This course trains you in the skills needed to program specific orientation and achieve precise aiming goals for spacecraft moving through three dimensional space. First, we cover stability definitions of nonlinear dynamical systems, covering the difference between local and global stability. We then analyze and apply Lyapunov's Direct Method to prove these stability properties, and develop a nonlinear 3-axis attitude pointing control law using Lyapunov theory. Finally, we look at alternate feedback control laws and closed loop dynamics.
After this course, you will be able to...
* Differentiate between a range of nonlinear stability concepts
* Apply Lyapunov’s direct method to argue stability and convergence on a range of dynamical systems
* Develop rate and attitude error measures for a 3-axis attitude control using Lyapunov theory
* Analyze rigid body control convergence with unmodeled torque
Этот курс входит в специализацию ''Специализация Spacecraft Dynamics and Control'
Control of Nonlinear Spacecraft Attitude Motion
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Программа курса: что вы изучите
Неделя
12 ч. на завершение
Nonlinear Stability Definitions
Discusses stability definitions of nonlinear dynamical systems, and compares to the classical linear stability definitions. The difference between local and global stability is covered.
12 видео ((всего 67 мин.)), 7 тестов
12 видео
Module 1 Introduction1мин
1: Overview of Nonlinear Control6мин
1.1: Overview Stability Definition Discussion5мин
1.2: Nonlinear Equations Representation8мин
2: Definition: Neighborhood3мин
3: Definitions: Lagrange Stability3мин
4: Definitions: Lyapunov Stability5мин
5: Definitions: Asymptotic Stability6мин
6: Definitions: Global Stability2мин
7: Linearizing a Dynamical System6мин
Optional Review: Stability Definitions16мин
7 практического упражнения
Concept Check 1 - State Vector Representation10мин
Concept Check 2 - State Neighborhood4мин
Concept Check 3 - Lagrange Stability4мин
Concept Check 4 - Lyapunov Stability6мин
Concept Check 5 - Asymptotic Stability4мин
Concept Check 6 - Global Stability Definitions10мин
Concept Check 7 - Linearization20мин
Неделя
25 ч. на завершение
Overview of Lyapunov Stability Theory
Lyapunov's direct method is employed to prove these stability properties for a nonlinear system and prove stability and convergence. The possible function definiteness is introduced which forms the building block of Lyapunov's direct method. Convenient prototype Lyapunov candidate functions are presented for rate- and state-error measures.
14 видео ((всего 129 мин.)), 7 тестов
14 видео
1: Overview of Definite Function15мин
2: Lyapunov Function Definition10мин
2.1: Lyapunov Asymptotic Stability17мин
3: Lyapunov Stability of Linear System4мин
4: Global Stability Applications2мин
Optional Review: Definiteness7мин
Optional Review: Stability Definitions3мин
Optional Review: Lyapunov's Direct Method9мин
5: General Elemental Velocity Lyapunov Function12мин
5.1 Example: Multi-Link System3мин
6: Rigid Body Detumble Control20мин
7: State-Based Lyapunov Functions14мин
Optional Review: Elemental Lyapunov Functions2мин
7 практического упражнения
Concept Check 1 - Definite Function20мин
Concept Check 2 - Lyapunov Functions45мин
Concept Check 3 - Asymptotic Stability40мин
Concept Check 4 - Global Stability Applications30мин
Concept Check 5 - General Elemental Rate5мин
Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function8мин
Concept Check 7 - General Elemental State Lyapunov Function20мин
Неделя
311 ч. на завершение
Attitude Control of States and Rates
A nonlinear 3-axis attitude pointing control law is developed and its stability is analyized using Lyapunov theory. Convergence is discussed considering both modeled and unmodeled torques. The control gain selection is presented using the convenient linearized closed loop dynamics.
8 видео ((всего 82 мин.)), 5 тестов
8 видео
1: Nonlinear Rigid Body State and Rate Control14мин
2: Global Stability of Nonlinear Attitude Control8мин
2.1 Example: Nonlinear Regulation Control11мин
2.2: Asymptotic Stability for Nonlinear Attitude Control5мин
3: Unmodeled Disturbance Torque15мин
4: Nonlinear Integral Control11мин
5: Feedback Gain Selection13мин
5 практического упражнения
Concept Check 1 - General 3-Axis Attitude Control30мин
Concept Check 2 - Asymptotic Stability30мин
Concept Check 3 - Unknown External Torques8мин
Concept Check 4 - Integral Feedback30мин
Concept Check 5 - Feedback Gain Selection30мин
Неделя
410 ч. на завершение
Alternate Attitude Control Formulations
Alternate feedback control laws are formulated where actuator saturation is considered. Further, a control law is presented that perfectly linearizes the closed loop dynamics in terms of quaternions and MRPs. Finally, the 3-axis Lyapunov attitude control is developed for a spacecraft with a cluster of N reaction wheel control devices.
6 видео ((всего 97 мин.)), 4 тестов
6 видео
1: Lyapunov Optimal Control30мин
2: Example: Numerical Control Simulation8мин
2.1: Linear Closed-Loop Dynamics21мин
3: RW Feedback Control Law22мин
Optional Review: Unconstrained Attitude Control13мин
3 практического упражнения
Concept Check 1 - Saturated Control45мин
Concept Check 2 - Linearized Closed Loop Dynamics30мин
Concept Check 3 - RW Feedback Control20мин
4.7
Рецензии: 5Лучшие рецензии
Excellent teaching from Professor Schaub ! Course has been very well organised and touches on the important aspects of nonlinear control. Looking forward to more courses from you.\n\nThank you !
Преподаватели
Hanspeter Schaub
Glenn L. Murphy Chair of Engineering, ProfessorDepartment of Aerospace Engineering Sciences
О Колорадский университет в Боулдере
CU-Boulder is a dynamic community of scholars and learners on one of the most spectacular college campuses in the country. As one of 34 U.S. public institutions in the prestigious Association of American Universities (AAU), we have a proud tradition of academic excellence, with five Nobel laureates and more than 50 members of prestigious academic academies.
О специализации ''Spacecraft Dynamics and Control'
Spacecraft Dynamics and Control covers three core topic areas: the description of the motion and rates of motion of rigid bodies (Kinematics), developing the equations of motion that prediction the movement of rigid bodies taking into account mass, torque, and inertia (Kinetics), and finally non-linear controls to program specific orientations and achieve precise aiming goals in three-dimensional space (Control). The specialization invites learners to develop competency in these three areas through targeted content delivery, continuous concept reinforcement, and project applications.
The goal of the specialization is to introduce the theories related to spacecraft dynamics and control. This includes the three-dimensional description of orientation, creating the dynamical rotation models, as well as the feedback control development to achieve desired attitude trajectories.
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