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.
Este curso forma parte de Programa Especializado - Spacecraft Dynamics and Control
Control of Nonlinear Spacecraft Attitude Motion
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Curso 3 de 4 en
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Nivel avanzado
Aprox. 25 horas para completar
Sugerido: Best completed in 4 weeks, with a commitment of between 2 and 5 hours of work per week.
Inglés (English)
Subtítulos: Inglés (English)
ofrecido por
Universidad de Colorado en 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.
Programa - Qué aprenderás en este curso
2 horas para completar
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.
2 horas para completar
12 videos (Total 67 minutos)
12 videos
Module 1 Introduction1m
1: Overview of Nonlinear Control6m
1.1: Overview Stability Definition Discussion5m
1.2: Nonlinear Equations Representation8m
2: Definition: Neighborhood3m
3: Definitions: Lagrange Stability3m
4: Definitions: Lyapunov Stability5m
5: Definitions: Asymptotic Stability6m
6: Definitions: Global Stability2m
7: Linearizing a Dynamical System6m
Optional Review: Stability Definitions16m
7 ejercicios de práctica
Concept Check 1 - State Vector Representation10m
Concept Check 2 - State Neighborhood4m
Concept Check 3 - Lagrange Stability4m
Concept Check 4 - Lyapunov Stability6m
Concept Check 5 - Asymptotic Stability4m
Concept Check 6 - Global Stability Definitions10m
Concept Check 7 - Linearization20m
5 horas para completar
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.
5 horas para completar
14 videos (Total 129 minutos)
14 videos
1: Overview of Definite Function15m
2: Lyapunov Function Definition10m
2.1: Lyapunov Asymptotic Stability17m
3: Lyapunov Stability of Linear System4m
4: Global Stability Applications2m
Optional Review: Definiteness7m
Optional Review: Stability Definitions3m
Optional Review: Lyapunov's Direct Method9m
5: General Elemental Velocity Lyapunov Function12m
5.1 Example: Multi-Link System3m
6: Rigid Body Detumble Control20m
7: State-Based Lyapunov Functions14m
Optional Review: Elemental Lyapunov Functions2m
7 ejercicios de práctica
Concept Check 1 - Definite Function20m
Concept Check 2 - Lyapunov Functions45m
Concept Check 3 - Asymptotic Stability40m
Concept Check 4 - Global Stability Applications30m
Concept Check 5 - General Elemental Rate5m
Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function8m
Concept Check 7 - General Elemental State Lyapunov Function20m
11 horas para completar
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.
11 horas para completar
8 videos (Total 82 minutos)
8 videos
1: Nonlinear Rigid Body State and Rate Control14m
2: Global Stability of Nonlinear Attitude Control8m
2.1 Example: Nonlinear Regulation Control11m
2.2: Asymptotic Stability for Nonlinear Attitude Control5m
3: Unmodeled Disturbance Torque15m
4: Nonlinear Integral Control11m
5: Feedback Gain Selection13m
5 ejercicios de práctica
Concept Check 1 - General 3-Axis Attitude Control1h 30m
Concept Check 2 - Asymptotic Stability1h 30m
Concept Check 3 - Unknown External Torques2h 8m
Concept Check 4 - Integral Feedback2h 30m
Concept Check 5 - Feedback Gain Selection2h 30m
10 horas para completar
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.
10 horas para completar
6 videos (Total 97 minutos)
6 videos
1: Lyapunov Optimal Control30m
2: Example: Numerical Control Simulation8m
2.1: Linear Closed-Loop Dynamics21m
3: RW Feedback Control Law22m
Optional Review: Unconstrained Attitude Control13m
3 ejercicios de práctica
Concept Check 1 - Saturated Control3h 45m
Concept Check 2 - Linearized Closed Loop Dynamics2h 30m
Concept Check 3 - RW Feedback Control20m
Revisiones
4.7
Principales revisiones sobre CONTROL OF NONLINEAR SPACECRAFT ATTITUDE MOTION
por SDFeb 3, 2018
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 !
por MAMay 29, 2019
Excellent course! Enjoyed it a lot. Learnt a lot as well. Thank you.
Acerca de Programa especializado 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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