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.
本课程是 Spacecraft Dynamics and Control 专项课程 专项课程的一部分
Control of Nonlinear Spacecraft Attitude Motion
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第 3 门课程（共 4 门）
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完成时间大约为25 小时
建议：Best completed in 4 weeks, with a commitment of between 2 and 5 hours of work per week.
英语（English）
字幕：英语（English）
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完成时间为 2 小时
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.
完成时间为 2 小时
12 个视频 （总计 67 分钟）
12 个视频
Module 1 Introduction1分钟
1: Overview of Nonlinear Control6分钟
1.1: Overview Stability Definition Discussion5分钟
1.2: Nonlinear Equations Representation8分钟
2: Definition: Neighborhood3分钟
3: Definitions: Lagrange Stability3分钟
4: Definitions: Lyapunov Stability5分钟
5: Definitions: Asymptotic Stability6分钟
6: Definitions: Global Stability2分钟
7: Linearizing a Dynamical System6分钟
Optional Review: Stability Definitions16分钟
7 个练习
Concept Check 1 - State Vector Representation10分钟
Concept Check 2 - State Neighborhood4分钟
Concept Check 3 - Lagrange Stability4分钟
Concept Check 4 - Lyapunov Stability6分钟
Concept Check 5 - Asymptotic Stability4分钟
Concept Check 6 - Global Stability Definitions10分钟
Concept Check 7 - Linearization20分钟
完成时间为 5 小时
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.
完成时间为 5 小时
14 个视频 （总计 129 分钟）
14 个视频
1: Overview of Definite Function15分钟
2: Lyapunov Function Definition10分钟
2.1: Lyapunov Asymptotic Stability17分钟
3: Lyapunov Stability of Linear System4分钟
4: Global Stability Applications2分钟
Optional Review: Definiteness7分钟
Optional Review: Stability Definitions3分钟
Optional Review: Lyapunov's Direct Method9分钟
5: General Elemental Velocity Lyapunov Function12分钟
5.1 Example: Multi-Link System3分钟
6: Rigid Body Detumble Control20分钟
7: State-Based Lyapunov Functions14分钟
Optional Review: Elemental Lyapunov Functions2分钟
7 个练习
Concept Check 1 - Definite Function20分钟
Concept Check 2 - Lyapunov Functions45分钟
Concept Check 3 - Asymptotic Stability40分钟
Concept Check 4 - Global Stability Applications30分钟
Concept Check 5 - General Elemental Rate5分钟
Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function8分钟
Concept Check 7 - General Elemental State Lyapunov Function20分钟
完成时间为 11 小时
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.
完成时间为 11 小时
8 个视频 （总计 82 分钟）
8 个视频
1: Nonlinear Rigid Body State and Rate Control14分钟
2: Global Stability of Nonlinear Attitude Control8分钟
2.1 Example: Nonlinear Regulation Control11分钟
2.2: Asymptotic Stability for Nonlinear Attitude Control5分钟
3: Unmodeled Disturbance Torque15分钟
4: Nonlinear Integral Control11分钟
5: Feedback Gain Selection13分钟
5 个练习
Concept Check 1 - General 3-Axis Attitude Control1 小时 30 分
Concept Check 2 - Asymptotic Stability1 小时 30 分
Concept Check 3 - Unknown External Torques2 小时 8 分
Concept Check 4 - Integral Feedback2 小时 30 分
Concept Check 5 - Feedback Gain Selection2 小时 30 分
完成时间为 10 小时
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.
完成时间为 10 小时
6 个视频 （总计 97 分钟）
6 个视频
1: Lyapunov Optimal Control30分钟
2: Example: Numerical Control Simulation8分钟
2.1: Linear Closed-Loop Dynamics21分钟
3: RW Feedback Control Law22分钟
Optional Review: Unconstrained Attitude Control13分钟
3 个练习
Concept Check 1 - Saturated Control3 小时 45 分
Concept Check 2 - Linearized Closed Loop Dynamics2 小时 30 分
Concept Check 3 - RW Feedback Control20分钟
审阅
4.7
来自CONTROL OF NONLINEAR SPACECRAFT ATTITUDE MOTION的热门评论
由 SD 提供Feb 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 !
由 MA 提供May 29, 2019
Excellent course! Enjoyed it a lot. Learnt a lot as well. Thank you.
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科罗拉多大学波德分校
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.
关于 Spacecraft Dynamics and Control 专项课程
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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