Acerca de este curso: 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
Para quién es esta clase: 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.
Creada por: University of Colorado Boulder
Enseñado por: Hanspeter Schaub, Alfred T. and Betty E. Look Professor of Engineering
Department of Aerospace Engineering Sciences
| Nivel | Advanced |
| Compromiso | Best completed in 4 weeks, with a commitment of between 2 and 5 hours of work per week. |
| Idioma | English |
| Cómo aprobar | Aprueba todas las tareas calificadas para completar el curso. |
| Calificaciones del usuario |
Programa
SEMANA 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 videos
- Vídeo: Module 1 Introduction
- Vídeo: 1: Overview of Nonlinear Control
- Vídeo: 1.1: Overview Stability Definition Discussion
- Vídeo: 1.2: Nonlinear Equations Representation
- Vídeo: 2: Definition: Neighborhood
- Vídeo: 3: Definitions: Lagrange Stability
- Vídeo: 4: Definitions: Lyapunov Stability
- Vídeo: 5: Definitions: Asymptotic Stability
- Vídeo: 6: Definitions: Global Stability
- Vídeo: 7: Linearizing a Dynamical System
- Vídeo: Optional Review: Stability Definitions
Calificado: Concept Check 1 - State Vector Representation
Calificado: Concept Check 2 - State Neighborhood
Calificado: Concept Check 3 - Lagrange Stability
Calificado: Concept Check 4 - Lyapunov Stability
Calificado: Concept Check 5 - Asymptotic Stability
Calificado: Concept Check 6 - Global Stability Definitions
Calificado: Concept Check 7 - Linearization
SEMANA 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 videos
- Vídeo: 1: Overview of Definite Function
- Vídeo: 2: Lyapunov Function Definition
- Vídeo: 2.1: Lyapunov Asymptotic Stability
- Vídeo: 3: Lyapunov Stability of Linear System
- Vídeo: 4: Global Stability Applications
- Vídeo: Optional Review: Definiteness
- Vídeo: Optional Review: Stability Definitions
- Vídeo: Optional Review: Lyapunov's Direct Method
- Vídeo: 5: General Elemental Velocity Lyapunov Function
- Vídeo: 5.1 Example: Multi-Link System
- Vídeo: 6: Rigid Body Detumble Control
- Vídeo: 7: State-Based Lyapunov Functions
- Vídeo: Optional Review: Elemental Lyapunov Functions
Calificado: Concept Check 1 - Definite Function
Calificado: Concept Check 2 - Lyapunov Functions
Calificado: Concept Check 3 - Asymptotic Stability
Calificado: Concept Check 4 - Global Stability Applications
Calificado: Concept Check 5 - General Elemental Rate
Calificado: Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function
Calificado: Concept Check 7 - General Elemental State Lyapunov Function
SEMANA 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 videos
- Vídeo: 1: Nonlinear Rigid Body State and Rate Control
- Vídeo: 2: Global Stability of Nonlinear Attitude Control
- Vídeo: 2.1 Example: Nonlinear Regulation Control
- Vídeo: 2.2: Asymptotic Stability for Nonlinear Attitude Control
- Vídeo: 3: Unmodeled Disturbance Torque
- Vídeo: 4: Nonlinear Integral Control
- Vídeo: 5: Feedback Gain Selection
Calificado: Concept Check 1 - General 3-Axis Attitude Control
Calificado: Concept Check 2 - Asymptotic Stability
Calificado: Concept Check 3 - Unknown External Torques
Calificado: Concept Check 4 - Integral Feedback
Calificado: Concept Check 5 - Feedback Gain Selection
SEMANA 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 videos
- Vídeo: 1: Lyapunov Optimal Control
- Vídeo: 2: Example: Numerical Control Simulation
- Vídeo: 2.1: Linear Closed-Loop Dynamics
- Vídeo: 3: RW Feedback Control Law
- Vídeo: Optional Review: Unconstrained Attitude Control
Calificado: Concept Check 1 - Saturated Control
Calificado: Concept Check 2 - Linearized Closed Loop Dynamics
Calificado: Concept Check 3 - RW Feedback Control
Calificado: Nonlinear Control Final Assignment
Preguntas Frecuentes
Cómo funciona
Trabalho
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Creadores
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.
Tarifa
| Comprar curso | |
|---|---|
| Accede a los materiales del curso | Disponible |
| Accede a los materiales con calificación | Disponible |
| Recibe una calificación final | Disponible |
| Obtén un Certificado de curso para compartir | Disponible |
Calificaciones y revisiones
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