CORE Metadata, citation and similar papers at core.ac.uk Provided by Scholar Commons | University of South Florida Research University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 7-30-2009 Autonomous Vertical Autorotation for Unmanned Helicopters Konstantinos Dalamagkidis University of South Florida Follow this and additional works at: https://scholarcommons.usf.edu/etd Part of the American Studies Commons Scholar Commons Citation Dalamagkidis, Konstantinos, "Autonomous Vertical Autorotation for Unmanned Helicopters" (2009). Graduate Theses and Dissertations. https://scholarcommons.usf.edu/etd/1921 This Dissertation is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. Autonomous Vertical Autorotation for Unmanned Helicopters by Konstantinos Dalamagkidis A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Computer Science and Engineering College of Engineering University of South Florida Co-Major Professor: Kimon P. Valavanis, Ph.D. Co-Major Professor: Les A. Piegl, Ph.D. Jay Ligatti, Ph.D. Ali Yalcin, Ph.D. Thomas Bieske, Ph.D. Date of Approval: July 30, 2009 Keywords: Helicopter Control, Non-linear Model-predictive Control, Neural Network, Autorotative Flight, Safety c 2009, Konstantinos Dalamagkidis To my parents. Table of Contents List of Tables iv List of Figures v Nomenclature x Abstract xiv Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Problem Statement 2 1.3 History and State of the Art of Autonomous Autorotation 2 1.4 Methodology 4 1.5 Summary of Contributions 5 1.6 Definitions 6 1.6.1 Air Traffic Control 6 1.6.2 Airworthiness 6 1.6.3 Federal Aviation Regulations (FAR) 6 1.6.4 Flare 6 1.6.5 General Aviation 7 1.6.6 National Airspace System 7 1.6.7 Public and Civil Aircraft 7 1.6.8 Sink Rate and Autorotative Sink Rate 7 1.6.9 Unmanned Aircraft System 7 1.7 Dissertation Outline 8 Chapter 2 Unmanned Aircraft Safety Considerations 9 2.1 Introduction 9 2.2 Current Certification Paths and Operational Guidelines in the U.S. 10 2.3 Equivalent Level of Safety 12 2.3.1 Manned Aviation Requirements 12 2.3.1.1 Applications 14 2.3.1.2 Sacrificability 14 2.3.1.3 Pilot Physically Removed from Cockpit 14 2.3.1.4 Take-off Weight 15 2.3.1.5 Payload 15 i 2.3.2 UAS Accident Types 15 2.3.3 Derivation of an ELOS for UAS 16 2.4 Ground Impact Requirements 17 2.4.1 UAS Equivalent Level of Safety 18 2.4.2 Target Reliability Level 19 2.5 Conclusions 23 Chapter 3 Helicopter Dynamics Model 25 3.1 Introduction 25 3.1.1 Dynamics 25 3.1.2 Control 27 3.2 Helicopter Failures and Recovery 28 3.2.1 Main Rotor Failures 28 3.2.2 Tail Rotor Failures 28 3.2.3 Autorotation 29 3.3 Hovering State 30 3.3.1 Momentum Theory 31 3.3.2 Blade Element Theory 33 3.4 Vertical Descent 35 3.4.1 Vortex Ring State and Turbulent Wake State 36 3.4.2 Ground Effect 38 3.4.3 Inflow Dynamics 39 3.5 Vertical Autorotation Model 40 3.6 Remarks 42 Chapter 4 Controller Design 43 4.1 Principles of Model Predictive Control 43 4.1.1 Fundamentals 43 4.1.2 Prediction 45 4.1.3 Optimization 45 4.1.4 Tuning 46 4.2 Collective Controller Design 47 4.2.1 Internal Vertical Autorotation Model 47 4.2.2 Non-linear Optimization using Recurrent Neural Networks 49 4.2.3 Controller Derivation 50 4.2.3.1 Prediction 50 4.2.3.2 Constraints 52 4.2.3.3 Non-linear Optimization 55 4.2.4 Design Summary 55 4.3 Vertical Autorotation Controller 56 4.3.1 Roll/Pitch/Yaw Controller 58 4.3.2 Sensor Fusion 59 4.3.3 Neural Network Filtering 60 4.3.4 Vertical Autorotation Controller Block Diagram 61 ii Chapter 5 Simulation Results 62 5.1 OH-58A HERS 63 5.1.1 Baseline Scenario 63 5.1.1.1 Cost Function 67 5.1.1.2 Non-linear Optimization Problem Convexity 67 5.1.1.3 Convergence Characteristics 68 5.1.1.4 Real-time Operation 69 5.1.2 Initial Altitude 71 5.1.3 Learning Rate 71 5.1.4 Noise 73 5.1.5 Reaction Time 73 5.1.6 Sampling Rate 78 5.2 X-Plane Simulation 78 5.3 Raptor 30v2 82 5.3.1 Baseline Scenario 82 5.3.1.1 Cost Function 83 5.3.1.2 Non-linear Optimization Problem Convexity 85 5.3.1.3 Convergence Characteristics 86 5.3.1.4 Real-time Operation 87 5.3.2 Alternative Cost Function 89 5.3.3 Initial Altitude 89 5.3.4 Learning Rate 92 5.3.5 Noise 92 5.3.6 Reaction Time 97 5.3.7 Sampling Rate 97 5.3.8 Stricter Constraint 97 Chapter 6 Conclusion and Future Extensions 101 6.1 Model Prediction Improvement 102 6.2 Ω-constraint Handling 103 6.3 Integration into an Emergency Landing System 103 6.4 The Issue of Finding a Suitable Landing Location 105 6.5 Use in Manned Aircraft 106 List of References 108 Appendices 116 Appendix A: Case Study 117 Appendix B: Ground Fatality Probability Model Sensitivity Analysis 120 About the Author End Page iii List of Tables Table 2.1 FAR Part 23 aircraft classes and corresponding acceptable failure condition probability based on severity as defined in AC 23-1309-1C. 13 Table 2.2 Fatality rates from all accidents based on analysis of NTSB accident data [62] between 1983 and 2006. 17 Table 2.3 Fatality rates for accidents where an in-flight collision with terrain or water occurred. 19 Table 2.4 Fatality rates for accidents where one or a combination of in-flight collision with terrain or water, hard/forced landing, runway overrun or ditching oc- curred. 19 Table 5.1 Vertical autorotation model parameters for a modified OH-58A helicopter with high energy rotor system. 64 Table 5.2 Sensor noise levels used in the case of the OH-58A helicopter. 73 Table 5.3 Model parameters for the Thundertiger Raptor 30v2 R/C model helicopter. 83 Table 5.4 Sensor noise levels in the case of the Thundertiger Raptor 30v2 simulation. 92 Table A.1 Characteristics of five fixed wing and five rotary-wing UAS of various sizes, used for the case analysis. 117 Table A.2 The parameters used for each test case and a description of a possible sce- nario corresponding to that case. 117 Table A.3 Fatality probability and reliability requirements with respect to ground impact accidents for ten UAS under three different cases. 118 Table A.4 The percentage of the US area over which each UAS can loiter without violat- ing set TLS requirement, based on exhibited reliability. 119 iv List of Figures Figure 2.1 Risk reference system for large manned aircraft (the grayed areas signify unacceptable risk). 13 Figure 2.2 Primary and secondary accidents that can result from the operation of UAS and their possible outcomes. 17 Figure 2.3 Fatality rates from general aviation, commuter and air carrier accidents as a function of time. 18 Figure 2.4 The probability of fatality as a function of kinetic energy impact as estimated by Weibel [84] and models derived in RCC321 [67] and RCC323 [66]. 21 Figure 2.5 The probability of fatality as a function of kinetic energy impact for the pro- 6 posed model with fα = 10 J, fβ = 100 J and for several values of fs. 23 Figure 3.1 The single main rotor with tail rotor helicopter design. 26 Figure 3.2 Helicopters have 6 degrees of freedom. 27 Figure 3.3 A typical helicopter H-V curve like the one available in helicopter manuals. 30 Figure 3.4 The flow model created by the main rotor as assumed by momentum theory. 31 Figure 3.5 The forces acting on a rotor blade section as a result of local air velocity. 33 Figure 3.6 The forces acting on a rotor blade section as a result of local air velocity during descent. 36 Figure 3.7 The rotor wake characteristics starting from axial climb or hovering (normal working state) and moving through the vortex ring, turbulent wake and wind- mill brake states as the descent velocity increases. 37 Figure 3.8 The induced velocity profile in the four operational states. 38 Figure 3.9 The forces acting on a helicopter during vertical autorotative descent. 40 v Figure 4.1 A diagram of the basic principle behind model predictive control. 44 Figure 4.2 Block diagram of the prediction module of the controller. 52 Figure 4.3 Block diagram of the NN-NMPC. 55 Figure 4.4 The NN-NMPC algorithm. 56 Figure 4.5 Overview of the calculations in the NN-NMPC loop that can run in parallel. 57 Figure 4.6 Block diagram of the RPY controller. 59 Figure 4.7 Block diagram of the vertical autorotation controller. 61 Figure 5.1 During the autorotative descent the helicopter traverses three distinct regions of operation: free, Ω-controlled and vH-controlled descent. 63 Figure 5.2 The sink rate, rotor rpm and control input of the OH-58A helicopter for a descent from an initial altitude of 120 m (Ns = 10, Nc = 5).