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
Este curso faz parte do Programa de cursos integrados Spacecraft Dynamics and Control
Control of Nonlinear Spacecraft Attitude Motion
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Programa - O que você aprenderá com este curso
Semana
12 horas para concluir
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 vídeos (total de (Total 67 mín.) min), 7 testes
12 videos
Module 1 Introduction1min
1: Overview of Nonlinear Control6min
1.1: Overview Stability Definition Discussion5min
1.2: Nonlinear Equations Representation8min
2: Definition: Neighborhood3min
3: Definitions: Lagrange Stability3min
4: Definitions: Lyapunov Stability5min
5: Definitions: Asymptotic Stability6min
6: Definitions: Global Stability2min
7: Linearizing a Dynamical System6min
Optional Review: Stability Definitions16min
7 exercícios práticos
Concept Check 1 - State Vector Representation10min
Concept Check 2 - State Neighborhood4min
Concept Check 3 - Lagrange Stability4min
Concept Check 4 - Lyapunov Stability6min
Concept Check 5 - Asymptotic Stability4min
Concept Check 6 - Global Stability Definitions10min
Concept Check 7 - Linearization20min
Semana
25 horas para concluir
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 vídeos (total de (Total 129 mín.) min), 7 testes
14 videos
1: Overview of Definite Function15min
2: Lyapunov Function Definition10min
2.1: Lyapunov Asymptotic Stability17min
3: Lyapunov Stability of Linear System4min
4: Global Stability Applications2min
Optional Review: Definiteness7min
Optional Review: Stability Definitions3min
Optional Review: Lyapunov's Direct Method9min
5: General Elemental Velocity Lyapunov Function12min
5.1 Example: Multi-Link System3min
6: Rigid Body Detumble Control20min
7: State-Based Lyapunov Functions14min
Optional Review: Elemental Lyapunov Functions2min
7 exercícios práticos
Concept Check 1 - Definite Function20min
Concept Check 2 - Lyapunov Functions45min
Concept Check 3 - Asymptotic Stability40min
Concept Check 4 - Global Stability Applications30min
Concept Check 5 - General Elemental Rate5min
Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function8min
Concept Check 7 - General Elemental State Lyapunov Function20min
Semana
35 horas para concluir
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 vídeos (total de (Total 82 mín.) min), 5 testes
8 videos
1: Nonlinear Rigid Body State and Rate Control14min
2: Global Stability of Nonlinear Attitude Control8min
2.1 Example: Nonlinear Regulation Control11min
2.2: Asymptotic Stability for Nonlinear Attitude Control5min
3: Unmodeled Disturbance Torque15min
4: Nonlinear Integral Control11min
5: Feedback Gain Selection13min
5 exercícios práticos
Concept Check 1 - General 3-Axis Attitude Control30min
Concept Check 2 - Asymptotic Stability30min
Concept Check 3 - Unknown External Torques8min
Concept Check 4 - Integral Feedback30min
Concept Check 5 - Feedback Gain Selection30min
Semana
45 horas para concluir
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 vídeos (total de (Total 97 mín.) min), 4 testes
6 videos
1: Lyapunov Optimal Control30min
2: Example: Numerical Control Simulation8min
2.1: Linear Closed-Loop Dynamics21min
3: RW Feedback Control Law22min
Optional Review: Unconstrained Attitude Control13min
3 exercícios práticos
Concept Check 1 - Saturated Control45min
Concept Check 2 - Linearized Closed Loop Dynamics30min
Concept Check 3 - RW Feedback Control20min
4.7
5 avaliaçõesMelhores avaliações
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 !
Instrutores
Hanspeter Schaub
Glenn L. Murphy Chair of Engineering, ProfessorDepartment of Aerospace Engineering Sciences
Sobre Universidade do Colorado em Boulder
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.
Sobre o Programa de cursos integrados 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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