Controller and Aeroelasticity Analysis for a Morphing Wing

American Institute of Aeronautics and Astronautics

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Controller and Aeroelasticity Analysis for a Morphing Wing

T. L Grigorie1, A. V. Popov2 and R. M. Botez3 École de Technologie Supérieure, Montréal, Québec H3C 1K3, Canada

M. Mamou4 and Y. Mébarki5 National Research Council, Ottawa, Ontario K1A 0R6, Canada

The main objectives of this research work are: the design and the wind tunnel testing of a controller for a new morphing mechanism using smart materials made of Shape Memory Alloy (SMA) for the actuators, and the aero-elasticity studies for the morphing wing. The finally obtained configuration for the controller is a combination of a bi-positional controller (on-off) and a PI (proportional-integral) controller, due to the two phases (heating and cooling) of the SMA wires’ interconnection. Firstly, the controller is used for the open loop development step of a morphing wing project, while, further, it is included as an internal loop in the closed loop architecture of the morphing wing system. In the controller design procedure four step are considered: 1) SMA actuators model numerical simulation for different loading force cases; 2) linear system approximation in the heating and cooling phases using Matlab’s System Identification Toolbox and the numerical values obtained in the first step; 3) selecting the controller type and its tuning for each of the two SMA actuators’ phases – heating and cooling; and 4) integration of the two controllers just obtained into a single controller. For the controller validation three actions are taken: 1) numerical simulation; 2) bench testing; and 3) wind tunnel testing. For the third part of this study, aeroelastic studies, the purpose is to determine the flutter conditions in order to be avoided during wind tunnel tests. These studies show that aeroelastic instabilities for the morphing configurations considered appears at Mach number 0.55, which is higher than the wind tunnel Mach number limit speed of 0.3.

Nomenclature a0÷a2 = coefficients of the Hh (s) transfer function nominator b0÷b3 = coefficients of the Hh (s) transfer function denominator CPI (s) = transfer function of the PI controller dY1opt = optimal vertical displacement of actuator 1 dY2opt = optimal vertical displacement of actuator 2 dY1real = real vertical displacement of actuator 1 dY2real = real vertical displacement of actuator 2 e = actuation loop error Faero = aerodynamic force Fpretension = pretension spring force Fskin = elastic force produced by the flexible skin FSMA = resultant force that acts on the SMA Fspring = elastic force of the gas spring

1 Postdoctoral Fellowship, Laboratory of Research in Active Controls, Avionics and AeroServoElasticity, 1100 Notre-Dame West Street. Member AIAA. 2 Ph.D. Student, Laboratory of Research in Active Controls, Avionics and AeroServoElasticity, 1100 Notre-Dame West Street. Member AIAA. 3 Professor, Laboratory of Research in Active Controls, Avionics and AeroServoElasticity, 1100 Notre-Dame West Street. Member AIAA. 4 Senior Research Officer, Aerodynamics Laboratory, Montreal Road, Uplands Building U66. Member AIAA. 5 Associate Research Officer, Aerodynamics Laboratory, Montreal Road, Uplands Building U66. Member AIAA.


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Gm = gain margin Hc(s) = identified transfer function for cooling phase Hcl(s) = closed loop transfer function of the controlled heating phase Hh(s) = identified transfer function for heating phase Hol(s) = open loop transfer function of the controlled heating phase i(t) = command variable (electrical current) KI = integral gain KP = proportional gain M = Mach number Pm = phase margin p0÷p4 = poles of the closed loop transfer function Hcl (s) q0÷q3 = coefficients of the Hcl (s) transfer function nominator Re = Reynolds number r0÷r4 = coefficients of the Hcl (s) transfer function denominator α = wing angle of attack δh, δv = horizontal and vertical actuated displacements ε = difference between the ideal and the real system outputs ωg = frequency associated with the gain margin ωc = frequency associated with the phase margin

I. Introduction ESEARCH into drag reduction, which often leads to fuel consumption reduction, was launched by the aerospace industry over the last few years, due to worldwide environmental concerns and rising fuel costs. Drag

reduction can be achieved by airfoil shape modification, with the aim of delaying the flow transition from laminar to turbulent, by moving the transition point close to the wing trailing edge. The laminar flow past an aerodynamically morphing wing can be improved so as to obtain significant drag reduction. This concept of modifying the airfoil for various flight conditions is known as a ‘morphing wing’.

Various morphing wing studies have been conducted. One consists of a symmetric wing structure with two tapered graphite/epoxy composite plates and a steel body. Four pairs of Shape Memory Alloy (SMA) wires are attached to the wings’ bottom surfaces in a chord-wise direction. Lift and drag forces are measured at various angles of attack. Dynamic vibration signals, measured by fiber Bragg grating (FBG) sensors at the wing root, are used to monitor aeroelastic unstable phenomena, such as flutter at various angles of attack1. Another wing structure, comprised of an optimized internal layout of cables and struts, was able to morph itself. Cables were used as actuators while struts provided rigidity to the wing. In addition to achieving continuous morphing by changing cable lengths, this structure had the advantages of being lightweight and having a distributed actuation. The Non-dominated Sorting Genetic Algorithm II (NSGA II) was used for the NASA HECS and the NextGen TSCh wing modeling2. Improved wing roll performance was achieved by use of articulated conformal control surfaces. The analysis results were compared to the experimental results obtained for a 16% scale model of a fighter wing equipped with embedded smart materials used to deform a control surface. The control surface design was found suitable for low-rate applications such as take-off and landing configurations3.

The present work refers to a rectangular morphing wing equipped with Shape Memory Alloys which modify the wing’s upper surface morphing flexible skin for various test cases. The ultimate goal of this research project is to obtain a drag reduction as a function of flow condition by changing the wing shape. This research work was a part of a morphing wing project developed by the Ecole de Technologie Supérieure in Montréal, Canada, in collaboration with the Ecole Polytechnique in Montréal and the Institute for Aerospace Research at the National Research Council Canada (IAR-NRC).

The rectangular wing model incorporated two parts: 1) A fixed rigid part of the wing’s lower surface, which sustains all of the resistance forces; and 2) The upper wing surface, consisting of a flexible skin which changes its shape through electrically controlled shape memory alloy actuators (see Fig. 1). Aerodynamic changes in the boundary layer flow took place over the morphing upper wing surface – therefore the transition point position changed and moved closer to the wing airfoil’s trailing edge.

The wing’s lower surface was designed and manufactured by a team from the Institute of Aerospace Research – Canada National Research Council, while the morphing upper wing surface and the Shape Memory Alloy (SMA) actuators were designed and manufactured by the Memory Alloys and Intelligent Systems Laboratory (LAMSI) team at ETS4.

R


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A laminar airfoil was considered as a reference airfoil shape for the morphing wing studied here, since a series of optimized airfoils had already been designed and calculated by the Ecole Polytechnique team using XFoil CFD code for various airflow conditions expressed as combinations of angles of attack and Mach numbers. Each optimized airfoil shape was characterized by its closest transition point location to the trailing edge. In total, 35 optimized airfoils were designed for the airflow combinations of Mach numbers 0.2, 0.225, 0.25, 0.275, 0.3 and angles of attack -1, -0.5, 0, 0.5, 1, 1.5 and 2 deg. These airfoils were used as a starting point in the actuation system design. Three steps were completed in the actuation system design phase: optimization of the number and positions of flexible skin actuation points, establishment of each actuation line’s architecture, and the analytical modeling of the smart materials actuators used in this application.

The next phase of the project was about the design of the actuation control, for which an integrated on-off versus PI architecture was chosen. In this design, numerical simulations of the open loop morphing wing integrated system, based on a SMA non-linear analytical model, were performed. As subsequent validation methods, a bench test and a wind tunnel test were conducted.

Also, aeroelastic analyses were performed on the flexible skin of the morphing wing for all 35 flight cases, prior to its testing in the wind tunnel, in order to determine if the wing would be stable in terms of flutter (i.e., no flutter would occur), and so the wing would therefore not be mechanically destroyed during its testing in the wind tunnel. Finite Element methods, coupled with KE methods, were used for structural and flutter analyses with the Nastran/Patran commercial software.

The wind tunnel tests were performed at the Institute for Aerospace Research at the National Research Council Canada in the 6 ft x 9 ft Subsonic Wind Tunnel. The purpose of these tests was to assess the performance of the wing model with a morphing skin with the goal of improving the laminar flow over the upper wing surface. The upper wing surface, made of flexible skin, was controlled and morphed by smart material actuators at two control points, such that any optimized upper airfoil shape for the 35 flow conditions could be achieved by adjusting the vertical displacements of both actuators.

The transition location detection was based on pressure signals measured by optical and Kulite sensors installed on the upper wing flexible surface. Depending on the project evolution phase, two architectures were considered for the morphing system: open loop and closed loop. The difference between these two architectures was done by the use of the transition point as feedback signal.

The work described here was developed in the open loop phase of the morphing wing system. In this phase, numerical and experimental studies were performed for the aerodynamics of the morphed wing, flexible skin structure, actuation hardware and the actuation system control. Also, the studies include the real-time determination and visualization of the transition point position using the pressure sensor system and infrared camera visualization. The functions of the optical and Kulite pressure sensors are limited to the monitoring of the pressure and its Root Mean Square (RMS) distribution in the boundary layer.

II. Controller Design

A. Actuation Mechanism The smart actuators modify the upper wing flexible skin surface, so that the laminar-to-turbulent transition point

moves close to the wing airfoil trailing edge. From the step regarding the optimization of the number and positions of flexible skin actuation points, derived the necessity to use two actuation rods incorporated at 25.3% and 47.6% of the chord, respectively. The shape memory actuator wires were made of nickel - titanium, and contract as muscles do when electrically excited. According to the adopted actuation mechanism in Fig. 25, the SMA wires were used as straight wires in our application (a cross section of the actuators is displayed in Fig. 1).

Each of our actuation lines assembly contains three SMA wires as actuators and a cam that is sliding spanwise on the supporting plate (on the x-axis as displayed in Fig. 2). The spanwise translating motion is translated into vertical displacement (z-direction) using rollers, at a rate of 3:1. A compression gas spring was also used as a recall. When the SMA is heated the actuator contracts and the cam moves to the right and upwards pushing the flexible skin outwards. Cooling of the SMA, results in a cam motion to the left and cause the skin to move inwards. From the

Figure 1. Cross-section of the morphing wing model.


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optimized airfoils shapes, an approximately 8 mm maximum vertical displacement was achieved for the rods, which thus required a maximum horizontal displacement of 24 mm from the actuators.

B. Controller Architecture The role of the controller was to drive the SMA actuators via

an electrical current supply, so that transducers position can be used to eliminate the deviation between the required values for vertical displacements (corresponding to the optimized airfoils) and their physical values. In open loop phase of the project, the actuation lines controller block diagram was organized as in Fig. 3.

Through optimization, for each of the 35 flight conditions, a pair of optimal vertical deflections (dY1opt, dY2opt) was obtained. Therefore, the SMA actuators aimed to morph the airfoil until the vertical deflections of the two actuation lines (dY1real, dY2real) became equal to the required deflections (dY1opt, dY2opt). The vertical deflections of the real airfoil at the actuation points were measured using two position transducers. The controller’s role is to send a command to supply an electrical current signal to the SMA actuators, based on the error signals (e) between the required vertical displacements and the obtained displacements. The designed controller was valid for both actuation lines, which are practically identical.

In the first step of the controller design, some numerical simulations were performed to see the SMA actuators behavior, taking into account the strongly non-linear character of its input-output dependencies. The SMA model used here is based on a numerical finite element method and was built by Terriault et al.6 using Lickhatchev’s theoretical model. For different loading forces, the actuators envelope in Fig. 4 was obtained. The gas spring has a preloaded force of 1500 N and a linear elastic coefficient of 2.95 N/mm. The flexible skin linear elastic coefficient of approximately 100 N/mm was considered in the simulations; the SMA initial wire length was equal to 1.8 m.

As seen in Fig. 4, to obtain a maximum vertical displacement (8 mm) of the flexible skin, in the absence of aerodynamic forces, an electrical current corresponding to a temperature of approximately 162˚C is needed to counteract the spring force. As the ability of the SMA wires to contract depends upon Joule heating to produce the required transformation temperature, the highest required temperature is the highest required electrical current. The required current and temperature values are decreased due to the reduction of the actuators’ load by aerodynamic forces; i.e. for Faero= 1800 N. Therefore, for the maximum vertical displacement the required temperature is approximately 90˚C.

With the current established actuation line architecture, it is suggested that the pretension force of the gas spring must have the value Fpretension= 1500 N. Thus, Faero= 1500 N value was chosen for the aerodynamic force in the numerical simulations. In these conditions, the chosen design procedure for the controller consisted of the following steps: 1) numerical simulation of the SMA model actuators for certain values of the forces in the system; 2) approximation with linear systems in the heating and cooling phases using Matlab’s System Identification Toolbox and the numerical values obtained in Step 1; 3) choosing the controller type and its tuning for each of the two SMA actuator phases – heating and cooling; and 4) integration of the two controllers into a single one, followed by its validation for the general model of the system (non-linear).

Simulating a cooling phase followed by a heating phase of the SMA actuators the characteristics in Fig. 5 were obtained. The first graphic window of the figure presents the SMA wire length changing over time (δh), while the second one shows the SMA wire temperature values in during two phases. An SMA wire dilatation occurs in the cooling phase, while a wire contraction is obtained in the heating phase. For a spanwise actuation distance of approximately 24 mm, the wire temperature reaches a value of 108˚C. Note that the transient times to reach the steady-state values for the two phases are approximately 60 s for the cooling phase and approximately 40 s for the heating phase. For the steady-state, after the cooling phase, the forces obtained by numerical simulation were:

HeatingCooling

Three SMA wires

Flexible skin

CamRoller

Support plate foractuation system

Rod

Compressionspring

x

z

Figure 2. The actuation mechanism concept.

, M,Re

Pilot

Control

Flightconditions

Optimisedairfoils

databasedY1opt

dY2opt

Real airfoil

Integratedcontroller

dY1realdY2real

SMAactuators

e=dYopt- dYreal

Airflowperturbations

Current

Positiontransducers

dY1real

dY2real

Figure 3. Operating scheme of the SMA actuators control.

Max v = 8 mm

Faero = 1800 N

Faero = 0 N

9

0

8

7

6

5

4

3

2

1

20 16040 60 80 100 120 140 180

Dis

plac

emen

t [m

m]

Temperature [oC]

Figure 4. SMA actuator simulated envelope.


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resultant force that acts on the SMA, FSMA= 1000 N; elastic force produced by the flexible skin, Fskin= 0 N, and elastic force of the gas spring, Fspring= 1500 N. In this steady-state, the system is not loaded and the vertical displacement of the actuator is null. After the cooling phase, the forces obtained by numerical simulation were: FSMA= 1337 N, Fskin= 266.1 N and Fspring= 1571 N. This steady-state corresponds to the actuation system’s maximal displacement of approximately 8 mm.

Using Matlab’s System Identification Toolbox and the numerical values characterizing the response δh, at a series of successive step inputs, two transfer functions (TF) were found for the two SMA heating, Hh(s), and cooling, Hc(s), phases:

,1012.1s94.1s

1067.2s1054.3)s(

,1002.1s1047.6s44.1s

1042.2s1002.4s10 77.1)s(

22

11

3123

2322

c

h

H

H (1)

The displacements δh, corresponding to the linear systems obtained through the two phases identification, are depicted in a dashed-line in Fig. 5. A very good approximation can be observed for the two phases. The previously established transfer functions help to determine the controller type choice for each phase.

Since the SMA wire must be heated to contract and then cooled to dilate by providing an appropriate electrical current from the control block, it is normal that in the cooling phase the actuators are not powered. This phase of cooling may not only occur when controlling a long-term phase, when a change between two values of the actuator displacements is ordered, but also it can occur in a short-lived phase, where the real value of the deformation exceeds its desired value. However, it is imperative that in the heating phase the actuators are controlled so that the stationary error of the automatic system goes to zero. Therefore, for this phase a simpler PI type (proportional-integral) of architecture works best for the controller. It combines the advantages of a proportional-type controller, which substantially reduces the overshoot and leads to a short transient time, with the benefits of an integral controller, which cancels the steady-state system error. As a consequence, the controller must behave like a switch between the cooling and the heating phase, situations where the output current is 0 A, or is controlled by a PI-type law. The two phases’ interconnection leads to an integrated controller, which can be viewed as a combination of a bi-positional (particularly an on-off one) and a PI (proportional-integral) controller.

The Ziegler-Nichols criterion used for the optimal tuning of the controller in the heating phase conducted to the following numerical values for the PI controller parameters: KP=1792.8 and KI=787.0061 s-1. As a consequence, the controlled system in heating phase can be modeled with an approximate linear system with the block schema in Fig. 6. The parameters a0÷a2 and b0÷b3 in the schema are the coefficients of the Hh(s) transfer function nominator and denominator in ascending power of s (eq. (1)). The open loop transfer function of the controlled heating phase results as the form

,ssss

sss)s()s()s(

0

2

1

3

2

4

3

01

2

2

3

3

bbbb

qqqqHCH hPIol

(2)

while the closed loop transfer function is

0 50 100 150 200 250 3000

30

60

90

120

0 50 100 150 200 250 300-6

0

6

12

18

24

heatingcooling

cooling

heating

SMA model

TF

Time [s]

Tem

pera

ture

[o C]

Dis

plac

emen

t h

[mm

]

Faero= 1500 N

Time [s]

Figure 5. Actuator displacement and temperature profile.

Current

SMA heatingmodel

012

23

3

01

2

2

sss

ss

bbbb

aaa

SMA realelongation

Wished SMAelongation

PI controller

sI

P

KK

Figure 6. The block schema with transfer functions of theheating phase linear model.


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.ssss

sss)s()s()s(

01

2

2

3

3

4

4

01

2

2

3

3

rrrrr

qqqqHCH hPIcl

(3)

The included coefficients are

19.0422,46.5396,21.1622,31.8021, 0010121223 aKqaKaKqaKaKqaKq IIPIPP (4)

respectively

19.0422.46.5386,

21.8096,30.3663,,1

001001

211222334

aKraKaKbr

aKaKbraKbrbr

IIP

IPP (5)

CPI (s) is the transfer function of the PI controller. The poles of the close loop transfer function Hcl (s) resulted with the values

.-0.4453,

,)Re( , i,1.1943 - -0.1187

,)Re( , i,1.1943 + -0.1187

,-29.6837,

14

333

222

11

R

RC

RC

R

pp

ppp

ppp

pp

(6)

One can observe that all poles of the transfer function are placed in the left-hand side of the s-plane, and the obtained system is stable. The system response for different step inputs and the Bode diagram starting from the Hol (s) transfer function are shown in Fig. 7; Fig. 7 confirm also the stability of the system, taking into account the values of the gain margin (Gm) and of the phase margin (Pm)

.rad/s75057.31frequencyassociateddeg,20777.86

,rad/s50665.1frequencyassociated,127023.0dB92.17

cm

gm

P

G (7)

Taking into account the previously considerations, the final form of the integrated controller law is

.0if,d)(0061.787)(8.1792

,0if,0)(

ettete

eti (8)

C. Controller Numerical Simulation Introducing the controller in a general block scheme, with the non-linear SMA model, the Simulink model

illustrated in Fig. 8 was obtained for the control of the SMA actuators. The input variable of the scheme is the desired skin deflection and the output is the real skin deflection. Information about the supplying current, the force loading the SMA actuators, which is a function of temperature and elongation, can be extracted from the scheme.

As displayed in Fig. 9, the “Integrated controller” block contains the implementation of the law described by equation (8) and the preliminary observations related to the SMA actuators’ physical limitations in terms of temperature and supplying currents. The block has as an input the control error (the difference between the desired and the obtained displacement) and the SMA wires temperatures. The output is the controlled electrical current

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

Time [s]

Dis

plac

emen

t h

[mm

]

h required

h obtained

-50

0

50

100

150

200

Mag

nitu

de (

dB)

10-4 10-3 10-2 10-1 100 101 102-720

-540

-360

-180

0

Phas

e (d

eg)

Bode Diagram

Frequency (rad/sec)

g=1.5066 c=31.75

Gm=17.92 dB

Pm=86.2077 deg

Figure 7. The step inputs system response and the Bode diagram.


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applied on the SMA actuators. There are two switches in the scheme; the first one chooses one of the two options in the control law (8) and the second one switches the electrical current value to 0 A when the SMA temperature value is over the imposed limit. In addition, a current saturation block is used to prevent the current increase over the physical limit supported by the actuation SMA wires.

Applying to the input of the controlled actuator a successive steps signal, the characteristics shown in Fig. 10 were obtained (Faero=1500 N). The numerical simulations confirm that the obtained integrated controller works well, the variant of the on-off controller combined with a well-tuned PI controller give very good results in booth phases (heating and cooling) of the SMA actuators. A few seconds lateness of the cooling phase vis-à-vis of the heating phase is observed. Also, it can be noticed that the amplitude of the temperature oscillations is getting higher with the actuation temperature increase. For Faero=1500 N, the FSMA varies between 1 kN and 1.33 kN.

III. Experimental Model The firsts experimental tests were performed in the LAMSI facility with the physical wing model installed on the

bench. The physical SMA actuators were connected to two AMREL SPS100-33 power supplies controlled by Matlab/Simulink through a Quanser Q8 communication board with 8 input and 8 output channels. The input

channels of the Quanser board were used for six thermocouples connected to a SMA actuators wires, and for two Linear Variable Differential Transformer (LVDT) potentiometers that sense the actuators positions (indicating the vertical displacements dY1 and dY2 of the actuation system using the ratio δh/δv=3/1) (Fig. 11). Two of the card output channels were used to control each power supply through analog/external control by means of a DB-15 I/O connector. The sampling rate of the acquisitioned signals was set at 0.01 seconds. The gas springs that maintained the SMA wires in tension had a preloaded value of 225 lbs (1000 N) since there was no aerodynamic force in the laboratory condition. The tests were performed using the configuration with the signal of the potentiometers measuring the displacements of the actuators used in control loop in order to obtain the desired positions of the actuators. The Matlab/Simulink model used in bench tests is shown in Fig. 12.

Temperature[K]

skin deflection [mm]

skindeflection

[mm]

desired deflection [mm]

SMA elongation[m]

skindeflection

[mm]

0

skin deflexion [mm]

1

1 4.5

desired skin deflection

[mm]

3/1000

cam factormm to m

XY Graph

Scope

0.078

SMA max set [m]

0

SMA elongation [m]

Current

Force

Displacement

Temperature

SMA Model1.8

SMA Initiallength [m]

1.8

SMA Initiallength

Diff error

Temperature

Current out

Integrated controller

Memory

F aero [N]

x [m]

F SMA [N]

y [mm]

Mechanical system

0

Current [A]

273.15

Celsius to Kelvin

1500

Aerodynamicforce [N]

Figure 8. The simulation model for the controlled SMA actuator with thenon-linear model.

1

Current out

Temperature limiter

Switch

-1

Gain 0

Current whencooling

Currentsaturation

0

Current whenreached limit

PI

Controller

|u|

Abs

2

Temperature

1

Diff error CurrentCurrent

Figure 9. “Integrated controller” block in Simulink.

0

5

10

0.9

1

1.1

1.2

1.3

1.4

20

40

60

80

100

120

0

5

10

20 30 40 50 60 70 80 90 100 110 120

Time [s]

Time [s]

Temperature [oC]

Tem

pera

ture

[o C

]D

ispl

acem

ent v

[mm

]D

ispl

acem

ent v

[m

m]

v required

v obtained

0 20 40 60 80 100 120 140 160 180 200

0 20 40 60 80 100 120 140 160 180 200

Time [s]0 20 40 60 80 100 120 140 160 180 200

FSM

A [

kN]

SMAinitialisation

SMAinitialisation

SMA initialisation

SMA actuation

SMAinitialisation

Figure 10. Response for a successive stepsinput, Faero=1500 N.

dY1 dY2

SMA#1 SMA#2

Deflections levelfor optimum airfoil

Output signal forpower supply control

AMREL SPS100-33power supplies

Positiontransducers

Quanser Q8 dataacquisition card

Signal from positiontransducers Real

dY1, dY2

...Signal from sixthermocouples

DesireddY1, dY2

Lower part ofthe morphing

wing

Deflections level forreference airfoil

Figure 11. Bench test model operating schema.


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The wind tunnel test runs were realized in the 6 × 9 ft2

wind tunnel at the Institute for Aerospace Research at the National Research Council Canada. Simultaneously with the actuation lines control validation, the 35 optimized airfoils were experimentally validated with the theoretically airfoils previously obtained. In this way, the transition point real time position detection and visualization were realized in wind tunnel test. The pressure data acquisition was performed using a NI-DAQ USB 6210 card with 16 analog inputs (Fig. 13), at a total sampling rate of 250 kS/s. The input channels were connected directly to the IAR-NRC analog data acquisition system, which in turn was connected to the Kulite pressure sensors mounted on the flexible skin. One extra channel was used for wind tunnel dynamic pressure acquisition and to calculate the pressure coefficient Cp from the pressure values measured by the pressure sensors. The sampling rate of each channel was 15 kS/s which allowed a boundary layer pressure fluctuation FFT spectral decomposition of up to 7.5 kHz for all channels. The signal was processed using Simulink, and displayed in real time.

IV. Aeroelastic Study

A. Analysis Step The commercial software for finite element analysis, MSC/NASTRAN, was used to build the 3D numerical

model of the flexible skin upper surface, situated between 3% and 70% of the wing chord, as shown in Fig. 14.

Finite Element Modeling The structural model was defined using the GRID and CQUAD4 shell elements given by the MSC/NASTRAN

commands7. The structure was divided into several bands of equal widths along the span, and formed elements in the chord-wise defining the airfoil shape; the whole formed a structure of 406 plane elements as shown in Fig. 15 a.

The internal elements were composed of four layers of composite materials. The MAT8 command defined the Young's modulus, the shear modulus, the Poisson's ratio and the density. All of the leading edge nodes were constrained to simulate a perfect clamp. In addition, the trailing edge was also well constrained, with the exception of the translation motion in its chord-wise aspect. To simulate the compensation spring, all the nodes along the actuators axis were constrained in translation and free in rotation, thus simulating the mechanism. Finally, all of the nodes were constrained against plane rotation, as the CQUAD4 element had no rigidity in this condition.

The ASET1 command was considered to reduce the problem size in order to restrict the number of freedom degrees for the wing normal deflection, i.e. the translation along the Z axis (the degree of freedom that allows wing bending and torsion), which is the only deflection required for aerodynamic force determination. It is important to note that the plan or shell model is often used because it provides results as close to reality as possible without overly complicating the problem. The material density, configured by entering the MAT8 command and the

0

Volts

Temp

StartVolt

termocouple1termocouple2termocouple3position 1

tempamps

control Vstart 5V

SMA1

Q8Quanser

Analog Input

Amps

Analog Input

0

Q8Quanser

Analog Output

Analog Output

termocouple1termocouple2termocouple3position 2

tempamps

control Vstart 5V

SMA2

Figure 12. Matlab/Simulink actuators control in benchtest.

dY1 dY2

SMA1 SMA2

...

Signal processingMatlab/Simulink

Optimumprofil

Referenceprofil

Computer

3 ThermocouplesSMA 1

PowerSupply

150V/20A/3kW

AMRELSPS

PowerSupply

150V/20A/3kW

AMRELSPS Output

analogsignal 0-10V

3 ThermocouplesSMA 2

LVDT position

sensor SMA 1

LVDT position

sensor SMA 2

QuanserQ8 /

QuaRC

Simulink(xPC)

Computer

15 Kulite pressuresensors

Data acquisition system for Kulitepressure sensors

(IAR-NRC signal conditioning andNi Daq 6210)

DesireddY1, dY2

Figure 13. Wind tunnel model operating schema.

Figure 14. Flexible extrados schematic with boundary and loading conditions.


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parameter COUPMASS, 1, resulted from generation of the coupled plate elements mass matrices, while the GRAV command introduced the model weight in the problem. Although the model weight in the wind tunnel was relatively low, it was not neglected, and the angles of attack remained small.

Aerodynamic Modeling The AERO command was used for the aerodynamic modeling, in which the basic coordinate system was used as

the aerodynamic coordinate system. Physical parameters were defined, such as the sea level density and the reference chord length equal to 334.8 mm. The commands SYMXZ = 1 for a complete wall reflection of the wind tunnel and SYMXY = 0 were defined, neglecting the floor tunnel or ceiling interference. The CAERO1 command, including a subsonic Mach number in the TRIM command, specified the use of the aerodynamic Doublet-Lattice Panel theory. A minimum of six equal strip widths along the span-wise was specified, along with a minimum of four equal strip widths along the chord-wise section. The aerodynamic and the structural models were interconnected with a spline surface, SPLINE1. The 24 aerodynamic boxes correspond to 232 nodes listed by the SET 1 command.

The 232 nodes were variously spaced along the span-wise section from one extremity to another. The PAERO1 command was required even if no interference problem occurred. The model division in aerodynamic boxes is shown in Fig. 15 b. The MKAERO1 command provided the required data for the aerodynamic matrix interpolation into the flutter solution. For each Mach number tested, the reduced frequencies k = 0.001 to k = 0.90 were specified to determine the flutter speed. The Lagrange method was used for the vibration analysis in the EIG|R command to obtain the ten modes that had the largest normalized assembly components. Each optimized airfoil shape was obtained by use of the XFoil CFD code.

Flutter Analysis Method The KE flutter analysis method was chosen for the system dynamics determination. This flutter method was

chosen based on its efficiency at producing well-behaved V-g curves. The structural damping was introduced by the parameter PARAM, KDAMP, -1 and the table TABDMP1. Since no damping data was known, we assumed g 0.01 at a frequency of 1000 Hz. The FLUTTER command specified the use of the KE flutter analysis method. The FLFACT command gives information during wind tunnel tests on the density ratio, the Mach number, and the reduced frequencies set, and specifies a linear interpolation of generalized aerodynamic force coefficients. The flutter speeds were converted from mm/s into m/s using the instruction PARAM, VREF, 1000.0.

B. Results and Discussion The mass and inertial data, the vibration frequencies and the deflection modes for the analyzed nodes (ASET1)

were calculated. The Lagrange method was used for vibration analysis, using the command EIGR to obtain ten modes which have frequencies up to 100 Hz.

Model’s Dynamic Response (Modal Analysis) In the modal analysis method, prior to the flutter analysis, two solving techniques were available to determine a

response to an imposed displacement. The first method is the large mass method, and the second is the Lagrangian multiplier method. The Lagrangian multiplier method required less computation and was very efficient for a small number of modes (in our case, the parameter PARAM, LMODES, 10 specified that the ten first modes of vibration be included in the flutter problem formulation for a frequency spectrum covering 100 Hz); this method was widely used for its efficiency in several aeroelastic dynamic response analyses and the results are presented in Table I.

Flutter analysis numerical results The structural stiffness, the mass and the damping matrices for the aeroelastic flutter analysis were generated by

use of MSC.Nastran by following an analysis of aeroelastic flutter. The aerodynamic operator matrix was generated

(a) Structural model

(b) Aerodynamic model

Figure 15. Structural and aerodynamic model.


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from data describing the aerodynamic finite elements’ geometry. The aerodynamic model choice of "grid points" was independent of the structural "grid points" positions called "nodes". The subsonic flow theory is the Doublets-method that allows coupling of the aerodynamical elements to the structural body. Thus, the vibration modes of the structure were used in the dynamic analysis and the following equation is used to determine the model characteristics, following the flutter analysis algorithm (SOL 145) proposed by the Nastran software

.0})]{2/()4/([ 22 h

R

hhhh

I

hhhhhh uQcVKpkcVQBpM (9)

This equation assumes a simple harmonic motion ti

h eutu }{)}({ , presented in the form of a second

order differential equation describing the dynamic linear behavior of the structure which is subject to forces and moments caused by the fluid flow. Figure 17 shows a flowchart that describes the software steps for this calculation.

The V-g flutter analysis method was used. In this method, the structural damping, g, of all of the vibration modes was assumed to be an unknown value. In Fig. 18, all of the mode shapes are shown, except for modes 5, 7 and 9, which correspond to under-damped modes. The first ten modes were analyzed and graphically presented in the forms of frequencies and damping versus speeds. It is known that the flutter speed is the speed at which the damping is zero (see the first curve showing the damping variation with speed). Then, the corresponding model’s flutter frequencies were calculated from the second graph which shows the frequency variation with speeds.

The advantage of the numerical approach is that only aerodynamic forces need to be determined for real frequencies. The disadvantage is that it is not possible to have a physical response overview. For a system with damping, only at the speed V=VF (i.e. where ω = ωR and ωI = 0) will the mathematical solution provides the physics of this problem.

Figure 16. First symmetric bending mode locatedbetween actuator #1 and the trailing edge (75.462 Hz).

Table I. Dynamic results of the flexible extrados. Mode Sorted Mode Remarks Freq (Hz)

MODE-1 1st Symmetric rotation (6 waves) between Act. #2 and T.E. 9.542 MODE-2 1st Asymmetric rotation (6 waves) between Act. #2 and T.E. 9.818 MODE-3 2nd Asymmetric rotation (6 waves) between Act. #2 and T.E. 26.198 MODE-4 2nd Asymmetric rotation (5 waves) between Act. #2 and T.E. 41.180 MODE-5 3th Asymmetric rotation (4 waves) between Act. #2 and T.E. 57.236 MODE-6 3th Symmetric rotation (3 waves) between Act. #2 and T.E. 58.037 MODE-7 4th Asymmetric rotation (2 waves) between Act. #2 and T.E. 58.872 MODE-8 1st Symmetric bending (2 waves) between Act. #2 and T.E. 75.462 MODE-9 1st Asymmetric rotation (8 waves) between Act. #1 and Act. #2 93.809

MODE-10 1st Symmetric rotation (7 waves) between Act. #1 et Act. #2 100.980

Figure 17. Flowchart of the flutter solution to the equation of motion(for one Mach number).


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Following a flutter analysis, the wing or aircraft design can be modified to prevent flutter, prior to its manufacturing or wind tunnel or in-flight testing. The key design parameter is the maximum flight speed Vd. The ratio between the absorbed energy and the dissipated energy depends on the flow speed. A stable oscillation could occur when this ratio is harmonic. The flow speed is critical when the oscillations become unstable. A model can have a variety of flutter modes. Ideally, the lowest critical speed exceeds the highest possible flight speed by a reasonable safety margin.

The critical flutter speeds for each configuration and their corresponding frequencies are shown in Table II. The safety factor offered by the FAR 258 standard specifies that the critical flutter speed is 1.2 times the flight design speed (Vd), which varies from 68m/s to 102 m/s depending on flight conditions. The (VP/Vd - 1)·100 value gives the model’s percentage margin and this value should be greater than 20%. The differences between flight configuration results are shown in Table II.

The flutter phenomenon only occurred for the Mach number of 0.55. For the flight configurations studied, the flutter margin was found to be 20% above the flight speed and thus met the FAR 25 standard. During wind tunnel tests for different configurations at the maximum Mach number of 0.3, no flutter problem occurred, thus demonstrating the efficiency of the wing aeroelastic analysis.

V. Controller Experimental Validation

A. Bench Tests The Matlab/Simulink implemented controller was used in the same way for both actuation lines of the morphing

wing system. The bench test validation of the controller started with the independent control in time for each of the two actuation lines. In this way, desired displacements (dY1 and dY2) under the form of successive steps signals were applied at the input of the actuation lines.

In the next phase of the controller bench tests validation, all pairs of the desired displacements characterizing the 35 optimized airfoil cases were imposed as input signals on the two actuation lines. A typical test run history is shown in Fig. 19 for α=2°, Mach=0.3 flight condition (dY1=6.26 mm, and dY2=7.88 mm).

-0,1

-0,08

-0,06

-0,04

-0,02

0

0,02

0,04

0,06

0,08

0,1

0 100 200 300 400 500 600

Dam

ping

Speed (m/s)

Speed vs Damping

MODE 1

MODE 2

MODE 3

MODE 4

MODE 6

MODE 8

MODE 10

-2

-1,8

-1,6

-1,4

-1,2

-1

-0,8

-0,6

-0,4

-0,2

Amor

tisse

men

t

25

35

45

55

65

75

85

95

Fre

quen

cy (

Hz)

Speed vs Frequency

Figure 18. Damping and frequency versus speeds.

Table II. Flutter results of the model. Flight speed

(Mach number) Flight speed (Vd) in m/s

Flutter speed (VF) in m/s

Flutter frequencies (Hz)

Differences (%)

0.2 68 186.122 67.2403 173.71 0.225 76.5 186.130 67.2434 143.31 0.25 85 186.141 67.2472 118.99 0.275 93.5 186.153 67.2516 99.09 0.3 102 186.167 67.2567 82.52


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The obtained results show that the controllers, in the two actuation lines, work even at zero values of the desired signal because of the pre-tensioned gas springs. Also, small oscillations of the obtained displacements are observed around their desired values. The amplitude of the oscillations in this phase is due to the LVDT potentiometers’ mechanical link (were not finally fixed because the model was not equipped with the flexible skin in this test) and to the SMA wires thermal inertia; the smallest amplitude is less than 0.06 mm. The heating phase is more rapid than the cooling phase; heating time is of the order of a few seconds, while the cooling time is around one minute.

From the numerical values obtained for all 35 optimized airfoil cases, it was observed that the position control error due to the heating-cooling cycles when the actuator maintains a desired position was smaller than 0.05 mm. The bench test results confirmed that the experimental version of the designed controller works well in the laboratory conditions, where no aerodynamic forces are loaded and the preloaded gas spring’s force is 1000N.

B. Wind Tunnel Tests With the confirmed good performance of the designed integrated controller, demonstrated on bench testing, the

next step in our morphing wing project was to validate the controller in a wind tunnel test with simultaneous real-time detection of the transition point and visualization for all the 35 optimized airfoils. The model was tested for all 35 theoretical flight conditions, with a comparative study realized based on the transition point position for the reference airfoil and for each optimized airfoil. Thus, a validation study for the aerodynamic part of the project was realized at the same time as the controller testing.

The transition detection was performed in real time using the pressure data signals obtained from the 32 Kulite and optical pressure sensors. The pressure data were acquired using the IAR-NRC analog data acquisition system, which was connected to the 32 sensors. The sampling rate of each channel was at 15 kHz, which allowed a pressure fluctuation FFT spectral decomposition of up to 7.5 kHz for all channels. The signals were processed in real time using Simulink. The pressure signals were analyzed using Fast Fourier Transforms (FFT) decomposition to detect the magnitude of the noise in the surface air flow. Subsequently, the data was filtered by means of high-pass filters and processed by calculating the Root Mean Square (RMS) of the signal to obtain a plot diagram of the pressure fluctuations in the flow boundary layer. This signal processing is necessary to disparate the inherent electronically induced noise, by the Tollmien-Schlichting waves that are responsible for triggering the transition from laminar to turbulent flow. The measurements showed that in the processed data, the transition appeared at frequencies between 3÷5kHz and the magnitude of the pressure variations in the laminar flow boundary layer are on the order of 5e-4 Pa. The transition from the laminar flow to turbulent flow was shown by an increase in the pressure fluctuation, which was indicated by a drastic variation of the pressure signal RMS.

For the wind tunnel test, the preloaded forces of the gas springs were reconsidered and increased to 1500 N because of the presence of the aerodynamic forces on the flexible skin of the wing. The control results for α=1° and Mach=0.2 with dY1=4.27 mm and dY2=7.08 mm, are presented in Fig. 20.

Also, from the experimental results, a high frequency noise influencing the LVDT sensors and the thermocouple’s instrumentation amplifiers is observed. The noise sources are the wind tunnel vibrations and the

=2o, Mach=0.3

-1

0

1

2

3

4

5

6

7

8

9

Dis

plac

emen

ts d

Y1

and

dY2

[mm

]

act #1 desiredact #1 obtainedact #2 desiredact #2 obtained

0 50 100 150 200 250 300Time [s]

act #2

act #1

Figure 19. Bench test for α=2° and M=0.3.

50 100 150 200 250 300 350-1

0

1

2

3

4

5

6

7

8

0

Time [s]

Dis

plac

emen

ts d

Y1,

dY

2 (

v) [

mm

]

=1°, Mach=0.2

act #1 desiredact #1 obtainedact #2 desiredact #2 obtained

400

20

30

35

40

45

50

55

65

Time [s]

Tem

pera

ture

[o C

]

act #1act #2

50 100 150 200 250 300 3500 400

25

70

60

Figure 20. Wind tunnel test for α=1° andM=0.2.


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instrumentation electrical fields. Even with this noise, the amplitude of the actuation error is less 0.07 mm, and this does not affect the transition location, which remains stable as detected by the sensor having a high RMS spike.

Figure 21 presents the results obtained by the transition monitoring for α=2° and Mach=0.225 with dY1=5.56 mm and dY2=7.91 mm. The actuation line control precision can have some influence on the transition location detection only if the density of the chord-disposed pressure sensors becomes greater. From the processed experimental data, it is concluded that, even if the value of the error is 1 mm around the optimized values, the transition location on the flexible skin is not significantly changed. The real-time Kulite pressure signals and their RMS are presented in Fig. 21. The left hand column presents the results for the reference airfoil, and the right hand side column display the results for the optimized airfoil. The spike of the RMS suggests that the flow is already turned turbulent on sensor on the channel 11, near the trailing edge.

The results obtained from the wind tunnel tests show that the actuator control – and the controller performed very well in enhancing the wind aerodynamic performance and fully satisfy the project requirements.

VI. Conclusions In this paper the design and the validation of a controller for a new morphing mechanism using smart materials

made of Shape Memory Alloy (SMA) for the actuators were presented. Also, an aeroelastic study for the morphing wing was performed.

The final configuration of the integrated controller resulted as a combination of a bi-positional controller (on-off) and a PI (proportional-integral) controller, due to the two phases (heating and cooling) of the SMA wires’ interconnection. This controller behaved like a switch between the cooling and the heating phases, situations where the output current was 0 A, or was controlled by a PI type law. The PI controller for the heating phase was optimal tuned using an integral criterion, the error minimum surface criterion (Ziegler-Nichols), and is numerically tested on the linear identified system in terms of time response, Bode diagram, amplitude and phase stability margins, and root-locus. Also, a validation step of the controller was performed by using numerical simulations, bench testing and wind tunnel testing. Before the wind tunnel validation step of the controller, an aeroelastic study was realized, with the aim to determine the flutter conditions to be avoided during wind tunnel tests. These studies show that aeroelastic instabilities for the morphing configurations considered appeared at Mach number 0.55, which was higher than the wind tunnel Mach number limit speed of 0.3. Also, all validation cases of the designed controller shown that controller performed very well in enhancing the wind aerodynamic performance and fully satisfy the project requirements.

Acknowledgments The authors would like to thank the Consortium for Research and Innovation in Aerospace in Quebec (CRIAQ),

Thales Avionics Inc., Bombardier Aerospace, and the National Sciences and Engineering Research Council (NSERC) for their financial support. We would like also to thank Dr. George Henri Simon for initiating the CRIAQ

Figure 21. Results obtained on the transition monitoring for α=2° andM=0.225.


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7.1 project and Dr. Philippe Molaret from Thales Avionics and Dr. Eric Laurendeau from Bombardier Aerospace for their help and fruitful discussions.

References 1Barrett, R., “Improvements to commercial and general aviation via adaptive aerostructures”, 7th AIAA Aviation Technology,

Integration and Operations Conference (ATIO), 18-20 September, Paper AIAA-2007-7873, pp. 1-9, 2007. 2Bharti, S. et al., “Optimal structural design of a morphing aircraft wing using parallel non- dominated sorting genetic

algorithm II (NSGA II)”, Smart Structures and Materials 2006: Industrial and commercial applications of smart structures technologies, Proceedings of SPIE Vol. 6166, pp. 1-12, 2006.

3Sanders, B. et al., “Aerodynamic and aeroelastic characteristics of wings with conformal control surfaces for morphing aircraft”, Journal of Aircraft, Vol. 40(1), pp. 94-99, 2003.

4Coutu, D., Brailovski, V. and Terriault, P., “Promising benefits of an active-extrados morphing laminar wing”, AIAA Journal of Aircraft, Vol. 46(2), pp. 730-731, 2009.

5Georges, T.,Brailovski, V., Morellon, E., Coutu, D. and Terriault, P., “Design of Shape Memory Alloy Actuators for Morphing Laminar Wing With Flexible Extrados”, Journal of Mechanical Design, Vol. 31, No. 9, September 2009, 091006.

6Terriault, P., Viens, F. and Brailovski, V., “Non-isothermal Finite Element Modeling of a Shape Memory Alloy Actuator Using ANSYS”, Computational Materials Science, Vol. 36, No. 4, July 2006, pp. 397-410.

7MSC/Nastran documentation (MSC software corporation, USA), 2001. 8FAR 25 Aviation Regulations, 2000.

Controller and Aeroelasticity Analysis for a Morphing Wing

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