MASTER'S THESIS Analysis of a Flutter Suppression System for an Efficiently Designed UAV Niclas Bramstång 2015 Master of Science in Engineering Technology Space Engineering Luleå University of Technology Department of Computer Science, Electrical and Space Engineering Masters Thesis Conducted at Aerospace Department at Collage of Engineering University of Illinois at Urbana-Champaign Analysis of a Flutter Suppression System for an Efficiently Designed UAV Examiner: Associate Professor Lars-G¨oranWesterberg Author: Supervisor: Niclas B. Bramst˚ang Professor Emeritus Harry H. Hilton September 2, 2015 Master Thesis Abstract With a market for Unmanned Aerial Aircrafts (UAV) exploding and in an age were composite materials are used to construct light and flexible structures it is of importance to have the knowledge of how the choice of material and model of plane will act together. UAV missions can vary with different flying conditions and loads and with high launching costs for satellites and the increasing amount of space debris, long endurance, high altitude UAVs might come to replace some of the functions that were previously handled by satellites. This thesis will study the influence of aeroelastic effects on an electric flexible tailless flying wing design UAV. A flying wing is chosen due to its efficiency, since less control surfaces means less drag and are therefore suitable for long endurance missions. Endurance of such plane can be enhanced by fitting of equipment such as piezo electric devices and solar panels. Different design options consists of, for example, choosing the optimum location of the center of gravity and the use of morphing control surfaces instead of conventional hinged ones. Due to lack of longitudinal stability compared to a conventional aircraft, aeroelastic effects such as flutter will have large consequences to the whole plane instead of just the wings. Long slender wings means less drag but more flexibility. Therefore, a flutter suppression system is the key to reach higher speeds with more efficient designs. Other aeroelastic effects such as divergence and control reversal also requires investigation since these effects cannot be suppressed and can have critical effects on the plane. Since UAVs are remote controlled, a flight control system (FCS) is often used in order to have it fly autonomous and stable during different maneuvers. Therefore a aero-servo-elastic analysis will be made to test the interaction between a FCS with the aeroelastic effects. The analysis may show whether it would be possible to suppress flutter and how the model handles wind gusts and turbulence. Keywords: Aeroelasticity, UAV, Flying wing, flutter suppression Acknowledgments Many thanks to Professor Emeritus Harry H. Hilton who agreed to su- pervise me during my thesis and has put in big effort to give me the opportunity to do my research at the Aerospace Department at the Col- lage of Engineering at University of Illinois at Urbana-Champaign. Personally I would also like to thank everyone who has supported me from home in my endeavour of learning and exploring new areas within the field of aerospace. i Master Thesis Contents Title Page i Abstract i Acknowledgments i Contents ii 1 Nomenclature 1 2 Introduction 3 2.1 Motivation . 3 2.2 Mission . 3 2.3 Design . 3 3 Aerodynamic Forces 5 3.1 Atmospheric Model . 5 3.2 Unsteady Aerodynamics . 6 3.3 Simplified Unsteady Aerodynamic Model . 7 3.4 Efficient Design . 8 4 Elastic Forces 13 4.1 Deformation of a Slender Beam . 13 4.2 Mode Shapes . 13 4.3 Deformation of the Wings . 14 4.3.1 Static Load . 15 4.3.2 Dynamic Load . 16 4.4 Energy Methods . 17 5 Flight Mechanics 18 5.1 Definitions . 18 5.2 Rigid Aircraft . 18 5.2.1 Dynamic model . 19 5.2.2 Longitudinal state-space model . 21 5.2.3 Pitch . 21 5.2.4 Pitch for flexible wings . 23 6 Stability 24 6.1 Static Stability . 25 6.2 Dynamic Stability . 25 6.2.1 Short Period . 26 6.2.2 Phugoid . 26 6.3 Pole Placement . 26 6.4 Flight Control System . 27 6.4.1 PID controller . 28 6.4.2 Full state feedback . 28 ii Master Thesis 7 Aeroelasticity 31 7.1 Basic Example . 32 7.2 Static Aeroelastic Effects . 32 7.2.1 Torsional Divergence . 33 7.2.2 Static aeroelastic effects on stability . 35 7.2.3 Control reversal . 35 7.3 Flutter . 37 7.4 Binary Aeroelastic Model . 38 7.4.1 Structural damping . 40 7.4.2 Moving flexural and mass axis . 41 7.5 Entire Aircraft Model . 41 7.6 Aeroelastic Model for Simulation . 42 7.7 Effects of Swept Wing and Low Aspect Ratio . 45 7.8 Viscoelasticity . 46 7.9 Maneuvers . 46 7.10 Turbulence and Gust Response . 46 7.10.1 Sharp edged gust . 46 7.10.2 1-cosine gust . 47 7.10.3 Turbulence Modeling . 47 7.11 Aero-servo-elasticity . 48 7.11.1 State-space modeling . 48 8 Analysis 50 8.1 Efficient Design . 51 8.2 Static Aeroelastic Effects . 52 8.3 Flutter Prediction . 52 8.4 Simulation . 53 9 Results 55 9.1 Efficient Design . 55 9.1.1 Airfoil Analysis . 55 9.1.2 3D model with hinged elevon . 56 9.1.3 3D model with morphed elevon . 58 9.2 Aeroelastic Effects . 59 9.3 Flutter Prediction . 60 9.3.1 Binary aeroelastic model . 60 9.3.2 Entire aircraft aeroelastic model . 61 9.3.3 3D Plots of entire aircraft model . 61 9.4 Simulation . 62 9.4.1 Linearized model without control . 62 9.4.2 Linearized model with control . 63 9.4.3 Simulink response without control . 64 9.4.4 Simulink response with LQR control . 64 9.4.5 Simulink response climb profile with LQR control . 65 9.4.6 Control Reversal . 66 9.4.7 Manual Tuning . 67 9.4.8 Simulink response climb profile with adaptive controller . 68 9.4.9 Poles and zeros plot . 69 9.5 Summary . 69 iii Master Thesis 10 Discussion 71 10.1 General Considerations . 71 10.2 Simulation . 71 10.3 Limitations of the Controller . 72 11 Conclusion 73 List of Tables 1 Design properties . 4 2 Aeroelastic velocities (m/s) at sea level . 69 3 Aeroelastic velocities (m/s) at 10,000 feet . 70 List of Figures 1 Swept unmanned flying wing design . 4 2 Flying wing airfoil MH 62 . 8 3 Weight and lift distribution of conventional aircraft [6] . 9 4 Design considerations flying wing [39] . 11 5 Hinged Design . 12 6 Wing morphing Design . 12 7 Coordinates and force vectors [33] . 20 8 Simple closed-loop with controller . 24 9 Effects of pole position on stability . 27 10 Full State Feedback control system . 29 11 Properties of the eigenvalues [41] . 30 12 Interaction between forces and their effects[1] . 31 13 Mechanical spring and damping system . 32 14 Divergence . 33 15 Flutter 2DOF . 37 16 Illustration of the 3 DOF wing-flap flutter model [18] . 43 17 Flow chart . 50 18 Flying wing 3D model in XFLR 5 with flaps down configuration 51 19 Flying wing 3D model in XFLR 5 with flaps down morphed con- figuration . 52 20 Flying Wing Flutter suppression system . 53 21 Lift to drag ratio for different flap settings and different Reynolds number . 55 22 Inviscid 3D analysis at different flap settings hinged elevon . 56 23 Viscous 3D analysis at different flap settings for hinged elevon . 57 24 Inviscid 3D analysis at different flap settings for morphed elevon 58 25 Viscous 3D analysis at different flap settings for morphed elevon 59 26 Aeroelastic response due to airspeed . 60 27 Flutter prediction of binary model . 60 28 Flutter prediction of entire aircraft model . 61 29 Damping ratio with respect to velocity and altitude . 61 30 Damping ratio with respect to velocity and pitch stiffness . 62 31 Linearized without control . 63 32 Step response of the linearized model with LQR control . 64 iv Master Thesis 33 Simulink response without control . 64 34 Simulink LQR response with control at 10,000 feet with airspeed of Mach 0.172 and 5 m/s gust at 10 seconds . 65 35 Simulink response with control at 10,000 feet with airspeed of Mach 0.172 with turbulence . 65 36 Climb and acceleration profile response for LQR controller with gusts and turbulence . 66 37 Control effectiveness for Simulink model . 67 38 Simulink response with manually tuned controller at 10,000 feet with airspeed of Mach 0.3 and 5 m/s gust at 5 seconds with turbulence . ..