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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


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


2.5 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

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