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
Ce cours fait partie de la Spécialisation Spacecraft Dynamics and Control
Control of Nonlinear Spacecraft Attitude Motion
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Programme du cours : ce que vous apprendrez dans ce cours
Semaine
12 heures pour terminer
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 vidéos (Total 67 min), 7 quiz
12 vidéos
Course Introduction1 min
Module 1 Introduction1 min
1: Overview of Nonlinear Control6 min
1.1: Overview Stability Definition Discussion5 min
1.2: Nonlinear Equations Representation8 min
2: Definition: Neighborhood3 min
3: Definitions: Lagrange Stability3 min
4: Definitions: Lyapunov Stability5 min
5: Definitions: Asymptotic Stability6 min
6: Definitions: Global Stability2 min
7: Linearizing a Dynamical System6 min
Optional Review: Stability Definitions16 min
7 exercices pour s'entraîner
Concept Check 1 - State Vector Representation10 min
Concept Check 2 - State Neighborhood4 min
Concept Check 3 - Lagrange Stability4 min
Concept Check 4 - Lyapunov Stability6 min
Concept Check 5 - Asymptotic Stability4 min
Concept Check 6 - Global Stability Definitions10 min
Concept Check 7 - Linearization20 min
Semaine
25 heures pour terminer
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 vidéos (Total 129 min), 7 quiz
14 vidéos
1: Overview of Definite Function15 min
2: Lyapunov Function Definition10 min
2.1: Lyapunov Asymptotic Stability17 min
3: Lyapunov Stability of Linear System4 min
4: Global Stability Applications2 min
Optional Review: Definiteness7 min
Optional Review: Stability Definitions3 min
Optional Review: Lyapunov's Direct Method9 min
5: General Elemental Velocity Lyapunov Function12 min
5.1 Example: Multi-Link System3 min
6: Rigid Body Detumble Control20 min
7: State-Based Lyapunov Functions14 min
Optional Review: Elemental Lyapunov Functions2 min
7 exercices pour s'entraîner
Concept Check 1 - Definite Function20 min
Concept Check 2 - Lyapunov Functions45 min
Concept Check 3 - Asymptotic Stability40 min
Concept Check 4 - Global Stability Applications30 min
Concept Check 5 - General Elemental Rate5 min
Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function8 min
Concept Check 7 - General Elemental State Lyapunov Function20 min
Semaine
35 heures pour terminer
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 vidéos (Total 82 min), 5 quiz
8 vidéos
1: Nonlinear Rigid Body State and Rate Control14 min
2: Global Stability of Nonlinear Attitude Control8 min
2.1 Example: Nonlinear Regulation Control11 min
2.2: Asymptotic Stability for Nonlinear Attitude Control5 min
3: Unmodeled Disturbance Torque15 min
4: Nonlinear Integral Control11 min
5: Feedback Gain Selection13 min
5 exercices pour s'entraîner
Concept Check 1 - General 3-Axis Attitude Control30 min
Concept Check 2 - Asymptotic Stability30 min
Concept Check 3 - Unknown External Torques8 min
Concept Check 4 - Integral Feedback30 min
Concept Check 5 - Feedback Gain Selection30 min
Semaine
45 heures pour terminer
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 vidéos (Total 97 min), 4 quiz
6 vidéos
1: Lyapunov Optimal Control30 min
2: Example: Numerical Control Simulation8 min
2.1: Linear Closed-Loop Dynamics21 min
3: RW Feedback Control Law22 min
Optional Review: Unconstrained Attitude Control13 min
3 exercices pour s'entraîner
Concept Check 1 - Saturated Control45 min
Concept Check 2 - Linearized Closed Loop Dynamics30 min
Concept Check 3 - RW Feedback Control20 min
4.7
5 avisMeilleurs avis
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 !
Enseignants
Hanspeter Schaub
Glenn L. Murphy Chair of Engineering, ProfessorDepartment of Aerospace Engineering Sciences
À propos de Université du Colorado à 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.
À propos de la Spécialisation 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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