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Control of Nonlinear Spacecraft Attitude Motion

Control of Nonlinear Spacecraft Attitude Motion

This course is part of Spacecraft Dynamics and Control Specialization

Instructor: Hanspeter Schaub

10,110 already enrolled

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4 modules

Gain insight into a topic and learn the fundamentals.

70 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.

70 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.

Module details

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 videosTotal 67 minutes

Course Introduction2 minutes
Module 1 Introduction1 minute
1: Overview of Nonlinear Control7 minutes
1.1: Overview Stability Definition Discussion5 minutes
1.2: Nonlinear Equations Representation9 minutes
2: Definition: Neighborhood4 minutes
3: Definitions: Lagrange Stability4 minutes
4: Definitions: Lyapunov Stability6 minutes
5: Definitions: Asymptotic Stability6 minutes
6: Definitions: Global Stability2 minutes
7: Linearizing a Dynamical System6 minutes
Optional Review: Stability Definitions16 minutes

1 readingTotal 1 minute

Course Updates and Accessibility Support1 minute

7 assignmentsTotal 200 minutes

Concept Check 1 - State Vector Representation30 minutes
Concept Check 2 - State Neighborhood30 minutes
Concept Check 3 - Lagrange Stability30 minutes
Concept Check 4 - Lyapunov Stability30 minutes
Concept Check 5 - Asymptotic Stability30 minutes
Concept Check 6 - Global Stability Definitions30 minutes
Concept Check 7 - Linearization20 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 videosTotal 129 minutes

Module 2 Introduction1 minute
1: Overview of Definite Function16 minutes
2: Lyapunov Function Definition11 minutes
2.1: Lyapunov Asymptotic Stability17 minutes
3: Lyapunov Stability of Linear System4 minutes
4: Global Stability Applications3 minutes
Optional Review: Definiteness8 minutes
Optional Review: Stability Definitions4 minutes
Optional Review: Lyapunov's Direct Method10 minutes
5: General Elemental Velocity Lyapunov Function13 minutes
5.1 Example: Multi-Link System4 minutes
6: Rigid Body Detumble Control20 minutes
7: State-Based Lyapunov Functions15 minutes
Optional Review: Elemental Lyapunov Functions3 minutes

7 assignmentsTotal 190 minutes

Concept Check 1 - Definite Function20 minutes
Concept Check 2 - Lyapunov Functions45 minutes
Concept Check 3 - Asymptotic Stability40 minutes
Concept Check 4 - Global Stability Applications30 minutes
Concept Check 5 - General Elemental Rate5 minutes
Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function30 minutes
Concept Check 7 - General Elemental State Lyapunov Function20 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 videosTotal 82 minutes

Module 3 Introduction1 minute
1: Nonlinear Rigid Body State and Rate Control14 minutes
2: Global Stability of Nonlinear Attitude Control8 minutes
2.1 Example: Nonlinear Regulation Control12 minutes
2.2: Asymptotic Stability for Nonlinear Attitude Control6 minutes
3: Unmodeled Disturbance Torque15 minutes
4: Nonlinear Integral Control12 minutes
5: Feedback Gain Selection14 minutes

5 assignmentsTotal 608 minutes

Concept Check 1 - General 3-Axis Attitude Control90 minutes
Concept Check 2 - Asymptotic Stability90 minutes
Concept Check 3 - Unknown External Torques128 minutes
Concept Check 4 - Integral Feedback150 minutes
Concept Check 5 - Feedback Gain Selection150 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.