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
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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教学大纲 - 您将从这门课程中学到什么
周
1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.
12 个视频 （总计 67 分钟）, 7 个测验
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
周
2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.
14 个视频 （总计 129 分钟）, 7 个测验
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
周
3完成时间为 5 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.
8 个视频 （总计 82 分钟）, 5 个测验
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 Control30分钟
Concept Check 2 - Asymptotic Stability30分钟
Concept Check 3 - Unknown External Torques8分钟
Concept Check 4 - Integral Feedback30分钟
Concept Check 5 - Feedback Gain Selection30分钟
周
4完成时间为 5 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.
6 个视频 （总计 97 分钟）, 4 个测验
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 Control45分钟
Concept Check 2 - Linearized Closed Loop Dynamics30分钟
Concept Check 3 - RW Feedback Control20分钟
4.7
5 个审阅热门审阅
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 !
讲师
Hanspeter Schaub
Glenn L. Murphy Chair of Engineering, ProfessorDepartment of Aerospace Engineering Sciences
关于 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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