Study and suppression of vibrations in rotary-wing Unmanned Aerial Vehicles

216 Pages·2017·8.15 MB·English

by  Neil Stewart

City Research Online
City, University of London Institutional Repository
Citation: Martinez Estelles, Sylvia (2016). Study and suppression of vibrations in rotary-
wing Unmanned Aerial Vehicles. (Unpublished Doctoral thesis, City, University of London)
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City University London
School of Mathematics, Computer
Science and Engineering
PhD thesis
Study and suppression of
vibrations in rotary-wing
Unmanned Aerial Vehicles
Silvia Estell´es Mart´ınez
supervised by
Dr. M. Toma´s-Rodr´ıguez
October 2015
London

School of Mathematics, Computer
Science and Engineering
City University London
Study and suppression of
vibrations in rotary-wing
Unmanned Aerial Vehicles
Silvia Estell´es Mart´ınez
1st Supervisor: 2nd Supervisor:
Dr. Mar´ıa Prof. George
Tom´as-Rodr´ıguez Halikias
Submitted as part of the requirements for
the degree of Doctor of Philosophy
in Aerospace Engineering
October 2015

Contents
Acknowledgments 21
Abstract 23
1 Introduction 33
1.1 Unmanned Aerial Vehicles (UAVs) . . . . . . . . . . . . . . . . . 33
1.2 Motivation and objectives . . . . . . . . . . . . . . . . . . . . . . 38
1.3 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.4 Thesis contributions . . . . . . . . . . . . . . . . . . . . . . . . . 41
2 Literature review 43
2.1 History of unmanned and rotary-wing vehicles . . . . . . . . . . . 43
2.2 Quadrotors in the modern era . . . . . . . . . . . . . . . . . . . . 51
2.3 Contribution to the state of the art . . . . . . . . . . . . . . . . . 62
3 Quadrotor modelling
65
3.1 Quadrotor dynamic and aerodynamic
overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.1.1 Quadrotor dynamics description . . . . . . . . . . . . . . . 66
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3.1.2 Aerodynamic forces involved . . . . . . . . . . . . . . . . . 72
3.2 Modelling tool: VehicleSim . . . . . . . . . . . . . . . . . . . . . . 75
3.2.1 VehicleSim modelling software, VS-Lisp . . . . . . . . . . . 77
3.2.2 Equations of motion . . . . . . . . . . . . . . . . . . . . . 81
3.2.3 VehicleSim solvers . . . . . . . . . . . . . . . . . . . . . . 84
3.2.3.1 Overview of numerical integration methods . . . 85
3.2.3.1.1 Adams-Moulton 2nd Order Method . . . 87
3.2.3.1.2 Adams-Moulton 3rd Order Method . . . 87
3.2.3.1.3 Adams-Moulton 4th Order Method . . . 88
3.2.3.1.4 Runge-Kutta 2nd Order Method . . . . . 88
3.2.3.1.5 Adams-Bashforth 2nd Order Method . . 89
3.3 Structural modelling . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.3.1 Rigid blades’ model. . . . . . . . . . . . . . . . . . . . . . 91
3.3.2 Elastic blades’ model. . . . . . . . . . . . . . . . . . . . . . 92
3.4 Aerodynamic modelling . . . . . . . . . . . . . . . . . . . . . . . . 97
3.4.1 Aerodynamic forces as a function of the rotational speed. . 99
3.4.2 Aerodynamic forces as a function of the rotational and
translational speed. . . . . . . . . . . . . . . . . . . . . . . 101
3.4.2.1 Aerodynamicforcesasafunctionoftherotational
and translational speed applied at the blade’s sta-
tionary pressure centre. . . . . . . . . . . . . . . 102
3.4.2.2 Aerodynamicforcesasafunctionoftherotational
andtranslationalspeedappliedattheblade’spres-
sure centre. . . . . . . . . . . . . . . . . . . . . . 104
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3.4.3 Aerodynamic forces for elastic blades. . . . . . . . . . . . . 105
3.4.4 Obtaining the aerodynamic parameters . . . . . . . . . . . 108
3.5 Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . . 110
4 Control system
113
4.1 Analysis of the nonlinear mathematical
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.2 Controllability of the platform . . . . . . . . . . . . . . . . . . . . 117
4.3 Control method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.3.1 Description of the algorithm . . . . . . . . . . . . . . . . . 122
4.3.2 Control of Drag Moments . . . . . . . . . . . . . . . . . . 127
4.3.2.1 Counter Drag Moment as a function of the rota-
tional speed. . . . . . . . . . . . . . . . . . . . . 128
4.3.2.2 Counter Drag Moment as a function of the rota-
tional and translational speed. . . . . . . . . . . . 129
4.3.2.3 Counter Drag Moment for elastic blades. . . . . . 130
4.3.3 Predefined smooth references . . . . . . . . . . . . . . . . 131
4.4 Trajectory tracking results . . . . . . . . . . . . . . . . . . . . . . 134
4.5 Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . . 140
5 Vibrations 143
5.1 Vibrational analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.1.1 Static and dynamic characterization of elastic blades . . . 144
5.1.2 Effect of elastic blades in the quadrotor motion . . . . . . 149
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5.2 Oscillations appearing in the angular acceleration. . . . . . . . . . 153
5.2.1 Predictor-corrector process for angular acceleration oscilla-
tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.3 Different blade mass and blade fracture . . . . . . . . . . . . . . . 159
5.3.1 Controllability of a different mass blade system. . . . . . . 160
5.3.2 Behaviourofamassdefectivebladeorfracturedbladequadro-
tor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
5.3.3 Adaptive control for moderate structural damage . . . . . 165
5.3.4 Isolating control device for severe structural damage . . . . 167
5.3.4.1 Description of the isolating control device . . . . 168
5.3.4.2 Preliminary study of the isolating control device . 168
5.3.4.3 Application of the isolating control device . . . . 170
5.4 Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . . 173
6 Conclusions and future work 175
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
6.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
6.3 Future work guidelines . . . . . . . . . . . . . . . . . . . . . . . . 178
6.4 List of contributions . . . . . . . . . . . . . . . . . . . . . . . . . 179
A Calculus of the representative point of the blade 181
B Calculus of the representative point of the blade’s segment for
elastic blades 185
C Calculus of the pressure centre of the blade 187
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D Calculus of the pressure centre of the blade’s segment for elastic
blades. 189
E Moments’ relation to maintain the forces balance 191
Bibliography 193
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