Incremental twisting fault tolerant control for hypersonic vehicles with partial model knowledge

A passive fault tolerant control scheme is proposed for the full reentry trajectory tracking of a hypersonic vehicle in the presence of modelling uncertainties, external disturbances, and actuator faults. To achieve this goal, the attitude error dynamics with relative degree two is formulated first by ignoring the nonlinearities induced by the translational motions. Then, a multivariable twisting controller is developed as a benchmark to ensure the precise tracking task. Theoretical analysis with the Lyapunov method proves that the attitude tracking error and its first-order derivative can simultaneously converge to the origin exponentially. To depend less on the model knowledge and reduce the system uncertainties, an incremental twisting fault tolerant controller is derived based on the incremental nonlinear dynamic inversion control and the predesigned twisting controller. Notably, the proposed controller is user friendly in that only fixed gains and partial model knowledge are required

대기바람을 고려한 비행체의 수직-접선벡터 가중치 기반 경로추종 제어

학위논문(박사) -- 서울대학교대학원 : 공과대학 기계항공공학부, 2023. 2. 김유단.In this dissertation, a versatile path-following control method for aerial vehicles that can effectively deal with an ambient wind shear is proposed. Novel equations of motion for aerial vehicles considering the effect of continuously differentiable time-varying ambient winds are derived, and a path-following control law in a three-dimensional Euclidean space, called the Weighted-Perpendicular-Tangent-based Path-Following Control (WPTPFC), that makes the vehicle asymptotically follow a given sufficiently smooth desired path is developed. The proposed equations of motion consist of the aerodynamic angles and the inertial flight path angles as state variables. The equations cover a large range of ambient wind speeds without any approximation or linearization. Two unique angles of sequential rotations called the path-relative wind angles are proposed to parametrize the difference between the air-relative velocity and the inertial velocity caused by ambient wind terms. The conventional aerodynamic roll angle is not defined in a wind condition; thus, a compatible modified version is also proposed. The resulting state equations are structured to form a cascade system, which helps designers interpret the physical and geometrical meaning of individual subsystems and efficiently design a corresponding feedback control law. The model particularly fits motion control problems such as trajectory tracking or path-following control of fixed-wing-type aerial vehicles in the presence of time-varying ambient wind. The properties and potential of the proposed formulation are discussed in depth by focusing on the meaning and use of each proposed angle and the wind estimation techniques. In the design of WPTPFC, a reference point called the perpendicular foot is proposed for path-following control as an alternative to the closest point. Though the notion of perpendicular foot suffers from a similar singularity issue that the closest point has, it guarantees the continuity of solution with respect to the motion of the vehicle provided that the point does not reach some geometrical region, and it is shown that the region can be effectively avoided by the proposed singularity avoidance strategies. A Velocity Direction Input (VDI) and Steering Input (SI), which are common input configurations for mobile robots with nonzero moving speed, are considered the inputs of the control system. In particular, a special barrier function-based method called the Barrier Weighting Method (BWM) is developed to fully utilize the characteristics of the backstepping control for a certain class of constrained systems. Using the proposed technique, it is demonstrated that the velocity direction control law can be efficiently reused for the steering input control design preserving the singularity avoidance capability. Finally, the flight control system and WPTPFC are unified based on the time-scale decomposition technique. The compatibility between the methods is investigated, and appropriate coordinate transformations and control allocation methods are developed. Numerical simulations are performed to demonstrate the effectiveness of the proposed control scheme.본 논문에서는 대기바람이 존재하는 환경에서 운용되는 비행체에 적용할 수 있는 경로추종 기법을 제안하였다. 연속 미분가능한 대기바람 속도를 고려하는 비행체 운동방정식을 유도하고, 이를 기반으로 한 비행제어 법칙을 설계하였다. 또한, 비행체가 충분히 매끈한 경로를 추종하도록 하는 수직-접선벡터 가중치 기반 경로추종 제어를 개발하고 비행제어 법칙과 통합하였다. 본 논문에서 제안한 운동방정식은 공력각과 관성 경로각을 상태변수로 가진다. 두 개의 경로대비 바람각(path-relative wind angle)을 정의하여 대기바람에 의해 발생하는 대기속도와 대지속도 벡터 성분의 차이를 매개화 하였다. 대기바람이 존재하는 상황에서 공력롤각을 정의하여 대기바람이 존재하는 환경에서도 균형선회가 수월하게 하였다. 제안한 운동방정식은 계단식 구조를 가지도록 정식화하여 제어법칙을 설계하는 데 도움이 되도록 하였다. 또한, 제안한 모델은 바람이 존재하는 상황에서도 관성 경로각의 거동을 효율적으로 표현하므로 경로추종 제어법칙을 설계하기에 유리하다. 한편, 수직-접선벡터 가중치 기반 경로추종 제어는 경로에 대한 수선의 발(perpendicular foot)을 기준점으로 채택하여, 기존 기법에서 널리 쓰이는 최단점이 가지는 특이점, 불연속성 등의 문제들을 보완하였다. 시스템 입력으로는 속도방향 벡터(velocity direction)와 조향 벡터(steering)을 고려하였다. 특히, 장벽가중치 기법(barrier weighting method)을 적용하여 조향벡터 입력 시스템에 백스텝핑 기법을 도입할 때 기준점 운동방정식이 가지는 특이점을 효과적으로 회피하도록 하였다. 위의 연구내용은 시간비례 분해기법(time-scale decomposition)을 적용하여 비행제어 법칙과 경로추종 제어기법을 통합하였다. 개별적으로 설계된 비행제어법칙 간의 호환성을 검토하고, 적절한 변환 및 조종할당 기법을 개발하였다. 본 논문에서 제안한 기법의 성능을 평가하기 위해 수치 시뮬레이션을 수행하였다.1 Introduction 1 1.1 Motivation and Objective 1 1.1.1 Effects of Wind Shear on Aerial Vehicles 1 1.1.2 Path-Following Control for Aerial Vehicles 3 1.1.3 Unification of Flight Controller and PFC 4 1.1.4 Study Objective 5 1.2 Literature Survey 6 1.2.1 Flight in Ambient Wind Shear 6 1.2.2 PFC for Aerial Vehicles 7 1.3 Research Contribution 9 1.3.1 Flight Dynamics 9 1.3.2 Weighted-Perpendicular-Tangent-based PFC 10 1.3.3 Summary 11 1.4 Dissertation Organization 13 2 Flight Dynamics Considering Time-Varying Ambient Wind 14 2.1 Derivation of Equations of Motion 15 2.1.1 External Force and Moment 20 2.1.2 Angular Velocity Dynamics 22 2.1.3 Aerodynamic Angle Dynamics 22 2.1.4 Flight Path Angle Dynamics 25 2.1.5 Airspeed Dynamics 26 2.1.6 Ground Speed Dynamics 27 2.1.7 Aerodynamic Roll Angle Dynamics 28 2.1.8 Overall Dynamics 36 2.2 Discussions 39 2.2.1 Aerodynamic Roll Angle 39 2.2.2 Path-Relative Wind Angles 40 2.2.3 Compensation of Unsteady Winds 40 2.2.4 Local Wind Field 42 2.2.5 Wind Estimation 43 3 Design of Flight Control System 49 3.1 State Representation 50 3.2 Cascade System Approximation 51 3.3 Angular Velocity Tracking Control 52 3.4 Aerodynamic Angle Tracking Control 54 3.5 Flight-path Angle Tracking Control 56 3.6 Numerical Examples 58 3.6.1 Example 3.1 59 3.6.2 Example 3.2 60 3.6.3 Example 3.3 65 4 Lyapunov Barrier Weighting Method 67 4.1 Notation 71 4.2 Mathematical Preliminary 72 4.3 Barrier Method 78 4.4 Lyapunov Barrier Weighting Method 83 5 Weighted-Perpendicular-Tangent-based Path-Following Control 90 5.1 Notation 91 5.2 Path-Following Problem 92 5.2.1 Perpendicular Foot 92 5.2.2 Vehicle Dynamics 94 5.2.3 Problem Statement 96 5.2.4 Path and Initial Position 99 5.2.5 Closest Point and Perpendicular Foot 99 5.3 Velocity Direction Control 104 5.3.1 Dynamics 104 5.3.2 Controller Design 105 5.3.3 Direct Approaching 113 5.3.4 Singularity Avoidance 114 5.3.5 Design Example 116 5.4 Steering Control 118 5.4.1 Dynamics 118 5.4.2 Controller Design 120 5.4.3 Singularity Avoidance 122 5.4.4 Design Example 125 5.5 Numerical Simulations 127 5.5.1 Rotation weighting function 127 5.5.2 Singularity Avoidance 130 5.5.3 Various Initial Position and Velocity 133 6 Unification of Flight Control System and WPTPFC 137 6.1 Parameter Normalization 138 6.2 WPTPFC: Velocity Direction Control 138 6.2.1 FPA Command Filter 140 6.3 WPTPFC: Steering Control 144 6.3.1 Normal Acceleration Control Allocation 146 6.3.2 Low-pass Filter for VDI Control 146 6.4 Numerical Simulation 147 6.4.1 Scenario 1: straight line tracking 147 6.4.2 Scenario 2: descending vertical helix tracking 153 6.4.3 Various simulation results 156 7 Conclusion 165 7.1 Concluding Remarks 165 7.2 Future Research 166 Appendices 166 A Flight Dynamics 167 A.1 Components of the Equations of Motion 167 A.2 Angle Conversion 169 B WPTPFC 172 B.1 Foot Dynamics 172 B.1.1 Curve Parametrization 172 B.1.2 Robust Foot Control 173 초록 184박

Fault Diagnosis and Fault-Tolerant Control of Unmanned Aerial Vehicles

With the increasing demand for unmanned aerial vehicles (UAVs) in both military and civilian applications, critical safety issues need to be specially considered in order to make better and wider use of them. UAVs are usually employed to work in hazardous and complex environments, which may seriously threaten the safety and reliability of UAVs. Therefore, the safety and reliability of UAVs are becoming imperative for development of advanced intelligent control systems. The key challenge now is the lack of fully autonomous and reliable control techniques in face of different operation conditions and sophisticated environments. Further development of unmanned aerial vehicle (UAV) control systems is required to be reliable in the presence of system component faults and to be insensitive to model uncertainties and external environmental disturbances. This thesis research aims to design and develop novel control schemes for UAVs with consideration of all the factors that may threaten their safety and reliability. A novel adaptive sliding mode control (SMC) strategy is proposed to accommodate model uncertainties and actuator faults for an unmanned quadrotor helicopter. Compared with the existing adaptive SMC strategies in the literature, the proposed adaptive scheme can tolerate larger actuator faults without stimulating control chattering due to the use of adaptation parameters in both continuous and discontinuous control parts. Furthermore, a fuzzy logic-based boundary layer and a nonlinear disturbance observer are synthesized to further improve the capability of the designed control scheme for tolerating model uncertainties, actuator faults, and unknown external disturbances while preventing overestimation of the adaptive control parameters and suppressing the control chattering effect. Then, a cost-effective fault estimation scheme with a parallel bank of recurrent neural networks (RNNs) is proposed to accurately estimate actuator fault magnitude and an active fault-tolerant control (FTC) framework is established for a closed-loop quadrotor helicopter system. Finally, a reconfigurable control allocation approach is combined with adaptive SMC to achieve the capability of tolerating complete actuator failures with application to a modified octorotor helicopter. The significance of this proposed control scheme is that the stability of the closed-loop system is theoretically guaranteed in the presence of both single and simultaneous actuator faults

Using learning from demonstration to enable automated flight control comparable with experienced human pilots

Modern autopilots fall under the domain of Control Theory which utilizes Proportional Integral Derivative (PID) controllers that can provide relatively simple autonomous control of an aircraft such as maintaining a certain trajectory. However, PID controllers cannot cope with uncertainties due to their non-adaptive nature. In addition, modern autopilots of airliners contributed to several air catastrophes due to their robustness issues. Therefore, the aviation industry is seeking solutions that would enhance safety. A potential solution to achieve this is to develop intelligent autopilots that can learn how to pilot aircraft in a manner comparable with experienced human pilots. This work proposes the Intelligent Autopilot System (IAS) which provides a comprehensive level of autonomy and intelligent control to the aviation industry. The IAS learns piloting skills by observing experienced teachers while they provide demonstrations in simulation. A robust Learning from Demonstration approach is proposed which uses human pilots to demonstrate the task to be learned in a flight simulator while training datasets are captured. The datasets are then used by Artificial Neural Networks (ANNs) to generate control models automatically. The control models imitate the skills of the experienced pilots when performing the different piloting tasks while handling flight uncertainties such as severe weather conditions and emergency situations. Experiments show that the IAS performs learned skills and tasks with high accuracy even after being presented with limited examples which are suitable for the proposed approach that relies on many single-hidden-layer ANNs instead of one or few large deep ANNs which produce a black-box that cannot be explained to the aviation regulators. The results demonstrate that the IAS is capable of imitating low-level sub-cognitive skills such as rapid and continuous stabilization attempts in stormy weather conditions, and high-level strategic skills such as the sequence of sub-tasks necessary to takeoff, land, and handle emergencies

A generalized framework for robust nonlinear compensation (application to an atmospheric reentry control problem)

Ce travail de thèse est consacré à l'extension de l'Inversion Dynamique non-linéaire (NDI-Nonlinear Dynamic Inversion) pour un ensemble plus grand de systèmes non-linéaires, tout en garantissant des conditions de stabilité suffisantes. La NDI a été étudiée dans le cas de diverses applications, y compris en aéronautique et en aérospatiale. Elle permet de calculer des lois de contrôle capables de linéariser et de découpler un modèle non-linéaire à tout point de fonctionnement de son enveloppe d'état. Cependant cette méthode est intrinsèquement non-robuste aux erreurs de modélisation et aux saturations en entrée. En outre, dans un contexte non-linéaire, l'obtention d'une garantie quantifiable du domaine de stabilité atteint reste à l'heure actuelle complexe. Contrairement aux approches classiques de la NDI, notre méthodologie peut être considérée comme un cadre de compensation non-linéaire généralisé qui permet d'intégrer les incertitudes et les saturations en entrée dans le processus de conception. En utilisant des stratégies de contrôle antiwindup, la loi de pilotage peut être calculée grâce à un simple processus en deux phases. Dans ce cadre de travail généralisé des transformations linéaires fractionnaires (LFT - Linear Fractional Transformations) de la boucle fermée non-linéaire peuvent être facilement déduites pour l'analyse de la stabilité robuste en utilisant des outils standards pour de systèmes linéaires. La méthode proposée est testée pour le pilotage d'un véhicule de rentrée atmosphérique de type aile delta lors de ses phases hypersonique, transsonique et subsonique. Pour cette thèse, un simulateur du vol incluant divers facteurs externes ainsi que des erreurs de modélisation a été développé dans Simulink.This thesis work is devoted to extending Nonlinear Dynamic Inversion (NDI) for a large scale of nonlinear systems while guaranteeing sufficient stability conditions. NDI has been studied in a wide range of applications, including aeronautics and aerospace. It allows to compute nonlinear control laws able to decouple and linearize a model at any operating point of its state envelope. However, this method is inherently non-robust to modelling errors and input saturations. Moreover, obtaining a quantifiable guarantee of the attained stability domain in a nonlinear control context is not a very straightforward task. Unlike standard NDI approaches, our methodology can be viewed as a generalized nonlinear compensation framework which allows to incorporate uncertainties and input saturations in the design process. Paralleling anti-windup strategies, the controller can be computed through a single multichannel optimization problem or through a simple two-step process. Within this framework, linear fractional transformations of the nonlinear closed-loop can be easily derived for robust stability analysis using standard tools for linear systems. The proposed method is tested for the flight control of a delta wing type reentry vehicle at hypersonic, transonic and subsonic phases of the atmospheric reentry. For this thesis work, a Flight Mechanics simulator including diverse external factors and modelling errors was developed in Simulink.TOULOUSE-ISAE (315552318) / SudocSudocFranceF

Supermanoeuvrability in a biomimetic morphing-wing aircraft

In this work we study the supermanoeuvrability of a biomimetic morphing-wing case study aircraft system. Analytical and computational models of biomimetic flight dynamics are developed, utilising multibody dynamics, computational fluid dynamics, and reduced-order aerodynamic models; and validated with respect to experimentally-derived flight dynamics of a Pioneer RQ-2 UAV. These models are used to explore the capability of this system for a wide range of biological and other supermanoeuvres: multi-axis quasistatic nose-pointing-and-shooting (NPAS) / direct force capability; multi-axis rapid-nose-pointing-and-shooting (RaNPAS) including Pugachev’s cobra; ballistic transition; and anchor turning. Novel contributions include the development of transient aerodynamic models for a three-dimensional flight-simulation context; the development of novel methods for assessing transient model validity; the development of improved methods of quaternion variational integration; the development of quasi-trim and continuation-based methods for the design, exploration, analysis and control of manoeuvres in biomimetic morphing-wing systems; an assessment of the complex spiral mode stability effects present in asymmetrically-morphed system trim states; and a demonstration of the wide-ranging potential for advanced supermanoeuvrability in biomimetic morphing-wing systems. Industrial applications include the design of high-precision guided missiles for use in complex, e.g. urban, environments.Cambridge Commonwealth Prince of Wales Scholarship (Cambridge Trust

Controller Design of Winged Rocket and Its Stability Analysis Based on Hierarchical Dynamic Inversion

本論文は非線形性の強いダイナミクスを持つ有翼式の宇宙輸送システムに対して有効な制御系の一設計手法について提案するものである．近年，世界中で精力的に開発が進められている再使用型の宇宙往還機であるが，揚力を利用する有翼式宇宙往還機は，エンジンの逆噴射による円筒式の宇宙往還機に比べて，打ち上げ後フライバックして任意の着陸地点までの帰還能力に優れている．また，宇宙への物資輸送や観光だけでなく大陸間弾道飛行などへの転用も可能であることからも，航空宇宙市場の拡大に貢献することが期待される．ところで，有翼式の宇宙往還機が利用する空力特性は，飛行速度や高度によって非線形に大きく変化する．加えて，宇宙往還機に求められる姿勢制御性能の要求は極めて高く，設計者の負担が大きい．そのため，自律飛行制御システムにおける姿勢制御系設計法の確立は重要研究課題の一つである．スペースシャトルに代表される従来の有翼式宇宙往還機の姿勢制御は，予め決められた軌道に沿った制御則の構築と安定性解析を行って決めたゲインスケジュールに基づいて行われてきた．しかし，これからの有翼式宇宙往還機には，多様な飛行環境に加えて，想定軌道からの逸脱や飛行安全の要求から咄嗟の飛行軌道の変更も想定しなければならず，飛行環境が既知の条件で用いられるゲインスケジューリングによる制御では，予め膨大な量の制御系設計が必要となり，実用的な制御システムの構築は困難となる．こうした多様な飛行環境や非線形システムに対応する制御系設計手法の一つとして，機体が持つ非線形な動特性をフィードバックによって打ち消し，任意の応答性能を実現するためのダイナミックインバージョン法がある．その一方で，宇宙往還機の制御システムは高次の非線形システムとなることもしばしばである．この場合，制御入力の導出には複雑な微分方程式を解かなければならず計算負荷が大きいという課題もある．近年では状態変数の動特性の違いに着目してシステムを階層構造化する手法が提案され，階層毎に線形化処理を行うような研究が進められ，実用化に近づいてきた．しかしながら，依然として階層構造を取り入れた制御システムの安定性解析には，複雑な微分方程式を解く必要があるため困難を極め，階層ごとに安定性は確保しているものの，経験的に階層ごとの動特性を調整する等して全体システムとしての安定性を担保しているという状況にある．本研究は，多階層ダイナミックインバージョン法における非線形システムが持つ動特性について，階層ごとに線形近似した支配的な伝達関数(以降，線形近似伝達関数と呼ぶ)を見出し，経験に頼らずに制御系のゲイン設定を容易に行うことができる方法を提案するところに独自性および新規性がある．その結果，階層ごとの線形近似伝達関数の導出により，階層間の動特性の連成も考慮することができるようになったことで全体システムの動特性を評価可能となり，従来法では評価が難しかった制御用アクチュエータの応答要求も陽に示せるようになった．この新しい理論構築は，多階層ダイナミックインバージョン法の制御系設計の簡便化が期待され，非線形制御系の実用化を容易にする．本論文では，先行研究と本研究の制御系設計例について説明した後，有翼式の宇宙往還機の縦の飛行運動を対象として，飛行制御系設計法について述べ，線形近似伝達関数と非線形飛行運動について比較評価する．最後に，実用化に向けた6自由度飛行運動を対象として，飛行制御系設計法について述べ，安定性について評価する．九州工業大学博士学位論文 学位記番号：工博甲第450号 学位授与年月日：平成30年3月23日第1章 序論|第2章 既存のダイナミックインバージョン法|第3章 多階層ダイナミックインバージョン法における線形近似応答を用いた制御系設計法|第4章 縦飛行運動の非線形制御系への応用|第5章 縦および横・方向連成運動の非線形制御系への応用|第6章 結論九州工業大学平成29年

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described