Control of Nonlinear Spacecraft Attitude Motion

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Control of Nonlinear Spacecraft Attitude Motion

This course is part of Spacecraft Dynamics and Control Specialization

Instructor: Hanspeter Schaub

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4 modules

Gain insight into a topic and learn the fundamentals.

68 reviews

Advanced level

Designed for those already in the industry

3 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

4 modules

Gain insight into a topic and learn the fundamentals.

68 reviews

Advanced level

Designed for those already in the industry

3 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

What you'll learn

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

Skills you'll gain

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Assessments

22 assignments¹

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Taught in English

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This course is part of the Spacecraft Dynamics and Control Specialization

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There are 4 modules in this course

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 The material covered is taking from the book "Analytical Mechanics of Space Systems" available at https://arc.aiaa.org/doi/book/10.2514/4.105210.

Discusses stability definitions of nonlinear dynamical systems, and compares to the classical linear stability definitions. The difference between local and global stability is covered.

What's included

12 videos1 reading7 assignments

12 videos Total 67 minutes

Course Introduction 2 minutes
Module 1 Introduction 1 minute
1: Overview of Nonlinear Control 7 minutes
1.1: Overview Stability Definition Discussion 5 minutes
1.2: Nonlinear Equations Representation 9 minutes
2: Definition: Neighborhood 4 minutes
3: Definitions: Lagrange Stability 4 minutes
4: Definitions: Lyapunov Stability 6 minutes
5: Definitions: Asymptotic Stability 6 minutes
6: Definitions: Global Stability 2 minutes
7: Linearizing a Dynamical System 6 minutes
Optional Review: Stability Definitions 16 minutes

1 reading Total 1 minute

Course Updates and Accessibility Support 1 minute

7 assignments Total 200 minutes

Concept Check 1 - State Vector Representation 30 minutes
Concept Check 2 - State Neighborhood 30 minutes
Concept Check 3 - Lagrange Stability 30 minutes
Concept Check 4 - Lyapunov Stability 30 minutes
Concept Check 5 - Asymptotic Stability 30 minutes
Concept Check 6 - Global Stability Definitions 30 minutes
Concept Check 7 - Linearization 20 minutes

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.

What's included

14 videos7 assignments

14 videos Total 129 minutes

Module 2 Introduction 1 minute
1: Overview of Definite Function 16 minutes
2: Lyapunov Function Definition 11 minutes
2.1: Lyapunov Asymptotic Stability 17 minutes
3: Lyapunov Stability of Linear System 4 minutes
4: Global Stability Applications 3 minutes
Optional Review: Definiteness 8 minutes
Optional Review: Stability Definitions 4 minutes
Optional Review: Lyapunov's Direct Method 10 minutes
5: General Elemental Velocity Lyapunov Function 13 minutes
5.1 Example: Multi-Link System 4 minutes
6: Rigid Body Detumble Control 20 minutes
7: State-Based Lyapunov Functions 15 minutes
Optional Review: Elemental Lyapunov Functions 3 minutes

7 assignments Total 190 minutes

Concept Check 1 - Definite Function 20 minutes
Concept Check 2 - Lyapunov Functions 45 minutes
Concept Check 3 - Asymptotic Stability 40 minutes
Concept Check 4 - Global Stability Applications 30 minutes
Concept Check 5 - General Elemental Rate 5 minutes
Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function 30 minutes
Concept Check 7 - General Elemental State Lyapunov Function 20 minutes

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.

What's included

8 videos5 assignments

8 videos Total 82 minutes

Module 3 Introduction 1 minute
1: Nonlinear Rigid Body State and Rate Control 14 minutes
2: Global Stability of Nonlinear Attitude Control 8 minutes
2.1 Example: Nonlinear Regulation Control 12 minutes
2.2: Asymptotic Stability for Nonlinear Attitude Control 6 minutes
3: Unmodeled Disturbance Torque 15 minutes
4: Nonlinear Integral Control 12 minutes
5: Feedback Gain Selection 14 minutes

5 assignments Total 608 minutes

Concept Check 1 - General 3-Axis Attitude Control 90 minutes
Concept Check 2 - Asymptotic Stability 90 minutes
Concept Check 3 - Unknown External Torques 128 minutes
Concept Check 4 - Integral Feedback 150 minutes
Concept Check 5 - Feedback Gain Selection 150 minutes

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.

What's included

6 videos3 assignments1 peer review

6 videos Total 97 minutes

Module 4 Introduction 1 minute
1: Lyapunov Optimal Control 31 minutes
2: Example: Numerical Control Simulation 9 minutes
2.1: Linear Closed-Loop Dynamics 21 minutes
3: RW Feedback Control Law 22 minutes
Optional Review: Unconstrained Attitude Control 13 minutes

3 assignments Total 395 minutes

Concept Check 1 - Saturated Control 225 minutes
Concept Check 2 - Linearized Closed Loop Dynamics 150 minutes
Concept Check 3 - RW Feedback Control 20 minutes

1 peer review Total 120 minutes

Nonlinear Control Final Assignment 120 minutes

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Instructor

Instructor ratings

(15 ratings)

Hanspeter Schaub

University of Colorado Boulder

10 Courses 37,036 learners

Offered by

University of Colorado Boulder

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Reviewed on Nov 26, 2020

The whole course is really good. The instructor is awesome at teaching concepts. I got to learn a lot of new things.

Reviewed on 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.Thank you !

Reviewed on Sep 26, 2020

Course is amazing and well detailed with different live perspectives.

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