Control of Nonlinear Spacecraft Attitude Motion

About 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

Who is this class for: 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.

Created by:  University of Colorado Boulder

• Taught by:  Hanspeter Schaub, Alfred T. and Betty E. Look Professor of Engineering

  Department of Aerospace Engineering Sciences

Level Advanced Commitment Best completed in 4 weeks, with a commitment of between 2 and 5 hours of work per week. Language English How To Pass Pass all graded assignments to complete the course. User Ratings 5.0 stars Average User Rating 5.0See what learners said Travail en cours

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Syllabus


WEEK 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 expand

1. Video: Course Introduction
2. Video: Module 1 Introduction
3. Video: 1: Overview of Nonlinear Control
4. Video: 1.1: Overview Stability Definition Discussion
5. Video: 1.2: Nonlinear Equations Representation
6. Video: 2: Definition: Neighborhood
7. Video: 3: Definitions: Lagrange Stability
8. Video: 4: Definitions: Lyapunov Stability
9. Video: 5: Definitions: Asymptotic Stability
10. Video: 6: Definitions: Global Stability
11. Video: 7: Linearizing a Dynamical System
12. Video: Optional Review: Stability Definitions

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

WEEK 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 expand

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

Graded: Concept Check 1 - Definite Function
Graded: Concept Check 2 - Lyapunov Functions
Graded: Concept Check 3 - Asymptotic Stability
Graded: Concept Check 4 - Global Stability Applications
Graded: Concept Check 5 - General Elemental Rate
Graded: Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function
Graded: Concept Check 7 - General Elemental State Lyapunov Function

WEEK 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 expand

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

Graded: Concept Check 1 - General 3-Axis Attitude Control
Graded: Concept Check 2 - Asymptotic Stability
Graded: Concept Check 3 - Unknown External Torques
Graded: Concept Check 4 - Integral Feedback
Graded: Concept Check 5 - Feedback Gain Selection

WEEK 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 expand

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

Graded: Concept Check 1 - Saturated Control
Graded: Concept Check 2 - Linearized Closed Loop Dynamics
Graded: Concept Check 3 - RW Feedback Control
Graded: Nonlinear Control Final Assignment