Immersion and Invariance-based Disturbance Observer and Its Application to Safe Control

When the disturbance input matrix is nonlinear, existing disturbance observer design methods rely on the solvability of a partial differential equation or the existence of an output function with a uniformly well-defined disturbance relative degree, which can pose significant limitations. This note introduces a systematic approach for designing an Immersion and Invariance-based Disturbance Observer (IIDOB) that circumvents these strong assumptions. The proposed IIDOB ensures the disturbance estimation error is globally uniformly ultimately bounded by approximately solving a partial differential equation while compensating for the approximation error. Furthermore, by integrating IIDOB into the framework of control barrier functions, a filter-based safe control design method for control-affine systems with disturbances is established where the filter is used to generate an alternative disturbance estimation signal with a known derivative. Sufficient conditions are established to guarantee the safety of the disturbed systems. Simulation results demonstrate the effectiveness of the proposed method

Sliding modes in constrained systems control

Abstract—In this paper, a sliding-mode-based design framework for fully actuated mechanical multibody system is discussed. The framework is based on the possibility to represent complex motion as a collection of tasks and to find effective mapping of the system coordinates that allows decoupling task and constraint control so one is able to enforce concurrently, or in certain time succession, the task and the constraints. The approach seems naturally encompassing the control of motion systems in interaction, and it allows application to bilateral control, multilateral control, etc. Such an approach leads to a more natural interpretation of the system tasks, simpler controller design, and easier establishment of the systems hierarchy. It allows a unified mathematical treatment of task control in the presence of constraints required to be satisfied by the system coordinates. In order to show the applicability of the proposed techniques, simulation and experimental results for high-precision systems in microsystem assembly tasks and bilateral control systems are presented

High order disturbance observer design for linear and nonlinear systems

© 2015 IEEE. In this paper, a disturbance observer is proposed for nonlinear systems with high order disturbance, where not only disturbance but also its high order derivatives are estimated. The relationship of the proposed observer with the existing results is discussed. Then, the result is further extended to the case of minimal-order output-based disturbance observer design for linear systems subject to high order disturbances. Two practical examples about actuator fault diagnosis for a nonlinear missile system and disturbance estimation for a double-effect pilot plant evaporator system with unobservable states are provided to illustrate the effectiveness of the proposed approaches

Reduced-order disturbance observer design for discrete-time linear stochastic systems

The conventional disturbance observers for discrete-time linear stochastic systems assume that the system states are fully estimable and the disturbance estimate is dependent on the estimated system states, hereafter termed Full-Order Disturbance Observers (FODOs). This paper investigates the design of Reduced-Order Disturbance Observers (RODOs) when the system state variables are not fully estimable. An existence condition of RODO is established, which is shown to be more easily satisfied than that of the conventional FODOs and consequently it has substantially extended the scope of applications of disturbance observer theory. Then a set of recursive formulae for the RODO is developed for on-line applications. Finally, it is furth er shown that the conventional FODOs are a special case of the proposed RODO in the sense that the former reduces to the RODO when the states become fully estimable in the presence of disturbances. Examples are given to demonstrate the effectiveness and advantages of the proposed approach

Safety Guaranteed Control for Spacecraft Inspection Mission

This paper investigates the safety guaranteed problem in spacecraft inspection missions, considering multiple position obstacles and logical attitude forbidden zones. In order to address this issue, we propose a control strategy based on control barrier functions, summarized as "safety check on kinematics" and "velocity tracking on dynamics" approach. The proposed approach employs control barrier functions to describe the obstacles and to generate safe velocities via the solution of a quadratic programming problem. Subsequently, we design a proportional-like controller based on the generated velocity, which, despite its simplicity, can ensure safety even in the presence of velocity tracking errors. The stability and safety of the system are rigorously analyzed in this paper. Furthermore, to account for model uncertainties and external disturbances, we incorporate an immersion and invariance-based disturbance observer in our design. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed control strategy.Comment: 22 pages, 9 figures, submitted to JGC

Multi-Objective Gust Load Alleviation Control Designs for an Aeroelastic Wind Tunnel Demonstration Wing

This paper presents several control and gust disturbance estimation techniques applied to a mathematical model of a physical flexible wing wind tunnel model used in ongoing tests at the University of Washington Aeronautical Laboratory's Kirsten Wind Tunnel. Three methods of gust disturbance estimation are presented, followed by three control methods: LQG, Basic Multi-Objective (BMO), and a novel Multi-Objective Prediction Correction (MOPC) controller. The latter of which augments a multi-objective controller, and attempts to correct for errors in the disturbance estimate. A simplified linear simulation of the three controllers is performed and a simple MIMO stability and robustness assessment is performed. Then, the same controllers are simulated in a higher fidelity Simulink environment that captures sampling, saturation and noise effects. This preliminary analysis indicates that the BMO controller provides the best performance and largest stability margins

해밀턴 구조와 외란 관측기 기법을 이용한 라그랑주 점 궤도 주변에서의 경계 상대 운동 및 궤도유지

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 기계항공공학부, 2020. 8. 김유단.In this dissertation, a novel strategy for station-keeping and formation flight of spacecraft in the vicinity of unstable libration point orbits is presented, and its performance and stability are analyzed. The presented control strategy leverages the Hamiltonian nature of the equations of motion, rather than simply applying the control theory from the perspective of ``signal processing". A filtered extended high-gain observer, a kind of disturbance observer, is designed to mitigate the performance degradation of the control strategy due to model uncertainties and external disturbances. Canonical coordinates are adopted to design a controller that exploits the mathematical structure of Hamiltonian system inherent in orbital mechanics, and then the equations of motion of spacecraft are represented in the form of Hamilton's equation with generalized coordinates and momenta. The baseline controller, utilizing the canonical form of the Hamiltonian system, is divided into two parts: i) a Hamiltonian structure-preserving control, and ii) an energy dissipation control. Hamiltonian structure-preserving control can be designed in accordance with the Lagrange-Dirichlet criterion, i.e., a sufficient condition for the nonlinear stability of Hamiltonian system. Because the Hamiltonian structure-preserving control makes the system marginally stable instead of asymptotically stable, the resultant motion of the Hamiltonian structure-preserving control yields a bounded trajectory. Through the frequency analysis of bounded relative motion, a circular motion can be achieved for particular initial conditions. By appropriately switching the gain of the Hamiltonian structure-preserving control, the radius of bounded motion can be adjusted systematically, which is envisioned that this approach can be applied to spacecraft formation flight. Furthermore, the energy dissipation control can be activated to make the spacecraft's bounded relative motion converge to the nominal orbit. On the other hand, a filtered extended high-gain observer is designed for the robust station-keeping and formation flight even under highly uncertain deep-space environment. The filtered extended high-gain observer estimates the velocity state of the spacecraft and disturbance acting on the spacecraft by measuring only the position of the spacecraft. The filtered extended high-gain observer includes an integral state feedback to attenuate navigation error amplification due to the high gain of the observer. The global convergence of the observer is shown, and it is also shown that the tracking error is ultimately bounded to the nominal libration point orbit by applying the Hamiltonian structure-based controller. Numerical simulations demonstrate the performance of the designed control strategy. Halo orbit around the L2 point of the Earth-Moon system is considered as an illustrative example, and various perturbations are taken into account.본 논문에서는 불안정한 동적특성을 갖는 라그랑주 점 궤도 주변에서 위성의 궤도유지 및 편대비행을 위한 제어기와 관측기를 설계하였으며, 설계된 제어기와 관측기의 안정성 그리고 전체 시스템의 안정성을 분석하였다. 설계한 기준 제어 전략은 신호처리 관점의 제어이론을 기반으로 하지 않고, 라그랑주 점 궤도의 자연적인 수학적 구조를 활용하였다. 모델 불확실성과 외부 외란으로 인한 기준 제어 전략의 성능저하를 완화하기 위해 외란관측기의 일종인 확장 고이득 관측기를 설계하였다. 본 논문에서는 궤도역학에 내재되어 있는 해밀턴 시스템의 구조를 활용하는 제어기를 설계하기 위해 정준좌표를 도입하였으며, 좌표변환을 통해 위성의 운동방정식을 해밀턴 시스템의 정준형식으로 나타내었다. 해밀턴 시스템의 정준형식으로 표현된 운동방정식을 이용해 설계한 기준 제어기는 해밀턴-구조 보존제어와 에너지 소산제어로 분리 설계된다. Lagrange-Dirichlet 기준은 정준형식으로 나타낸 해밀턴 시스템의 비선형 안정성을 판별하는 충분조건으로, 해밀턴-구조 보존제어 설계의 기준이 된다. 기준 라그랑주 점 궤도 주위에서 해밀턴-구조 보존 제어를 적용한 결과, 위성은 기준궤도로 수렴하지 않고 기준궤도와 유한한 거리를 유지하는 경계운동을 하였다. 경계운동의 주파수 분석을 통하여 특정한 초기조건 하에서는 원형 경계운동이 가능하였으며, 더 나아가 해밀턴-구조 보존제어의 제어이득 값을 적절히 설정함으로 원형 경계운동의 크기를 체계적으로 조절할 수 있고 이를 위성 편대비행에 응용할 수 있음을 보였다. 추가적으로 에너지 소산제어 입력을 설계하여 위성이 기준 라그랑주 점 궤도로 점근 수렴하는 운동도 가능함을 수학적으로 증명하였다. 한편, 심우주상의 예측하기 어려운 섭동력 및 불확실성 하에서도 강건한 궤도유지와 편대비행을 수행하기 위해 확장 고이득 관측기를 설계하였다. 확장 고이득 관측기는 위성의 위치 정보만을 이용하여 위성의 속도와 위성에 작용하는 외란을 동시에 추정하며, 추정된 상태변수를 이용하여 기준이 되는 피드백 제어입력을 생성한다. 추정된 외란은 피드포워드 형태의 제어입력으로 구성되어 제어기의 성능을 강건하게 만든다. 심우주 공간상의 위성의 궤도결정 결과로 얻어지는 위치정보는 상대적으로 큰 오차를 갖는데, 확장 고이득 관측기는 위치 오차를 증폭시킨다는 단점이 있다. 본 연구에서는 이러한 단점을 완화하고자 적분 관측기 형태로 개선된 필터링된 확장 고이득 관측기를 설계하고 수렴성을 분석하였다. 그리고 필터링된 확장 고이득 관측기와 시스템의 해밀턴 구조를 활용하는 제어기를 적용한 전체 시스템의 안정성을 분석하였다. 불안정한 라그랑주 점 궤도 주변에서 위성의 궤도유지와 편대비행을 위해 설계된 제어기법의 성능을 확인하고자 수치 시뮬레이션을 수행하였다. 수치 시뮬레이션을 위해 지구-달 시스템의 L2 주변 헤일로 궤도를 기준궤도로 설정하였으며, 심우주 공간에서의 다양한 섭동력 및 모델 불확실성을 고려하였다. 궤도결정 오차로 인한 위성의 위치 및 속도 불확실성이 존재 하더라도 제안한 제어기법을 통해 위성이 궤도유지와 편대비행을 만족스럽게 수행함을 보였다.1 Introduction 1 1.1 Background and Motivation 1 1.2 Literature Review 3 1.2.1 Spacecraft Station-Keeping in the Vicinity of the Libration Point Orbits 3 1.2.2 Spacecraft Formation Flight in the Vicinity of the Libration Point Orbits 5 1.3 Contributions 7 1.4 Dissertation Outline 10 2 Background 13 2.1 Circular Restricted Three-Body Problem 14 2.1.1 Equilibrium Solutions and Periodic Orbits 16 2.1.2 Stability of Periodic Orbits 20 2.2 Hamiltonian Mechanics 21 2.2.1 Hamiltonian Approach to CR3BP 21 2.2.2 Hamiltonian Approach to LPO Tracking Problem 22 3 Hamiltonian Structure-Based Control 25 3.1 Classical Linear Hamiltonian Structure-Preserving Control 27 3.2 Switching Hamiltonian Structure-Preserving Control 29 3.2.1 Orbital Properties of Spacecraft 33 3.2.2 Switching Point 1: From a Circular Orbit to an Elliptical Orbit 34 3.2.3 Switching Point 2: From an Elliptical Orbit to a Circular Orbit 37 3.3 Hamiltonian Structure-Based Control 39 3.3.1 Potential Shaping Control 39 3.3.2 Energy Dissipation Control 45 4 Filtered Extended High-Gain Observer and Closed-Loop Stability 49 4.1 Filtered Extended High-Gain Observer and Its Convergence 51 4.2 Closed-Loop Stability Analysis 56 5 Numerical Simulations 67 5.1 Disturbance Model 67 5.2 Navigation Error Model 68 5.3 Simulation Results 69 5.3.1 Simulation 1 71 5.3.2 Simulation 2 77 5.3.3 Simulation 3 81 5.3.4 Simulation 4 93 5.3.5 Simulation 5 98 6 Conclusion 101 6.1 Concluding Remarks 101 6.2 Further Work 103 Bibliography 105 국문초록 127Docto