Об этом курсе: 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

Для кого этот курс: This class is for working engineering professionals looking to add to their skill sets, graduate students in engineering looking to fill gaps in their knowledge base, and enterprising engineering undergraduates looking to expand their horizons.

Автор: University of Colorado Boulder

Преподаватели: Hanspeter Schaub, Alfred T. and Betty E. Look Professor of Engineering
Department of Aerospace Engineering Sciences

Уровень	Advanced
Выполнение	Best completed in 4 weeks, with a commitment of between 2 and 5 hours of work per week.
Язык	English
Как пройти курс	Чтобы пройти курс, выполните все оцениваемые задания.
Оценки пользователей	4.9 звезды Средняя оценка пользователей: 4.9Посмотрите, что пишут учащиеся

Программа курса

НЕДЕЛЯ 1

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

Видео: Module 1 Introduction
Видео: 1: Overview of Nonlinear Control
Видео: 1.1: Overview Stability Definition Discussion
Видео: 1.2: Nonlinear Equations Representation
Видео: 2: Definition: Neighborhood
Видео: 3: Definitions: Lagrange Stability
Видео: 4: Definitions: Lyapunov Stability
Видео: 5: Definitions: Asymptotic Stability
Видео: 6: Definitions: Global Stability
Видео: 7: Linearizing a Dynamical System
Видео: Optional Review: Stability Definitions

Оцениваемый: Concept Check 1 - State Vector Representation

Оцениваемый: Concept Check 2 - State Neighborhood

Оцениваемый: Concept Check 3 - Lagrange Stability

Оцениваемый: Concept Check 4 - Lyapunov Stability

Оцениваемый: Concept Check 5 - Asymptotic Stability

Оцениваемый: Concept Check 6 - Global Stability Definitions

Оцениваемый: Concept Check 7 - Linearization

НЕДЕЛЯ 2

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

Видео: 1: Overview of Definite Function
Видео: 2: Lyapunov Function Definition
Видео: 2.1: Lyapunov Asymptotic Stability
Видео: 3: Lyapunov Stability of Linear System
Видео: 4: Global Stability Applications
Видео: Optional Review: Definiteness
Видео: Optional Review: Stability Definitions
Видео: Optional Review: Lyapunov's Direct Method
Видео: 5: General Elemental Velocity Lyapunov Function
Видео: 5.1 Example: Multi-Link System
Видео: 6: Rigid Body Detumble Control
Видео: 7: State-Based Lyapunov Functions
Видео: Optional Review: Elemental Lyapunov Functions

Оцениваемый: Concept Check 1 - Definite Function

Оцениваемый: Concept Check 2 - Lyapunov Functions

Оцениваемый: Concept Check 3 - Asymptotic Stability

Оцениваемый: Concept Check 4 - Global Stability Applications

Оцениваемый: Concept Check 5 - General Elemental Rate

Оцениваемый: Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function

Оцениваемый: Concept Check 7 - General Elemental State Lyapunov Function

НЕДЕЛЯ 3

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

Видео: 1: Nonlinear Rigid Body State and Rate Control
Видео: 2: Global Stability of Nonlinear Attitude Control
Видео: 2.1 Example: Nonlinear Regulation Control
Видео: 2.2: Asymptotic Stability for Nonlinear Attitude Control
Видео: 3: Unmodeled Disturbance Torque
Видео: 4: Nonlinear Integral Control
Видео: 5: Feedback Gain Selection

Оцениваемый: Concept Check 1 - General 3-Axis Attitude Control

Оцениваемый: Concept Check 2 - Asymptotic Stability

Оцениваемый: Concept Check 3 - Unknown External Torques

Оцениваемый: Concept Check 4 - Integral Feedback

Оцениваемый: Concept Check 5 - Feedback Gain Selection

НЕДЕЛЯ 4

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

Видео: 1: Lyapunov Optimal Control
Видео: 2: Example: Numerical Control Simulation
Видео: 2.1: Linear Closed-Loop Dynamics
Видео: 3: RW Feedback Control Law
Видео: Optional Review: Unconstrained Attitude Control

Оцениваемый: Concept Check 1 - Saturated Control

Оцениваемый: Concept Check 2 - Linearized Closed Loop Dynamics

Оцениваемый: Concept Check 3 - RW Feedback Control

Оцениваемый: Nonlinear Control Final Assignment

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Авторы

University of Colorado 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.

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