Control of Nonlinear Spacecraft Attitude Motion (Coursera)

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

Course 3 of 4 in the Spacecraft Dynamics and Control Specialization.

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.

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.

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.

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.