关于此课程： 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
此课程适用人群： 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.
制作方： University of Colorado Boulder
教学方： Hanspeter Schaub, Alfred T. and Betty E. Look Professor of Engineering
Department of Aerospace Engineering Sciences
| 级别 | Advanced |
| 承诺学习时间 | Best completed in 4 weeks, with a commitment of between 2 and 5 hours of work per week. |
| 语言 | English |
| 如何通过 | 通过所有计分作业以完成课程。 |
| 用户评分 |
授课大纲
第 1 周
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
- 视频: Module 1 Introduction
- 视频: 1: Overview of Nonlinear Control
- 视频: 1.1: Overview Stability Definition Discussion
- 视频: 1.2: Nonlinear Equations Representation
- 视频: 2: Definition: Neighborhood
- 视频: 3: Definitions: Lagrange Stability
- 视频: 4: Definitions: Lyapunov Stability
- 视频: 5: Definitions: Asymptotic Stability
- 视频: 6: Definitions: Global Stability
- 视频: 7: Linearizing a Dynamical System
- 视频: Optional Review: Stability Definitions
已评分: Concept Check 1 - State Vector Representation
已评分: Concept Check 2 - State Neighborhood
已评分: Concept Check 3 - Lagrange Stability
已评分: Concept Check 4 - Lyapunov Stability
已评分: Concept Check 5 - Asymptotic Stability
已评分: Concept Check 6 - Global Stability Definitions
已评分: Concept Check 7 - Linearization
第 2 周
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
- 视频: 1: Overview of Definite Function
- 视频: 2: Lyapunov Function Definition
- 视频: 2.1: Lyapunov Asymptotic Stability
- 视频: 3: Lyapunov Stability of Linear System
- 视频: 4: Global Stability Applications
- 视频: Optional Review: Definiteness
- 视频: Optional Review: Stability Definitions
- 视频: Optional Review: Lyapunov's Direct Method
- 视频: 5: General Elemental Velocity Lyapunov Function
- 视频: 5.1 Example: Multi-Link System
- 视频: 6: Rigid Body Detumble Control
- 视频: 7: State-Based Lyapunov Functions
- 视频: Optional Review: Elemental Lyapunov Functions
已评分: Concept Check 1 - Definite Function
已评分: Concept Check 2 - Lyapunov Functions
已评分: Concept Check 3 - Asymptotic Stability
已评分: Concept Check 4 - Global Stability Applications
已评分: Concept Check 5 - General Elemental Rate
已评分: Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function
已评分: Concept Check 7 - General Elemental State Lyapunov Function
第 3 周
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
- 视频: 1: Nonlinear Rigid Body State and Rate Control
- 视频: 2: Global Stability of Nonlinear Attitude Control
- 视频: 2.1 Example: Nonlinear Regulation Control
- 视频: 2.2: Asymptotic Stability for Nonlinear Attitude Control
- 视频: 3: Unmodeled Disturbance Torque
- 视频: 4: Nonlinear Integral Control
- 视频: 5: Feedback Gain Selection
已评分: Concept Check 1 - General 3-Axis Attitude Control
已评分: Concept Check 2 - Asymptotic Stability
已评分: Concept Check 3 - Unknown External Torques
已评分: Concept Check 4 - Integral Feedback
已评分: Concept Check 5 - Feedback Gain Selection
第 4 周
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
- 视频: 1: Lyapunov Optimal Control
- 视频: 2: Example: Numerical Control Simulation
- 视频: 2.1: Linear Closed-Loop Dynamics
- 视频: 3: RW Feedback Control Law
- 视频: Optional Review: Unconstrained Attitude Control
已评分: Concept Check 1 - Saturated Control
已评分: Concept Check 2 - Linearized Closed Loop Dynamics
已评分: Concept Check 3 - RW Feedback Control
已评分: Nonlinear Control Final Assignment
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制作方
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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