Modeling and Simulation for an Aircraft of

Seamless Aeroelastic Wing

Wang Zheng Ping School of Aerospace and Science Engineering

Beijing Institute of Technology Beijing,China

wzp@bit.edu.cn

Guo Shi Jun Aerospace Engineering

Cranfield University Bedford,UK

s.guo@cranfield.ac.uk

Abstract—The purpose of this paper is to discuss the method of modeling and simulation software design for an aircraft of seamless aeroelastic wing. An aeroelastic wing structure model is established, and then a flight control model is linearized by small disturbance method. The characteristic for aeroelastic wing aerodynamic force varying with the flight speed and the control surface deflection is analyzed through some numerical calculation curves. The analyzing results show that the main challenge is how to achieve a specified rolling rate for the aircraft when the control effectiveness drops down within the flight envelope. In order to resolve this problem, the simulation software integrated dynamics force calculating and control system design is developed and a PID control law is designed. The simulation results show that the control plans are feasible to meet the requirement for rolling control of aeroelastic wing aircraft designed by this paper.

Keywords- seamless aeroelastic wing; active control; Integrated Software

I. INTRODUCTION Active aeroelastic wing technology (AAWT) integrates

multidisciplinary technologies in structures, aerodynamics and controls to improve aircraft performance [1]. The original goal for developing the AAWT was to achieve the required controllability and performance of an aircraft without paying excessive weight penalty for adequate wing structural stiffness [2].

One of the investigations was made to extend the AAWT to a small unmanned aircraft vehicle (UAV) design[3] . A small UAV normally has a much lower wing load and stress level and has more potential of weight saving. However significant weight saving is only possible if the aircraft with reduced wing stiffness and control effectiveness can be controlled by applying the AAWT. [4] presents an integrated trim and structural method for controller design. It applies an optimization algorithm such as simplex method to calculate the desired deflection of control surface. This design philosophy, in theory, may provide an exact control signal for the aircraft, but difficult to apply to resolving the control problem in practice for its complex optimization process.

This paper firstly presents the aircraft model including a SAW structural model in section II; followed by analysis results for the model in section III; the integrated simulation

software developed for the SAW aircraft and the simulation results to track the planned trajectory in section IV; and conclusions in section V.

II. AIRCRAFT MODELING

A. Aeroelastic Wing Structure Model[5] In this paper, a small aircraft is investigated. The aircraft

has a large sweptback seamless aeroelastic wing (SAW). The wing box is made of composite materials and modeled by using 15 span wise single-cell thin-walled beams along the elastic axis as shown in Figure 1. The LE and TE control surfaces are positioned in the 15th wing section.

The equations of motion for each of the thin-walled box beams were represented as follows:

0=⋅⋅−⋅+′′′⋅+′′′′⋅ φφ αXmhmCKhEI 0=⋅−⋅⋅+′′′⋅+′′⋅ φφ α pIhXmhCKGJ (1) Where 4 4h h y′′′′ = ∂ ∂ , 2 2h h t= ∂ ∂ , 3 3h yφ′′′ = ∂ ∂ and 2 2h tφ = ∂ ∂ .

A dynamic stiffness matrix for a box beam can be subsequently created by relating the displacements to the bending moment and torque at both ends of the beam. A dynamic stiffness matrix for the whole wing box structure is obtained by assembling all the wing box beam stiffness matrices along the wingspan.

For static aeroelastic analysis, the aerodynamic coefficients for each of the wing sections with deflected TE are calculated by employing the panel method. By assembly of the spanwise beam models and 2D aerodynamic forces, the

TE control surface

LE control surface

Figure 1. A seamless aeroelastic wing platform and beam sections.

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static aeroelastic equation of the wing can be established and written in matrix form as:

[ ]{ } ( ){ }LETEdAFdK δδ ,,= (2) Where[K] is the stiffness matrix of the whole wing,{d} is the vector of the wing box beam transverse displacement h and Φ; {AF(d,δTE, δLE)} is the vector of aerodynamic lifting force and pitching moment acting on the wing, which depends upon {d} especially the twist angle, and the flexible TE and LE section deflection. For the highly flexible and large sweptback angle SAW, a geometrically nonlinear and large bending-torsion coupled deformation is expressed in the following form and solved in an iterative procedure: [ ]{ } ( ){ }LETEjj dAFdK δδ ,,1 =+ (3)

B. Lateral Directional Linearized Aerodynamic Model The dynamic behavior of the SAW small-sized UAV is

modeled by nonlinear six degree-of-freedom equation. The equations are written in two sets of equations. These are the longitudinal equation of motion and the lateral directional equation of motion. This paper focuses on discussing the aircraft roll maneuver, the roll moment equation of motion and the kinematic equation are expressed as: ( ) ( )xx zz yy xzPI QR I I R PQ I L+ − − + = (4)

sinP = − ΘΨ + Φ (5) Where P, Q and R are the roll, pitch and yaw rates, respectively, expressed in the body axis. Ixx,Iyy and Izz are the moments of inertia about the x axis, y axis and z axis, and Ixx is the product of inertia y x-z plane of the aircraft. L is the rolling moment. Θ,Φ and Ψ are pitch angle, heading angle and roll angle of the body axis.

By using the small perturbations assumption, and neglecting derivatives that have negligible values, the lateral-direction model becomes [6]

xz

p rzz

Ip L L p L r L rIβ δβ δ= + + + +

(6) Where, β is the angle of sideslip, and p, r presents the roll rate and the yaw rate respectively. The variable δ presents the deflection angle of control surface. The stability parameters Lβ, Lp, Lr and Lδ can be seen to be simply a group of the terms multiplying each control parameter. TABLE I summaries some lateral-directional stability parameters associated with (6).The overall response of the aircraft rolling maneuver can be assessed from the relative magnitude of these stability parameters.

In an attempt to simplify discussion on the roll maneuver, the variables (β, r and r ) are temporarily removed from the

TABLE I. LATERAL-DIRECTIONAL STABILITY PARAMETERS

Stability Parameters Definition Units

Lβ ρV2SbClβ/2Ixx s-2

Lp ρV2Sb2Clp/2IxxU1 s-1

Lr ρV2Sb2Clr/2IxxU1 s-1

Lδ ρV2SbClδ/2Ixx s-2

above equation. It is focused on studying the roll maneuver determined by the wing control. (6) can then be represented as:

LE TELE TEpp L p L Lδ δδ δ= + + (7) Notice that the control variables here are divided into two term, that are δLE and δTE, which present deflection angle of leading edge control surface and that of the tailing edge control surface. By using the power of Laplace transforms, (7) can then be represented as a function:

LE TE

LE TE( ) ( ) ( )( ) ( )p p

L Lp s s s

s L s Lδ δδ δ= +

− − (8) The roll approximation transfer function becomes:

TE LE

)

( )( ) (p p

L Ls

s s L s s Lδ δφ = +− − (9)

Equation (9) shows that the roll mode will be excited by the inputs of leading edge and trailing edge control surfaces. It is easier to characterize the roll mode when studying response to the trailing edge control surface or the leading edge control surface input.

III. AEROELASTIC WING AERODYNAMIC FORCE ANALYSIS It is helpful for aero-elastic wing control system design

to understand the effect of each control surface on aircraft rolling moment. It is evident that the lift generated by trailing edge control surface deflection varies significantly with the speed. At low speed, the twist on the wing is small. As a result, the lift decreases with the trailing edge control surface deflecting from negative to positive. At the higher speed, a large amounts of wing twist caused by trailing edge control surface deflection that reduces the wing effective angle of attack. Note that the wing lift generate by trailing edge control surface negative deflection decreases significantly after the critical speed due to the twisting of the elastic. Calculating results shows, the opposing wing twist and wing camber are balanced at this critical speed, which means any deflection of the trailing edge control surface always generates the nearly constant lift, as shown in Fig.2.

Fig.3 shows that at the critical speed, the left and right wing generates the same lift, which will make the rolling moment equal to zero.

20 30 40 50 60 70 80 90 100-500

0

500

1000

1500

2000

2500

Ela

sitc

Win

g L

ift(N

)

Speed(m/s)

TEF_L=-10TEF_R=10

AOA=5

AOA=2

AOA=0

Figure 2. Lift against the speed

2

The critical speed point divides the region of rolling moment generated by trailing edge deflection with the speed varying into different parts. Fig.4 shows, in both of the lower and higher regions, the aircraft rolling movement can be controlled by trailing edge control surface, but it is noted that in the lower region, the rolling moment produced primarily using lift derived from wing camber, alternately, in the higher region, the rolling moment is created by lift from wing twist. That is, in order to maintain the idea rolling moment, the trailing edge control strategy should be transited from conventional to wing twist control method. A simple method is to make the tailing edge flap deflect to the opposite direction.

IV. SIMULATION

A. The Integrated Software Design The simulation software block is shown in Fig.5 and

consists of the non-linear aircraft model module, the rolling control module and the aerodynamic forces of elastic wing module. The subsystem aerodynamic forces is used to compute the elastic wing aerodynamic lifts using the embedded structural and aerodynamic optimization software AEROBEAMSAW, which is complied and linked into a shared MATLAB library-aerobeamsaw.mex, and it can run in MATLAB. The following flow diagram illustrates data flow, shown in Fig.6.

In Fig.6, a call to aerobeamsaw tells MATLAB to pass variables u (1), u (2), u (3) and u(4)to aerobeamsaw.mex.

B. Mathematic Simulation [7]

In the simulation, the small aircraft with the SAW is supposed to move along the flight speed trajectory. By applying the Simulink Response Optimization Toolbox, a PID-type roll control law for Active Aeroelastic Wing small aircraft has been designed.

The whole flight speed range is divided into four stages within a time scale. In the first stage up to 40 m/s, the speed remains constant. The second and third stages are connected from speed of 40m/s up to 60m/s with different accelerations. In the final speed stage of 60m/s, two types of wind turbulence are considered. One is a constant turbulence, which lasts about 20 seconds and makes the flight speed change to 65m/s; another is a random wind turbulence, which abruptly makes the flight speed change up to 72m/s. The aim of considering the above flight trajectory is to test the adaption performance of the designed control law.

For the different speed segment, it is supposed to trace the reference roll rate. Fig.7 presents the actual roll rate, shown in the solid line. From the above figure, we can see the output settling time is satisfied with the control target.

V. CONCLUSIONS The model of aeroelastic wing structure and flight control

model are developed. Based on analyzing the characteristic of aerodynamic force varying with the flight speed and control surface deflection, the roll maneuver control trajectory is proposed, and the control law is reinforced by the optimization PID algorithm. The flight simulation results demonstrate that effective roll control can be achieved through the use of wing twist.

Extension to this work will go no studying the dynamic aeroelastic wing and other control methodologies such as intelligent control will be investigated as a means of controlling the faster wing.

REFERENCES [1] Andersen, G., Forster, E., and Kolonay,R., ‘Multiple control surface

utilization in active aeroelastic wing technology’, Journal of aircraft, Vol.34,No.4, 1997, pp.552-531.

-10 -5 0 5 1050

52

54

56

58

60

62

64

66

68

70

Lift

(N)

Trailing edge deflection(degree)

AOA=0.4v=54m/s

Figure 3. Lift at the critical speed

30 40 50 60 70 80 90 100

-800

-600

-400

-200

0

200

roll reserval point2

Rol

ling

Mom

ent(N

m)

Speed(m/s)

1 TEF_LEF_dif2 TEF_LEF3 LEF4 TEF

roll reserval point1

AOA=2

Figure 4. Rolling moment

0 10 20 30 40 50

-2

-1

0

1

2

Rol

l Rat

e(de

g/s)

Time(second)

Reference Actual Output

Figure 7. Rolling rate

3

[2] Diebler, C.G. and Cumming, S.B., ‘Active aeroelastic wing aerodynamic model development and validation for a modified F/A-18A airplane’, NASA/TM-2005-213668, 2005

[3] Allegri, G. and Guo, S. and Trappani, M. On the design of an aeroservoelastic fin for a flight demonstrator, International Forum on Aeroelasticity and Structural Dynamics, Stockholm, Sweden, 18-20 Jun., 2007.

[4] Samarch, J.A., Chwalowsk, P., Horta, L.G., Piatak,D.J., ‘Integrated aerodynamic/structural/dynamic analysis of aircraft with large shape changes’, 48th AIAA/ASME/ASCE/AHS/ASC Structure, Structural Dynamics, and Materials Conference, 2007.

[5] Perera M., Guo S.J., ‘Optimal Design of a Seamless Aeroelastic Wing Structure’, AIAA Conference,2009, unpublished.

[6] Thomas R.Yechout, ‘Introduction to aircraft flight mechanics’, AIAA education series.

[7] Wang, Z.J., Guo, S.J. and Yang, D.Q., ‘Rolling active control for an aircraft of seamless aeroelastic wing’, International Journal of Modeling, Identification and Control, 2009.in press.

Figure 5. Simulation software block

A call to MEX-file aerobeamsaw:y=arobeamsaw(u(1),u(2),u(3),u(4))tells MATLAB to pass variables u(1),u(2),u(3) and u(4) to MEX-file

FortranAerobeamsaw.for

subroutine mexFunction(nlhs,plhs,nrhs,prhs) integer plhs(*),prhs(*) integer nlhs,nrhs C creat the output arguments arrays plhs(1) = mxCreateDoubleMatrix(m,n,0) C use the mxGet function to extract data from prhs(1) u1_pr = mxGetPr(prhs(1) … u4_pr = mxGetPr(prhs(4)) y_pr = mxGetPr(plhs(1))C call Fortran subroutine-AEROC use %val to pass the input and output data pointers AERO(%val(y_pr),%val(u1_pr),%val(u2_pr),& %val(u3_pr), %val(u4_pr),size)

C the original Fortran program SUBROUTINE AERO(Y,U1,U2,U3,U4,SIZE) REAL *8 Y(1),U1(1),U2(1),U3(1),U4(1) INTEGER SIZE ...

MATLAB- Simulink

MATLAB Functionaerobeamsaw

Cl_L Output

TEF,LEF,alpha,vtInput

On return from MEX-fileaerobeamsaw:y=aerobeamsaw(u(1),u(2),u(3),u(4))plhs(1)is assigned to y

Figure 6. Sequential Fortran－Mex running process

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