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Control of Nonlinear Spacecraft Attitude Motion
  • Level Expert
  • Duration 31 hours
  • Course by University of Colorado Boulder
  • Offered by

About

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

Modules

Introductions

    • 2 Videos
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2 Videos

  • Course Introduction
  • Module 1 Introduction

Fundamental Definitions

    • 4 Videos
    • 2 Assignment
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2 Assignment

  • Concept Check 1 - State Vector Representation
  • Concept Check 2 - State Neighborhood

4 Videos

  • 1: Overview of Nonlinear Control
  • 1.1: Overview Stability Definition Discussion
  • 1.2: Nonlinear Equations Representation
  • 2: Definition: Neighborhood

Nonlinear Stability Definitions

    • 6 Videos
    • 5 Assignment
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5 Assignment

  • Concept Check 3 - Lagrange Stability
  • Concept Check 4 - Lyapunov Stability
  • Concept Check 5 - Asymptotic Stability
  • Concept Check 6 - Global Stability Definitions
  • Concept Check 7 - Linearization

6 Videos

  • 3: Definitions: Lagrange Stability
  • 4: Definitions: Lyapunov Stability
  • 5: Definitions: Asymptotic Stability
  • 6: Definitions: Global Stability
  • 7: Linearizing a Dynamical System
  • Optional Review: Stability Definitions

Lyapunov's Direct Method

    • 9 Videos
    • 4 Assignment
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4 Assignment

  • Concept Check 1 - Definite Function
  • Concept Check 2 - Lyapunov Functions
  • Concept Check 3 - Asymptotic Stability
  • Concept Check 4 - Global Stability Applications

9 Videos

  • Module 2 Introduction
  • 1: Overview of Definite Function
  • 2: Lyapunov Function Definition
  • 2.1: Lyapunov Asymptotic Stability
  • 3: Lyapunov Stability of Linear System
  • 4: Global Stability Applications
  • Optional Review: Definiteness
  • Optional Review: Stability Definitions
  • Optional Review: Lyapunov's Direct Method

Prototype Lyapunov Functions

    • 5 Videos
    • 3 Assignment
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3 Assignment

  • Concept Check 5 - General Elemental Rate
  • Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function
  • Concept Check 7 - General Elemental State Lyapunov Function

5 Videos

  • 5: General Elemental Velocity Lyapunov Function
  • 5.1 Example: Multi-Link System
  • 6: Rigid Body Detumble Control
  • 7: State-Based Lyapunov Functions
  • Optional Review: Elemental Lyapunov Functions

Lyapunov Attitude Control Development

    • 5 Videos
    • 2 Assignment
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2 Assignment

  • Concept Check 1 - General 3-Axis Attitude Control
  • Concept Check 2 - Asymptotic Stability

5 Videos

  • Module 3 Introduction
  • 1: Nonlinear Rigid Body State and Rate Control
  • 2: Global Stability of Nonlinear Attitude Control
  • 2.1 Example: Nonlinear Regulation Control
  • 2.2: Asymptotic Stability for Nonlinear Attitude Control

Lyapunov Attitude Control Properties

    • 3 Videos
    • 3 Assignment
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3 Assignment

  • Concept Check 3 - Unknown External Torques
  • Concept Check 4 - Integral Feedback
  • Concept Check 5 - Feedback Gain Selection

3 Videos

  • 3: Unmodeled Disturbance Torque
  • 4: Nonlinear Integral Control
  • 5: Feedback Gain Selection

Attitude Control Implementations

    • 6 Videos
    • 3 Assignment
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3 Assignment

  • Concept Check 1 - Saturated Control
  • Concept Check 2 - Linearized Closed Loop Dynamics
  • Concept Check 3 - RW Feedback Control

6 Videos

  • Module 4 Introduction
  • 1: Lyapunov Optimal Control
  • 2: Example: Numerical Control Simulation
  • 2.1: Linear Closed-Loop Dynamics
  • 3: RW Feedback Control Law
  • Optional Review: Unconstrained Attitude Control

Nonlinear Control Peer Assignment

    • 1 PeerReview
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1 Peer Review

  • Nonlinear Control Final Assignment

Auto Summary

Explore the intricacies of spacecraft maneuvering with the "Control of Nonlinear Spacecraft Attitude Motion" course. This expert-level program delves into the realm of personal development, offering a specialized focus on achieving precise spacecraft orientation in three-dimensional space. Guided by Coursera, the course kicks off with an introduction to stability definitions of nonlinear dynamical systems, distinguishing between local and global stability. Learners will then master Lyapunov's Direct Method to validate these stability properties and will develop a robust nonlinear 3-axis attitude pointing control law using Lyapunov theory. The curriculum also explores alternative feedback control laws and examines closed-loop dynamics. Upon completion, participants will be equipped to: - Differentiate between various nonlinear stability concepts. - Utilize Lyapunov’s direct method to ensure stability and convergence across dynamical systems. - Formulate rate and attitude error measures for 3-axis control using Lyapunov theory. - Assess rigid body control convergence in the presence of unmodeled torque. The course spans 1860 minutes and is available through multiple subscription options: Starter, Professional, and Paid. Designed for those with an advanced understanding of the subject, this course is ideal for professionals seeking to sharpen their expertise in spacecraft attitude control.

Hanspeter Schaub
Instructor

Hanspeter Schaub