWA and guarantee a satisfactory dynamic performance. Keywords: Oblique wing aircraft; Dynamic characteristics; Decoupling; Control allocation; Model-reference dynamic inversion ciency than traditional fixed-wing designs.3 1. Introduction1 Compared to variable-sweep wing aircraft, the neutral point of OWA shifts in a small range with Oblique wing aircraft (OWA) can vary wing sweep configuration change, reducing trim drag and load for optimal configuration at various flight speeds and on the fuselage and empennage. The wave drag of extension of their flight envelope.1-2 Compared to OWA is also smaller in transonic and supersonic conventional fixed-wing aircraft, an OWA maintains flight. The lift dependent wave drag and the volume excellent low-speed, takeoff and landing performance dependent wave drag of OWA are 1/4 and 1/16 less at no sweep while being capable of large lift to drag than those of variable sweep aircraft, respectively.4 ratio via high skew angle in supersonic flight. Cruise Furthermore, oblique wing designs are simple and and maneuvering performance can also be enhanced reliable in structure, thus reducing the complexity of when the wings are at a moderate oblique angle. As a fuselage structure and related aerodynamic drag.5 result, OWA have the ability to adapt to mul- However, the asymmetry of OWA introduces special ti-mission flight and possess higher operational effi- flight dynamics problems and challenges for flight control.6-8 The asymmetric configuration will pro- *Corresponding author. Tel.: +86 10 82338821 duce side force, rolling moment and yawing moment E-mail address: [email protected] in level flight, which do not exist in conventional

·2 · Chinese Journal of Aeronautics aircraft, leading to severe coupling and nonlinearity The asymmetry of an OWA significantly affects its of the aircraft. Moreover, aileron deflection induces aerodynamic characteristics. The pressure distribu- not only rolling moment but also pitching moment, tion along the chord direction changes due to the and rolling effectiveness is insufficient at high skew spanwise flow of air. The aerodynamic load of the angle. Only with flight control systems can the lon- right forward-swept wing is concentrated on the gitudinal and lateral motions of OWA be decoupled wing root; thus the leading-edge suction of the right to meet operational requirements of pilots and wing tip and the lift coefficient decrease. The left achieve good flight quality. backswept wing is the opposite: aerodynamic load is Currently, the flight controllers for OWA are concentrated on the wing tip, and the leading-edge mostly designed by linear control methods based on suction and lift coefficient increase, which can be linear equations.9-15 For example, Alag et al.13 and seen in Fig. 2(a). Since leading-edge suction makes a Pahle14 used linear quadratic optimal control theory greater contribution to lift, the left wing has a lift based on model-following technology to design con- increment. As seen in Fig. 2(b), the lift increment of 15 trol laws. Clark and Letron proposed a command left wing ∆LL is greater than the lift increment of and stability augmentation system where right wing ∆L , which produces nose-down pitch- eigenstructure assignment techniques are combined R ing moment ∆M and rolling moment ∆L that with an optimization procedure to determine the make the right wing move downward. feedback matrix for approximating the desired The asymmetric wings of an OWA generate side eigenstructure. Evaluation of these controllers on force that symmetric wings do not have. In Fig. 2 (c), nonlinear equations of motion seems to be less de- the velocity of airflow V can be divided into veloc- sirable with certain time delays and great oscilla- 0 16 tions. With regard to the research on applying ity normal to the leading edge Vn and velocity par- modern control technologies, such as intelligent con- allel to the leading edge Vt . Regardless of viscosity, trol theory, to OWA with high cross-coupling and V has no effect on the pressure distribution of the nonlinearity, Pang16 designed an attitude controller t D V with a sliding mode control method for near-space wing surface. The drag n corresponding to n vehicles with an oblique wing. However, the over- can be divided into Dx and Dy in the wind coor- shoot of this closed-loop system was relatively high, dinate system. In symmetric swept back wings, the and no reports are available about OWA in the con- two side-components DyL and DyR offset each ventional flight envelope. This paper investigates the nonlinear dynamic other. But, for the oblique wing, the lack of symmetry model of OWA, and dynamic response is numerically introduces a side component that increases as the simulated and analyzed. According to the highly skew angle becomes larger. The side force is large cross-coupled and nonlinear properties of OWA, enough that it cannot be ignored when contrasted model-reference dynamic inversion is used for flight with the magnitude of drag. control law design. Differential horizontal tail and The leading edge suction of the left backswept ailerons are allocated for roll control. This approach wing is larger than that of the right forward-swept can successfully maintain multivariate decoupling wing at subsonic speed, and the lift vector of the left control for OWA. wing inclines forward (see Fig. 2(b)), which results in smaller drag of the left wing. At supersonic speed, 2. Layout and aerodynamic characteristics the wave drag of the right wing is larger. Conse- quently, the drag of the left wing is larger than that The OWA investigated in this paper is presented in of the right wing at subsonic and supersonic speed, Fig. 1. The oblique wing is designed to pivot from 0° i.e. DDnL< nR . Fig. 2(c) shows that the asymmetric to 60° with the right wing forward. drag produces a yawing moment ∆N > 0 N m that tends to reduce the skew angle.

Fig. 1 Oblique wing aircraft.

Chinese Journal of Aeronautics · 3 ·

Fig. 3 Decrease of aileron moment arm caused by oblique wing.

3. Modeling and dynamic characteristics analys es

3.1. Flight dynamic modeling

The aerodynamic forces and moments of OWA become highly nonlinear and cross-coupled as the skew angle becomes larger. In addition, the inertia is also cross-coupled between an aircraft’s 1ongitudinal and 1ateral-directional axes. So the flight motion of OWA should be modeled by six-degree-of-freedom nonlinear equations and cannot be divided into longitudinal and lateral equations. Compared with conventional fixed-wing aircraft, OWA’s asymmetry leads to great changes in moments of inertia and cross products of

inertia; the cross products of inertia I xy and I yz are no longer zero. Therefore, the moment equations cannot be simplified like with conventional fixed-wing aircraft, and they are expressed in Eq. (1).5

 2 2 L= Ix p&& − I yz()() q − r − I zx r + pq Fig. 2 Influence of oblique wing on aerodynamic force   −Ixy()() q& − rp − I y − I z qr and moment.  2 2 The right aileron is ahead of the left on the oblique M= Iy q&& − I yz()() r − p − I xy p + qr  (1) wing, and the difference of lift caused by aileron de-  −Iyz()() r& − pq − I z − I x rp flection introduces pitching moment. So, apart from  2 2 the rolling moment caused by aileron deflection, the N= Iz r&& − I xy()() p − q − I yz q + rp additional pitching moment should also be consid-   −Izx()() p& − qr − I x − I y pq ered in flight trimming and maneuvering. Moreover, the aileron moment arm la decreases when the where L, M and N are total moment components in wings are oblique (see Fig. 3); thus the rolling effec- body axes; p, q and r are roll, pitch and yaw angular tiveness of ailerons will decrease with the increase of rate in body axes respectively; Ix , I y , I z , I xy skew angle Λ . This will lead to insufficient rolling and Izx are moments of inertia and cross products effectiveness of the ailerons. It is therefore necessary of inertia in body axes. to use horizontal tail to help roll control when the Due to its asymmetry, OWA wing rotation, lift, wings are highly skewed. drag and pitching moment vary greatly, and asym- metrical side force, rolling moment and yawing moment are generated. The nonlinear aerodynamic forces and moments can be expressed as follows:

·4 · Chinese Journal of Aeronautics

Λ zontal tail are regarded as independent control varia- X= X0 ( u,,,α β ) +Xp p + X q q + X r r  bles. The allocation of control moments are the only  +XXδδeL + δ δ eR eL eR factor to be considered in flight control surfaces.  Y= Y u,,,α βΛ +Y p + Y q + Y r + Y δ Therefore, moment equations can be written as  0 () p q r δr r  Z= Z u,,,α βΛ +Z α + Z p + Z q + Z r  0 () α& & p q r p&      +ZZZZδδeL + δ δ eR + δ δ aL + δ δ aR q&  =ff() x + g f () x u  eL eR aL aR (2) Λ r  L= L0 () u,,,α β α +Lp p + L q q + L r r &  +LLLδ + δ + δ   g g g g g   δaLaL δ aR aR δ r r f ()x p p p p p p  δaL δ aR δ r δ eL δ eR   Λ   M= M0 () u,,,α β +Mα α& + Mp p + M q q + Mr r =f()x  + g g g g g (3)  & q qδ q δ q δ q δ q δ   aL aR r eL eR   +MMMMδ + δ + δ + δ f x   δeLeL δ eR eR δ aL aL δ aR aR r ()  g g g g g rδ r δ r δ r r δ  aL aR rδeL eR  N= N u,,,α βΛ +N p + N q + N r + N δ  0 () p q r δr r T [,,,,]δaL δ aR δ r δ eL δ eR where XYZ, and are aerodynamic force compo- where x = [,,,,,,,,]p q rα β µ u γ H T are state variables nents in body axes; XYZLMN, , , , and are 0 0 0 0 0 0 related to control allocation, with γ and H are flight aerostatic forces and moments; u,α and β are the path angle and flight altitude; airplane speed, angle of attack and sideslip angle, u = [,,,,]δ δ δ δ δ T ; f( x) is a nonlinear respectively; δ, δ , δ , δ and δ are the control aL aR r eL eR f aL aR r eL eR three-element vector function varied with state varia- inputs of left aileron, right aileron, rudder, left hori- g x zontal tail and right horizontal tail, respectively; the bles, and f ( ) is a nonlinear 3×5 matrix function representing the control matrix. partial derivatives XYZLMi,,,, i i i i and Ni To avoid a situation where deflection of the differ- i= p,,,,,,,, q r δ δ δ δ δ α are aerodynamic ( eL eR r aL aR & ) ential horizontal tail approaches full but deflection of derivatives corresponding to variables. The aerostatic ailerons is still small, forces and moments and dynamic derivatives are ∆ = diag(δ , δ , δ , δ , δ ) is in- related to u,α , β and Λ can be obtained by interpo- aLmax aRmax rmax eLmax eRmax troduced for weighting. Therefore, Eq. (3) can be lation during simulation. rewritten as: Eq. (2) shows that OWA are highly coupled in aerodynamics, and triaxial state variables all have p&  influences on longitudinal and lateral aerodynamic   ∆∆−1 ∆ q&  =ff + g fu = f f + g f uˆ (4) forces/moments. The cross static derivatives r&  XYZLMNβ,,,,, α β α β α and cross dynamic derivatives YZZLMMNq,,,,,, p r q p r q exist in OWA, but where uˆ = [,,,δaL δ aLmax δ aR δ aRmax δ r δ rmax T they are zero for conventional airplanes. The change δeL δ eLmax,] δ eR δ eRmax . According to Eq. (4), the of moment arm and aerodynamic efficiency of ailer- optimal control u can be gotten by pseudo-inverse. ons has obvious effects on rolling effectiveness. The The control deflection has the smallest two-norm, left and right ailerons have distinctly different con- corresponding to the smallest control power, theoret- trol effectiveness due to asymmetry of the flow field; ically. The expression is thus, the left and right ailerons should be considered separately in the design of flight control laws. While p&   +    the ailerons produce a pitching moment, i.e. M , u =∆ g ∆ q − f (5) δa ()f&  f    the asymmetric wing has little effect on the actions of r&   the rudder and horizontal tail. The rolling effectiveness of OWA is insufficient at where the superscript “+” symbolizes pseudo-inverse. high skew angles, so a differential horizontal tail is needed for roll control. For optimal control, ailerons 3.2. Dynamic characteristics and the differential horizontal tail should be allocated properly, which is an important problem for OWA (1) Trimming in different skew angles in trimming and the design of flight control laws. OWA can vary skew angle at different speeds for a This paper employs the concept of pseudo-controls17 multi-mission flight. The following three typical to facilitate the efficient use and combination of con- conditions are chosen for trimming and the trimming trol power. Both ailerons and the differential hori- parameters are presented in Table 1, where φ is the

Chinese Journal of Aeronautics · 5 · bank angle. Table 1 Trimming parameters at typical conditions

Parameter Condition Sweep (°) Ma H (m) α(°) δeL (°) δeR (°) φ (°) δr (°) δaL (°) δaR (°)

1 0 0.3 3000 0.51 －7.10 －7.10 0 0 0 0 2 30 0.8 10000 －0.86 －2.85 －5.53 －11.97 －4.22 －2.67 1.28 3 60 1.4 10000 －0.93 －1.91 －4.51 －25.64 －4.4 －4.45 3.16 shown in Fig. 4(a). This phenomenon is mostly The results in Table 1 show that: caused by the cross static derivatives L and N . (a) To trim the asymmetric aerodynamic moments α α caused by an oblique wing, the triaxial control sur- In Fig. 4(a), ∆α , ∆ β , ∆ θ and ∆ φ are variations of faces should deflect in a coordinated way. At the angle of attack, sideslip angle, angle of pitch and same time, OWA make use gravity to balance the bank angle. In the phugoid mode, bank angle also side force by rolling an angle. changes, as seen in Fig. 4(b). This is because the side (b) As the angle of attack for trimming decreases force varies with flight speed; thus the bank angle for with the increase of flight speed, the resulting balancing side force also changes. In Fig. 4(b), ∆V nose-down pitching moment decreases. Thus the is variation of airplane speed. Nevertheless, the horizontal tail takes up less to trim the pitching mo- changes in lateral mode shape are generally small. ment. The motion responses are similar to that of the (c) The bank angle and the deflection of lateral straight wing, and longitudinal parameters have no control surfaces become larger, since the asymmetric significant variations in lateral modes. aerodynamic forces and moments increase with the increase of flight speed and skew angle. (d) Because of the allocation by pseudo-controls, the left and right ailerons hold different deflection areas based on different control effectiveness. The differential horizontal tail takes part in roll control; thus it decreases the deflection of ailerons and facilitates their efficient use. (2) Natural modes The linear equations of motion can be derived from the six-degree-of-freedom nonlinear equations by utilizing the small-disturbance theory. Based on these linear equations, five modes corresponding to the modes of conventional airplanes can be obtained. Taking Condition 2 as an example, the eigenvalues of modes are presented in Table 2. Table 2 Eigenvalues of modes

Mode Eigenvalues Short period －1.51 ± 6.70i Phugoid －0.0018 ± 0.058i Rolling convergence －39.68 Dutch roll －0.52 ± 6.70i Spiral mode －0.0074

Five modes of OWA are similar but not identical to Fig. 4 Eigenvectors of short-period mode and phugoid those of conventional airplanes. The short-period mode. mode of straight wings is seen to be a motion in which longitudinal parameters α and q are present (3) Control characteristics with significant magnitude. But the short-period The open-loop control characteristics of OWA are mode of OWA is highly longitudinal/lateral coupled, analyzed for Condition 2. The responses to square and all rotation parameters changes significantly, as wave input of asymmetric aileron ∆δa_asym =2 ° ,

·6 · Chinese Journal of Aeronautics

rudder ∆δr =2 ° and a symmetric horizontal tail ∆t = 2 s ).

∆δe_sym =2 ° are presented in Fig. 5 (pulse width

Fig. 5 Responses to square wave input of asymmetric aileron, rudder and a symmetric horizontal tail for Condition 2. longitudinal motion parameters. Fig. 5 shows that an oblique wing makes the longitudinal and lateral motions highly coupled: 4. Flight control design based on model-reference (a) Although the symmetric deflection of the hori- dynamic inversion zontal tail only generates pitching moment, the response of OWA is a fairly large roll angular rate p. Nonlinear dynamic inversion (NDI) is a kind of This is because OWA do not have the bilateral sym- modern control method aimed directly at nonlinear metry. The lift of the left wing is no longer equal to motion models. Because unsteady aerodynamic forc- that of the right wing when the angle of attack es of OWA are obvious and triaxial motion is highly changes; thus the rolling moment changes greatly cross-coupled and nonlinear, it is difficult to build an with variation in angle of attack. Moreover, the mo- accurate motion model for OWA. Without an accu- ment of inertia I decreases obviously with rota- xx rate model, the control effectiveness of pure NDI is tion of the wing. Consequently, symmetric deflection unsatisfying. Hence, ideal models established ac- of the horizontal tail introduces a large rolling rate. cording to the requirements for handling qualities are (b) As the right aileron is ahead of the left aileron introduced based on NDI. OWA can track these on the oblique wing, ailerons generate rolling mo- models by NDI, thereby ensuring the controlled air- ment and pitching moment. The pitching moment craft enjoys satisfactory flight qualities in quite a changes angle of attack; thus the rolling moment will large flight envelope.18-20 be greatly influenced. This results in a more obvious coupling between longitudinal and lateral axes. 4.1. Flight control structure (c) Rudder deflection produces sideslip and rolling angles, but, since these have little effect on longitu- As shown in Fig. 6, the flight control system based dinal aerodynamics, these result in little change to on model-reference dynamic inversion includes four

Chinese Journal of Aeronautics · 7 ·

parts: ideal reference models, compensators, NDI control command of outer loop while qRM is di- inner loop and NDI outer loop. Each part is intro- rectly taken as the pitching control command of in- duced as follows: ner loop q . (1) Ideal models form the ideal control response c (3) The NDI outer loop is used to generate control µ&RM , qRM and βRM under the control command commands of the inner loop. [,]β& µ T is re- T cmd& cmd [,,]µ&cq c β c , where µ& is the velocity bank angle. solved to [,]p r T , which combines with the pitch- According to the low-order equivalent system meth- c c od for assessing flying qualities, the low-order equiv- ing control command of inner loop qc to generate alent models are chosen as ideal models, and their the commands of inner loop. According to Ref.21, the parameters are determined by requirements for han- control forces resulting from control surfaces are dling qualities. The ideal models are expressed in Eq. much smaller than aerodynamic forces; thus the ef- (6). fect of these small perturbations on dynamics is neg- ligible and can be canceled in steady state by incor-  porating integrators into the control law. So the con- µ&RM 1 = trol forces can be neglected when designing the outer  µ&cs + ω p  loop, and the differential equation of [,,]α β µ T can qRM 2 s+1 Tθ 2  = ωsp 2 2 (6) be expressed as  qc s+2ξsp ω sp s + ω sp  µ  p  β ω &  RM = β      α& =fm() x + g m () x q   βc s + ωβ β&  r  (7) where the reciprocal of rolling time constant ωp is   fµ cosα cos β 0 sin α cos β   p  4 rad/s; ω and ξ are the frequency and damp       sp sp =fα  + −cosα tan β 1 − sin α tan β   q        of short-period mode, respectively, taken as ωsp =5 fβ  sinα 0− cos α   r  rad/s, ξ =1.2; time constant T can be solved by sp θ 2 where f( x) is a nonlinear three-element vector control anticipation parameters (CAP), and the value m of CAP is 1; the desired response for sideslip angle is function varied with state variables; and gm ( x) is taken as the first order inertia link, and a nonlinear 3×3 matrix function varied with α and

ωβ = 3 rad/s . β ; fµ, f α and f β are continuous functions related (2) PI compensators are used to generate the con- to state variables. trol commands for the NDI loop and timely track the response of ideal models. It compensates for errors of loop and the external disturbance. βRM , µ&RM and the corresponding feedback signals pass through the compensator to generate β&cmd and µ&cmd as the

Fig. 6 Flight control system scheme based on model-reference dynamic inversion. According to the time-scale separation meth- pseudo-inverse: od,10,20,21 the dynamic responses of fast variables are p  µ   f   considered to have arrived at steady state when de- c & µ  21  +     signing the outer loop. Ref. demonstrates that this qc =g m  α&  −  fα   (8) approximation justifies slow-state control law. So the        rc  β&   fβ  control commands of the inner loop can be solved by  

·8 · Chinese Journal of Aeronautics

In Eq. (7), the equations of β& and µ& do not zontal tail by pseudo-controls. The expression is presented in Eq. (4). contain q, which means that the command of β& According to the characteristic response of the first and µ& can be realized just by controlling p and r, order inertia link to the step signal, the output and the pitching control command of inner loop qc [,,]p q r is designed to track the command T is free from the influence of βc and µ&c . By mak- [,,]pc q c r c asymptomatically by making ing pitching control command α =0 ° , q can TTω ω c RM [p&&& , q , r ]c = f [ p c− p , q c − q , r c − r ] . f = diag replace the pitching command generated by the outer ( ωp,, ω q ω r ) = diag (15,10,10) rad/s is taken to loop, which is intended to be the pitching control command of inner loop. achieve good tracking results, where ωqand ω r are (4) The NDI inner loop calculates the required reciprocals of time constant of first order inertia link. T The structure of inner loop is shown in Fig. 7. control surfaces to track the command [,,]pc q c r c and achieve the desired control. Based on the princi- ples of NDI, a control law of the inner loop can be obtained that allocates ailerons and differential hori-

Fig. 7 Structure of inner loop considering control saturation. rolling maneuvers are simulated. Condition 2 is tak- 4.2. Closed-loop flight simulation and analysis en as an example, and the dynamic response curves are presented in Fig. 8. To validate the control law based on model-reference dynamic inversion, the pitching, side slipping and

Chinese Journal of Aeronautics · 9 ·

Fig. 8 Closed-loop response to triaxial input.

In Fig. 8(a), the velocity bank angle µ& does not moment and yawing moment that symmetric wings appear to oscillate; it tracks the commands quickly do not have. To trim the asymmetric aerodynamic and almost matches with the response of the ideal moments, triaxial control surfaces should deflect in a model. Meanwhile, β does not exceed 0.5° in ma- coordinated way that balances the asymmetric moments. Meanwhile, OWA should roll on an angle to neuvering flight. During the pitching maneuver, the balance the side force. curve of pitch angular rate q also coincided with that (2) OWA have significant aerodynamic and inertial of the ideal model. β and p change little and cross-coupling between the longitudinal and recover to zero quickly, as seen in Fig. 8(b). This 1ateral-directional axes. The short-period mode of an demonstrates that the flight control system success- OWA is highly coupled, and all rotation parameters fully maintains decoupling control between the lon- take on a substantial amount of variation. In the gitudinal and lateral axes. In side slipping maneuvers, phugoid mode, the bank angle also changes. Never- the response of sideslip angle has a little delay com- theless, the changes in lateral mode shape are gener- pared to the ideal model, but they are still pretty ally small. The motion responses are similar to those close, as seen Fig. 8(c). Therefore, the flight control of straight wings, and longitudinal parameters have system enables the OWA to track commands quickly no significant variations in lateral modes. and maintain decoupling control. (3) The control characteristics of OWA are quite dis- The actual responses are close to those of the ideal tinct from those of conventional aircraft. Although model, so good handling qualities can be achieved by symmetric deflection of the horizontal tail only gen- these designs. According to the response of the con- erates pitching moment, the response has a fairly trol surfaces in Fig. 8, it can be found that the dif- large rolling rate p. Ailerons generate both rolling ferential horizontal tail takes part in roll control for moment and pitching moment; thus coupling be- the allocation by pseudo-controls. Thus it decreases tween longitudinal and lateral axis becomes more the deflection of ailerons and facilitates their efficient obvious. The deflection of rudder introduces both use. sideslip and rolling angles, which have little effect on longitudinal motion parameters. 5. Conclusions (4) The aileron moment arm shortens in OWA, which leads to insufficient rolling effectiveness. So (1) Oblique wings change the lift, drag and pitching they need a differential horizontal tail to assist roll moment greatly, and generate side force, rolling

·10 · Chinese Journal of Aeronautics control at high skew angles. Ailerons and the differ- for the F-8 oblique wing research aircraft. IEEE ential horizontal tail are allocated by pseudo-controls Control Systems Magazine 1988; 8(2):81-6. to facilitate efficient use and combine control power. 12. Jeffery J, Hall SEJC, Perkins J. The design and This decreases the deflection of ailerons and has sat- control of an oblique winged remote piloted vehicle. isfactory control effect. Reston: AIAA; 1995 Jan. Report No.: (5) The control law based on model-reference dy- AIAA-1995-0744. namic inversion maintain decoupling control for 13. Alag GS, Kempel RW, Pahle JW, Bresina JJ, OWA. The actual response is close to that of the ideal Bartoli F. Model-following control for an model, and good handling qualities can be realized oblique-wing aircraft. Washington, D.C.: NASA; from ideal model designs. 1986. Report No.: NASA-TM-88269. 14. Pahle JW. Output model-following control syn- References thesis for an oblique-wing aircraft. Washington, D.C.: NASA; 1990. Report No.: NASA-TM-100454. 1. Hirschberg MJ, Hart DM, Beautner TJ. A sum- 15. Clark RN, Letron XJY. Oblique wing aircraft mary of a half-century of oblique wing research. flight control system. Journal of Guidance, Control, Reston: AIAA; 2007 Jan. Report No.: and Dynamics 1989; 12(2):201-8. AIAA-2007-0150. 16. Pang J. Modeling and flight control for 2. Espinal D, Im H, Lee B, Dominguez J, Sposato H, near-space vehicles with an oblique wing [disserta- Kinard D, et al. Supersonic bi-directional flying wing, tion]. Nanjing: Nanjing University of Aeronautics Part II: Conceptual design of a high speed civil and Astronauts; 2013 [Chinese]. transport. Reston: AIAA; 2010 Jan. Report No.: 17. Reigelsperger WC, Banda SS. Nonlinear simula- AIAA-2010-1393. tion of a modified F-16 with full-envelope control 3. Nelms WP. Applications of oblique wing technol- laws. Control Engineer Practice 1998; 6(17):309-20. ogy-An overview. Proceedings of AIAA aircraft sys- 18. Long JW, Pan WJ, Wang LX. A comparison of tems and technology meeting; 1976 Sep 27-29; Dal- nonlinear dynamics inversion control law designs for las, Texas. Reston: AIAA; 1976. a fighter aircraft. Flight Dynamics 2013; 4. Cheng SY. Aerodynamic design and preliminary 31(4):297-300[Chinese]. flight dynamics study on oblique flying wing [disser- 19. Walker GP, Allen DA. X-35B STOVL flight con- tation]. Xi’an: Northwest Polytechnical University; trol law design and flight qualities. Reston: AIAA; 2007 [Chinese]. 2002 Nov. Report No.: AIAA-2002-6018. 5. Qiu L, Gao ZH, Liu Y. Research on oblique wing 20. Knöös J, Robinson JWC, Berefelt F. Nonlinear aircraft’s flight dynamics model. Flight Dynamics dynamic inversion and block backstepping: A com- 2015; 33(2):106-10 [Chinese]. parison. Reston: AIAA; 2012 Aug. Report No.: 6. Hu SY, Jiang CW, Gao ZX, Li CX. Oblique flying AIAA-2012-4888. wing supersonic airliner aerodynamic configuration 21. Snell SA, Nns DF, Arrard WL. Nonlinear inver- parameters selection method. Journal of Beijing sion flight control for supermaneuverable aircraft. University of Aeronautics and Astronautics 2014; Journal of Guidance, Control, and Dynamics 2012; 40(4):551-7 [Chinese]. 15(4):976-84. 7. Hao NS, Liu Y, Wang J, Yang WC, Yang JM. Wind tunnel investigation of a low speed oblique plate. Wang Lixin is a professor and Ph.D. supervisor at Beihang University. His main research interests lie in air- Acta aerodynamica sinica 2013; 31(3):344-9 [Chi- craft design, flight dynamics, and flight control. nese]. E-mail: [email protected] 8. Curry RE, Sim AG. Unique flight characteristics of the AD-1 oblique-wing research airplane. Journal of Xu Zijian received his B.S. from Beihang University and Aircraft 2015; 20(6):564-8. is now Ph.D. student. His main research interests are flight 9. Alag GS, Kempel RW, Pahle JW. Decoupling con- dynamics, flight simulation and flight control. trol synthesis for an oblique-wing aircraft. Washing- E-mail: [email protected] ton, D.C.: NASA; 1986. Report No.: NASA-TM-86801. Yue Ting is an assistant professor at Beihang University. 10. Pang J, Mei R, Chen M. Modeling and control He received his B.S., M.S. and Ph.D. in aircraft design for near-space vehicles with oblique wing. Proceed- from Beihang University in 2004, 2006 and 2010 respectively. His main research interests are aircraft fight dy- ings of the 10th world congress on intelligent control namics and control. and automation; 2012 Jul 6-8; Beijing. Piscataway E-mail: [email protected] (NJ): IEEE Press; 2012. p. 1773-8. 11. Enns DF, Bugajski DJ, Klepl MJ. Flight control