smart-structures-and-materials-2017

146 B. Mokrani et al.

7.5.2 Electrical Circuits

The voltage controlled synthetic inductor is implemented based on the schematic

shown in Fig. 7.9, referred to as Antoniou circuit. The value of the inductor can be

tuned by simply tuning the resistor R4, using a resistive optoisolator, called vactrol.
Figure 7.10 shows the control circuit of the resistor R4, involving a vactrol; by varying
the voltage source from 0 to 10 V, the value of the resistor varies from 100 kΩ to 2 kΩ.
One should notice that the relationship between R4 and the command voltage is not
linear [1], but this non-linearity has no big effect on the tuning since the system is

controlled in closed loop.

The Phase Shift to Voltage Converter circuit has been built using two different

blocks, as shown in Fig. 7.11. The first block is used to convert the harmonic signals

to two square signals. Then, these square signals are used by the phase detector of a

Phase Locked Loop integrated circuit (74HC4046A). The output of the phase detec-

tor circuit is a voltage proportional to the relative phase between the two signals VL
and Vref : the relationship between the output of the circuit and the relative phase is
linear and varies from 0 to 10 V. Finally, a low-pass filter is used at the output of the

Fig. 7.9 Voltage controlled synthetic inductor based on Antoniou circuit

Voltage to current Photoresistive opto-isolator

converter Vactrol

4-20mA

LED 4

in Light

0-10V

Photoresistor

Fig. 7.10 Voltage controlled resistor R4, involving a resistive optoisolator, Vactrol

7 Adaptive Inductor for Vibration Damping in Presence of Uncertainty 147

Fig. 7.11 Phase shift to voltage converter circuit based on a phase locked loop circuit (PLL)

Fig. 7.12 Frequency response of the beam for various values of e

PLL circuit in order to keep only the average phase shift between the two signals;
this filter has a bandwidth of about 10 Hz and it should be taken into account for the
design of the controller. Indeed, due to this filter, the bandwidth of the controller is
set to be about 0.1 Hz in order to preserve the stability of the control loop.

7.5.3 Results

Figure 7.12 shows the frequency response of the beam to a band limited white noise
in the frequency range [80–180] Hz (including only the first flexural mode). The
figure shows the effect of the electrical frequency tuning e on the RL shunt perfor-
mance.

148 B. Mokrani et al.

Fig. 7.13 Measured magnitude and phase of VL∕Vref for various values of e

Figure 7.13 shows the magnitude and the phase of VL∕Vref for the various tuning
of e. In agreement with the simulations, when e = n, the relative phase is
exactly5 + ∕2 at = n. When the electrical frequency is mistuned, the relative
phase becomes smaller or greater than ∕2, depending whether e > n or e < n.

Figure 7.14 shows the time response of VL and Vref for the various tuning of the
electrical frequency e. When the vibration is dominated by the targeted mode (i.e.
the instantaneous frequency is n), the relative phase shift between the signals is in
a good agreement with the predictions, for the various values of e.
Adaptive RL Shunt
Figure 7.15 shows the response of the structure when the adaptive RL shunt is imple-
mented according to the schematic of Fig. 7.8. The value of L is tuned automatically
in real time, via the feedback loop, where the controller is a simple integrator. Since
the adaptive inductor has a long time response (of about 0.1 s), and due to the pres-
ence of a low pass filter at the output of the Phase Shift to Voltage Converter circuit
(of bandwidth 10 Hz), the bandwidth of the controller is set to be about 0.1 Hz (cor-
responding to a settling time of about 6 s) in order to preserve the stability of the
control system.

Figure 7.16 shows the measured relative phase in volts, and the evolution of
the command of the voltage controlled synthetic inductor. First, the cantilever beam

5Because the reference PZT is mounted with opposite polarization, a phase shift of 180◦ is intro-
duced in the frequency response of VL∕Vref .

7 Adaptive Inductor for Vibration Damping in Presence of Uncertainty 149
1 = 1,07

Normalized voltage [/] 0

-1
1 =1

0

-1
1 = 0,88

0 0.05 t [sec]

-1
0 0.01 0.02 0.03 0.04

Fig. 7.14 Time response of VL and Vref for various values of e

Massless
configuration

0.01

0.6 0.8 0.88 1 1.2

Fig. 7.15 Frequency response function of the beam tip with and without the optional mass, when
the adaptive RL shunt is used

is equipped with the optional mass and the RL shunt is tuned such that e ≪ n; at
t0, the Phase Shift to Voltage Converter circuit is plugged and the control is turned on.
Few seconds are needed by the circuit to measure the relative phase shift, and as long

as < ∕2 (or 4.8 V), the voltage commanding the synthetic inductor increases

until t1 where ≤ − ∕2 (corresponding to e = n). At t2, the optional mass is
removed from the beam and becomes larger than ∕2, leading to a reaction of

the controller to compensate this change, and at t3 the control system converges to

150 B. Mokrani et al.

180 3.8 Command to photoresistor [V]

Removing 3.4
the mass

3

2.6

2.2
10 20 30 40 50 60 70

[sec]

Fig. 7.16 Command voltage of the photoresistor and the corresponding measured relative phase
shift

the optimal value of L. The fluctuation of the measured is due to the fact that

the instantaneous frequency is not exactly n, however, the average value of
corresponds to the relative phase at the average frequency n.

7.6 Conclusion

This paper investigates the linear RL shunt damping when a single mode is targeted.
The importance of the relative phase shift between the strain at the location of the
transducer and the electrical charge of the RL circuit is highlighted and supported
experimentally. At resonance, this relative phase shift must be equal to ∕2 in order
to preserve the optimal performance of the RL shunt.

The problem related to the robustness of the RL shunt with respect to the variabil-
ity of the resonance frequency has been solved by adapting the value of the inductor
L, via a voltage controlled synthetic inductor. A Phase Shift to Voltage Converter,
inspired from a Phase Locked Loop circuit, offers the possibility to measure accu-
rately the relative phase shift between two signals, and the output is used to adapt the
value of the inductor. The adaptation procedure has been demonstrated experimen-
tally when the structural response is dominated by one mode. The behavior when the
structural response combines several modes remains to be investigated.

Acknowledgements This research is supported by the Wallonia Region of Belgium through the
Mecatech M4 Project. The comments of the reviewers are gratefully acknowledged.

7 Adaptive Inductor for Vibration Damping in Presence of Uncertainty 151

References

1. Elmer P (2001) Optoelectronics, Photoconductive cells and analog optoisolators (VactrolsⓇ)
2. Forward RL (1979) Electronic damping of vibration in optical structures. J Appl Opt

18(5):690–697
3. Forward RL (1979) Electromechanical transducer-coupled mechanical structure with negative

capacitance compensation circuit. US Patent 4,158,787
4. Hagood NW, von Flotow A (1991) Damping of structural vibrations with piezoelectric mate-

rials and passive electrical networks. J Sound Vib 146(2):243–268
5. Hollkamp JJ (1994) Multimodal passive vibration suppression with piezoelectric materials and

resonant shunts. J Intell Mater Syst Struct 5(1):49–57
6. Hollkamp JJ, Starchville TF (1994) A self-tuning piezoelectric vibration absorber. J Intell

Mater Syst Struct 5(4):559–566
7. Lefeuvre E, Badel A, Petit L, Richard C, Guyomar D (2006) Semi-passive piezoelectric struc-

tural damping by synchronized switching on voltage sources. J Intell Mater Syst Struct 17(8–
9):653–660
8. Mokrani B, Rodrigues G, Burda I, Bastaits R, Preumont A (2012) Synchronized switch damp-
ing on inductor and negative capacitance. J Intell Mater Syst Struct
9. Niederberger D, Morari M, Pietrzko SJ (2003) Adaptive resonant shunted piezoelectric devices
for vibration suppression. Smart Struct Mater 213–224. International Society for Optics and
Photonics
10. Niederberger D, Fleming A, Moheimani SR, Morari M (1025) Adaptive multi-mode resonant
piezoelectric shunt damping. Smart Mater Struct 13(5):2004
11. Philbrick Researchers, Inc (1965) Application manual for computing amplifiers for modeling,
measuring, manipulating and much else. Nimord Press, Boston
12. Preumont A (2006) Mechatronics, Dynamics of electromechanical and piezoelectric systems.
Springer
13. Richard C, Guyomar D, Audigier D, Bassaler H (2000) Enhanced semi passive damping using
continuous switching of a piezoelectric device on an inductor. In: Proceeding of the SPIE
international symposium on smart structures and materials. Conference, Passive damping and
isolation, Newport Beach, vol 3989, pp 288–299

Chapter 8

Active Control of the Hinge of a Flapping
Wing with Electrostatic Sticking to Modify
the Passive Pitching Motion

Hugo Peters, Qi Wang, Hans Goosen and Fred van Keulen

Abstract Wing designs for Flapping Wing Micro Air Vehicles (FWMAVs) might
use a properly tuned elastic hinge at the wing root to obtain the required passive
pitching motion to achieve enough lift production to stay aloft. Practical use of this
type of FWMAVs requires some form of control which can be achieved by actively
adjusting the elastic hinge stiffness and, thus, the pitching motion and lift produc-
tion of the wing. This paper studies an elastic hinge design consisting of stacked
layers which can be sticked together using electrostatics. This sticking changes the
bending stiffness of the hinge. The voltage-dependent behavior of this elastic hinge
during the large pitching motion are described in detail. The passive pitching motion
is governed by the equation of motion which is a function of the elastic hinge stiffness
and the applied control voltage. The lift generated by the passive pitching wings is
predicted by a quasi-steady aerodynamic model. Numerical simulations show signif-
icant changes of the passive pitching motion and, consequently, of the lift production,
if slipping stacked layers stick together. Experiments are conducted to study the prac-
tical applicability of this method on FWMAVs. The experiments show similar trends
as the numerical simulations in modifying the pitching motion although the effect is
less significant which is mainly due to manufacturing difficulties. This approach is,
in conclusion, promising to control FWMAV flight.

H. Peters ⋅ Q. Wang (✉) ⋅ H. Goosen ⋅ F. van Keulen 153

Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
e-mail: [email protected]

H. Peters
e-mail: [email protected]

H. Goosen
e-mail: [email protected]

F. van Keulen
e-mail: [email protected]

© Springer International Publishing Switzerland 2017
A.L. Araujo and C.A. Mota Soares (eds.), Smart Structures and Materials,
Computational Methods in Applied Sciences 43,
DOI 10.1007/978-3-319-44507-6_8

154 H. Peters et al.

8.1 Introduction

The design and realization of lightweight Flapping Wing Micro Air Vehicles
(FWMAVs) have attracted much attention over the last decades. Potential applica-
tions of FMWAV designs are in, among others, surveillance (e.g., police and secu-
rity) and inspection of inaccessible or dangerous locations (e.g., disaster scenes and
sewers). The design and realization of FWMAVs is complicated by weight con-
straints as a result of the limited lift production of the wings. Consequently, designers
aim for lightweight, smart and highly integrated systems. This has resulted in sev-
eral ways of achieving flapping kinematics for sufficient lift production. To decrease
the actuation mechanism complexity, some wing designs integrate elastic hinges that
allow the wing pitching motion to be passive during the flapping motion [3, 22]. Due
to the inertial and aerodynamic loading, a properly tuned elastic hinge results in the
required pitching motion to achieve enough lift production to stay aloft.

For stable flight and maneuvering, FWMAV designs require some form of con-
trol. In fact, constant control will be necessary because of the intrinsic dynamic insta-
bility of the designs. Recent work on the Harvard Microrobotic Fly (i.e., a FWMAV
design which exploits passive pitching) applied aerodynamic dampers for stabiliza-
tion [17], complex mechanisms to induce asymmetric flapping wing kinematics to
produce control torques [7], and separate actuators for each wing [11]. Additionally,
control torques were created by integrating a piezoelectric bimorph actuator in the
wings’ elastic hinge to induce a bias during the wing stroke [18]. To control light-
weight FWMAV designs, actively adjusting the dynamic properties (i.e., structural
damping and stiffness) of the wings’ elastic hinge appears to be a promising, ele-
gant, and integrable approach to change the passive pitching motion during flight
and, hence, the stroke-averaged lift force. This control approach is not well estab-
lished within literature.

To actively change the dynamic properties of the wings’ hinge, the elastic hinge
needs to be replaced by an active hinge which properties change due to some external
stimuli (e.g., an electric field). Methods to actively change the dynamic properties
of an elastic element are, for example: (i) smart fluids (i.e., magnetorheological or
electrorheological fluids) for which the properties transform rapidly upon exposure
to an external magnetic or electric field [12], (ii) piezoelectric polymer films (e.g.,
PVDF) for which the properties change as a function of the connected electrical
circuit [4], and (iii) sticking stacked layers using, for example, electrostatics [2, 15].

This paper investigates the method with the stacked layers for which the con-
ceptual idea is shown in Fig. 8.1. Figure 8.1a shows a capacitor-like clamped-free
beam which consists of two layers which can slide with respect to each other when
deflected by the end-load F. Each layer consists of a conducting layer (e.g., steel)
and a dielectric layer (e.g., Mylar). Figure 8.1b shows that, during deflection, the
two layers slip with respect to each other if the applied voltage V = 0. For a specific
voltage Vst, the electrostatic loading causes the layers to stick to each other during
deflection, see Fig. 8.1c. Whenever these layers stick, the second moment of area
increases, which effectively increases the bending stiffness of the beam.

8 Active Control of the Hinge of a Flapping Wing with Electrostatic Sticking . . . 155

(a) (b) (c)

conductor V =0 V ≥ Vst

dielectric

F =0 F =0

F =0

Fig. 8.1 Conceptual idea to change the bending stiffness of stacked layers. a Capacitor-like
clamped-free beam with end-load F. b For V = 0, the layers slip with respect to each other during
deflection. c For V ≥ Vst , the layers stick together which effectively increases the bending stiffness

This work aims to actively control the wing’s passive pitching motion by sticking
stacked layers using electrostatics. These stacked layers need to be integrated into a
lightweight wing design (i.e., total wing design is about 200 mg) and should allow
for large passive pitching deflections. This study investigates the influence of electro-
statics on the dynamic properties of this active hinge during these large deflections.
The wing is assumed to be a thin, rigid plate for simplicity. This work uses a quasi-
steady aerodynamic model to obtain the equation of motion of the passive pitching
motion as a function of the elastic hinge properties. Experiments are conducted to
study the practical applicability of this active element for small-scale and lightweight
FWMAV applications.

This paper is organized as follows. Section 8.2 introduces a flapping wing design
and the description of the flapping kinematics with, in particular, the passive pitch-
ing motion. The theory of the electrostatically controlled structural properties of the
elastic hinge is discussed in Sect. 8.3. Section 8.4 presents the equation of motion
of a passive pitching flapping wing as a function of the elastic hinge stiffness and
the applied control voltage. Section 8.5 discusses the realization of the active hinge,
the experimental setup, the obtained measurement results, and a comparison with
analytical results. Section 8.7 gives conclusions and recommendations for further
research.

8.2 Passive Pitching Flapping Motion

8.2.1 Flapping Wing Design

Both insects and FWMAVs show flapping wings with different outlines, stiffness dis-
tributions and materials. Generally, the pitching motion is partly generated passively
with the help of wing flexibility. This wing flexibility can, for instance, be realized
with: (i) a flexible veins-membrane structure as known from insect wings [6], (ii) a
carbon-fiber-reinforced polymer film as commonly used in FWMAV wing designs

156 H. Peters et al.

zc wing holder

yc xc

L wing c

elastic b
hinge
R

Fig. 8.2 Schematic drawing of the wing design for a zero pitching angle with the elastic hinge
connecting the wing holder to the wing

elastichinge wing
wingholder
krot = EI
L

Fig. 8.3 Side-view sketch of the wing design, rotated through an angle , showing the replacement
of the compliant elastic hinge with length L by a rotational spring with stiffness krot

[5], or (iii) an elastic hinge at the wing root to represent the wing stiffness [21]. This
work uses the latter approach which is generally used for experimental studies.

Figure 8.2 shows the wing design as studied in the present work, consisting of
a rectangular, thin plate which is assumed to be rigid. The mass distribution over
the wing surface is assumed to be uniform. Since the focus of the current work is
primarily on the active hinge design, such a simple wing layout design is justified.
The wingspan and chord length are denoted by R and c, respectively. The elastic
hinge is located at the wing root and has width b, length L and thickness t. This
elastic hinge is essentially a compliant hinge, which is primarily loaded in bending.
The effective rotational stiffness can, consequently, be given by [10]:

krot = EI , (8.1)
L

where E and I are the Young’s modulus and second moment of area of the hinge,
respectively. Figure 8.3 shows a schematic side-view of the wing design which is
rotated through an angle to visualize the result of replacing the compliant elastic
hinge with length L by a rotational spring with stiffness krot. For pure bending, this
simple equation is accurate for large deflections. Although the loading of the elastic
hinge is more complex during the flapping motion, Eq. (8.1) is assumed to hold
during the entire flapping cycle.

8 Active Control of the Hinge of a Flapping Wing with Electrostatic Sticking . . . 157

8.2.2 Passive Pitching and Wing Kinematics

The flapping wing motion is a spatial wing movement that can be decomposed into
three successive motions, namely sweeping motion (or yaw), pitching motion (or
pitch), and heaving motion (or roll). The sweeping motion drives the wing to sweep
reciprocally in a stroke plane with a specified stroke amplitude. The pitching motion
controls the geometrical angle of attack (AOA) of the flapping wings. For flapping
wings, the highest AOA (i.e., 90◦) is, generally, experienced during wing reversal
phases while the lowest AOA shows up during the middle of the strokes. The heaving
motion represents the out-of-stroke-plane movement which amplitude is generally
one order smaller than for the other two motions. Hence, it is ignored in this study.
Therefore, the flapping kinematics can be fully determined by the sweeping motion
and the pitching motion.

Two Euler angles are used to quantify the wing kinematics: the sweeping angle ,
and the pitching angle , as shown in Fig. 8.4. The pitching angle is visualized
in Fig. 8.3. Additionally, two coordinate frames are specified which are of partic-
ular interest for the study of flapping wing motion: the fixed inertial frame xiyizi
and the co-rotating frame xcyczc which co-rotates with the wing (see Fig. 8.2). The
angular velocity and acceleration of a flapping wing in the co-rotating frame can be
expressed by

c = [ ̇ sin( ), ̇ cos( )]T , (8.2)
̇ ,

and c = ̇ c = [ ̇ ̇ cos( ) + ̈ sin( ), ̈ cos( ) − ̇ ̇ sin( )]T , (8.3)
̈ ,

respectively. The AOA can be simply obtained by ‖90◦ − ‖. The inertial and aero-
dynamic load can be fully determined if Eqs. (8.2) and (8.3) are known. For a given
prescribed sweeping motion (t), the tuned elastic hinge stiffness fully determines
the (passive) pitching motion and, therefore, the aerodynamic load generation (e.g.,

Fig. 8.4 Visualization of zi

the flapping kinematics zc yc yi
η(+) xi
determined by the sweeping
angle and pitching angle . LE
Additionally, the fixed
φ(−)
inertial frame xiyizi and the
co-rotating frame xcyczc are
shown

xc TE

158 H. Peters et al.

lift force). Consequently, changing the elastic hinge stiffness in an active manner
would lead to changes in the aerodynamic load generation and, hence, to a way to
control FWMAV flight.

8.3 Electrostatically Controlled Hinge Theory

This section discusses a model to electrostatically control the dynamic properties of
the active hinge. First, it presents the proposed hinge design followed by a description
of the voltage-induced normal stress between the stacked layers. Subsequently, it
describes the voltage-dependent behavior during the flapping motion (i.e., whether
the layers slip or stick). After that, the voltage-dependent properties of the active
hinge (i.e., its rotational stiffness and power dissipation) during the flapping motion
are presented.

8.3.1 Proposed Elastic Hinge Design

The elastic hinge in the wing design of Fig. 8.2 is replaced by an active hinge for
which an enlarged side-view is shown in Fig. 8.5a. The hinge is symmetric in thick-
ness direction. The hinge has length L and width b. It consists of a conducting core
which is covered on both sides by dielectric layers and two conducting facings. The
core connects the wing holder to the wing while the two facings are attached to the
wing holder only. The two facings can slide with respect to the core. The thickness
of the core, the dielectric layers, and the facings are denoted by tc, td, and tf , respec-
tively (see Fig. 8.5b). Two clamps are attached to the wing to prevent the layers from
separating during the pitching motion. Hence, all layers will always contribute to the
resulting bending stiffness. The facings are assumed to slip freely with respect to the
clamps.

(a) clamp (b) L
xc
wing holder slip tf yc
interfaces td

zc tc

conducting facings wing
dielectric layers
conducting core

Fig. 8.5 Symmetric active hinge design. a Side-view. b Dimensions

8 Active Control of the Hinge of a Flapping Wing with Electrostatic Sticking . . . 159

(a) (b) (c)

Fig. 8.6 Zoom-in of the active hinge during electrostatic loading. a Electric field over dielectric

layer due to applied voltage V. b Normal stress N due to the electrostatic loading. c Shear stress
distribution N at the interface

8.3.2 Voltage-Induced Stresses Between Stacked Layers

By applying a voltage V to the conducting facings of the active hinge while connect-
ing the conducting core to ground, an electric field is created over the dielectric lay-
ers, see Fig. 8.6a. This electric field induces a normal stress at the interface between
the facings and the dielectric layers, see Fig. 8.6b, which is given by [2]

1 0 r V 2
2 td2
N (V ) = , (8.4)

where 0 represents the vacuum permittivity and r is the material-dependent relative
permittivity. The normal stress depends quadratically on the applied voltage V and

inversely quadratic on the gap between the conducting layers (i.e., the dielectric layer

thickness td). The normal stress introduces friction between the stacked layers to
resist slip during deflection. The shear stress that can be transferred from one layer

to the other due to this friction, see Fig. 8.6c, is given by

N (V) = N (V) , (8.5)

where represents the material-dependent friction coefficient at the interface which
depends on whether there is relative displacement at the interface (i.e., dynamic fric-
tion) or not (i.e., static friction). The sticked layers start to slip with respect to each
other if the shear stress at the interface due to deflection becomes higher than the
friction-induced shear stress of Eq. (8.5). Thus, Eq. (8.5) determines the threshold
value at which the transition from stick to slip at the interface takes place. This work
assumes the static and dynamic friction coefficient to be equal to improve the under-
standing of the active hinge behavior.

160 H. Peters et al.

8.3.3 Behavior of the Active Hinge During Large Deflections

This section describes the stick-slip phenomena of the active hinge as a function
of the applied voltage V during large deflections to understand its rather complex
behavior (i.e., the active hinge is not a simple spring anymore). The hinge deflects
according to the wing pitching motion (t) and it is assumed that the stacked layers
slip over the entire interface without restriction for V = 0. For V > 0, the voltage-
induced normal stress tries to prevent slip by introducing friction. The required fric-
tion to prevent slip increases if the hinge deflection increases. The required voltage
to stick the layers together up to the maximal deflection is denoted by Vst (i.e., the
layers do, in that case, not slip throughout the entire pitching motion). In the fol-
lowing, two phases are distinguished: the layers either completely slip or completely
stick over the entire interface.

Figure 8.7 shows conceptual steady-state stick-slip behavior of the hinge layers
during a pitching motion (t) for a voltage 0 < V < Vst. The essential step in under-
standing the hinge behavior is the investigation of the interface shear stress in dur-
ing the pitching motion. It is assumed that, at the start of the graph, increases (i.e.,
deflection increases) and the layers slip. During slip, the interface shear stress in is
constant and equal to the friction-induced threshold shear stress (i.e., N(V)). The
constant interface shear stress results in a constant shear deformation of the layers,
see State 1 in Fig. 8.8. The layers continue to slip until the maximum pitching angle

Fig. 8.7 Conceptual steady-state stick-slip behavior of the voltage-controlled active hinge during
the pitching motion (t) for a voltage 0 < V < Vst with the corresponding interface shear stress
in. Additionally, it shows the pitch-duration ∗ for which the layers stick together. The dotted
green line represents the friction-induced threshold shear stress N (V). Characteristic layer off-set
configurations are indicated by Configurations 1–5

8 Active Control of the Hinge of a Flapping Wing with Electrostatic Sticking . . . 161

Fig. 8.8 Sketches of the shear deformation of two layers of the voltage-controlled active hinge
during the pitching motion (t) for a voltage 0 < V < Vst at different interface shear stress values
in. States 1–10 represent characteristic shear deformation sketches

(i.e., maximum hinge deflection) is reached, resulting in a hinge layer off-set, see
Configuration 1 in Fig. 8.7.

There is no relative motion at the interface at the maximal pitching angle, which
initiates stick between the layers. At the start of the reversal motion (i.e., decreases),
the layers remain sticking since the interface shear stress in becomes lower than the
friction-induced threshold shear stress N(V). The interface shear stress decreases
during this reversal until in = − N(V) (i.e., until the maximum friction-induced
shear stress N is reached again). At that point, the layers have not slipped yet as illus-
trated by Configurations 1 and 2 in Fig. 8.7 where the layer off-set did not change.
The shear deformation of the layers changes according to the changing interface
shear stress as represented by States 1–5 in Fig. 8.8. During the remainder of the
reversal motion (i.e., until the maximum negative ), the layers slip and result in a
layer off-set opposite to the one at the start of the pitching reversal, see Configura-
tion 1–3 in Fig. 8.7. During this slip, the interface shear stress and, hence, the shear
deformation is constant, see States 5–7 in Fig. 8.8.

Thereafter, a similar but opposite cycle starts followed by identical consecutive
cycles. If the layers stick, the off-set between the layers remains the same (see, for
example, Configuration 3 and 4 in Fig. 8.7) while the interface shear stress and, con-
sequently, the layer shear deformation changes (e.g., States 7–10 in Fig. 8.8). On the
other hand, if the layers slip, the off-set changes (e.g., from Configuration 4 to 5
in Fig. 8.7) while the interface shear stress and, consequently, the layer shear defor-
mation, is constant. The complexity that might be caused by the marginal off-set
between stacked layers (e.g., buckling), is neglected.

During sticking, the interface shear stress in changes with an amplitude of
in = 2 N(V) before the layers start to slip again as shown by the difference between
the horizontal dashed threshold lines in Fig. 8.8. The pitch-duration for which the
layers stick is denoted by ∗, see Fig. 8.7. To determine ∗, the relation between
the change of the pitching angle (i.e., ) and the known change of the interface
shear stress (i.e., in) is used. This relation is clarified in the following based on the
flowchart of Fig. 8.9 and the sketches of Fig. 8.10.

162 H. Peters et al.

Fig. 8.9 Graphical interpretation of the relation between the change of the pitching angle and

the interface shear stress in. P and Q represent the change of the external load on the wing and
the shear force at the cross-section, respectively

(a) lCOL (b)

COL wing yi Q M
holder
wing elastic wing
holder hinge P yc

Fig. 8.10 Side-view sketches of the wing design to determine the interface shear stress, in, and
pitch angle, , due to the external load P. a center of load (COL) with the external load P. b zoom-in

of the active hinge with moment M and shear force Q at the cross-section due to load P

Firstly, the change of the pitching angle is discussed. During flapping flight, the

wing loading can be captured by an external load P which is assumed to remain per-

pendicular to the wing surface (see Fig. 8.10a) for all angles of attack. This assump-

tion is justified since the strength of the bound circulation at a post-stall angle of

attack, that results in a net force perpendicular to the incoming flow, is negligible as

compared to the vorticity-induced circulation that results in the load perpendicular to

the wing surface [8]. Although the location of the center of load (COL) varies slightly

during a flapping cycle we assume it to be constant at a distance lCOL = 0.5L + 0.5c
from the wing holder [23], where L is the hinge length and c is the chord length (see

Fig. 8.2). The load P causes the wing to pitch through an angle . The change of the

pitching angle due to a change of the external load P is, using a linear spring

model, given by

= PlCOL , (8.6)
krot

where krot represents the effective rotational stiffness (see Eq. (8.1)).
Secondly, the change of the interface shear stress in is discussed. The external

load P results in a moment M and a shear force Q (i.e., Q = P) at the cross-section

of the sticked layers (see Fig. 8.10b). Q is assumed to be constant along the length of

the hinge L. From ordinary sandwich beam theory, the change of the shear stress in
at a depth yi = 0.5tc + td (i.e., at the interface) due to a change of the shear force Q
at the cross-section, is given by [1]

in () = Q ∑ (8.7)
yi Db (SE) ,

8 Active Control of the Hinge of a Flapping Wing with Electrostatic Sticking . . . 163

wofhtehreeaDctriveperheisnegnetsatthteheflienxtuerrafal creig, iadnitdy∑of(tShEe)ernetpirreescernotssstsheecstiuomn,obf gives the width
the products of

the first moment of area S and the Young’s modulus E of all parts of the cross section

for which yc > yi. Due to symmetry in the thickness direction, the shear stress at the
other interface (i.e., yc = −yi) is identical.

Finally, given the known voltage-induced in, the change of the shear force Q
can be obtained from Eq. (8.7). Since P = Q, the change of the pitching angle

can be determined from Eq. (8.6). This change of the pitching angle gives, conse-
quently, the pitch-duration ∗ for which the layers stick.

In conclusion, stick and slip alternate during the pitching motion. The properties

of the hinge depend on whether the layers stick or slip as discussed in the next section.
Hence, it is important to know the pitch-duration ∗ for which the layers stick. This

pitch-duration is, in this work, directly related to the change of the friction-induced

shear stress in using the external load P. Hence, this enables the determination of
the stick-slip behavior of the active hinge during large deflections.

8.3.4 Voltage-Dependent Hinge Properties

The property changes of the active hinge as a function of the applied voltage are
twofold: (1) rotational stiffness changes, and (2) energy dissipation changes due to
friction at the interfaces. Both influence the passive pitching response.

Depending on whether the layers stick or slip, the tangent rotational stiffness is
denoted by

∙ krsot t if the layers stick. In this case, the active hinge consists, basically, of one single
bending element, and

∙ krsol t if the layers slip. In this case, the active hinge consists, basically, of three
individually bending layers.

The tangent rotational stiffness of the sticking layers is significantly higher compared
to the slipping layers case. For example, for a beam consisting of n stacked layers with
width b and thickness t, the ratio between the second moments of area for sticking
and slipping cases is n2 (i.e., Istick∕Islip = (n3bh3∕12)∕(nbh3∕12)). Subsequently, the
tangent rotational stiffness is n2 times higher if the layers stick.

For 0 < V < Vst, the layers sequentially stick and slip during the pitching motion.
Whenever the layers slip, energy is dissipated due to friction which leads to mechan-
ical damping. The resulting dissipated power due to friction between the layers (i.e.,
there are two sliding interfaces in the current hinge design) can be given by

L ( )
v1 t)
Pf r (V , t) = d N (V ) b ∫0 ( , t) + v2 ( , d , (8.8)

where represents a coordinate along the active hinge and v1 ( , t) and v2 ( , t) rep-
resent the relative velocity between the slipping layers at the upper interface (i.e., at

164 H. Peters et al.

yc = −yi, see Fig. 8.10b) and lower interface (i.e., at yc = yi), respectively. The rela-
tive velocity along the hinge is determined by the pitching motion (t) and the thick-
ness of the layers. It is assumed that the relative velocity at the interface increases
linearly from zero at the wing holder (i.e., at = 0) to its maximal value at the
end of the hinge (i.e., at = L) although the velocity distribution might be more
complex in reality. During slip, the counteracting moment due to the friction can,

subsequently, be obtained by

{ 0 for V = 0,
Pfr (V, t) ∕ ̇ for V ≠ 0.
Mxfcr = (8.9)

Equation (8.9) explicitly assumes that the dissipated power is equal to zero for
V = 0 although this assumption oversimplifies the occurring slip behavior due to
the inevitable normal stress between slipping layers which are jointly bending. This
description allows, despite the limitations, to study the influence of an electrostati-
cally controlled active hinge on the passive pitching motion of a flapping wing.

8.4 Equation of Motion of Passive Pitching Motion

Since the sweeping motion (t) is prescribed, the rigid wing model involves only
one degree of freedom, the pitching angle . The equation of motion that governs
can be obtained by applying Euler’s second law of motion. That is,

Mxacpplied + Mxincer = 0, (8.10)

where the inertial torque, Mxincer, in the co-rotating frame is given by

Mxinc er = Ixc xc [1 sin (2 ) ̇ 2 − ] − Ixczc ̈ cos ( ), (8.11)
2 ̈

where Ixcxc and Ixczc are moment of inertia terms. The applied torque, Mxacpplied, acting
around the pitching axis consists of three components: (i) the elastic torque from the
active hinge, Mxeclas, (ii) the voltage-dependent torque due to the friction between the
layers, Mxfcr, as calculated by Eq. (8.9), and (iii) the aerodynamic torque Mxacero.

A quasi-steady aerodynamic model is used to calculate the transient aerodynamic

loads. This paper only shows the terms relevant for this work without going into

much detail on the specific terms. For more details the reader is referred to [20]. The

aerodynamic model assumes the resultant aerodynamic load acting on the wing to

be always perpendicular to the chord over the entire stroke (i.e., in yc-direction). For
thin plates, this assumption is justified due to a negligible leading-edge suction load

and wing surface viscous drag compared to the dominant pressure load. The loads

are decomposed into four components as illustrated in Fig. 8.11 and originate from
different sources: (1) from the wing translational velocity, leading to Fytrcans and Mytrcans

8 Active Control of the Hinge of a Flapping Wing with Electrostatic Sticking . . . 165

pitching axis (angular) velocity (angular) acceleration

xc v = v+ vzc xc +a
a xc
+
xc
xc

aerodynamic loads on 1) translational 2) coupling 3) rotational 4) added mass
flapping wing load load load load

circulatory loads non-circulatory load

Fig. 8.11 Decomposition of the flapping wing aerodynamic loads from a quasi-steady model in
which a and v are the acceleration and velocity of the wing at the pitching axis, respectively

(see, for example, [14]), (2) from the coupling effect between wing translational and

rotational eFffyrocetcat,ndleMadyriocntg, atnodF(y4cco)upfrl oamndthMeycacodupdle, d(3m) afsrosmefftehcet,pluearedirnogtattoioFnyaacml velocity,
leading to and Myacm

(see, for example, [13]). The resultant aerodynamic loads can be calculated by

Fyacero = −sgn( zc ) 1 f cR3 cFytrcans ( 2yc + z2c ) + 3 f c2 R2 xc yc
6 8
⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏟

Fytrcans Fyccoupl

⏟− ⏞16⏞⏞ ⏞ ⏞⏞f⏞c⏞⏞3⏞⏞R⏞⏟Crot⏞ ⏞⏞ ⏞x⏞⏞c⏞|⏞⏞ ⏞ ⏞⏞x⏟c | + ⏟ 8 ⏞ ⏞ ⏞f⏞⏞c⏞⏞2⏞⏞R⏞⏞⏞[⏞⏞−⏞⏞⏞R⏞⏞⏞(⏞ ⏞ ⏞z⏞⏟c + ⏞ ⏞ ⏞⏞x⏞c⏞ ⏞⏞ ⏞y⏞⏞c⏞)⏞⏞⏞−⏞⏞⏞⏞c⏞⏞ ⏞ ⏞x⏞⏟c ],

Fyroct Fyacm

and Myacero = −sgn( zc ) 1 f c2 R3 cFytrcans ẑtcrpans ( y2c + 2zc )
6
⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟

Mytrcans

+ 3 f c3 R2 xc yc − 1 f c4 RCrot xc | xc |
32 8
⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟

[Myccoupl Myroct ]
c3R −R( zc ,
+ f + xc yc) − 9 c xc (8.12)
16 8
⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟

Myacm

respectively, where f is the density of the fluid, ẑctrpans is the position of the center
of pressure due to the translational force which is calculated using an empirical for-

mula (i.e., ẑctrpans = 0.261 (AOA) + 0.05), and Crot is the drag coefficient for a plate
revolving at an AOA of 90◦. An analytical model proposed by Taha et al. [16] is

used to calculate the lift coefficient cFytrcans due to the wing translational velocity. This
analytical formula provides a good prediction of the lift coefficients of translational

flapping wings with different aspect ratios according to the comparison with exper-

imental data from bumble bees, fruit flies and hawk moths.

166 H. Peters et al.

Eventually, the voltage-dependent equation of motion of the wing passive pitching
can be expressed as

Ixcxc ̈ + krot = Myacero + f ( , ̇ ) + Mxfcr ( ̇ , V) , (8.13)
where the inertial drive torque f ( , ̇ ) is given by

f ( , ̇ ) = 1 Ixc xc ̇ 2 sin(2 ) − Ixczc ̈ cos ( ). (8.14)
2

Finally, Eq. 8.12 will be used to determine the average lift generated by the flap-
ping wing with the actively controlled elastic hinge. It should be mentioned that
the introduced quasi-steady model cannot capture some unsteady effects (e.g., wake
capture effect and Wagner effect). Rather good agreements can, however, be found
between the results from the quasi-steady model and experiments [20] since the most
important unsteady effect (i.e., the prolonged attached of the leading edge vortex) is
captured. As such, the model is adequate for this work.

8.5 Experimental Analysis

To validate the presented approach on changing the dynamic properties of wing
hinges, experiments are done. First, the manufactured wing equipped with an active
hinge is discussed together with the experimental setup. After that, the change of
the passive pitching motion due to different applied voltages is shown. Finally, the
experimentally and analytically obtained results are compared.

8.5.1 Realization of Wing with Active Hinge

The wing design consists of three parts: (i) the wing planform, (ii) the active hinge
at the wing root, and (iii) the wing holder, see Fig. 8.12. The first part, the wing
planform, is composed by gluing two rectangular, 1 mm thick sheets of blue foam
(i.e., Expanded PolyStyrene (EPS) with Young’s modulus EEPS = 3 GPa) on top of
each other. The wingspan R = 50 mm and its chord length c = 20 mm. The core layer
of the active hinge is clamped between these two sheets.

The second part, the active hinge, consists of a conducting core which is on both
sides covered by, consecutively, a dielectric layer and a conducting facing. For all
conducting layers, spring steel strips are used (i.e., Young’s modulus Es = 210 GPa).
These spring steel strips are tough and allow for a large number of cyclic, large
deflections. The strips have a width b of 12.7 mm and the thickness of the core and
the facings is 20 µm and 5 µm, respectively. For the dielectric layers two different
approaches can be followed: (1) spin coat a thin polymeric film onto the conducting
layer(s) (e.g., the photo-resist SU-8), or (2) use thin sheets of dielectric polymer
film (e.g., Mylar). In this work, 5 µm thick Mylar films are tightly attached to the

8 Active Control of the Hinge of a Flapping Wing with Electrostatic Sticking . . . 167

(a) (b)

Fig. 8.12 Wing design consisting of: (i) the wing planform, (ii) the active hinge, and (iii) the wing
holder. a Planform with core layer covered by Mylar film. b Realized wing design

core conducting layer by gluing its two edges to the spring steel while squeezing

the air layer out, see Fig. 8.12a. For the Mylar, the Young’s modulus Ed = 4.25 GPa,
the dielectric constant r = 3.25, the static and dynamic friction coefficients with
respect to steel are assumed to be equal, that is, s = d = 0.2,1 and the dielectric
strength is Vd = 500 V∕µm [9, 19]. The total length of the active hinge L = 5 mm.

To prevent the layer from separating during the pitching motion, clamps are added

on both sides. The bending stiffness EI of the blue EPS plate is about 1000× higher

in chordwise direction compared to that of the hinge. Therefore, the wing planform

can be regarded as a rigid plate.

The third part, the wing holder, is made from 3D-printed plastic. The wing holder

is extended over the entire wing span to constrain the movement of the wing tip via

a strip of spring steel with a relatively high bending compliance. This constraint

prevents warping of the active hinge during large deflections which would lead to

undesired large deflections in spanwise direction. The resulting wing design is shown

in Fig. 8.12b.

The total mass of the realized wing (excluding the wing holder) is around 300 mg

which is relatively high compared to wings found in nature with similar dimensions

(e.g., 50 mg) due to glue and the additional clamps. With the currently used layer

thicknesses, the ratio between the b+en2dtfi)n3g∕st(ifftc3n+es2stfo3)f the sticked layers, krsot t , and
the slipping ( = 2.34.
layers, krsol t , is tc + 2td

8.5.2 Experimental Setup

Figure 8.13 shows a picture of the experimental setup as positioned on a vibration-
isolating table. The key components of this setup are: (1) the active wing, (2) a non-
conducting clamping mechanism to apply the voltage to the facings and to ground

1Since no appropriate information was found about the friction coefficient between Mylar (PET,
Polyethylene terephthalate) and spring steel, the friction coefficient between the similar material
PE (Polyethylene) and steel was used instead.

168 H. Peters et al.

Fig. 8.13 Experimental setup indicating the key components

the core layer, (3) a DC high-voltage source to apply the voltage to the active hinge,
(4) a driving mechanism to enforce a harmonic sweeping motion (t) to the wing,
(5) a tachoprobe to measure the driving frequency, and (6) a high-speed camera with
a flashlight to capture the flapping motion.

To capture the pitching motion, two black markers are glued onto the wing tip of
the wing design in chord-wise direction. The distance on the captured image between
these markers when the wing planform is perpendicular to the optical axis of the
camera, is taken as the reference length and denoted by db. The high-speed camera
(2000 fps) captures images and, thus, the distance between the black markers during
the flapping motion. By relating this distance to the reference length db, the pitching
angle (t) can be calculated.

8.5.3 Experimental Results

This section shows experimental results of one specific wing design. Although simi-
lar trends were found for other wing designs, this design shows the trend most clearly
over a large range of applied voltages. Due to wing fabrication difficulties it was hard

8 Active Control of the Hinge of a Flapping Wing with Electrostatic Sticking . . . 169

angle (degrees) 80 , experimental
60 , fitted
40 , exp. (0 V)
20 , fitted (0 V)
, exp. (600 V)
0 , fitted (600 V)
-20
-40 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
-60 time (s)

0

Fig. 8.14 Lapping kinematics of a passive pitching wing design for which the pitching amplitude
decreases if the applied voltage to the active hinge increases

to compare different designs over a large range of applied voltages. These difficulties

were, among others, handling the extremely thin spring steel and Mylar sheets (i.e.,
5 µm) and preventing a remaining air layer between the stacked layers. This air layer
has a negative influence on the voltage-induced normal stress (see Eq. (8.4)). Hence,

the number of well succeeded wing designs was limited.
The driving frequency was constant for all experiments and restricted to 12.5 Hz

to prevent excessive pitching amplitudes (i.e., (t) > 90◦). Figure 8.14 shows the
resulting flapping kinematics: the sweeping motion (t) and the passive pitching
motion (t). The passive pitching motion lags behind the sweeping motion by about
30◦. The amplitude of the sweeping motion is 37.5◦. The maximum passive pitching
angle decreases if the applied voltage to the active hinge increases (i.e., the maximum
pitching angle decreases from about 84◦ for 0 V to about 78◦ for 600 V) and the

phase lag becomes slightly bigger (i.e., a few degrees). The asymmetry of the passive

pitching motion is caused by inaccuracies of the realized flapping wing design. The

small irregularities or disappearance of measurement points for the pitching motion

is caused by the difficulties in tracking the markers on the flapping wing, especially
around (t) = 0◦.

Figure 8.15 shows the change of the average pitching amplitude (using both the

maximum and minimum pitching angle) as a function of the applied voltage to the
active hinge. To get these results, the flapping frequency was fixed to 12.5 Hz and the
applied voltage was increased in steps of 100 V to the maximum of 600 V. For each

measurement point, a wait of a couple of seconds was introduced to be assured of

steady-state motion before taking images. For some images, the exact location of the
black markers was hard to identify. This resulted in a non-smooth pitching angle (t)
as shown by some outliers in Fig. 8.14. This, consequently, complicates the determi-

nation of the maximum pitching angle. The error bars indicate the uncertainty of the

maximum pitching angle as determined by the spread in the measurements.

170 H. Peters et al.

76

pitching amplitude (degrees) 74

72

70

68

66 100 200 300 400 500 600
0
applied voltage (V)

Fig. 8.15 Average pitching amplitude as a function of the applied voltage V. The error bars indi-
cate the measurement uncertainty as determined by the non-smoothness of the measured pitching
motion (t)

Figure 8.15 shows an increase of the average passive pitching amplitude up to
200 V followed by a monotonic decrease of this amplitude for higher voltages. A
possible explanation for this initial amplitude increase is the presence of the clamps
on the wings to keep the layers from separating. The friction between these clamps
and the outer facings decreases if the voltage-induced sticking of the stacked layers
increases. The reduction of friction reduces the energy loss and, hence, increases the
average pitching amplitude.

The targeted gap between the core conducting layer and the outer facings was
5 µm as determined by the thickness of the Mylar sheet. Since the electric strength
of Mylar is 500 V∕µm, the maximum possible applied voltage to the active hinge
is, theoretically, restricted to 2500 V. Figures 8.14 and 8.15 show only results up to
600 V since the hinge failed for higher voltages. This could have several reasons,
for example: (i) due to Mylar sheet irregularities (e.g., a small scratch) the practical
dielectric strength is lower than the theoretical value, or (ii) due to the presence of
the very thin air gap between the conducting layers and the dielectric sheet. If the
breakthrough voltage of the air gap is reached, a current is going to flow which might
locally burn the dielectric Mylar layer.

8.6 Numerical Analysis and Comparison
to Experimental Results

The numerical analysis to determine the passive pitching motion is complicated by
the abrupt jump in the hinge stiffness if the layers of the active hinge change from
stick to slip, or visa versa. To solve this problem the jump of the hinge stiffness is

8 Active Control of the Hinge of a Flapping Wing with Electrostatic Sticking . . . 171

angle (degrees) 80
60
40 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
20 time (s)
0
-20
-40
-60
-80

0

Fig. 8.16 Numerical results of the flapping kinematics for different applied voltages to the active
hinge. Segments in red show the pitch-duration ∗ (i.e., just after the maximum pitching angle)

for which the layers stick

smoothed by a C∞ function, and the ode15s solver from MatlabⓇ is used to solve this
stiff problem. Figure 8.16 shows the sweeping motion (t) and numerical steady-
state passive pitching (t) for different applied voltages V to the active hinge. The
figure clearly shows the decrease in the pitching amplitude for an increase of the volt-
age. The passive pitching motion without voltage (i.e., 0 V) lags behind the sweeping
motion by about 30◦, which is comparable to the experimental results. The phase
lag increases slightly if the voltage increases. Additionally, the figure indicates the
locations at which the layers stick (i.e., just after the maximum pitching angle). The
pitch-duration ∗ for which the layers stick increases if the applied voltage increases
although it remains relatively short with respect to the entire flapping cycle.

Figure 8.17 shows the numerical change of the average pitching amplitudes as a
function of the applied voltages. The average pitching angle decreases monotoni-
cally, almost linearly, if the voltage increases. The cycle-average lift force decreases
accordingly, see Fig. 8.18. The average lift force decreases by about 31 % if the
voltage is increased from 0 to 250 V, which is sufficient in controlling lightweight
FWMAV designs. The maximum applied voltage is set to 250 V. For voltages higher
than 250 V, the passive pitching motion (t), as shown in Fig. 8.16, starts to devi-
ate significantly from being harmonic. Additionally, the convergence becomes poor
such that a steady-state solution can not be found.

The numerical passive pitching amplitude change due to the applied voltage (i.e.,
Figs. 8.16 and 8.17) is more significant compared to the experimental results of
Figs. 8.14 and 8.15 although the trend is similar (i.e., decreasing amplitude and
increasing phase lag when the applied voltage increases). The discrepancy can be
explained by: (1) the simplifying assumptions in the theoretical model, (2) the diffi-
culties in the manufacturing process, and (3) the presence of additional air between
the conducting layers and the Mylar.

172 pitching amplitude H. Peters et al.
Fig. 8.17 Numerical (degrees)
average passive pitching 78
amplitudes as a function of average lift force (mN) 74
the applied voltages 70
66
Fig. 8.18 Numerical
average lift force as a 0 50 100 150 200 250
function of the applied
voltages applied voltage (V)

2.6
2.4
2.2
2.0

0 50 100 150 200 250

applied voltage (V)

8.7 Conclusions and Recommendations

This paper presents a method to actively control the passive pitching motion of a
flapping wing using electrostatic sticking of stacked layers. These stacked layers con-
stitute the elastic hinge at the wing root in a FWMAV design. Actively modifying
the structural properties of that hinge (e.g., damping and stiffness) results in signifi-
cant changes of the wing’ passive pitching motion and, hence, of its lift production.
The hinge in this work consists of three conducting spring steel layers which are
separated from each other by dielectric Mylar films.

During the pitching motion, the layers, consecutively, stick and slip with respect
to each other. The layers stick due to the voltage-induced normal stress between the
layers. Whenever the layers stick, the bending stiffness of the hinge is significantly
higher compared to the case when the layers slip (i.e., 2.34 × for our hinge). If the
layers slip, power is dissipated due to friction which is induced by the normal stress
between the layers. This friction results in an additional moment that dampens the
passive pitching motion.

Numerical simulations show significant changes of the pitching amplitude if the
applied voltage to the active hinge increases. The pitch-duration for which the layers
stick increases with the applied voltage, although it remains relatively short com-
pared to the duration for which the layers slip. The resulting average lift force changes

8 Active Control of the Hinge of a Flapping Wing with Electrostatic Sticking . . . 173

corresponding to the different applied voltages are sufficient for control purposes of
lightweight FWMAV designs. The theoretical model gives, despite the introduced
limitations, a clear insight into the voltage-controlled stick-slip behavior of the active
hinge during large deflections.

Experiments are conducted to study the practical applicability of this active elastic
hinge for small-scale and lightweight FWMAV applications. To obtain experimental
results, several fabrication difficulties have been tackled, for example, the handling
of the very thin Mylar films (i.e., 5 µm). The experimental results show, although
suppressed, the same trends compared to the numerical simulations. The results are
less significant, mainly due to: (1) the presence of an air layer between the conducting
layers and the dielectric layers, (2) the presence of Mylar film irregularities. Despite
of these shortcomings, the results clearly show a decrease of the pitching amplitude
as a function of the applied voltage. Hence, it shows the potential of this method to
control FWMAVs.

In future work, the numerical model might be improved to model the stick-slip
behavior of the active hinge more accurately (e.g., the friction between the layers
in the absence of a control voltage). Additionally, long lasting experiments need to
be conducted to study the influence of wear due to friction between the Mylar and
the conducting sheets. Alternatively, it is interesting to change the applied voltage
during a flapping cycle and study the occurring transient behavior. The fabrication
process can be optimized by preparing jigs or well-designed tools.

Acknowledgements This work is part of the Atalanta project from Cooperation DevLab and is
supported by Point One - UII as project PNU10B24, Control of Resonant Compliant Structures.
This work is also financially supported by Chinese Scholarship Council (CSC NO. 201206290060).
Additional thanks to the technical staff of PME for their support with the experimental setup.

References

1. Allen H (1969) Analysis and design of structural sandwich panals. Pergamon Press, Oxford
2. Bergamini A, Christen RX, Maag B, Motavalli M (2006) A sandwich beam with electrostat-

ically tunable bending stiffness. Smart Mater Struct 15(3):678–686. doi:10.1088/0964-1726/
15/3/002
3. Bolsman CT, Goosen JFL, van Keulen F (2009) Design overview of a resonant wing actuation
mechanism for application in flapping wing mavs. Int J Micro Air Veh 1(4):263–272. doi:10.
1260/175682909790291500
4. Clark WW (2000) Vibration control with state-switched piezoelectric materials. J Intell Mater
Syst Struct 11(4):263–271. doi:10.1106/18CE-77K4-DYMG-RKBB
5. de Croon G, de Clercq K, Ruijsink R, Remes B, de Wagter C (2009) Design, aerodynamics, and
vision-based control of the delfly. Int J Micro Air Veh 1(2). doi:10.1260/175682909789498288
6. Dudley R (2000) The biomechanics of insect flight: form, function, evolution. Princeton Uni-
versity Press
7. Finio BM, Wood RJ (2012) Open-loop roll, pitch and yaw torques for a robotic bee. In: IEEE
International conference on intelligent robots and systems, pp. 113–119. doi:10.1109/IROS.
2012.6385519. Art. no. 6385519
8. Ford C, Babinsky H (2014) Impulsively started flat plate circulation. AIAA J 52(8):1800–1802
9. Free Flight Supplies (2015). www.freeflightsupplies.co.uk/mylarspec.pdf

174 H. Peters et al.

10. Howell LL (2001) Compliant Mechanisms. Wiley
11. Ma KY, Felton SM, Wood RJ (2012) Design, fabrication, and modeling of the split actua-

tor microrobotic bee. In: IEEE international conference on intelligent robots and systems, pp.
1133–1140. doi:10.1109/IROS.2012.6386192. Art. no. 6386192
12. Majidi C, Wood RJ (2010) Tunable elastic stiffness with micro confined magnetorheological
domains at low magnetic field. Appl Phys Lett 97(16). http://dx.doi.org/10.1063/1.3503969.
Art. no. 164104
13. Newman J (1977) Marine hydrodynamics. The MIT Press
14. Sane SP, H, DM (2002) The aerodynamic effects of wing rotation and a revised quasi-steady
model of flapping flight. J Exp Biol 205(8):1087–1096. http://jeb.biologists.org/content/205/
8/1087.short
15. Tabata O, Konishi S, Cusin P, Ito Y, Kawai F, Hirai S, Kawamura S (2001) Micro fabricated
tunable bending stiffness devices. Sens Actuators, A 89(1–2):119–123. doi:10.1016/S0924-
4247(00)00538-0
16. Taha HE, Hajj MR, Beran PS (2014) State-space representation of the unsteady aerodynamics
of flapping flight. Aerosp Sci Technol 34:1–11. doi:10.1016/j.ast.2014.01.011
17. Teoh ZE, Fuller SB, Chirarattananon P, Prez-Arancibia NO, Greenberg JD, Wood RJ (2012)
A hovering flapping-wing microrobot with altitude control and passive upright stability. In:
IEEE international conference on intelligent robots and systems, pp. 3209–3216. doi:10.1109/
IROS.2012.6386151
18. Teoh ZE, Wood RJ (2014) A bioinspired approach to torque control in an insect-sized flapping-
wing robot. In: Proceedings of the IEEE RAS and EMBS international conference on biomed-
ical robotics and biomechatronics, pp. 911–917. doi:10.1109/BIOROB.2014.6913897. Art. no.
6913897
19. Toolbox TE (2015). http://www.engineeringtoolbox.com/friction-coefficients-d_778.html
20. Wang Q, Goosen JFL, van Keulen F (2016) A predictive quasi-steady model of aerodynamic
loads on flapping wings. J Fluid Mech 800:688–719
21. Wood R (2007) Design, fabrication, and analysis of a 3dof, 3cm flapping-wing mav. In:
IEEE/RSJ international conference on intelligent robots and systems, 2007. IROS 2007, pp.
1576–1581. doi:10.1109/IROS.2007.4399495
22. Wood RJ (2008) The first takeoff of a biologically inspired at-scale robotic insect. IEEE Trans
Robot 24(2):341–347. doi:10.1109/TRO.2008.916997
23. Zhao L, Huang Q, Deng X, Sane SP (2010) Aerodynamic effects of flexibility in flapping
wings. J R Soc Interface 7:44. doi:10.1098/rsif.2009.0200

Chapter 9

Control System Design for a Morphing
Wing Trailing Edge

Ignazio Dimino, Monica Ciminello, Antonio Concilio, Andrè Gratias,
Martin Schueller and Rosario Pecora

Abstract Shape control of adaptive wings has the potential to improve wing
aerodynamic performance in off-design conditions. A possible way to attain this
objective is to implement specific technologies for trailing edge morphing, aimed at
changing the airfoil camber. In the framework of SARISTU project (EU-FP7), an
innovative structural system incorporating a gapless deformable trailing edge was
developed. A related key technology is the capability to emulate and maintain
pre-selected target wing shapes within an established margin, enabling optimal
aerodynamic performance under current operational pressure loads. In this paper,
the actuation and control logics aimed at preserving prescribed geometries of an
adaptive trailing edge under variable conditions are numerically and experimentally
detailed. The actuation concept relies on a quick-return mechanism, driven by
load-bearing actuators acting on morphing ribs, directly and individually. The
adopted unshafted distributed electromechanical system arrangement uses
servo-rotary actuators, each rated for the torque of a single adaptive rib of the
morphing structure. The adopted layout ensures compactness and weight limita-
tions, essential to produce a clean aerodynamic system. A Fiber Bragg Grating
(FBG)-based distributed sensor system generates the information for appropriate
open- and closed-loop control actions and, at the same time, monitors possible
failures in the actuation mechanism.

I. Dimino (✉) ⋅ M. Ciminello ⋅ A. Concilio 175

CIRA, The Italian Aerospace Research Centre, Via Maiorise,
81043 Capua, CE, Italy
e-mail: [email protected]

A. Gratias ⋅ M. Schueller
Department MDI, Fraunhofer ENAS, Technologie-Campus 3,
09126 Chemnitz, Germany

R. Pecora
Department of Industrial Engineering Aerospace Division, University of Naples
“Federico II”, Via Claudio, 21, 80125 Naples, Italy

© Springer International Publishing Switzerland 2017
A.L. Araujo and C.A. Mota Soares (eds.), Smart Structures and Materials,
Computational Methods in Applied Sciences 43,
DOI 10.1007/978-3-319-44507-6_9

176 I. Dimino et al.

9.1 Introduction

Changing aircraft wing shape or geometry for maneuver and general control
purposes has its roots at the very early stage of the modern aviation. The Wright
Flyer, the first engined aircraft, enabled roll control by changing the twist angle of
its wing, by using cables directly actuated by the pilot. The increasing demand for
higher cruise speeds and payloads led to more rigid aircraft structures, unable to
change their shape to different aerodynamic conditions. Nowadays, conventional
flaps or slats are a typical example of such an adaptive wing geometry arrangement
(examples are the variable wing planform geometry on the Grumman F14 Tomcat
or the Aerospatiale/British Aerospace Concorde nose) to increase wing lift coeffi-
cient. However, their use leads to discontinuities, in turn producing geometry
sharpening, aerodynamic efficiency worsening and also noise emissions increase. It
becomes clear then the associated benefits could be increased if an inherent
deformable wing would be referred to, either globally or locally (see for instance
[1], for general aerodynamic performance enhancement or [2], for radiated noise
reduction) to fly at sub-optimal wing performance levels.

Wing shape morphing is a very promising area of research enabling dramatic
improvements in aircraft aerodynamic performance. It has interested researchers
and designers over the years; a quite thorough survey may be found in [3], while
early works may be found in the far past [4]. Novel strategies have been considered
in the last decade: for example, the idea of producing smooth variations of the
geometry even in presence of large displacements distributed over a wider portion
of the wing, is well documented [5].

Shape morphing structures, however, gives rise to an interesting paradox: the
same structure that has to withstand the external aerodynamic loads without suf-
fering appreciable deformations, has to allow dramatic strains to let its shape match
the target flight condition. Morphing structures require then a compromise between
high load-carrying capacity and adequate flexibility. This target necessitates inno-
vative structural and actuation solutions. When dealing with adaptive structures for
lifting surfaces, the level of complexity naturally increases as a consequence of the
augmented functionality. In specific, an adaptive structure ensures a controlled and
fully reversible transition from a baseline shape to a set of different configurations,
each one capable of withstanding the associated external loads. To this aim, a
dedicated actuation system shall be designed. In addition, the adopted morphing
structural kinematics shall demonstrate complete functionality under operative
loads.

Several international researchers have been working on this topic by following
different approaches. Some efforts were made on morphing skins to delay
the laminar transition point [6, 7], to modify the local or global camber [8–10], or
the wing span itself [11, 12] or the twist angle [13, 14]. Others focused on the
development of actuation kinematics [15, 16] or compliant structures [17, 18].
These are designed to achieve large deformations by relying only upon the elastic
properties of their structural components. This requires the balance between high

9 Control System Design for a Morphing Wing Trailing Edge 177

load-carrying capabilities to sustain external forces and sufficient flexibility to
smoothly realize the target shape under the actuation forces. Rigid-body mecha-
nisms offer a direct solution to the morphing paradox. Actuation is carried out via
lever mechanisms driven by load-bearing actuators combing load carrying and
actuation functions. Fewer actuators are typically required to control the morphing
process whose overall benefit expected on the system level drives the additional
mass, volume, force and power required by the actuation system.

Morphing is then a very general concept, applicable to a huge set of wing
functionalities. So, it is necessary to specify an application in order to translate this
idea into a device. Herein, cruise performance is addressed. Large commercial
airplanes weight reduces up to 30% during a long range mission due to fuel con-
sumption [19, 20]. Such consistent changes in flight conditions can be compensated
by varying the wing camber during the mission to obtain a near optimum geometry
in order to preserve aerodynamically efficient flight. To reach this aim, several
chord and span-wise concepts are developed in the literature.

Within the frame of SARISTU, project (EU-FP7), an innovative structural
system incorporating a gapless adaptive trailing edge device (ATED) has been
developed. Actuation is carried out via a lever mechanism driven by load-bearing
actuators, which combine load carrying and actuation capacities. Such an actuation
architecture allows the control of the morphing structure by using a reduced mass,
volume, force and consumed power with respect to conventional solutions. ATED
function may thus be referred to as a continuous and quasi-static wing TE shape
optimization control [21]. By properly adapting the chord-wise trailing edge
camber, the wing shape is controlled during cruise in order to compensate the
weight reduction due to the fuel burning. As a result, it allows the trimmed con-
figuration to remain optimal in terms of efficiency (L/D ratio) or minimal drag (D).
Key benefits may be measured as reduction of fuel consumption or increase of
range, expected to amount to 3% or more. Because span-wise variations can be also
attained, design weight decrease could be also potentially achieved by reducing the
root bending moment (RBM).

9.2 System Architecture

Civil aircraft flight profiles are quite standard but different missions may be flown
(fast or slow, at low or high altitude). Lift coefficient can span over tenth to unit
while weight reduces by around a quarter as the fuel burns. The best aerodynamic
configuration then changes, having to match new conditions. SARISTU project
addresses medium-range aircraft (around 3 h cruise flight). Chord-wise camber
variations are implemented through trailing edge (TE) adaptations to get the optimal
geometry for different flight conditions. The trailing edge portion spans 3.0 m along
the inner wing (kink) and 9.6 m along the outer wing region (Fig. 9.1). The
required chordwise extensions is equal to the 10% of the wing Mean Aerodynamic
Chord (MAC) (nearly 3.5 m) respectively for the inner and the outer segments.

178 I. Dimino et al.

Fig. 9.1 Morphing trailing edge regions of the A/C wing [22]

Target morphed shapes—to be reproduced in flight—were determined through
CFD-based optimization analyses. Aerodynamic enhancements are herein estimated
in terms of reduction of mission fuel or range increase, expected to amount to 3% or
more. Lift-to-drag (L/D) ratio is the referenced parameter to catch those perfor-
mance improvements, kept to its optimal value while weight and angle of attack
change. Morphing is enabled by a multi-finger architecture driven by load-bearing
actuators systems (hidden in Fig. 9.2), designed to work synchronously to provide
camber variation. After information gained from a widely distributed strain sensor
network, the control system drives actuators action. An adaptive, highly deformable
skin, (shown in Fig. 9.3), consisting of hard and soft segments, absorbs part of the
external loads and insures a smooth profile. While the soft skin segments release a
smooth, gapless transition between movable and fixed parts of the underlying
kinematic structure, the hard skin segments compensate deformations due to air

Fig. 9.2 The adaptive trailing edge (ATED) device [23]

9 Control System Design for a Morphing Wing Trailing Edge 179

Fig. 9.3 The morphing skin consists of hard and soft segments. Elastomer foam is used for soft
segments which are located above and under the rib hinges. Hard segments are alumium profiles
(grey). Hard and soft segments are covered with a thin elastomer layer [23]

pressure gradients. The soft segments are based on elastomer foam while the hard
segments consist of aluminum profiles. Both segments are covered by a thin layer to
ensure a smooth surface. The system keeps its structural properties while actuated,
then allowing the preservation of a specific target shape regardless the action of the
operational loads. The soft segments are located above and under the rib hinges
while the hard segments are connected to the rib structure. Static & dynamic
responses under external excitation, are considered.

9.3 Actuators Selection and Layout

Contrary to flexural joints-based compliant morphing mechanisms, the morphing
trailing edge device combines a rigid-body mechanical system with a compliant
adaptive skin. The adaptive ribs are segmented in three different parts connected by
standard revolute hinges, which ensure larger motion range and stiffness in all
directions except the revolution axis. The actuation kinematics is based on a
“direct-drive” actuation consisting of an arm (actuation beam) that is rigidly con-
nected to the B2 block shown in Fig. 9.4. This arm rotates the resulting
1-DOF-based mechanical system and transmits the actuation torque from the
actuator to the adaptive rib, as shown in Fig. 9.5.

Fig. 9.4 Morphing rib architecture: a Blocks and links, b Hinges [22]

180 I. Dimino et al.

Fig. 9.5 Details of the actuation system assembly

In order to minimize the actuation torque necessary to hold and move the ATE
device, different actuation kinematics were assessed during the design phase. The
size and shape of a suitable actuator were in turn estimated taking into account
weight and safety constraints. The torque needed to activate the device is generated
by an actuation force acting perpendicularly to this arm (if the friction can be
considered equal to zero) resulting from the contact between a carriage and a linear
guide. This force is generated by a rotational actuator via a crank rotating with the
actuator shaft. A simplified sketch of the mechanism is shown in Fig. 9.6.

The actuation arm rotates around the “virtual hinge” (the point around which the
second rib block rotates during the movement of the ATE device) and transmits the
actuation load (torque) from the actuator to the second rib block. The mechanical
advantage (MA) (ratio between the loading moment and the driving moment) of the
resulting mechanism and the relation between the actuator rotation angle and the rib
block rotation is:

MA = LOAD = Mrib#2 = F BL = BL
DRIVER Matt F BR BR

BR = R cosγ; BL = BR + L cosα

9 Control System Design for a Morphing Wing Trailing Edge 181

Fig. 9.6 The actuation system layout [24]

MA = BL = Lcos α + 1
BR Rcos γ

− 1
L α
Rsin γ = Lsin α → γ = sin
sin
R

As shown in Fig. 9.7, the mechanical advantage increases with the morphing angle
and this is much more evident as higher is the ratio between the arm length L
(distance between the second rib block virtual hinge) and the actuation crank radius
R. However, the higher the L/R ratio is, the higher the actuator rotation angle has to
be. This limits the palette of Commercial Off-The-Shelf (COTS) servo actuators
suitable for the actual application.

Fig. 9.7 Mechanical advantage and actuator shaft angles of the actuation system

182 I. Dimino et al.

Table 9.1 Servoactuators specifications

Parameter Assumption Units
Type of actuator Piezoelectric or electromechanical (stepped motor)
Max torque 6 (dynamic) or 15 (static) [Nm]
Displacement ±45 (pk to pk) [°]
Resolution 0.55 ÷ 1.1 (max actuator backlash) 0.1 − 0.05 (ATE [°]
device resolution)
Dimensions 100 × 50 × 200 (W × H × L) [mm]
Weight <1 [N]
Number of actuators 10 –
Actuator speed >10 [°/s]
Actuation signal max <10 [ms]
latency
Nominal voltage 12 or 24 [V]
Power consumption <100 [W]

Following these results, the main actuator specifications were defined, as listed
in Table 9.1.

A number of certified servoactuators were mapped on the market in order to find
the most suitable for the morphing trailing edge application. The Bental RSA-06
actuator demonstrated to match the expected performance. Its contained weight
(less than 0.5 kg), dimensions and available torque were in accordance with the
established specifications. As shown in Fig. 9.5, the actuation arm is fastened to the
mechanical box spar, which is rigidly connected to the second rib block.

Linear static analyses under limit load condition were carried out in corre-
spondence of locked actuator shafts. Limit load condition was simulated through
piecewise pressure distributions acting on upper (suction) and lower skin (com-
pression); pressure distributions were obtained by referring to the dynamic pressure
of 26000 N/m2 (dive speed, sea-level) and to Cp trends evaluated through inviscid
3D vortex lattice method. In order to be more conservative, no inertial alleviation
was taken in account.

Non-linear static analysis was then addressed to evaluate deformation and stress
up to ultimate load condition (defined as limit loads multiplied by the reserve factor
of 1.5).

9.4 Sensor System Layout

A sensor system was necessary to reconstruct the ATED shape during operation by
using the strain data retrieved from span-wise tip section and chord-wise middle
bays sections.

9 Control System Design for a Morphing Wing Trailing Edge 183

Fig. 9.8 Sensor architecture sketch

In order to reduce any kind of assembly chain interferences, two kind of sensor
systems were selected: shape beams and ribbon tapes, Fig. 9.8. The shape beam is a
sensorized cantilevered beam with integrated fiber optics (FO). The sliding beam is
guided to copy the skin profile as an independent structural system able to measure
camber variations. The guide itself is designed to compensate the air gap due to the
different thickness of the skin and allowing the skin profile to transfer its curvature
to the beam. Basically at least three point of interest are considered corresponding
to the rib hinges.

The ribbon tape is a very thin and flexible glass fiber reinforced patch. The
span-wise deformation is expected to be coherent with standard glass FO so that
ribbon tapes can be directly bonded in the inner side of the metallic tip cover and
then connected to form two measurement lines in order to drastically reduce the
number of channels. Structural reshape for a circular recess allow the patch-cord
cable to be safely hosted inside the tip without any interference with the skin
installation.

Two effects are envisaged for sensors aimed at monitoring the camber shape
variations of the ATE:

• ATE span-wise bending;
• ATE chord-wise bending and torsion.

Span-wise torsion is not directly detected but can be determined through the
relative bending of the different ribs. All the strain data detected by this sensors net,
are read and then stored by a data acquisition system that is to be used for the
morphing trailing edge contains the following components

• Deminsys Interrogator
• A laptop or equivalent for monitoring the signals.
• An optical switch for multiplexing signals.
• Power supply for the Deminsys system and the PC.

184 I. Dimino et al.

Table 9.2 Sensor system components Properties
Deminsys
System Characteristics 2
Interrogator System 20 kHz
Number of systems 3 pm
Chord-wise sensors Frequency rate 4
Span-wise sensors Resolution 8
Channels 600 gr
Max number of multiple readings 20 W
Weight Sensor beam
Power supply 40
Assembly 5
Total number of FBG Ribbon tape
Total channels 10
Assembly 2
Total number of FBG
Total channels

The max system sampling frequency being 20 kHz, the needed interrogation
time periods can be up to 9 min. As a quasi-static structural behaviour is investi-
gated, the sensors do not need a simultaneous recording, but can be alternatively
sampled by using an optical switch. Established the max number of FBG to be
deployed over the structure, the system configuration resulted as detailed in
Table 9.2.

9.5 Control Logic

The designed adaptive control system uses individual rotary actuators driven by
PWM signals to achieve prescribed target shapes enabling enhanced aircraft
aerodynamic performance. No roll, yaw, pitch control is considered. Both morphing
and load-carrying capabilities are introduced through the actuation mechanism
driven by rotary actuators. A multiple segmented trailing edge that forms a variable
camber continuous trailing edge surface is hence obtained. Servo-rotary actuators
with both feed-forward and feed-back control logics are considered to control the
system mechanical components. In comparison with the currently-used discontin-
uous solutions such as flaps which are typically actuated independently, a smooth
morphing trailing edge ensures a further drag reduction in addition to the advantage
due to variable camber.

As shown in Fig. 9.9, the process starts from a given set of desired wing shapes
generated with the objective of minimizing drag while maintaining optimal lift
coefficient. They result from an accurate aerodynamic analysis involving a number
of flight conditions and lead to optimized shapes relying on complex numerical

9 Control System Design for a Morphing Wing Trailing Edge 185

START
Start control

Actuation

Sensing

ATE shape reconstruction Strain DataBase
module

Actual Unknown static and
ATE System State, dynamic disturbances

S Optimal
ATE System State,
+-
Sopt
ATE Control System Shape Error Error
Estimator E= S-Sopt Optimal
ATE Shape
no Is the Shape Error for actual condition

lower than the [W(t), V(t), rho(t), ...]
threshold value?

yes

Optimal ATE
configuration

no
Is the mission
concluded?
yes
END

Fig. 9.9 Flowchart for shape control of morphing aircraft wings

routines involving both theory and interpolation methods. First, these optimal ATE
shapes are stored in a database. Then, the structural response to the actuation loads
is numerically predicted by FEM simulations.

186 I. Dimino et al.

Fig. 9.10 Adaptive trailing edge control system platform [25]

The architecture developed for the control of the morphing wing trailing edge
model is illustrated in Fig. 9.10. The optimal airfoils are prescribed at a single flow
condition (Mach = 0.75 in cruise) and for different combinations of angle of attack.
For such conditions, theoretical smooth trailing edge shapes are generated by using
polynomial functions and then aerodynamically studied to calculate the optimal
performance. A continuous wing camber variation corresponding to a rigid TE
deflection from −5° to 5° is here considered. The optimized airfoil database (blue
box) contains information about the stain vector corresponding to the target TE
shapes on specific points of interest. Off-line aerodynamic simulations may be
required to estimate the impact of the difference between the actual and the desired
shape on the achieved aerodynamic performance and reduced fuel consumption.
However, this target remains out of the scope of the controller whose performance
will be estimated only by structural parameters describing the capability of
achieving the target shape. The shape reconstruction module (red box) includes the
software and hardware needs for measuring strain data through FBG sensors. Such
data will be on-line processed by the controller (green box) to calculate the error
signal and hence the control action driving the actuators. Moreover, the actual
angular position reached by the actuator will be provided by a rotary encoder and
compared to the expected rotation value. The controller compares the information
received from sensors with the information stored in a database in the computer
memory.

9 Control System Design for a Morphing Wing Trailing Edge 187

9.6 Results

The controller was real-time implemented in a Digital Signal Processing
(DSP) Board. Two architectures were considered: open loop and closed loop. In the
former, the controller executed the driving command on the basis of the off-line
predictions of the actuator shaft rotations needed to reach specific ATED morphing
angles. In this case, the control strategy is defined open loop (feed-forward). As a
result, the controller gives no feedback on the achieved trailing edge shape. In the
latter, the controller monitored the actual ATED shape information either given by
the FBG-based sensor system distributed over the structure or the actuator rotation
levels given by the servo so that the controller actions could be real-time adjusted.
Then, the control strategy is defined as closed loop (feedback control). Both open
and closed loop control architectures were developed and tested.

In both experimental campaigns, the actuation mechanism was driven to enforce
the structure to the desired shape (±5° of morphing). The experimental results were
compared with the CAD model expectations, as sketched in Fig. 9.11. The actual
displacements of the morphed ATED structure were firstly measured and then
compared with the numerical predictions. The measurement points are shown in
Fig. 9.12. The error was evaluated by the sum of square errors between the
experimental and simulated data. The position of the ATED device in terms of
morphing angle was obtained by minimizing this error function. The results of the
closed loop control obtained with external loading applied are reported in Fig. 9.13.
The range of ATED morphing, assessed by the minimum of the error function, was
estimated in the range [−4.91°, 5.21°]. The deviations with the respect to the CAD
shape are given in Figs. 9.14, 9.15 and 9.16 for the baseline and the full morphing
deployment (+5°, −5°) respectively. Control system performance, such as actuation
time, slew rate, resolution and stability were also in this way validated.

Fig. 9.11 Baseline and morphed airfoils

188 I. Dimino et al.

Fig. 9.12 Location of measurement points used for shape reconstruction

Fig. 9.13 Comparison between actual and expected shapes

Shape recovery capability of the feed-back control architecture was evaluated
along with controller stability and robustness. Such tests were performed by
impacting the trailing edge tip with an hammer after commanding the morphing
deployment, Fig. 9.17. Strain map distribution sensed by the sensor system was
also off-line processed in order to reconstruct ATED shape in morphing conditions.
The differences between the actual and target shape was identified by the respective
correlations with the strain levels and found satisfactory.

9 Control System Design for a Morphing Wing Trailing Edge 189

-3 Experimental measurements and comparison with CAD data

2.5 x 10 Baseline
2

1.5

distance [m] 1

0.5

0

-0.5

-1

-1.5

-2
100 101 102 103 104 105 106 107 108 109 110 111 112 113 114
Measurement Points

Fig. 9.14 Shape deviation in baseline configuration

3 x 10-3 Experimental measurement and comparison with CAD data
2.5
Morphed down +5°

2

1.5

Distance [m] 1

0.5

0

-0.5

-1

-1.5
100 101 102 103 104 105 106 107 108 109 110 111 112 113 114
Measurement Points

Fig. 9.15 Shape deviation in morphed down configuration

190 I. Dimino et al.

1 x 10-3 Experimental measurements and comparison with CAD data
0.5
Morped Up +5°

0

-0.5

Distance [m] -1

-1.5

-2

-2.5

-3

-3.5

-4 100 101 102 103 104 105 106 107 109 110 111 112 113 114

Measurement Points

Fig. 9.16 Shape deviation in morphed up configuration

Fig. 9.17 Controller
robustness tests through
hammer excitation

9 Control System Design for a Morphing Wing Trailing Edge 191

9.7 Conclusions and Future Developments

The herein presented work deals with the development and implementation of a
morphing system made of integrated actuators and sensors, driven by a control
architecture. An innovative smart configuration is achieved by the properly
assembly of standard components. In this way, many of the complications con-
nected to the realization of a novel device are skipped, dealing with reliable, already
tested components. The adaptive trailing edge changes the global wing curvature in
order to compensate the weight variation of the aircraft during cruise, as a conse-
quence of the fuel consumption. In the same way, it can adapt the same wing
camber as a function of the actual take-off weight, depending on the hosted pas-
sengers and their luggage (or the boarded goods—cargo).

Nevertheless, some open issues still remain on the developed architecture,
installation aspects and implementation strategy. The specifications should be
improved by considering a complete aircraft, so to compute the overall effect of the
trailing edge device on the overall aircraft aerodynamic polar. The layout of the
device shall also derive from the global reference geometry, so to find the best
arrangement along the wing span and its chord. Further complications are also
expected, following the implementation of a complex kinematic system on a
movable surface such as a flap. On the other hand, the available room should be far
more adequate to host the innovative components with respect to the wing tip zone.
Indeed, studies to verify the possibility of inserting such systems in the aileron are
currently performed by this same team and other researchers.

The actuator system design shall be integrated within the structural design, so to
come to a unique active structural, load-bearing system, instead of merging to
components, separately developed. Sensor system is constructed on the basis of an
extended network, made of fiber optic FBGs. This reduces the cables number
drastically. However, for a real implementation, it comes up that this number
remains high. In order to further improve this aspect, wireless systems should be
addressed, irrespective of the nature of the sensor material or nature. Of course,
such an architecture leads to further complications, mainly associated with the inner
architecture (need of defining a suitable path of signal transmission), to the sensors
feeding and the compatibility with the other, existing aircraft systems. Control
system capability should move from adaptive feedforward architectures, based on
pre-built strain maps, to real-time feedback systems, sensible to the selected
objective parameter; therefore included into the overall aircraft avionics.

Acknowledgements The research leading to these results has gratefully received funding from
the European Union’s Seventh Framework Programme for research, technological development
and demonstration under grant agreement no 284562.

192 I. Dimino et al.

References

1. Botez RM, Molaret P, Laurendeau E (2007) Laminar flow control on a research wing project
presentation covering three year period. In: Canadian aeronautics and space institute annual
general meeting, Montreal, Canada

2. Scarselli G, Marulo F, Paonessa A (2010) Sensitivity investigation of aircraft engine noise to
operational parameters. In: Proceedings of the 16th AIAA/CEAS aeroacoustics conference
(31st AIAA aeroacoustics conference), Stockholm (Sweden)

3. Barbarino S, Bilgen O, Ajaj RM, Friswell MI, Inman D (2011) A review of morphing aircraft.
J Intel Mater Syst Struct 22:823–877

4. Chopra I (2002) Review of state of art of smart structures and integrated systems. AIAA J 40
(11):2145–2187

5. Vasista S, Tong L, Wong KC (2012) Realization of morphing wings: a multidisciplinary
challenge. J Aircraft 49:11–28

6. Grigorie LT, Botez RM, Popov AV, Mamou M, Mébarki Y (2012) A hybrid fuzzy logic
proportional-integral-derivative and conventional on-off controller for morphing wing
actuation using shape memory alloy, Part 1: morphing system mechanisms and controller
architecture design. Aeronaut J 40(1179):433–449

7. Grigorie LT, Botez RM, Popov AV, Mamou M, Mébarki Y (2012) A hybrid fuzzy logic
proportional-integral-derivative and conventional on-off controller for morphing wing
actuation using shape memory alloy, Part 2: controller implementation and validation.
Aeronaut J 116(1179):451–465

8. Spillman J (1992) The use of variable camber to reduce drag, weight and costs of transport
aircraft. Aeronaut J 96:1–8

9. Wildschek A, Grünewald M, Maier R, Steigenberger J, Judas M, Deligiannidis N, Aversa N
(2008) Multi-functional morphing trailing edge device for control of all-composite, all-electric
flying wing aircraft. In: Proceedings of the 26th congress of international council of the
aeronautical science (ICAS), Anchorage (Alaska, US)

10. Ameduri S, Brindisi A, Tiseo B, Concilio A, Pecora R (2012) Optimization and integration of
shape memory alloy (SMA)-based elastic actuators within a morphing flap architecture. J Intel
Mater Syst Struct 23(4):381–396

11. Blondeau J, Pines D (2004) Pneumatic morphing aspect ratio wing. In: Proceedings of the
45th AIAA/ASME/ASCE/AHS/ASC Structures, structural dynamics and materials confer-
ence, Palm Springs, California, US

12. Bye DR, McClure PD (2007) Design of a morphing vehicle. In: Proceedings of the 48th
AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference,
Honolulu (Hawaii, US)

13. McGowan AR, Horta LG, Harrison JS, Raney DL (1999) Research activities within NASA’s
morphing program. In: Proceedings of the RTO AVT specialists’ meeting on structural
aspects of flexible aircraft control, Ottawa (Canada)

14. Pecora R, Amoroso F, Lecce L (2012) Effectiveness of wing twist morphing in roll control.
J Aircraft 49(6):1666–1674

15. Popov AV, Grigorie TL, Botez RM, Mébarki Y, Mamou M (2010) Modelling and testing of a
morphing wing in open-loop architecture. J Aircraft 47(3):917–923

16. Pecora R, Barbarino S, Concilio A, Lecce L, Russo S (2011) Design and functional test of a
morphing high-lift device for a regional aircraft. J Intel Mater Syst Struct 22:1005–1023

17. Monner HP, Sachau D, Brietbach E (1999) Design aspects of the elastic trailing edge for an
adaptive wing. In: Proceedings of the RTO AVT specialists’ meeting on structural aspects of
flexible aircraft control, Ottawa (Canada)

18. Barbarino S, Pecora R, Lecce L, Concilio A, Ameduri S, De Rosa L (2011) Airfoil structural
morphing based on S.M.A. actuator series: numerical and experimental studies. J Intel Mater
Syst Struct 22:987–1003

9 Control System Design for a Morphing Wing Trailing Edge 193

19. Ahrend H, Heyland D, Martin W (1997) Das Leitkonzept ‘Adaotiver Flugel’ (ADIF).
DGLR-Jahrestagung, DGLR-JT97-147, Munchen

20. Monner HP, Sachau D, Breitbach E (1999) Design aspects of the elastic trailing edge for an
adaptive wing. Presented at RTO AVT specialists’ meeting on structural aspects of flexible
aircraft control, held in Ottawa, Canada, 18–20 October 1999, and Published in RTO MP-36

21. Dimino I, Concilio A, Pecora R (2016) Safety and reliability aspects of an adaptive trailing
edge device (ATED). In: 24th AIAA/AHS adaptive structures conference, AIAA SciTech,
4–8 Jan 2016

22. Pecora R, Amoroso F, Magnifico M, Dimino I, Concilio A (2016) KRISTINA: kinematic rib
based structural system for innovative adaptive trailing edge. SPIE Smart Structures/NDE,
Las Vegas, Nevada (USA)

23. Schorsch O, Lühring A, Nagel C, Pecora R, Dimino I (2015) Polymer based morphing skin
for adaptive wings. In: Proceedings of the 7th ECCOMAS conference on smart structures and
materials – SMART2015, 3–6 June 2015, Azores

24. Dimino I, Flauto D, Diodati G, Concilio A, Pecora R (2014) Actuation system design for a
morphing wing trailing edge. Recent Patents Mech Eng 7:138–148

25. Dimino I, Flauto D, Diodati G Schueller M, Gratias A (2013) Adaptive shape control
architecture for morphing wings. In: 6th conference on smart structure and materials,
ECCOMAS 2013, Torino, 24–26 Jun 2013

Chapter 10

Towards the Industrial
Application of Morphing Aircraft
Wings—Development of the Actuation
Kinematics of a Droop Nose

Stefan Storm and Johannes Kirn

Abstract This paper describes the design process of a simple actuation system
capable of deforming an extensive flexible skin of a leading edge droop nose
designated for laminar wings. Special note has to be taken of a least complex
actuation system which has to be smoothly modified between the shape for high-lift
and cruise flight. To meet the joint aviation requirements a separation of actuation
and skin is mandatory. The design of the kinematics is therefore a key element for
the development of a droop nose. The SARISTU project (Smart Intelligent Aircraft
Structures‚ EU-FP7 project-consortium‚ [1]) utilizes a planform with a wing span of
16 m from which a 4 m outboard segment was selected for detailed studies. To
deform the flexible skin in this region seven kinematic stations with different-sized
lever kinematics are required. The objective is to develop an interconnected
mechanical kinematic system actuated with a single actuator, taking into account
the need of simultaneous and uniform deformation of the skin. For optimization
purposes the kinematic system is simplified to a reduced subsystem that consists of
a single load introduction point linked by a crank mechanism with the actuation
system. Its interconnection is achieved by equal rotational angle of each main lever.
The possible kinematic points lie along a straight line, which is exclusively
depending on the selected rotational angle of the main lever and is named therefore
isogonic line. A geometrical methodology to generate the isogonic line is described
for the case that the movement of all kinematic points are in-plane, and also for the
general case that rotational movement and linked trajectories are arbitrarily arran-
ged in a three-dimensional space. This newly developed methodology enables not
only to find a very precise kinematic solution for interconnected crank mechanisms
in a convenient way, but shows the impact of parameter variation which are coming
along with inaccuracy of production. A full-scale demonstrator of the enhanced

S. Storm (✉) ⋅ J. Kirn 195

Airbus Group Innovations (AGI), Munich, Germany
e-mail: [email protected]

J. Kirn
e-mail: [email protected]

© Springer International Publishing Switzerland 2017
A.L. Araujo and C.A. Mota Soares (eds.), Smart Structures and Materials,
Computational Methods in Applied Sciences 43,
DOI 10.1007/978-3-319-44507-6_10

196 S. Storm and J. Kirn

adaptive droop nose was designed with this geometrical construction method and its
functionality verified in a wind tunnel under realistic flow conditions and during a
life-cycle ground test.

⋅ ⋅ ⋅ ⋅Keywords Morphing Adaptive aircraft System design Kinematics
⋅ ⋅Actuation systems Laminar wing Optimization tool

10.1 Introduction

The idea of morphing wings goes all the way back to the Wright brothers who used
wing warping to control their flying machines at the end of 19th century [2]. Since
then many experimental and numerical studies [3] showed the aerodynamic benefit
of morphing wings in various application scenarios but until now, over one century
after its first application, morphing is still not a state-of-the-art technology in civil
transport aircraft. Some necessary steps towards the industrialization of morphing
have been taken in the framework of the SARISTU project.

The application case is a seamless and gapless Enhanced Adaptive Droop Nose
(EADN) for a single aisle transport aircraft. The droop nose enables laminar wings
with up to 6% drag reduction and thus leads to positive implications on fuel con-
sumption as well as required take-off fuel load [4, 5]. The selected droop nose
concept consists of a flexible skin being actuated by a composition of kinematics
and actuators [6, 7].

The actuation of the leading edge poses a huge challenge for the internal
kinematics as it has to arrange with other functionalities like bird strike protection,
de-icing, surface and lightning-strike protection. The design of the kinematics is
therefore a key element for the development of a droop nose. In this context this
paper focuses on a geometrically-based numerical optimization as a design tool.

10.2 Development of the Actuation Kinematics of a Droop
Nose

Work on an adaptive droop-nose kinematic actuation system started in the previous
publicly funded projects “Innovative High Lift Devices” (InHiD, LuFo IV) and
“Smart High Lift Devices for Next Generation Wings” (SADE, EU-FP7) where the
basic feasibility of such a system was demonstrated. The work was conceptually
based on a patent by Dornier [8]. In the project SADE studies with different kind of
actuation mechanism for smart leading edges were performed such as eccentric
beam mechanism, horn concept, fluidic actuator concept, kinematic chain. Elec-
tromechanical or hydraulic devices are feasible actuator solutions, whereas the
utilization of piezoelectric or magneto-resistive material integrated into the structure

10 Towards the Industrial Application of Morphing Aircraft … 197

of the flexible leading edge was ruled out due to unsolved manufacturing, main-
tenance issues and power requirement [9].

As opposed to SADE where the enhanced adaptive droop nose was simply an
extruded 2D wing cross-section, within the SARISTU project it represents a 3D
free-formed surface, which has to be smoothly modified between the shape for
high-lift and cruise flight [10, 11]. The objective is to develop a mechanical
kinematic system with minimal deviation from the optimal kinematical path in
consideration of limited available design space, aerodynamic loads and manufac-
turing constrains. Taking into account the need of simultaneous and uniform
deformation of all differently sized kinematic stations implies great effort in the
design phase [12].

The loads introduced by the skin are distributed at discrete support points along
the span and in chordwise direction of the wing. The large deflection versus little
space allocation ratio removes the possibility for directly reaching the support
points with the actuator which has the consequence that a new kinematic
drive-chain is utilized, as depicted in Fig. 10.1. This new kinematic drive-chain
translates the linear motion of the main drive actuator into a synchronous, rotatory
movement of a main lever. As the rotatory movement has to be synchronous for

Fig. 10.1 Cross-section of an enhanced adaptive droop nose with an integrated kinematic system
for a morphing wing at cruise and (graying out) at drooped position