An adaptive feed-forward controller for active wing bending vibration alleviation on large transport aircraft [Elektronische Ressource] / Andreas Wildschek

Rmawilds

Informations

• Publié par: technische_universitat_munchen
• Publié le: 01 janvier 2009
• Nombre de lectures: 35
• Langue: English
• Poids de l'ouvrage: 5 Mo

Extrait

I
Lehrstuhl für Leichtbau
der Technischen Universität München



An Adaptive Feed-Forward Controller for Active
Wing Bending Vibration Alleviation on Large
Transport Aircraft





Andreas Wildschek


Vollständiger Abdruck der von der Fakultät für Maschinenwesen der Technischen
Universität München zur Erlangung des akademischen Grades eines

Doktor-Ingenieurs

genehmigten Dissertation.






Vorsitzender: Univ.-Prof. Dr.-Ing. habil. B. Lohmann


Prüfer der Dissertation:


1. Univ.-Prof. Dr.-Ing. H. Baier

2. Univ.-Prof. Dr.-Ing. F. Holzapfel




Die Dissertation wurde am 04. Juni 2008 bei der Technischen Universität München
eingereicht und durch die Fakultät für Maschinenwesen am 21. Januar 2009
angenommen.II

III



Preface


This PhD thesis arose from almost four years of research on adaptive aeroelastic
control at EADS Innovation Works in Ottobrunn, Germany.

I would like to thank Professor Horst Baier, head of the Institute for Lightweight
Structures at Technische Universität München, Germany for his encouragement,
supervision, and support. I am also grateful to Professor Florian Holzapfel, head of the
Institute of Flight System Dynamics at Technische Universität München for his
expertise and co-supervision.

Moreover, I would like to express my sincere gratitude to Dr. Rudolf Maier, with
EADS Innovation Works for his exceptional support, and the fruitful technical
discussions. My thanks also go to Dr.-Ing. Matthieu Jeanneau and Dipl.-Ing. Nicky
Aversa, both with Airbus France, as well as to Dr.-Ing. Simon Hecker with the Institute
of Robotics and Mechatronics at the German Aerospace Center (DLR)
Oberpfaffenhofen, and to Professor Zbigniew Bartosiewicz, head of the Department of
Mathematics at Bialystok Technical University, Republic of Poland, for their
invaluable suggestions.

I would also like to thank Dr. Ravindra Jategaonkar and his colleagues at the Institute
of Flight Systems at DLR Braunschweig for the fruitful discussions and their support,
in particular for providing me with flight test data of their ATTAS research aircraft.

Many thanks go to Dr.-Ing. habil. Christian Breitsamter, with the Institute for
Aerodynamics at Technische Universität München and his team for their exceptional
support with the wind tunnel test. In this context I would also like to thank my
colleagues at EADS Germany, particularly Dipl.-Ing. Falk Hoffmann, Josef
Steigenberger, and Karl-Heinz Kaulfuss, as well as Dipl.-Ing. Theodoros
Giannopoulos, with Airbus Deutschland GmbH, and Dr.-Ing. Athanasios Dafnis, with
the Department of Aerospace and Lightweight Structures at the RWTH Aachen,
Germany for their invaluable suggestions and support with the design of the wind
tunnel test setup, and the realization of the wind tunnel test.

Last but not least, my family and friends, in particular my wife Marriah deserve my
gratefulness for their loving support and continuous encouragement.


Ottobrunn
June 2008 Andreas Wildschek IV
V
Contents

Preface............................................................................................................................III
Contents.......................................................................................V
Nomenclature.............................................................................VI
Abstract...................................................XIII
Kurzfassung...................................................................................XV
1 Introduction......................................................................................................................... 1
1.1 State of the Art............................................................................................................. 2
1.2 The Main Research Objective of this Thesis............................................................... 6
1.3 Organization of the Thesis........................................................................................... 7
2 Analysis of the Control Problem ......................................................................................... 9
2.1 The Example Aircraft Model..................................................................................... 10
2.2 Concepts for Active Wing Bending Vibration Control............................................. 23
2.3 Estimation of Expected Performance of Feed-Forward Control ............................... 28
2.4 Using the Alpha Probe as a Reference Sensor .......................................................... 32
2.5 Conclusions of Chapter 2 – The Hybrid Control Concept ........................................ 33
3 Wing Bending Vibration Controller Synthesis.................................................................. 35
3.1 Design of the Adaptive Feed-Forward Controller..................................................... 36
3.2 Stability Analysis of the Adaptive Control Algorithm.............................................. 44
4 Numeric Simulations.........................................................................................................55
4.1 Modeling of the Turbulence and of the Reference Measurement ............................. 56
4.2 Performance of the Converged Controller................................................................. 58
4.3 ance with Modeling Errors ........................................................................... 61
4.4 Introduction of a Mean Plant Model.......................................................................... 69
4.5 Transition Between Different Mass and Mach Cases ............................................... 71
4.6 Response of the Converged Controller to a Discrete Gust........................................ 75
5 Wind Tunnel Testing of the Adaptive Control System ..................................................... 81
5.1 The Experimental Setup ............................................................................................ 81
5.2 Wind Tunnel Test Results ......................................................................................... 91
6 An Infinite Impulse Response Controller as a Perspective ............................................. 103
7 Conclusions and Outlook................................................................................................. 109
aAppendix A – Series Expansion of the Term .................................................................... 112 ∆
Appendix B – Stability Bounds for the Convergence Coefficient c........................................ 114
Appendix C – Derivation of the Optimum Convergence Coefficient c ............................... 116 opt
Appendix D – Assumption of a Quasi-Steady State Feed-Forward Controller ...................... 117
Appendix E – Justification of Neglecting Parasitic Feedback ................................................ 119
Appendix F – Performance of the Converged Controller for Different Cases........................ 120
Appendix G – Definition of Transforms Used in this Thesis.................................................. 134
Appendix H – Measured Coherence for the ATTAS Aircraft................................................. 136
Bibliography ............................................................................................................................ 139 VI
Nomenclature

Symbols frequently used in this thesis are listed below alphabetically. In addition, the
place of their first occurrence in the text is given in the very right column. The state
space matrices A, B, C, and D are only used in Eq. 2-1, and are not noted here. Neither
are the counting variables i, k, and m, or the discrete frequency domain auxiliary
functions, such as a()f , a()f , b()f , b()f , g()f , g()f , v()ω , w()ω in this list. 1 k ∆ k k k 1 k ∆ k

Latin Symbols

Symbol Meaning First occurrence
jωTA()e Fourier transform of the reference signal Eq. (2-13)
A()z numerator of discrete transfer function of IIR controller Eq. (6-2)
tha i coefficient of A()z i
distance between the points “a” and “b” Eq. (2-14) ab
B()z denominator of discrete transfer function of IIR controller Eq. (6-2)
thb ()k coefficient of B z k
jωTB()e multiplicative magnitude error Eq. (4-5)
c convergence coefficient for FIR controller update Eq. (3-15)
c , c convergence coefficients for IIR controller update Eqs. (6-3), (6-4) 1 2
jωTD()ed, disturbance signal and its Fourier transform Figure 2-11
jωTe, E()e error signal and its Fourier transform Eq. (2-3)
F()s closed loop transfer function Eq. (2-6)
parasitic feedback transfer function, i.e. from u to α F ()s Eq. (2-19) FFP
F (s) aileron actuation mechanism’s transfer function Eq. (2-2) δ
f frequency Eq. (2-14)
thf k discrete frequency Eq. (3-16) k
G()z plant transfer function seen by the digital controller H()z Figure 3-2
G()f estimated value of 2N-point DFT of plant impulse response Eq. (3-37) k
~ jωTG()fbiased approximation of by evaluating G()e