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.
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.
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
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.
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
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.
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
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.
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
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