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Design, Implementation and Testing of Advanced Control Laws for Fixed-Wing Uavs

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Design, Implementation and Testing of Advanced Control Laws for Fixed-Wing Uavs Politecnico di Torino Porto Institutional Repository [Doctoral thesis] Design, Implementation and Testing of Advanced Control Laws for Fixed-wing UAVs Original Citation: Sartori D. (2014). Design, Implementation and Testing of Advanced Control Laws for Fixed-wing UAVs. PhD thesis Availability: This version is available at : http://porto.polito.it/2571146/ since: October 2014 Published version: DOI:10.6092/polito/porto/2571146 Terms of use: This article is made available under terms and conditions applicable to Open Access Policy Article ("Creative Commons: Attribution-Noncommercial-Share Alike 3.0") , as described at http://porto. polito.it/terms_and_conditions.html Porto, the institutional repository of the Politecnico di Torino, is provided by the University Library and the IT-Services. The aim is to enable open access to all the world. Please share with us how this access benefits you. Your story matters. (Article begins on next page) POLITECNICO DI TORINO SCUOLA DI DOTTORATO Dottorato di Ricerca in Ingegneria Aerospaziale - XXVI ciclo Tesi di Dottorato Design, Implementation and Testing of Advanced Control Laws for Fixed-wing UAVs Daniele Sartori Tutori Coordinatore del corso di dottorato Prof. Giorgio Guglieri Prof.ssa Fulvia Quagliotti Prof.ssa Fulvia Quagliotti Prof. Matthew Rutherford Prof. Kimon Valavanis 2014 ABSTRACT The present PhD thesis addresses the problem of the control of small fixed-wing Unmanned Aerial Vehicles (UAVs). In the scientific community much research is dedicated to the study of suitable control laws for this category of aircraft. This interest is motivated by the several applications that these platforms can perform and by their peculiarities as dynamical systems. In fact, small UAVs are characterized by highly nonlinear behavior, strong coupling between longitudinal and latero-directional planes, and high sensitivity to external disturbances and to parametric uncertainties. Furthermore, the challenge is increased by the limited space and weight available for the onboard electronics. The aim of this PhD thesis is to provide a valid confrontation among three different control techniques and to introduce an innovative autopilot configuration suitable for the unmanned aircraft field. Three advanced controllers for fixed-wing unmanned aircraft vehicles are designed and implemented: PID with H1 robust approach, L1 adaptive controller and nonlinear back- stepping controller. All of them are analyzed from the theoretical point of view and validated through numerical simulations with a mathematical UAV model. One is implemented on a microcontroller board, validated through hardware simulations and tested in flight. The PID with H1 robust approach is used for the definition of the gains of a commer- cial autopilot. The proposed technique combines traditional PID control with an H1 loop shaping method to assess the robustness characteristics achievable with simple PID gains. It is demonstrated that this hybrid approach provides a promising solution to the problem of tuning commercial autopilots for UAVs. Nevertheless, it is clear that a tradeoff between robustness and performance is necessary when dealing with this standard control technique. The robustness problem is effectively solved by the adoption of an L1 adaptive controller for complete aircraft control. In particular, the L1 logic here adopted is based on piecewise constant adaptive laws with an adaptation rate compatible with the sampling rate of an au- topilot board CPU. The control scheme includes an L1 adaptive controller for the inner loop, while PID gains take care of the outer loop. The global controller is tuned on a linear decou- pled aircraft model. It is demonstrated that the achieved configuration guarantees satisfying performance also when applied to a complete nonlinear model affected by uncertainties and Abstract parametric perturbations. The third controller implemented is based on an existing nonlinear backstepping tech- nique. A scheme for longitudinal and latero-directional control based on the combination of PID for the outer loop and backstepping for the inner loop is proposed. Satisfying results are achieved also when the nonlinear aircraft model is perturbed by parametric uncertainties. A confrontation among the three controllers shows that L1 and backstepping are comparable in terms of nominal and robust performance, with an advantage for L1, while the PID is always inferior. The backstepping controller is chosen for being implemented and tested on a real fixed- wing RC aircraft. Hardware-in-the-loop simulations validate its real-time control capability on the complete nonlinear model of the aircraft adopted for the tests, inclusive of sensors noise. An innovative microcontroller technology is employed as core of the autopilot sys- tem, it interfaces with sensors and servos in order to handle input/output operations and it performs the control law computation. Preliminary ground tests validate the suitability of the autopilot configuration. A limited number of flight tests is performed. Promising results are obtained for the control of longitudinal states, while latero-directional control still needs major improvements. iii CONTENTS Abstract :::::::::::::::::::::::::::::::::::::::::::: ii Contents ::::::::::::::::::::::::::::::::::::::::::: iv List of Figures :::::::::::::::::::::::::::::::::::::::: vii List of Tables ::::::::::::::::::::::::::::::::::::::::: xi Nomenclature ::::::::::::::::::::::::::::::::::::::::: xiii Acknowledgments :::::::::::::::::::::::::::::::::::::: xvi 1. Preface :::::::::::::::::::::::::::::::::::::::::: 1 2. Introduction :::::::::::::::::::::::::::::::::::::::: 4 2.1 Overview of UAV technology . 4 2.2 Control problem and proposed solutions . 11 2.3 PID with H1 related work and contribution . 13 2.4 L1 related work and contribution . 15 2.5 Backstepping related work and contribution . 16 3. Fixed-wing Aircraft Mathematical Model ::::::::::::::::::::::: 18 3.1 Reference frames . 18 3.1.1 Generic body axes . 18 3.1.2 Wind axes . 18 3.1.3 NED axes . 19 3.1.4 ECEF axes . 20 3.2 Euler angles . 20 3.3 Notable Euler angles . 22 3.3.1 Body axes - Wind axes . 22 Contents 3.3.2 Body axes - NED axes . 23 3.4 Nonlinear mathematical model . 24 3.4.1 Forces equation . 24 3.4.2 Moments equation . 25 3.4.3 Attitude equation . 25 3.5 Linear mathematical model . 26 3.6 Aircraft models . 29 3.6.1 MH850 UAV model . 30 3.6.2 MH850 UAV actuators model . 33 3.6.3 C172P aircraft model . 36 3.6.4 Ultrastick 25e aircraft model . 37 4. H1 Robust Approach to PID Design :::::::::::::::::::::::::: 40 4.1 Introduction to PID technique . 40 4.2 Introduction to H1 approach . 41 4.3 Problem formulation and proposed control design . 43 4.4 Practical application and simulation results . 49 4.5 Conclusions . 60 5. L1 Adaptive Controller ::::::::::::::::::::::::::::::::: 61 5.1 Introduction to L1 adaptive controller . 61 5.2 Problem formulation and proposed control approach . 62 5.3 Implementation and simulation results . 65 5.3.1 Linear case design and simulation results . 66 5.3.2 Nonlinear case simulation results . 69 5.3.3 Parametric robustness validation . 73 5.4 Conclusions . 73 6. Backstepping Nonlinear Controller ::::::::::::::::::::::::::: 76 6.1 Introduction to backstepping nonlinear controller . 76 6.2 Problem formulation and proposed control approach . 77 6.2.1 Shaping of the equations of motion . 78 6.2.2 Backstepping controller design . 80 6.2.3 Control strategy . 84 6.3 Simulation results . 87 6.3.1 Parametric robustness validation . 89 v Contents 6.3.2 Confrontation among backstepping, L1 and PID controllers . 92 6.4 C172P SIL simulation results . 95 6.5 C172P HIL simulation results . 98 6.6 Conclusions . 101 7. Experiments and Flight Tests :::::::::::::::::::::::::::::: 103 7.1 Sensors noise model . 103 7.1.1 Velocity measurement . 103 7.1.2 Altitude measurement . 105 7.1.3 Attitude measurement . 106 7.2 Kalman filter . 107 7.3 Ultrastick 25e simulation results . 108 7.4 Ultrastick 25e HIL simulation results . 112 7.5 Aircraft - Controller integration . 112 7.6 Command - Deflection correlation . 119 7.7 Preliminary ground tests . 120 7.8 Preliminary flight tests . 121 7.9 Conclusions . 125 8. Conclusions :::::::::::::::::::::::::::::::::::::::: 128 Appendices :::::::::::::::::::::::::::::::::::::::::: 131 A. Evaluation of an L1 Controller for Wing Rock Suppression ::::::::::::: 132 A.1 Introduction . 132 A.2 Wing rock model . 134 A.3 Controller design . 139 A.4 Implementation and simulation results . 142 A.5 Conclusions . 145 B. Ultrastick 25e onboard connections schemes :::::::::::::::::::::: 148 Bibliography ::::::::::::::::::::::::::::::::::::::::: 151 vi LIST OF FIGURES 2.1 Tupolev Tu-143 reconnaissance drone [9]. 5 2.2 Aerosonde Mark 4.7 UAV for Antartic climate studies [14]. 6 2.3 Example of GCS from Aeronautics Defense Systems [21]. 8 2.4 Example of EO/IR payload from Controp [22]. 9 3.1 Generic body axes . 19 3.2 Wind axes . 19 3.3 NED and ECEF axes orientation . 20 3.4 Two generic reference frames . 21 3.5 Euler angles for body axes - wind axes rotation . 23 3.6 Sequence of rotations to align FN to FB ..................... 23 3.7 MH850 UAV . 31 3.8 MH850 UAV model in ACI software tool . 32 3.9 GWS IQ-100 analog servo. 34 3.10 Time domain normalized input and output series for V = 7:5 m/s. 34 3.11 Bode plot for the servo transfer function . 35 3.12 Cessna 172P aircraft . 36 3.13 Ultrastick 25e aircraft . 37 4.1 Longitudinal control scheme . 43 4.2 Latero-directional control scheme . 44 4.3 Root locus plot . 45 4.4 Robust control scheme . 46 4.5 P − K − ∆ framework (a) and M − ∆ framework (b) . 48 4.6 MicroPilot MP2028 autopilot [109] . ..
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