Perpetual Flight in Flow Fields
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Perpetual Flight in Flow Fields by Ricardo Ayres Gomes Bencatel A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Electrical and Computer Engineering) in the University of Porto, School of Engineering Faculdade de Engenharia da Universidade do Porto 2011 Doctoral Committee: Professor Fernando Lobo Pereira, Chair Professor Anouck Girard Associate Lu´ısaBastos Doctor Jos´eMorgado c Ricardo Ayres Gomes Bencatel 2012 All Rights Reserved To my family and my girlfriend, who supported my endeavors and endured the necessary absences. v ACKNOWLEDGEMENTS I thank with all my heart my family and my girlfriend for the support in the easy and the hard times, and for the encouragement to always do my best and surpass myself. Furthermore, I would like to thank the friendship of Nuno Costa with whom I developed and tested several model aircraft, which contributed to the knowledge required for this work. I would like to thank the support from AsasF group and the researchers from the Un- derwater Systems and Technology Laboratory, specially Jo~aoSousa and Gil Gon¸c´alves, and Pedro Almeida for their support, and in particular Jo~aoCorreia, Joel Gomes, Eduardo Oliveira, Rui Caldeira, Filipe Ferreira, Bruno Terra, Filipe Costa Ferreira, Joel Cardoso, and S´ergioFerreira for their friendship, support, and assistance. I gratefully acknowledge the support of the Portuguese Air Force Academy, specially Cap. El´oiPereira, Lt. Tiago Oliveira, Cap. Jos´eCosta, Sgt. Joaquim Gomes, Sgt. Paulo Teixeira, Lt. Gon¸caloCruz, Lt. Col. Morgado, Maj. Madruga, Lt. Jo~aoCaetano, and Sgt. Fernandes. I'm most grateful for the time I spend at the Aerospace Department from the University of Michigan. I enjoyed everyone's friendliness and support, in particular Anouck Girard and all Aerospace & Robotic Controls Laboratory people, specially Baro Hyun, Justin Jackson, Mariam Faied, and Zahid Hasan. The research leading to this work was partly funded by Financiamento pluri-anual of the R&D unit FEUP Instituto de Sistemas e Rob´otica- ISR - Porto. It was also funded by the Portuguese Foundation for Science and Technology (FCT - Funda¸c~aopara a Ci^encia e a Tecnologia) under PhD grant SFRH/BD/40764/2007, co-financed by the Portuguese Human Potential Operational Program (POPH - Programa Operacional Potencial Humano) and the European Social Fund (FSE - Fundo Social Europeu). vi TABLE OF CONTENTS DEDICATION :::::::::::::::::::::::::::::::::::::: v ACKNOWLEDGEMENTS :::::::::::::::::::::::::::::: vi LIST OF FIGURES :::::::::::::::::::::::::::::::::: x LIST OF TABLES ::::::::::::::::::::::::::::::::::: xv LIST OF ABBREVIATIONS ::::::::::::::::::::::::::::: xvi NOMENCLATURE ::::::::::::::::::::::::::::::::::: xviii ABSTRACT ::::::::::::::::::::::::::::::::::::::: xix CHAPTER I. Introduction ..................................1 1.1 Motivation & Background . .1 1.2 Existing Work . .2 1.3 Technical Approach . .6 1.3.1 Perpetual Flow Field Flight . .6 1.3.2 Standard Unmanned Aerial Vehicles (UAVs) . .6 1.3.3 Control Tools . .7 1.4 Original Contributions . .7 1.4.1 Flight Perpetuity Requirements . .7 1.4.2 Flow Field Phenomena Localization . .7 1.4.3 Control Tools . .8 1.5 Scenario - Team Cooperation with Flow Field Supported Flight . .8 1.6 Thesis Organization . .9 II. Models ...................................... 11 2.1 Introduction . 11 2.2 Frames . 11 2.3 Aircraft . 12 2.4 UAV Dynamic Models . 15 2.4.1 Holonomic Models . 16 vii 2.4.2 2D 3DOF Kinematic Model . 16 2.4.3 2D 4DOF Kinematic Model . 17 2.4.4 3D 4DOF Kinematic Model . 17 2.4.5 3D 5DOF Kinematic Model . 18 2.4.6 3D Stabilized Motion Model . 18 2.4.7 Full 3D Dynamics Model . 20 2.4.8 Propeller/Motor Propulsion Model . 24 2.4.9 Simplified Propulsion Model . 30 2.5 Environment Models . 31 2.5.1 Wind Shear . 31 2.5.2 Updraft . 39 2.5.3 Gust Models . 63 2.6 Conclusions . 64 III. Perpetual Flight Conditions ........................ 66 3.1 Introduction . 66 3.2 Energy Dynamics . 66 3.2.1 Airmass-relative Energy . 67 3.2.2 Goal-relative Energy . 67 3.2.3 Airplane Nominal Power . 68 3.2.4 Flow Conveyed Power . 68 3.3 Perpetual and Sustainable Flight Definitions . 68 3.4 Perpetuity Conditions in Thermal Fields . 70 3.4.1 Altitude Hold Derivation . 72 3.4.2 Energy Balance Derivation . 74 3.4.3 Discussion . 76 3.5 Perpetuity Conditions in Wind Shear . 77 3.6 Perpetuity Conditions in Gusts . 79 3.7 Conclusions . 80 IV. Flow Field Estimation ............................ 82 4.1 Introduction . 82 4.2 Observability of Nonlinear Systems . 83 4.3 Thermal Estimation . 84 4.3.1 Thermal Observability . 85 4.3.2 Chimney Thermal Estimator . 90 4.3.3 Flight Results . 97 4.3.4 Bubble Thermal Estimation . 97 4.4 Wind Shear Estimation . 98 4.4.1 Wind Observability . 98 4.4.2 Wind Shear Propagation Models . 100 4.4.3 Wind Shear Observation Models . 101 4.4.4 Particle Filter (PF) . 102 4.5 Conclusions . 105 viii V. Control ..................................... 106 5.1 Introduction . 106 5.2 Collision Avoidance System for Close Proximity Operations . 107 5.2.1 Related Work . 107 5.2.2 General Problem . 107 5.2.3 Nomenclature . 108 5.2.4 Mathematical Background . 109 5.2.5 System Definitions . 111 5.2.6 Collision Avoidance Control . 114 5.2.7 System Models . 121 5.2.8 Flight Results . 134 5.3 Formation Control . 134 5.3.1 General Problem . 135 5.3.2 Literature Review . 135 5.3.3 Current Approach . 136 5.3.4 Sliding Mode Control . 137 5.3.5 Formation Controller - Kinematic Derivation . 138 5.3.6 Formation Controller - Corrections for Aircraft Dynamics 142 5.3.7 Collision Avoidance Logic . 145 5.3.8 Global Position Control . 146 5.3.9 Formation Definition . 148 5.3.10 Distributed Controller . 150 5.3.11 Preliminary Simulation Results . 151 5.3.12 Simulation Results - Leaderless Formation . 154 5.3.13 Flight Results . 161 5.4 Conclusions . 162 VI. Conclusions ................................... 164 6.1 Conclusions . 164 6.2 Future Work . 165 6.2.1 Open questions . 166 6.2.2 Future developments . 167 APPENDICES :::::::::::::::::::::::::::::::::::::: 171 B.1 Properties proof: Model 1 - Single integrator . 175 B.2 Properties proof: Model 2 - Double integrator . 187 B.3 Properties proof: Model 3 - Control delays . 190 BIBLIOGRAPHY :::::::::::::::::::::::::::::::::::: 193 ix LIST OF FIGURES Figure 1.1 Observations of soaring birds by S. E. Peal (Illustration from [1]) . .3 1.2 Column thermal updraft 3D representation. .4 1.3 Surface Wind Shear 3D representation . .5 2.1 Euler rotation angles (illustration from [2]) . 12 2.2 Velocity vector diagram (illustration from [2]) . 13 2.3 Aircraft forces diagram. In this illustration the pitch angle θ is represented by #. ....................................... 14 2.4 Aerodynamic coefficients through the full range of the Angle-of-Attack (AOA). ..................................... 15 2.5 Wind reference frame (illustration from [3]) . 19 2.6 Propeller forces and torque diagram. T is the propeller thrust, B is the resistant torque, L and D are the aerodynamic lift and drag forces, #P is −1 the propeller advance angle, #F = tan (Va=r!) is the flow advance angle, αP = #P − #F is the propeller angle-of-attack, r is the a radius over the propeller blade, ! is the propeller angular rate, Va is the aircraft air speed, and xB is the body frame longitudinal axis. 25 2.7 Propeller thrust and torque curves with the airspeed, for a set of angular rates. The illustrated angular rates range from 0 to 10000 Rotations Per Minute (RPM). The solid lines represent the thrust and torque predictions of (2.50) with 100 section partitions, which should represent (2.48) quite accurately. The dashed lines use the same approximation but with only 4 partitions. 27 2.8 Propeller thrust and torque curves with the angular rate (in RPM), for a set of airspeeds. The illustrated airspeeds range from 0 to 100 m/s. The solid lines represent the thrust and torque predictions of (2.50) with 100 section partitions, which should represent (2.48) quite accurately. The dashed lines use the same approximation but with only 4 partitions. 27 2.9 Propeller thrust and torque curves with the airspeed, for a set of angular rates. The illustrated angular rates range from 0 to 10000 RPM. The approximated model (2.51) is illustrated in dashed lines. 28 2.10 Internal Combustion (IC) engine power and torque curves, with useful RPM range, i.e., from engine stall to the maximum achievable RPM in level flight. 29 2.11 Electric motor power and torque curves, with useful RPM range, i.e., from null RPM to the maximum achievable RPM in level flight. 29 2.12 Dynamics of a propeller/motor pair. 30 2.13 Surface Wind Shear profile . 32 x 2.14 Sach-daCosta Layer Wind Shear model. 33 2.15 Gaussian Layer Wind Shear model. 34 2.16 Quadratic Layer Wind Shear model. 35 2.17 Linear and quadratic Layer Wind Shear model. 36 2.18 Variation of wind speed over a Ridge Wind Shear with altitude and distance to the ridge crest. 37 2.19 Zhao Generic Wind Shear quadratic model. 38 2.20 Thermal updraft Gaussian model . 40 2.21 Thermal updraft Gedeon model . 41 2.22 Updraft velocity magnitude . ..