Research Collection
Doctoral Thesis
Closed-Loop Control of Spanwise Lift Distribution for MorphingWing Applications
Author(s): Quack, Manfred
Publication Date: 2014
Permanent Link: https://doi.org/10.3929/ethz-a-010400041
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Dissertation ETH No. 22350
Closed-Loop Control of Spanwise Lift Distribution for
Morphing Wing Applications
A thesis submitted to attain the degree of
Doctor of Sciences of ETH Zurich
(Dr. sc. ETH Zurich)
presented by
Manfred Quack
MSc ME ETH Zurich, Switzerland
born on 11.11.1982
citizen of Fällanden (Zurich)
citizen of Germany
accepted on the recommendation of
Prof. Dr. Manfred Morari (examiner)
Dr. Rafael Palacios (co-examiner)
2014
© 2014 Quack ManfredAll Rights Reserved
ISBN 978-3-906031-93-4
to my wife, Yukiko Ishigaki Quack,
for always supporting me.
Acknowledgments
First of all, I want to thank Prof. Dr. Manfred Morari, for giving me the opportunity to
work on this exciting and highly interdisciplinary topic. At the Automatic Control Lab (IfA),
Prof. Morari provides a research environment which allows to address all questions in a very
open-minded way – a research environment where I never felt constrained and for which I am
extremely grateful.
I want to thank all members of the CHIRP project, Prof. Dr. Ermanni, Prof. Dr. Jenny, Prof.
Dr. Mazza, Vitaly Dmitriev, Francesco Previtali and Giulio Molinari. The close collaboration
with all members and in particular with Giulio on topics like fluid-structure interaction, multi-
disciplinary optimization, structural integration and control of macro fiber composite (MFC)
piezo actuators enabled the interdisciplinary approach, for which the project has actually re-
ceived its funding. Dr. Andres Arrieta has brought an important and appreciated turning-point
to the project, when he introduced the potential of MFC piezo actuators to the group. Dr.
Sébastién Mariéthoz gave much valuable advice during discussions on the design of high voltage
supplies and Oliver Schulthess helped me with designing my first decent PCB.
The excellent work contributed as part of semester and master thesis projects by students I
supervised, including Timon Achtnich, Lukas Bühler, Flavio Gohl and Philippe Petit helped
to address many practical aspects of this project. I want to thank the RC-pilots Flavio Gohl
and Ernst Arnold, for their valuable time and great piloting skills, which allowed to use the
test-platform for many flights and to collect much experimental data.
I am very thankful to Dr. Rafael Palacios for being my co-examiner and for his interest in my
research.
I want to thank my current office mates at IfA, Claudia Fischer, Dr. Henrik Hesse and my
former office mates, Dr. Joe Warrington (thanks for the tea), Dr. Alexander Fuchs and Dr.
Jack DiGiovanna for always providing a good atmosphere in the office, the Kite-folks Aldo
Zgraggen, Tony Wood, Dr. Lorenzo Fagiano for the many interesting discussions and meetings
related to research and other things, Robert Nguyen for all the good cakes, Dr. Christian
Conte, Andreas Hempel, Dr. Tyler Summers for his musical support to IfA, Dr. Stefan Huck
and Tobias Baltensperger for joining me for a sandwich once in a while and all the other many
great members at IfA including the administrative staff, which I have not listed yet explicitly.
Thanks also to all the former and current members and visitors from the structural lab, Dr.
Wolfram Raither (thanks for the Espresso), Dr. Tommaso Delpero, Dr. Luigi di Lillio, Dr.
Andreas Bergamini, Dr. Joanna Wong, Dr. Shinya Honda, Simon Steiner, Bryan Louis, Mario
Danzi, Davi Montenegro and all the others not listed explicitly.
Thanks to Dr. Urban Mäder and all other instructors for teaching me to fly and all members
at the glider club (SG Zürich), for making flying as part of a glider club possible and Peter
Nyffeler for technical discussions on cross-country soaring.
i
Having a great family around you that not only supports you in all the hard times, but also
vividly discusses scientific and other questions of all kinds, had probably the most formative
impact on me and for this I am extremely grateful to my mother Dr. Roswitha Quack, my
father Prof. Dr. Dr. h.c. Martin Quack and my brothers Dr. Niels Quack and Dr. Till Quack.
I would not have had the endurance required to finish a PhD and maybe not even started the
research presented here, without the support from my beloved wife, Yukiko Ishigaki Quack.
Zurich, October 2014
ii
Contents
Contents iii
Abstract vi
Zusammenfassung viii
Dissertation Structure x
Summary of Contributions xii
List of Figures xv
List of Tables xvi
Nomenclature xvii
List of Acronyms xxiii
1 Introduction 1
1.1 Background of the Subject and Literature Review . . . . . . . . . . . . . . . . 1
1.2 Research Needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 A Showcase Mission for Morphing Wings 11
2.1 Glider Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 A Thermal Soaring Glider . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Speed-to-Fly in Straight Flight . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Turning Flight & Minimal Sink Rate . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Tailless Glider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
iii
I Adaptive Lift Distribution With Conventional Actuators 25
3 Showcase Model: Six-Flapped Flying Wing 27
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.1 Considered Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 Flight Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.2 Aerodynamic Forces and Moments . . . . . . . . . . . . . . . . . . . 34
3.2.3 Dynamic Lookup-Table Based on 3D Panel-Code Data . . . . . . . . . 36
3.2.4 Extended Lifting Line: Standard Formulation . . . . . . . . . . . . . . 38
3.2.5 Extended Lifting Line: Parameterization & Coupling . . . . . . . . . . 40
3.3 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3.1 Optimal Flap Deflections for Gliding and Turning Flight . . . . . . . . 47
3.4 Development of a Test-Platform . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.1 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.2 Test-Platform Specifications . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.3 Control Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.5 Test Flight Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.5.1 Attitude Controller Performance . . . . . . . . . . . . . . . . . . . . . 63
3.5.2 Airspeed Controller Performance . . . . . . . . . . . . . . . . . . . . 63
3.5.3 Performance Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.5.4 Flight Tests Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.6 Parameter Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.6.1 Collocation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.6.2 Gradient-Free Single Shooting . . . . . . . . . . . . . . . . . . . . . 72
3.6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
II Adaptive Lift Distribution with Smart Actuators 79
4 Adaptive Span-Wise Lift Distribution on a Morphing Wing with Smart Actu-
ators 81
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2.1 2D Airfoil Parameterization . . . . . . . . . . . . . . . . . . . . . . . 82
4.2.2 Fluid-Structure Interaction in 2D . . . . . . . . . . . . . . . . . . . . 84
4.3 Design Optimization (2D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3.1 Design Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3.2 Airfoil Requirements for Morphing: Morphability . . . . . . . . . . . . 86
4.3.3 Multidisciplinary Concurrent Optimization . . . . . . . . . . . . . . . . 87
4.3.4 Structural Design Concept Example . . . . . . . . . . . . . . . . . . . 89
iv
4.3.5 Results and Comparison . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.3.6 Conclusions on the 2D Optimization . . . . . . . . . . . . . . . . . . 101
5 Macro Fiber Composite Piezo Actuators 103
5.1 Closed-Loop Control of MFC-Piezo-Actuated Wing . . . . . . . . . . . . . . . 103
5.1.1 Wind-Tunnel Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.2 High Voltage Driver for Multiple MFC-piezos . . . . . . . . . . . . . . . . . . 111
6 Conclusions 115
6.1 Conclusions on Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.2 Conclusions on Part II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.3 Overall Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7 Ongoing & Future Work 121
7.1 Ongoing Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.1.1 Related to Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.1.2 Related to Part II . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8 Outlook 125
Bibliography 129
Publication List 136
Curriculum Vitae 137
v
Abstract
The work presented here, is part of the SmartAirfoil Project, a collaborative highly interdis-
ciplinary research project (CHIRP) at ETH Zurich with the goal to enable shape adaptation
techniques for aircraft airfoils and to investigate the potential of this technology in combination
with wing morphing. For the formulation of requirements on morphing airfoils, a tailless glider
in cross-country flight with a minimal time objective is considered as a showcase mission. This
mission is well suited to demonstrate the potential of wing morphing, since such a tailless glider
relies on the adaptation of span-wise lift distribution to generate control moments and needs
to operate efficiently at a wide range of operating points to achieve good overall performance.
Effective wing morphing requires careful system integration and adequate control strategies.
The considered morphing wing concept provides a high number of actuators and a control
strategy to make optimal use of this redundancy at a wide range of operating conditions is
necessary. A 3.3m-span six-flapped tailless RC model glider with conventional servo-actuators
is considered in the first part of this thesis as an approximation to a morphing wing and has
been used as a basis for a test-platform. Flight tests demonstrated the feasibility of sensor
integration and closed-loop control of the span-wise lift distribution providing stable straight
and turning flight at different airspeeds. Stable flight allowed data acquisition over extended
flight periods and hence acquired data can be used for averaged performance data as well as
for parameter identification.
A parametric numerical model explaining the effect of changes in span-wise lift distribution on
the flight trajectory has been developed. The model is in differential algebraic equation (DAE)
formulation and couples an extended lifting line method to the flight dynamic equations. Due
to its low complexity and the parametric description, which allows to treat sectional aerody-
namic coefficients as uncertain parameters, it is well suited for parameter identification, on-line
estimation and model-based control methods.
The second part of this thesis addresses design and control methods, necessary to enable
wing morphing based on macro fiber composite (MFC) piezo actuators. First, a novel multi-
disciplinary design optimization methodology is presented, which not only employs a 2D aero-
structural simulation method, but is also able to exploit aero-structural coupling, since it
concurrently optimizes structural and aerodynamic parameters. The method has been applied
to a morphing concept example using dielectric elastomer actuators and provides significantly
better results in comparison to the commonly applied sequential optimization approach.
Closed-loop control of multiple MFC-piezo actuators is presented and demonstrated on a mor-
phing wing prototype featuring multiple MFC-piezo actuators in bi-morph configuration. A
simple feedback control law is used in combination with flexural strain gauge sensor signals to
overcome the hysteresis and creep behavior, which is typically found in MFC piezo-actuators.
Robustness of the control method to external disturbance has been experimentally validated in
Wind Tunnel tests.
A light-weight, small-size integrated electronic circuit design suitable to drive independently
vi
multiple active sections using MFC-piezos in bi-morph configuration in closed-loop control is
presented. In combination with compact off-the-shelf high voltage power supplies, a rise time
of less than 200 ms for the trailing edge deflection is expected. Furthermore, the solution is
designed to scale up to at least six independent active sections, which will allow to apply the
control methods from the six-flapped flying wing platform to a new prototype employing the
same number of active sections.
With this, the thesis presents all the building blocks necessary to enable the closed-loop control
of span-wise lift distribution on a morphing tailless glider at UAV scale.
vii
Zusammenfassung
Diese Arbeit ist Teil des “SmartAirfoil” Projektes, einem interdisziplinären Forschungsprojekt
(Collaborative Highly Interdisciplinary Research Project – CHIRP) der ETH Zürich, mit dem
Ziel der Realisierung von Formanpassung von Tragflächenprofilen und der Erforschung des Po-
tentials dieser Technologie für den Einsatz in adaptiven Flügeln. Um präzise Anforderungen
an solche form-adaptive Tragflächenprofile zu formulieren, wird das Beispiel eines Nurflüglers
im Streckensegelflug betrachtet, wobei angenommen wird, dass der Pilot zeit-minimal fliegt.
Diese Flugaufgabe bietet aus zwei Hauptgründen den idealen Hintergrund um das Potential
von adaptiven Flügelstrukturen zu erklären. Erstens muss ein Nurflügler zur Erzeugung von
Steuermomenten die Auftriebsverteilung entlang der Spannweite anpassen und zweitens muss
der Flieger für ein weites Spektrum von Betriebspunkten gute Flugleistungen aufweisen um
insgesamt sein Ziel zu erreichen.
Die effektive Anwendung von adaptiven Flügeln erfordert eine sorgfältige Integration aller Sy-
stemkomponenten, sowie die Verwendung von adäquaten Regelungsstrategien. Das in dieser
Arbeit verwendete Konzept für einen adaptiven Flügel, führt zu einer hohen Anzahl von un-
abhängigen Aktuatoren und erfordert daher einen Regelungsansatz, der die optimale Ausnut-
zung dieser redundanten Aktuatoren über einen weiten Bereich von Betriebspunkten ermöglicht.
Im ersten Teil dieser Arbeit wurde in erster Annäherung an einen kontinuierlich form-adaptiven
Flügel, ein ferngesteuertes Nurflüglermodell mit einem Sechs-Klappen-Mechanismus als Ver-
suchsträger verwendet. Die Klappen-Ansteuerung basiert hierbei zunächst auf konventionellen
Servo-aktuatoren. Mit Hilfe von Flugversuchen konnte die Machbarkeit der Sytem-Integration
aller notwendingen Sensoren und die Regelung der Auftriebsverteilung mit Zustandsrückführung
im geschlossenen Regelkreis dargelegt werden. Die Verwendung dieser Regelstrukturen er-
laubten einen stabilen teil-automatisierten Flug, was Messungen über längere Flugperioden
ermöglicht und durch die Mittelung der Daten über grössere Zeitdauer Rückschlüsse auf die
Flugleistungen erlaubt. Die gewonnen Daten können ausserdem für die Schätzung von unsi-
cheren oder unbekannten Parametern verwendet werden.
Ein parametrisches numerisches Modell in Form einer differential-algebraischen Gleichung wurde
unter Berücksichtigung der Kopplung zwischen flugmechanischen und aerodynamischen Glei-
chungen hergeleitet. Aufgrund seiner Einfachheit und dank der parametrischen Formulierung
ist dieses Modell gut für die Lösung von Schätzungsproblemen in Echtzeit, zur Parameteriden-
tifikation und für modell-basierte Zustandsregelung geeignet.
Der zweite Teil dieser Arbeit behandelt Entwurfs- und Regelungs-Methoden, die für die Umset-
zung von form-adaptiven Flügelstrukturen mit Hilfe von Macro Fiber Composite (MFC)-Piezo-
Aktuatoren benötigt werden. Zunächst wird eine neue multi-disziplinäre Design-Optimierungs-
Methode vorgestellt, welche nicht nur zwei-dimensionale Fluid-Struktur Interaktionsmodelle
verwendet, sondern welche auch gezielt diese Kopplungseffekte auszunutzen vermag. Dies wird
durch die simultane Optimierung struktureller und aerodynamischer Parameter erreicht. Im
Vergleich mit der üblicherweise sequentiellen Vorgehensweise zeigt die Methode für ein Beispiel
viii
eines Konzeptes zur Form-Adaption basierend auf dielektrischen Elastomeren zur Aktuation,
bedeutend bessere Resultate.
Die Regelung mehrerer MFC-Piezo-Aktuatoren im geschlossenen Regelkreis wird anhand ei-
nes Prototypen vorgeführt. Dieser Prototyp verwendete mehrere solcher Aktuatoren in einer
paarweisen Konfiguration in der sich der Effekt bei gegenseitiger Ansteuerung verstärkt. Eine
einfache Regelstruktur welche die Messwerte eines Dehnmessstreifens in einem geschlosse-
nen Regelkreis verwendet, erlaubt es die Probleme von Hysterese und Kriechverhalten welche
typischerweise bei MFC-Piezo-Aktuatoren auftreten, zu bewältigen. Die Robustheit dieser Me-
thode gegen äussere Störeinflüsse wurde in Windkanal-versuchen vorgeführt. Ein Entwurf eines
leichten, kleinen integrierten Schaltkreises welcher die Ansteuerung mehrerer form-adaptiver
Segmente basierend auf MFC-Piezo-Aktuatoren erlaubt, wird erläutert. In Kombination mit
leichten, kompakten Hochspannungsmodulen, wie sie auf dem Markt erhätlich sind, wird eine
Anstiegszeit von weniger als 200 ms erwartet. Desweiteren ist dieser Lösungsansatz bis zu min-
destens sechs unabhängigen Segmenten skalierbar, wodurch die Erfahrungen mit dem Sechs-
Klappen-Mechanismus auf einen neuen Prototypen mit der gleichen Anzahl von form-adaptiven
Segmenten übertragbar sind. Damit präsentiert diese Arbeit alle notwendigen Grundsteine für
die Regelung der Auftriebsverteilung entlang der Spannweite auf einem form-adaptiven Nur-
flügler im Grössenmasstab unbemannter Flugzeuge.
ix
Dissertation Structure
Chapter 1 is an introduction to the subject of wing morphing and provides an overview over
the relevant literature. Research needs in this field are identified and explained in section 1.2
of this chapter, and the approach taken to address these research needs, are described in 1.3.
Chapter 2 introduces a showcase mission for morphing, namely that of a tailless glider in cross-
country soaring with a minimal time objective. Based on existing work, the optimal speed to fly
and optimal bank angle for minimal sink rate in turning flight are explained. From the optimal
solution for these problems, it is shown that such a glider has to operate at a wide range of
operating points in terms of lift coefficient CL and that therefore wing morphing can increase
the performance in such a setting.
After this introductory part, the thesis is divided into two parts: Part I focuses on the problem of
feed-back control for the span-wise lift-distribution, based on conventional actuators, whereas
Part II focuses on the design and control problems which need to be solved to enable span-wise
lift adaptation using smart actuators.
Part I, Chapter 3, introduces a showcase model for span-wise morphing based on conventional
actuators. Section 3.1.1 displays the geometry of the considered model, which is a tailless six-
flapped RC-glider. In section 3.2 the modeling of such a six-flapped flying glider is explained
from a top-down approach, in the sense that first the relevant equations for a six degree of
freedom (6-dof) model of the flight dynamics are considered in section 3.2.1, before the problem
of computing the aerodynamic forces and moments appearing in these equations is addressed
in section 3.2.2.
Section 3.2.5, presents a parametric model in differential algebraic equation (DAE) formulation,
which couples an aerodynamic model based on the extend Lifting Line Theory to the 6-dof
model of the flight dynamic, and yet is simple enough for the use in control and estimation
methods.
In section 3.4, the development of a test-platform for controller evaluation, model validation
and performance comparisons is presented. Details of the control scheme used on this platform
are presented in section 3.4.3 and flight test results with this platform are presented in section
3.5.
Data acquired during these test flights are used for identification of uncertain model parame-
ters, described in section 3.6. Flight trajectories predicted with the estimated parameters are
compared to flight test data in 3.6.3.
Conclusions to Part I are presented in section 6.1 of the separate chapter 6.
Part II, Chapter 4, discusses numerical design methods and solutions of control problems
related to smart actuators, and more specifically MFC-piezo actuators.
x
Section 4.2.1, presents a 2D airfoil shape parameterization, suitable to describe a large number
of airfoil profiles for the use in morphing and section 4.2.2 presents a numerical simulation
method, to account for the aero-structural coupling for the flow around a 2D airfoil, under
assumption of steady-state aerodynamics.
The numerical methods from the previous sections are used in a multidisciplinary concurrent
design optimization method, presented in section 4.3.3. This section contains the definition
of requirements on 2D airfoils for morphing (section 4.3.2) and the 2D example of a trim-tab
assisted morphing concept (section 4.3.4). Results obtained, when applying the method to this
example are presented in section 4.3.5.
In Chapter 5, control and electronic circuit design problems related to MFC-piezo actuators are
discussed. Section 5.1 presents a simple feedback control approach based on flexural strain-
gauge readings, which has successfully been applied to the control of an MFC-actuated active
section on a morphing wing prototype. Section 5.2 discusses the design and implementation
of an electronic circuit to drive multiple active sections actuated by MFC-piezo patches.
Conclusions to Part I and Part II of this thesis are presented in chapter 6 and ongoing and
(short-term) future work is discussed in 7.
The thesis closes with Chapter 8, where an outlook on the potential of the presented work is
discussed in a wider sense.
xi
Summary of Contributions
The main contributions of this thesis are:
1. The derivation of a parametric numerical model in differential algebraic equation (DAE)
formulation, coupling an extended lifting line method to the flight dynamic equations.
The model describes the effect of changes in the span-wise lift distribution on the tra-
jectory. (section 3.2.5)
2. The development of a test-platform, suitable to investigate different control strategies for
the feedback control of the span-wise lift-distribution on a six-flapped flying wing and for
the acquisition of flight test data for parameter estimation and performance comparison.
(section 3.4)
3. The estimation of uncertain model parameters for the model from point 1, based on
flight test data acquired with the test-platform. (section 3.6)
4. A multi-disciplinary concurrent design optimization method, including 2D fluid-structure
interaction (FSI) models to account for the aero-structural coupling encountered in com-
pliant structures for morphing wing applications. (section 4.3.3)
5. The definition of a performance measure for 2D morphing airfoils as presented in section
4.3.2.
6. The implementation and demonstration of simple feedback-control based on strain gauge
measurements to overcome hysteresis effects and creep effects in MFC-piezo actuators.
(section 5.1)
7. The design and testing of an electronic circuit based on solid-state-relays, able to inde-
pendently control many active sections equipped with MFC-piezo actuators. (section:
5.2)
xii
List of Figures
2.1 Flight track of a typical glider competition day. Red crosses mark the turn-
points, which the pilots has to surround, round markers start and final. (track
from www.onlinecontest.org) . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 A glider in a typical situation in cross-country flight. Numbers indicate the
expected achievable climb-rate for the upwind. Which speed to fly and which
thermal to climb? Clearly, the operating points of a glider are dictated by
external (meteorological) factors. (schematically after [Rei05]) . . . . . . . . . 16
2.3 Construction of the speed-to-fly after MacCready [Mac49] from plane polar for
the example of a Discus b [SH84] with a 70 kg pilot. The expected vertical
climb rate in the next polar is read at the ordinate, and at the tangent point of
the tangent to the polar the optimal speed can be read from the abscissae . . 16
2.4 Turning flight polar with minimal sink rate envelope for a typical 15m span glider
(wing loading 33kg/m2) using equation 2.20 and based on a cubic polynomial
fit to straight-flight polar data from [SH84] . . . . . . . . . . . . . . . . . . 21
2.5 Resulting climb-rates in different thermal updraft distributions modeled with
thermal model from [All06]. The vertical lines indicate the radii corresponding
to flight at CL,max and CL,min.sink . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6 Schematic of the placement of control surfaces for stability and controllability
about the pitch axis (after [NW90]) . . . . . . . . . . . . . . . . . . . . . . . 23
3.1 Planform of the six-flapped flying wing RC-model ‘Taborca’, after [Haa14] . . 29
3.2 Definition of speeds and rates in body-fixed coordinate system . . . . . . . . . 31
3.3 Schematic of the working principle of a dynamically growing lookup-table. Only
colored data-points are occupying memory. . . . . . . . . . . . . . . . . . . . 38
3.4 Arrangement of horseshoe vortices for the extended lifting line analysis: the
boundary of the wing is printed in black, the horseshoe vortices in colors. Black
circular arrows indicate the sign of vortex strength and blue dots are the points,
where the flow tangency boundary condition is enforced . . . . . . . . . . . . 39
3.5 Sparse structure of the Jacobian of the DAE defined by 3.1, to 3.4 & 3.19 . . 46
xiii
www.onlinecontest.org
3.6 Turning flight performance for a six-flapped flying wing, with direct access to the
flaps compared to use of static mixing. blue: assumes xδ = δpitch,flaperon,slow/fast,
red: solved by gridding and turquoise: direct flap access, i.e. xδ = δ1..δ6 . . . 48
3.7 Control-Scheme for attitude and airspeed control, implemented on the six-
flapped flying wing test-platform. . . . . . . . . . . . . . . . . . . . . . . . . 57
3.8 Static Mixing, relating the control inputs for the principal axes to predefined
flap-deflections. The effects from each principal axis are summed up. Number
indicate deflections in degrees, positive downwards. Slow flight mode deploys
flaperons and is intended for powered climb, loiter and during landing. (after
[Haa14]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.9 Relais-Controller for PID-controller tuning with the method from [AH95] . . . 61
3.10 Airspeed and pitch response, during relay-control with relay-height dφref = 10.
Vertical lines indicate the critical period Pu = 3.4 s . . . . . . . . . . . . . . . 61
3.11 Attitude Control performance for step inputs of −10◦ and 10◦ . . . . . . . . . 633.12 Airspeed Control Performance at low speed in calm and windy situations . . . 64
3.13 Airspeed Control Performance at high speed in calm and windy situations . . . 65
3.14 Projected Flight Trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.15 Total Energy Decay in turning flight at U∞ = 15m/s and φ = 13◦ . . . . . . . 67
3.16 Drag polar derived from turning flight data. During flight 19, weather conditions
were particularly calm (in terms of thermals). The plane was equipped with an
additional pitot-tube mount but otherwise clean configuration. Samples have
been selected, based on monotonous decay of total energy. Flight speeds ranged
from 12m/s to 26m/s and bank angles from 4◦ to 32◦, flaps were always set to
slow flight mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.17 Comparison of measured and simulated data for identification dataset. sim
refers to simulation with identified parameters, init with initial parameters and
exp to data from experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.18 Comparison of measured and simulated data for dataset not used in identifica-
tion. sim refers to simulation with identified parameters and exp to data from
experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1 Airfoil shape parameterization based on 11 geometrical parameters. The explicit
airfoil representation is handled by 4th order polynomials, separately for the front
and back segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2 Static aeroelastic analysis tool working principle . . . . . . . . . . . . . . . . 86
4.3 Outline of the design procedure . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.4 Multidisciplinary concurrent optimizer working principle . . . . . . . . . . . . 88
4.5 Trim tab-based structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.6 Convergence of the concurrent optimization. The line indicates the mean value
per generation and the bars indicate the maximal and minimal values within
that generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
xiv
4.7 Drag polars of the initial (dotted lines) and optimized (solid lines with circular
markers) airfoil at constant angle of attack and different morphing states; su-
perimposed, a conventional drag polar of a rigid NACA0012 airfoil (solid black
line). A 25% reduction in drag at cl = 0.5 and at a wide range of cl-coefficients
in comparison to the initial guess of the optimized airfoil is visible. . . . . . . . 97
4.8 Concurrent optimization: base shape and morphed states of the initial and best
candidate solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.9 Concurrent optimization: structural details of the best candidate (deformed
states) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.10 Envelopes of the drag polars of the optimized airfoil at the design angle of attack
and different morphing states (solid black line); superimposed, drag polars of
the optimised airfoil at constant angle of attack and different morphing states;
for comparison, drag polar of the rigid optimized airfoil at different angles of
attack (dashed black line). All polars have been obtained for Re=700’000. . . 98
4.11 Comparison of the drag polars of the concurrently optimized profile, sequentially
optimized profile geometry (pure aerodynamic analysis) and resulting sequen-
tially optimized morphing airfoil. For reference, polar of a NACA0012 rigid
profile and of a morphing NACA0012 airfoil, used as the initial point for the
concurrent optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.12 Sequential optimization: comparison between aerodynamic target shapes and
corresponding achieved deformed structural shapes. . . . . . . . . . . . . . . . 100
5.1 Straight NACA0012 wing with 3x6 MFC-piezo actuators (image from [MQA+14])104
5.2 Schematic of electronic controlled MFC driving circuit . . . . . . . . . . . . . 105
5.3 Schematic of the resulting feed-back control loop . . . . . . . . . . . . . . . . 106
5.4 Closed-Loop Controller performance . . . . . . . . . . . . . . . . . . . . . . . 107
5.5 Compensation of hysteretic effect through feedback control. . . . . . . . . . . 107
5.6 Comparison: strain gauge measurement vs. trailing edge deflection . . . . . . 108
5.7 Feedback-Control based on flexural strain-gauge readings under loaded condi-
tion in Wind-Tunnel tests at an onflow of U∞ = 30m/s and angle of attack of
α = 4.8. ∆CL has been multiplied by a factor 5. . . . . . . . . . . . . . . . 109
5.8 Linear relationship between strain-gauge signal and CL in contrast to relation-
ship between MFC-Voltage and CL, which is affected by actuator hysteresis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.9 Schematic Dual Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.10 Cascaded Control-Loop to drive one active section using 2 groups of MFC-piezo
actuators in bi-morph configuration . . . . . . . . . . . . . . . . . . . . . . . 113
xv
List of Tables
3.1 Key Properties of the Taborca flying wing model. . . . . . . . . . . . . . . . . 28
3.2 Comparison of different numerical methods to compute aerodynamic forces and
moments of a flying wing in free flight. Please note that this representation is
only to give a rough indication and accuracies achieved depend on details of
the implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Coefficients and parameters appearing in DAE (eq. 3.1, to 3.4 and 3.19 ) . . . 45
3.4 Sensors installed on the test-platform. Barometric sensor and IMU sensors are
integrated in the logic-board (Pixhawk) . . . . . . . . . . . . . . . . . . . . . 52
3.5 Comparison of expected error in airspeed at different airspeeds for different
differential pressure sensors. The expected error is computed from information
provided in the respective datasheets . . . . . . . . . . . . . . . . . . . . . . 54
3.6 Radio communication devices on board of the test-platform. . . . . . . . . . . 54
3.7 Controller gains used in the attitude control loops. Attitude angles are measured
in centi-degrees and output is normalized between -1 and 1. Gains are for a
trim speed of U0 = 15m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.8 Controller gains computed based on Ziegler-Nichols and data from relay-controller
experiment. Input units are ms and output units are degrees . . . . . . . . . . 60
3.9 Measurements used in parameter identification . . . . . . . . . . . . . . . . . 70
3.10 Parameters to be identified with initial guess and final value . . . . . . . . . . 75
4.1 Comparison of the contribution of the different terms of the cost function for
the initial and best case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2 Optimization variables and values for the initial and best candidate of both
the concurrent and sequential optimization. The geometrical parameters are
explained in figure 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
xvi
Nomenclature
α Angle of attack
αTE Airfoil parameterization: trailing edge exit angle
αcorr,i Correction for αi due to fixed body rates (see sect. 3.2.5)
αeff.,i Effective angle of attack at vortex element i, including all effects
αtwist,i Geometrical (twisting) angle of attack at vortex element i
αlp Recursive low-pass filter constant
A Wing Aspect Ratio
ᾱ Design angle of attack
c̄ Mean aerodynamic chord (m.a.c.)
c̄l Design lift coefficient
q̄ Dynamic Pressure q̄ = ρ2
(U2 + V 2 +W 2)
s̄i Local offset in chord-wised direction due to sweep at point i
ȳi Span wise distance at point i to the center of gravity
β Sideslip angle
βTE Airfoil parameterization: trailing edge wedge angle
`j Line length of vortex singularity element j
Γ Vector of circulation strengths
∆`i Overall length of line-segment i
∆cm Change in sectional pitching moment coefficient (due to morphing)
∆Tth Temperature change (imposed, actuation level)
∆yi Extension of element i in span-wise direction
xvii
∆zi Local offset in vertical direction due to dihedral at point i
δi Deflection angle of flap number i
δflaperon Flaperon input command
δpitch Pitch input command
δroll Roll input command
δslow/fast Flaperon mode input command
δyaw Yaw input command
�mech Mechanical DE material strain
�thermal Actuation (or thermal) DE material strain
�tot Resulting total DE material strain
Γj Circulation strength (of vortex singularity j)
(̂·) Circumflex/hat: Estimated quantity
(·)? Super-script ?: location of optimum, or optimizer
(·)ref Subscript ref: Reference quantity
dRLE,i Vector from xCOG to midpoint at leading edge of element i
Fj Resultant force vector at control point j
K∞ Influence matrix (used in extended Lifting Line Method)
nj Normal vector at element j
p Vector of unknown parameters
p2D Airfoil parameterization: Structural and geometrical parameters
r1 Vector pointing from origin to point 1
uk Vector of control inputs at kth time step
vj Velocity vector at element j
vind,i→j Velocity vector at control point j, due to singularity at point i
xδ Vector of optimization variables (flap deflections or main axes input)
xalg. Lower part of stacked state vector: algebraic states of the DAE
xDAE (Stacked) state vector in DAE (see eqn. 3.17)
xdyn. Upper part of stacked state vector: differential states of the DAE
xviii
dCM,yaw,β Side-slip damping factor (estimated parameter)
ν Kinematic viscosity of air
νP Poisson ratio
φ Bank (or roll) angle (Euler angle)
ψ Yaw angle (Euler angle)
ρ Density (of air, surrounding the aircraft)
τ1,PWM Pulse-Length of PWM-signal in µs
Re Reynolds number (typically based on m.a.c.: Re = Uc̄ν
)
θ Pitch angle (Euler angle)
θcorr Pitch-offset (estimated parameter)
δ̃scaled,i Scaled flap deflection at element i (not the same as δi)
ω̃ Reduced frequency
ỹk,j jth Entry of measurements at time tk
A Projected area of lifting surface
a Output amplitude at critical gain
ar Centrifugal acceleration in turning flight
Amin Minimal cross-sectional area
Ac Cross-sectional area of airfoil (2D)
b Projected span of lifting surface
blow,i Airfoil parameterization: Lower bound for parameter i
bup,i Airfoil parameterization: Upper bound for parameter i
cd Sectional (2D) drag coefficient
cj Chord length at vortex singularity element j
cl Sectional (2D) lift coefficient
cm Sectional (2D) pitching moment coefficient
CD,fast Drag coefficient in fast flight mode
CD,slow Drag coefficient in slow flight mode
CD Drag Coefficient of whole aircraft , see equation (2.6), page 18
xix
CL,max Maximum whole aircraft lift coefficient, limited by stall
cl,max Maximal sectional lift coefficient
CL,min.sink Lift coefficient at which minimal sink rate in straight flight occurs
cl,min Minimal sectional lift coefficient
cl0 Sectional (2D) lift coefficient at zero angle of attack
CL Lift Coefficient of whole aircraft , see equation (2.5), page 18
CMpitch Non-dimensional pitching moment in wind-axis FoR (see eq. 3.7)
CMroll Non-dimensional rolling moment in wind-axis FoR (see eq. 3.7)
CMyaw Non-dimensional yawing moment in wind-axis FoR (see eq. 3.7)
Cth Expected achievable climb-rate in the upcoming thermal
CY Lateral force coefficient of whole aircraft
D Drag force
d Relay height
Dd Down-draft strength between the thermals
E Total Energy
e Error: i.e. difference between reference and system output
F{x,y,z} Resultant (aerodynamic) force projected onto body {X, Y, Z}-axis
fmap Mapping function: relates flap deflection δj to δ̃i at vortex element i
g Earth’s standard acceleration due to gravity (g = 9.80665 m/s)
Ixx, Iyy, ... Entries of aircraft inertia tensor
J Cost term in optimization problem
KI Integral gain of PI-controller
KP Proportional gain of PI-controller
Ku Critical gain
kth Linear coefficient of thermal expansion
kdamp. Numerical damping factor (in solution of Lifting Line problem)
ksc Exponent used in gain scheduling
KI,U∞ Integral gain of airspeed-controller
xx
KI,{φ,θ,ψ} Integral gain in φ,θ or ψ-axis,respectively
KP,U∞ Proportional gain of airspeed-controller
KP,{φ,θ,ψ} Proportional gain in φ,θ or ψ-axis,respectively
kU∞ Gain factor for airspeed reading (estimated parameter)
L Lift force
m Aircraft mass
m (·) Measurement function
mth Airfoil parameterization: maximum profile thickness
Mx Resultant Moment projected on to body x-axis
My Resultant Moment projected on to body y-axis
Mz Resultant Moment projected on to body z-axis
m{α,Re,δ} Mid-value used for scaling of αi,Rei and δ̃i, respectively
n{α,β,δi,Re} Number of (virtual) gridding points in respective dimension
P Body axis roll rate, i.e. rotational rate of aircraft about longitudinal axis in body-
fixed frame
Pu Critical period
p1...p11 Parameters in 2D airfoil parameterization
p2D,i Airfoil parameterization: Parameter i
pa,i Polynomial coefficients in approximation of 2D aerodynamics (3.21)
Q Body axis pitch rate, i.e. rotational rate of aircraft about lateral axis in body-fixed
frame
R Body axis yaw rate, i.e. rotational rate of aircraft about vertical axis in body-fixed
frame
Rc,CL,max Turning radius ( equation 2.9 ), evaluated at φ? and CL,max
Rc,CL,min sink Turning radius ( equation 2.9 ), evaluated at φ? and CL,min.sink
Rc Turning radius
rk,j Residual at kth time step related to jth measurement vector entry
T Mission horizon
t Time (in seconds)
xxi
U Longitudinal component of aircraft velocity in body-fixed frame
u Control Input
U0 Trim speed (used in gain scheduling)
U∞ Flight speed magnitude (indicated airspeed)
Ucorr,i Inflow correction in X-direction due to fixed body rates (sect. 3.2.5)
V Lateral component of aircraft velocity in body-fixed frame
V0,V1,V2 Voltage at terminal 0,1 or 2, respectively
Vs Resulting sinking speed of aircraft , see equation (2.15), page 19
vind Induced velocity at specific point
Vavg Average cross-country speed , see equation (2.1), page 14
Vg Glide speed between thermals
Vs Sink rate during the glide phase in calm air
W Vertical component of aircraft velocity in body-fixed frame
w (cl (i)) Weighting attributed to cl-bin i
wj Weighting of residual related to jth entry in the measurement vector
Wcorr,i Inflow correction in Z-direction due to fixed body rates (sect. 3.2.5)
X,Y ,Z Coordinates in Inertial (earth-fixed) reference system (Z downwards)
Xl Airfoil parameterization: location lower maximum
Xu Airfoil parameterization: location upper maximum
xCOG Location along longitudinal axis of center of gravity
Z\xx,l Airfoil parameterization: curvature at lower maximum
Z\xx,u Airfoil parameterization: curvature at upper maximum
ZLE Airfoil parameterization: leading edge deflection
ZTE Airfoil parameterization: trailing edge deflection
Zbaro Barometric altitude
δTE Airfoil parameterization: trailing edge thickness
xxii
List of Acronyms
CMA-ES Covariance Matrix Adaptation Evolutionary Strategies
COG Centre of Gravity
DAE Differential Algebraic Equation
DE Dielectric Elastomer
EKF Extended Kalman Filter
eLLT extended Lifting Line Theory
FoR Frame of Reference
GPS Global Positioning System
HV High Voltage
IMU Intertial Measurement Unit
LE Leading Edge
m.a.c. mean aerodynamic chord length
MFC Macro Fiber Composite
PI Proportional-Integral Controller
PID Proportional-Integral-Derivative Controller
RC Remote Controll(ed)
STL Standard Template Library
TE Trailing Edge
UAV Unmanned Aerial Vehicle
VLM Vortex Lattice Method
xxiii
Chapter 1
Introduction
1.1 Background of the Subject and Literature Review
The idea of morphing wings has been there since the early days of manned flight, when the
Wright brothers were using wing twisting to provide roll control. A recent review by Barbarino
et al. [BBA+11] provides an overview of the many morphing concepts that have been developed
since then, with specific focus on recent ones based on so called ‘Smart Materials’ [Cho02] for
actuation.
The review by Lachenal et al. [LDW13] discusses the recently growing interest of the wind
power community in wing morphing solutions. Jha et al. [JK04] classify different morphing
concepts and the review by Sofla et al [SMTY10] discusses specifically concepts based on Smart
Materials.
Motivation for Morphing
The reasons to consider the use of morphing in the design of an aeronautical structure are
typically based on one or a combination of the following goals:
• to create control moments for attitude control (e.g. [PAL12])
• to provide some form of load alleviation for static or dynamic loads (e.g. [DW11])
• to provide optimal performance (in terms of drag, lift-to-drag, maximal lift etc.) atdifferent operating points (e.g. [KOE+09])
• to increase functionality
Morphing concepts for fixed wing aircraft can be grouped according to the following adaptation
mechanisms:
1
1. Introduction
• change of planform parameters: sweep, span or chord (e.g. [NGJ+04] )
• change of out-of-plane parameters: twist (e.g. [BCWM+04]) or dihedral
• change of airfoil: camber (e.g. [SH88]) or thickness ([PLFB08] )
• direct flow control (e.g. Plasma actuators [PNV+07])
Typically the performance of a morphing design concept can only be expressed in the context
of the overall airplane or airfoil mission. Only in this context can the corresponding trade-offs
be made and the overall performance evaluated. Szodruch and Hilbig [SH88] discuss a typical
transport aircraft and how variable camber morphing concepts could increase the performance
in such a setting and Gamboa et al. [GVLS09] formulate performance in terms of different
mission parts like cruise speed, cruise endurance, rate of climb etc. Significant advantages due
to morphing can only be expected if the underlying airplane mission requires not only good
airfoil performance at a single design operating point but also at a wide range of different
operating points. In chapter 2 of this thesis, the mission of a tailless glider in cross-country
soaring will be used as a showcase mission for morphing and is discussed in detail. The reason
to consider a tailless aircraft is given by the fact, that for this type of aircraft the only means
of creating control moments aerodynamically, is by altering the span-wise lift-distribution over
the wing. If this is achieved by changing the camber at different span-wise locations through
morphing, the drag attributed to solutions with a hinge-gap could be overcome. Tailless aircraft
in general have the potential of reducing the skin friction drag by minimizing the wetted area
and have regained interest in studies on blended wing body designs [Lie04]. Design aspects on
tailless aircraft are discussed in great detail in the book by Nickel and Wohlfahrt [NW90].
Smart Materials
Recent work on the structural design concepts has been focusing a lot on new materials such
as Dielectric Elastomers (DE) (e.g. [KARE13]), Shape Memory Alloys (SMA) (e.g. [PGB+10])
or macro fiber composite (MFC) piezos (e.g. [Bil10]). These new materials provide certain
features that would be difficult achieve with conventional actuators. MFC-piezo actuators
provide, for instance, a much higher actuation bandwidth, than conventional actuators and
they can in principle be directly integrated in a laminated structure. A hinge-less design with
this type of actuator, would allow to design laminar flow airfoils where the flow in the boundary
layer remains much longer laminar compared to current designs, as there is no hinge-gap which
would typically trigger the transition to a turbulent boundary layer, typically attributed with
higher drag.
With the growing interest in the use of Smart Materials, the focus has shifted more on purely
structural aspects, and publications focusing on these aspects, as listed for instance in the
review by Sofla et al. [SMTY10], only provide very little information about the aerodynamic
performances achieved. In order to develop a design that provides an increased performance
2
1.1. Literature Review
compared to conventional designs, a multi-disciplinary approach is necessary, not only to model
the flow-structure interaction, but also to include the requirements arising from the control and
the aerodynamic perspective in the design process. These points have been addressed in this
thesis in section 4.2.2 and 4.3, where a numerical analysis method for aero-structural coupling
in 2D is presented. Furthermore, a concurrent multidisciplinary optimization method, able to
optimally trade-off compliance and stiffness, has been presented. This concurrent optimization
method is different from the sequential approach which is commonly reported in literature,
as for instance by Gamboa et al. [GVLS09]. In the concurrent approach, both structural
and aerodynamic parameters are optimized at the same time to achieve improved performance
in terms of an aerodynamic performance measure. We found, that for settings where the
structural and aerodynamic interplay play an important role, the concurrent approach provides
better performing solutions than the sequential approach. Although the design models were
based on a 2D assumption and as specific smart actuator the characteristics of DEs have been
used, the methodology can be easily extended to different actuator types, such as MFC piezos,
and with some effort also three-dimensional effects can be included in the models, as has been
shown within the scope of this research project by Molinari [MAE14].
The use of MFC piezos in a UAV to demonstrate the feasibility of the underlying morphing
concept poses additional difficulties, in particular the need for small weight and bulk High
Voltage electronics to drive the actuators, which require voltages in the range from −500 V to1500 V. This problem is often neglected in early design phases. In the design of an UAV with
all solid state actuated control surfaces, Bilgen et. al [BBD+12] use a Voltage divider circuit
based on completely passive components [BKIO10] to generate the two bi-polar voltages for
each independent channel. Although this solution could be integrated in the fuselage of the
small one-meter-span UAV, the actuation band-width was much too slow and additionally the
system did not provide any feedback or compensation for the hysteresis of the MFC-actuators.
These deficiencies in combination with unfavorable wind conditions eventually lead to a crash
of the UAV after a short flight. This failure underlines the need for closed-loop control in the
context of adaptive wing structures, but more importantly it also shows that the success of
the design depends on all parts involved, including all their structural, aerodynamic, electrical
and control aspects. To overcome the problem of hysteresis, a simple feedback control scheme
based on the strain measured by a strain-gauge is presented as part of this thesis in chapter
5.1. For the specific problem of designing an electronic circuit which is able to drive multiple
independent MFC-piezo-actuated sections, a solution using solid-state relays has been devised
and is presented in section 5.2.
Control Aspects
Literature related to control aspects of airfoil morphing is less frequent than literature related
to structural aspects: Popov et al. present methods related to shape memory alloy morphing
structures [PLFB08], [PGB+10] and Grigoire et al. [GBP09] present a fuzzy controller, trained
3
1. Introduction
to relate flap deflections to operating points characterized by the Mach number and angle of
attack. Poggie et al. [PTF+10] present a closed-loop stall control system which combines
plasma actuators for flow control with a compliant morphing flap. Baldelli et al. [BLSPC08]
derive a linear parameter varying model for an envisioned out-of-plane morphing aircraft and
design a multi-loop controller using robust controller reduction schemes. In a wider sense the
publications related to the research for flutter or buffet suppression as part of NASA’s morphing
project [MWM+98] also address control related problems by investigating the effect of actu-
ator placement on the control derivatives. Finally, Gopalarathnam and Cusher [GN09],[CG12]
present ideal lift distributions for a wing with multiple trailing edge flaps. Such ideal lift distri-
butions can be seen as the open-loop problem formulation of the control problems described
in section 3.4.3, where a simple control scheme is used to adapt the span-wise lift-distribution
on a tailless model glider in a feed-back loop to provide attitude control.
1.2 Research Needs
From the literature review and as part of the project proposal the following research needs have
been identified:
RN1 In order to concretize the project goal, it is necessary to identify one or several airplane
missions, where wing morphing can potentially bring performance improvements.
RN2 A methodology to derive precise requirements on a morphing airfoil, based on the con-
sidered airplane mission(s)
RN3 Coupled structural and aerodynamic models to predict the effect of aerodynamic loads
on a compliant morphing wing
RN4 Design optimization strategies and algorithms capable to tune the local stiffness and
compliance, such that an optimal solution can be found, which fulfills the requirements
on the morphing airfoil. The design strategy should also consider the need to integrate
load carrying elements, actuators, sensors and auxiliary systems.
RN5 Reduced or simplified models for implementation in the control system.
RN6 Control algorithms to achieve optimized and stable flight, while suppressing possible
dynamic instabilities.
Furthermore, the success of morphing clearly also depends on specific details related to man-
ufacturing, system integration and controller implementation. Therefore, it was defined as a
clear goal of the project to build a final prototype in the form of a UAV and/or of a wind-tunnel
model to demonstrate the feasibility and potential of airfoil morphing.
4
1.3. Approach
1.3 Approach
The research needs stated in the previous section underline that design of a morphing wing is
a highly interdisciplinary research topic and therefore needs to be addressed in an integrated
interdisciplinary approach. The research presented in this thesis has been part of a ETH-
funded collaborative highly interdisciplinary research project (CHIRP), where professors and
PhD students from three different institutes were collaborating from the beginning of the
project:
• Prof. Dr. Paolo Ermanni and Giulio Molinari (PhD Student) from the Laboratory ofComposite Materials and Adaptive Structures
• Prof. Dr. Edoardo Mazza from the Institute of Mechanical Systems
• Prof. Dr. Patrick Jenny and Vitaly Dmitriev (PhD Student) from the Institute of FluidDynamics
• Prof. Dr. Manfred Morari and myself, (Manfred Quack, PhD Student) from the Auto-matic Control Lab
Furthermore, Francesco Previtali (PhD student) and later also Dr. Andres Arrieta, both from
Prof. Ermanni’s Laboratory, were also closely involved in the project. Involving researchers
from the different disciplines (i.e. from structural, aerodynamic and control laboratories )
allowed to discuss interdisciplinary aspects quickly already at an early project phase.
Short Overview
In short, the approach taken in this research project to address the research needs listed above
can be split into three phases:
1. In a first phase, feasibility of developing a morphing airfoil based on DE elastomer actu-
ators has been investigated. A concurrent multidisciplinary design optimization method
has been developed to investigate this question and addressed in 2D the research needs
RN2, RN3 and RN4. At the same time Dmitriev investigated feasibility of energy ex-
traction from span-wise onflow inhomegenenity by means of wing morphing to address
RN1.
2. In a second phase, in order to address research needs RN5 and RN6, a test-platform
based on a six-flapped flying wing RC model has been developed as part of this thesis.
This test-platform served for controller design and investigation on system integration
of sensors and logic boards. In the mean-time Molinari extended the methods of phase
1 from 2D to 3D at the same time the focus shifted from DE actuators to MFC-piezo
5
1. Introduction
actuators. Dmitriev extended the research to investigations on a closed flapping wing as
a new field for adaptive airfoils.
3. In a final phase, a parametric model has been developed as part of this thesis and param-
eter identification based on test-flight data from the test-platform has been carried out.
Analysis of test-flight data showed the feasibility of extracting performance information
from such data. At the same time a feed-back controller and electronic drivers have been
designed for a MFC-piezo actuated morphing prototype. This prototype is based on a
structural design optimization by Molinari. The design, and the overall design method
as well as the robustness of the feed-back controller for the MFC-piezo actuators has
been validated in wind-tunnel tests. Free flight tests with the morphing prototype are in
preparation as part of this final phase, but are yet to be completed. These free flight tests
are planed, in order to validate, that all research needs have been successfully addressed.
Chronological Overview
In a first phase of the project, I was focusing on finding an appropriate description of the possible
shapes that could be achieved with morphing and formulated the airfoil shape parameterization
presented in section 4.2.1. Molinari was comparing morphing concepts based on different
actuation mechanisms and investigating ways to integrate models for the non-linear behavior of
dielectric materials in Finite Element models. After some discussion, we came to the conclusion
that the shape of the airfoil it its morphed state should not be modeled by a pre-described
set of parameters, but it should be the solution to an aero-structural simulation, which takes
the structural forces, the actuator forces and the aerodynamic forces into account. Therefore,
the 2D FSI-model presented in section 4.2.2 has been developed, which was done in close
collaboration with Molinari.
In the meantime Dmitriev was working on a top-down approach to evaluate the potential of
using morphing wings to extract energy from onflow inhomogeneity in the spanwise direction,
which was later published in [DJ13]. Dmitriev investigated this question by the use of trajectory
optimization where the control parameters were the circulation at span-wise stations. Although
these results were not yet available at that time, it was clear, that a coupling between the results
of the trajectory optimization and the design of the morphing airfoil should be considered. With
this in mind the requirements on the airfoil have been formulated as described in section 4.3.2.
During the work on the 2D FSI-model, we also noted, that since the design-methodology for a
morphing airfoil also needs to take the aero-structural coupling into account, a corresponding
design optimization method is required. This led to the formulation of a concurrent multi-
disciplinary design optimization method as presented in section 4.3.3. Key points of this method
are, that it directly optimizes for aerodynamic performance goals and that it concurrently
optimizes the geometrical parameters defining the initial profile and the structural parameters
6
1.3. Approach
related to the dimensioning of the inner structure. The method has been applied to a design
example which was based on a morphing concept using dielectric elastomer materials and the
results have been published in the journal paper [MQD+11].
With this the research needs RN2,RN3 and partially also RN4 have been addressed, in prin-
ciple. However, because the models used up to this point were only two-dimensional, several
decisions had to be made for the extension of the work to 3D and related to this the following
questions arose:
1. Are the actuation strains predicted by the 2D-model also achievable, when integrated in
a 3D structure?
2. How can the two-dimensional morphing concept be extended to 3D?
3. Which numerical models should be used for a three-dimensional description of the
aerostructural coupling?
4. Assuming that the final prototype will use multiple active sections along the span-wise
direction, how should the lift-distribution be controlled to provide stable flight and later
also optimal performance?
5. Which cost function should be used to define optimal performance and to derive an
optimal lift-distribution?
6. How can the effect of changes in the span-wise lift distribution on the flight trajectory
be modeled?
7. How accurate are the three-dimensional aerodynamic models, and how can the related
model uncertainties be taken into account during controller design?
8. Which sensors will be available on the final prototype and which states will be measurable
and at which accuracy and bandwidth?
The first three questions were closely related to structural aspects and have therefore been
addressed by Molinari.
In order to define optimality (question 5) and as part of RN1 a more precise mission profile
had to be considered and I therefore suggested to consider a tailless glider in cross-country
soaring as a showcase mission for morphing, described in detail in chapter 2. This airplane
mission allowed to clearly define and quantify performance goals, which in principle should even
be measurable in free flight tests. Claimed improvements due to morphing could therefore be
validated in such tests.
At this stage of the project, I suggested the use of a test-platform based on conventional
actuators for free-flight tests, which should help to find an answer to questions 4 to 8. The
test-platform is based on a commercially available flying wing RC-model of 3.3 m span and is
described in section 3.4. Part of the development of the test-platform, including sensor and
7
1. Introduction
actuator integration, attitude control and later also airspeed control have been carried out as
part of Semester Thesis [AB12] and Master Thesis [Pet14] projects, which I was supervising
at that time. This test-platform allowed to investigate and test available sensors in the same
environment as it would be expected for the final prototype and hence allowed to provide an
answer to question 8.
Part of question 4 has been investigated with this RC-model: Feedback control methods for
flight stabilization has been designed, implemented and tested for this model, which uses six
independently actuated control surfaces at the trailing edge of the wing. Based on existing
static mixing laws for the flap-deflections, relating the moments around the principal axis to
deflections of the six control surfaces, an attitude feedback controller acting on the principal
axes has been implemented. An outer control-loop for airspeed control, in cascade to the pitch
attitude controller, has also been implemented and tested. Airspeed control is important to
provide repeatable measurement conditions and to be able to average over longer measurement
intervals when performance data is to be acquired. The feedback control schemes are presented
in section 3.4.3 and provide a partial answer to RN6, since they provide stabilizing, but not
yet optimal control.
The use of static mixing laws for the flap-deflections, allowed in combination with simple
PI-control loops to provide stable flight even without a detailed model describing the interac-
tion between span-wise lift distribution and flight-dynamics. Although this approach allowed
to quickly acquire first valuable data from free flight tests, for optimal control and optimal
flap-deflections providing minimal drag, such a model is required. To be able to incorporate
knowledge from test-flight data, and in order to be able to quantify the uncertainty in the mod-
els, a parametric description has been devised. The parametric modeling approach presented
in 3.2.5, makes use of the finding, that the coupling between the extended Lifting Line Theory
(eLLT) and the flight dynamic equations can be elegantly expressed in form of a differential
algebraic equation (DAE). This description also allows to introduce model parameters and to
compute the sensitivities on these parameters very easily and provides an answer to question 6
and is simple enough to be used in model-based controllers and therefore at the same time also
provides an answer to RN5. The description as DAE allows the use of existing numerical tools
for the numerical integration of these equations for simulation purposes, such that experimental
flight trajectory data can be compared with the ones predicted by the model.
The limited accuracy of available aerodynamic models when applied for the simulation of flow
regimes at low Reynolds-numbers – as encountered in UAV-flight (Re ≈ 1e5 to Re ≈ 5e5 ) –makes the derivation of optimal spanwise lift-distribution under realistic assumptions a difficult
task. A possible approach to address these challenges, is to use parameter identification meth-
ods to first identify the uncertain model parameters from experimental flight data. For the
model description based on the DAE formulation, different numerical tools for optimal control
and parameter identification exist. Collocation methods, for instance, allow to use gradient-
based numerical optimization methods and provide therefore good convergence rates. The
8
1.3. Approach
application of such a method (PSOPT, [Bec11]) to identify a set of uncertain model parame-
ters, including a parametric description of the sectional airfoil profile polar, has been outlined
in section 3.6.1. However, since the results of this method have not been satisfactory, an alter-
native approach based on gradient-free single-shooting has been applied to the same problem
and is presented in section 3.6.2. The alternative approach converges significantly slower, but
the resulting trajectories are always fulfilling the system dynamic constraints, and can therefore
always be forward integrated. A set of test-flight data has been used to estimate uncertain
model parameters. The L2-error in predicted flight trajectories and measured trajectories is
significantly smaller for the parameters returned by the identification methods, compared to
the initial guess of parameters. The L2-error in predicted airspeed is for instance reduced by
70% for a specific dataset. Nevertheless, the method does not provide any guarantees, that
the identified parameters are matching the physical parameters, but data shows at least that
locally the model predicts correctly the evolution of the states, which is sufficient for the use
in model-based controllers.
The concurrent multi-disciplinary design optimization for 2D airfoils presented in 4.3.3 has
been extended to 3D and applied to maximize roll authority on a morphing-wing prototype, by
my colleagues Molinari et al. [MAE14]. The wing is equipped with multiple active sections,
actuated by macro fiber composite piezos. The input-output relation of these actuators in
terms of voltage to strain, is very non-linear and features hysteresis and creep effects. A simple
feed-back controller based on flexural strain-gauge readings has been used to overcome these
non-linear effects and is presented in section 5.1.The robustness of the approach has been
tested in wind-tunnel tests, also under loaded conditions up to 30m/s
For the use of MFC-piezo actuators on a wing with many independent active sections, it is
necessary to provide small and lightweight electronic circuitry and control methods to drive
these MFC-piezo actuators independently of each other. Due to the high driving voltages of
−500 V to 1500 V and in combination with requirement of a light-weight small size solution,this is a challenging task. A electronic circuit based on solid-state relays, suitable to drive many
independent active sections has been designed and manufactured. The design is expected to
scale up to at least six independent sections. Preparation and integration of the circuit for free-
flight tests for 1 independent output-channel is currently ongoing and flight tests are planned
for the near future.
9
Chapter 2
A Showcase Mission for Morphing
Wings
The benefits of morphing airfoils can only be described properly if the performance is evaluated
with respect to its original objective. In the context of aeronautical applications – which is
however not the only potential application field of morphing airfoils – the objective of the airfoil
is directly connected to the mission of the airframe in which it is embedded. Taking this into
account, it is obvious, that a morphing airfoil can only outperform a classical design if the
underlying airplane mission requires that the airfoil has to provide good performance for a wide
spectrum of different operating points.
The showcase mission being considered in this thesis is a thermal soaring tailless glider. In
summary this mission is an excellent showcase mission for the following reasons:
1. a thermal soaring glider is operating at two very distinct operating conditions: a gliding
phase and a thermal soaring phase. Both phases have significant influence on the overall
performance.
2. within the gliding phase, a glider with a minimal-time objective has to fly at an optimal
speed which can be shown to be a function of changing external factors (i.e. the average
thermal strength at that period of time).
3. within the thermal soaring phase, the optimal radius and speed to fly are again a function
of changing external factors (i.e. the radius of the thermal updraft and the updraft
distribution within the thermal).
4. The permissible flight speeds of a standard glider (usually dictated by a flutter limit) are
typically Ma ≈ 0.2, which allows the assumption of incompressible flow, simplifying themodeling significantly.
5. In contrast to classical airframe designs, where the attitude is also controlled through
11
2. A Showcase Mission
control surface deflections at the tail, a tailless airplane design can only control its
attitude by changing the span-wise lift distribution on the wing. This poses additional
requirements and constraints on the airfoil.
In particular points 2 and 3 underline, that a glider in cross-country soaring requires good airfoil
performance over a wide spectrum of different operating points. In the following sections these
statements will be elaborated in more detail.
2.1 Glider Competition
To provide the necessary background information on the gliding sport, the typical settings
in glider competition shall be explained. The descriptions here are not precise in the sense,
that many variations of the regulations exist, but they usually adhere to the FAI Sporting
Code [FAI13]. Today, gliding has become an international sport, with many competitions on
local,regional,national and international level. A typical competition lasts 1 or 2 weeks, with
several competition days. On each day, a committee will define a competition task based on the
meteorological conditions and forecasts. The task is typically published shortly before the start
and contains a circuit defined by a few turn-points that have to be passed. Typical distances
are on the range between 100km to 500km, but under exceptional weather conditions also tasks
for 1000km have been defined. After publication of the task, the pilots prepare their gliders
(assembly, programming navigation computer etc.). The standard equipment of a competition
glider usually consists of the following on-board instruments:
• An altimeter which can be set to a reference pressure (QNH, published by the airfield),indicating altitude in meters above sea level.
• An airspeed indicator providing airspeed measurement in km/h. Note that the indicatedairspeed is not the true airspeed, due to changing density with altitude. For most purposes
the indicated airspeed is more relevant to the pilot since the forces scale with the density
and therefore the critical velocities, like the stalling speed, are indicated correctly by the
instrument. (An important exception is the flutter speed which is also a function of true
airspeed).
• An analog variometer, to indicate the vertical movement of the plane. Typically thevariometer provides total energy compensation, which means that the change in potential
energy due to a change in kinetic energy (e.g. during a pull-up maneuver) is subtracted.
In most cases the variometer is calibrated to the plane polar and subtracts the planes
sinking speed (in straight flight). Such a netto variometer provides a reading for the
vertical movement of the air parcel in which the plane is currently flying.
• An electronic variometer providing additionally and audible signal to indicate the currentclimb-rate to facilitate feedback to the pilot.
12
2.2. Soaring Glider
• A gps-based navigational computer, which usually also provides an estimate of the currentwind-speed and direction.
• A collision avoidance system (e.g. FLARM ([FLA14], [Mäd10])).
• A certified gps flight logger (often integrated in either the navigational computer orcollision avoidance system)
• A two-way communication radio.
After preparation on the field, the gliders are towed into a defined waiting space, where the
pilots loiter until the start signal is given. After the start signal the gliders are free to commence
the race, where the exact timing is defined based on a start-line that has been published in the
task description. The goal is then, to pass through all turn-points and return to the final target
in minimal time. Certain turn-points may be defined rather as a turn-region, in which case the
final score will also take the traveled distance into account. The final score will be evaluated
based on the flight logs, that have been recorded with gps-loggers. Missed turn-points, out-
landings etc. will be penalized according to the specific regulations.
In such a competition, the glider pilot has not only to show his piloting skills, but he also
faces many tactical decisions, which need to be taken on a short time-frame. The pilot will
try to gain altitude either in thermal updrafts, which stem from convective flow in an unstable
atmosphere or from orographic lift caused by advective flows over the terrain, or from large-
scale lee-waves behind large mountain areas. There is also the possibility to extract energy
from wind-gradients through dynamic soaring, but this is rarely used in cross-country flight
and usually not an option during competitions. In this thesis we are considering only thermal
updrafts, since they can be considered the most common means of gaining altitude for gliders.
However, it should be noted, that most of the long-distance world records (usually not during
competitions), have been made in lee-wave situations. A typical competition circuit is displayed
together the winners gps-log in figure 2.1.
2.2 A Thermal Soaring Glider
To describe the situation of a glider pilot in cross-country flight, we will first consider the
simplest situation, as depicted in figure 2.2. This corresponds to a day without horizontal wind
but well defined updrafts, which are clearly marked by cumulus clouds. Under competition
conditions the pilot needs to make the following choices:
1. at which speed should the pilot fly between the thermals?
2. should the glide be interrupted for the weaker thermal B or C, or should the pilot continue
directly to thermal D?
3. at which altitude should the pilot exit the thermals?
13
2. A Showcase Mission
0 100 200 300 400 500 600 700500
1000
1500
2000
2500
3000
3500
4000
Distance flown [km]
Altitute
[m
]
(a) Altitude vs Distance flown
−50 −40 −30 −20 −10 0 10−20
0
20
40
60
80
100
120
140
160
(x) East [km]
(y)
Nort
h [km
](b) Flight path
Figure 2.1: Flight track of a typical glider competition day. Red crosses mark the turn-points, which
the pilots has to surround, round markers start and final. (track from www.onlinecontest.org)
4. at which bank angle and speed should the pilot fly inside the thermal?
The first question has been addressed in 1949 by Paul MacCready [Mac49], the second and
third question are both addressed in the works of Helmut Reichmann [Rei05] and [Rei76] and
will be discussed in more detail in 2.3. Eppler [Epp54] has discussed the optimal turning flight
for gliders in a calm atmosphere and a discussion of the effect of different thermal profiles are
discussed also in [Rei05].
2.3 Speed-to-Fly in Straight Flight
Classical MacCready Theory
In the following the classical speed-to-fly theory after MacCready [Mac49] is explained in more
detail. MacCready starts with the following equation for the average cross-country-speed Vavg,
which has been originally published by Nickel in [Nic49]:
Vavg =VgCth
Vs + Cth +Dd(2.1)
Where Cth is the expected achievable climb-rate in the upcoming thermal, Vg is the glide
speed between the thermals, Vs is the sink rate during the glide phase in calm air and Dd is
the down-draft strength between the thermals. MacCready then makes the argument, that
the same way as the maximum glide ration in calm air i.e. the maximum for the term VgVs
is
14
www.onlinecontest.org
2.3. Speed-to-fly
determined by drawing a tangent to the glider polar curve through the origin, one can also
determine the the maximum for the term VgVs+Cth+Dd
by drawing a tangent at the aircraft polar,
but this time through a point that is shifted by Dd + Vs from the origin along the vertical axis
as shown in figure 2.3. This tangency condition can also be derived by minimizing the total
travel time (based on the average cross-country speed in eq. 2.1), as explained in more detail
in [Rei05].
Due to the simple tangency-condition the optimal speed-to-fly can be easily derived graphically
from the aircraft polar for different values of Cth and written down in tabulated form. Mac-
Cready also suggested to print this tabulated information on a rotatable ring-scale, mounted
over the variometer. With this equipment, which quickly became a standard tool in gliding,
the glider pilot will set the expected average climb-rate (the MacCready value), and since the
variometer will show the current sink-speed during glide, the indicator of the variometer will
actually point directly to the optimal speed-to-fly in the case of a down-draft during the glide
phase. A pilot flying optimal in the MacCready-sense will therefore not only adjust his speed
due to a changed value in the expected average climb-speed Cth, but he will also speed up
when he encounters a down-draft during the glide-phase or slow down when encountering a
(weak) updraft. This explains why a glider flying with a minimal-time objective after Mac-
Cready has to be designed for minimal drag over a wide range of operating points in terms
of airspeed. Furthermore, the pilot will use the MacCready-setting to make the decision when
to exit a thermal and for which updraft strength he is willing to interrupt the glide-phase.
If the climb-rate starts dropping below the MacCready-setting he will leave the thermal and
correspondingly he will ignore small thermals that are below the MacCready-setting.
Extended MacCready Theory
The MacCready theory has later been extended to incorporate some parts of the stochastic
nature of the problem. Cochrane [Coc99] solved the optimal speed-to-fly problem under con-
sideration of uncertain lift and limited altitude with a dynamic programming approach. In
addition to the minimal-time cost term, his approach also keeps the risk of an out-landing
below a certain threshold. This will lead to lower MacCready values at low altitudes and higher
values at high altitudes. Almgren [AT14] solved the Hamilton-Jacob-Bellman equations for the
optimal-soaring problem and derived what the optimal MacCready-setting would have been for
the problem assuming once complete knowledge and once the realistic case of no predictive
knowledge of the updraft distribution. For the scenario that he considered the MacCready-
setting would have been approximately 2 in average but with variations between 0.5 and more
than 3. For an average glider in the 15m-span class (i.e. a Schempp-Hirth Discus b glider
[SH84], 350kg mass, wing loading of 33kg/m2, best glide ratio of 42 at 100km/h), this would
correspond to an optimal glide-speed between 115km/h and 165km/h in calm atmosphere
and even up to 180km/h for a 1 m/s down-draft. Therefore, it can be stated, that a glider
15
2. A Showcase Mission
2.5 m/s0.5 m/s 1.5 m/s 3.0 m/s
A B C D
Figure 2.2: A glider in a typical situation in cross-country flight. Numbers indicate the expected
achievable climb-rate for the upwind. Which speed to fly and which thermal to climb? Clearly, the
operating points of a glider are dictated by external (meteorological) factors. (schematically after
[Rei05])
0 50 100 150−3
−2
−1
0
1
2
3
4
5
U∞[km/h]
dZ
dt[m
/s]
Figure 2.3: Construction of the speed-to-fly after MacCready [Mac49] from plane polar for the
example of a Discus b [SH84] with a 70 kg pilot. The expected vertical climb rate in the next polar
is read at the ordinate, and at the tangent point of the tangent to the polar the optimal speed can
be read from the abscissae
16
2.4. Turning Flight
pilot flying with a minimal-time objective taking the extensions by Cochrane and Almgren into
account, will use the glider in an even wider spectrum of operating points. Summarizing,
questions 1-3 at beginning of section 2.2 can be answered as follows:
1. Depending on the expected climb-rate, the pilot will determine the MacCready value.
According to [Coc99] and [AT14], the value has to be decreased at low al