Dynamics, Estimation, and Control for Stabilizing the Attitude and Shape of a Flexible Spacecraft

Abstract

Advances in technology have enabled the development of large spacecraft structures such as solar sails, expansive antennas, and large solar arrays. A critical design constraint for these structures is mass, necessitating lightweight construction which, in turn, increases structural flexibility. This flexibility poses significant challenges resulting from structural deformations and vibrations that complicate attitude control and can degrade the performance and lifespan of the spacecraft. The goal of this research is to develop estimation and control strategies to mitigate the effects of spacecraft flexibility.A flexible spacecraft model is derived using a hub and appendage framework. In this model one or more flexible appendages attach to a central rigid hub. The model represents the appendages as a discretized set of flexibly connected elements called panels. Stiff springs connect the panels, and the dynamic model of the system’s internal forces and moments uses coordinates in the hub’s reference frame. Reaction wheels on the hub perform attitude control, while distributed pairs of magnetic torque rods on the appendage influence its shape. Initially, the model restricts flexibility to one direction, resulting in a planar model. A Lyapunov-based control design provides a feedback law for the reaction wheel and torque rods in the planar model. Numerical simulations demonstrate that the proposed controller meets the control objectives and compares favorably to other controllers. An Extended Kalman Filter is applied to the system to perform state estimation and output feedback control, which performs at nearly the same level as state feedback control. The modeling framework and flexibility are extended to three dimensions. The development of a control law for the magnetic torque rods considers the attitude control of a single panel using two magnetic torque rods. Due to the system being underactuated, the attitude error is defined in terms of the reduced-attitude representation. Lyapunov analysis yields a control law that stabilizes the reduced attitude and angular velocity of a rigid panel using only two magnetic torque rods. Numerical simulations validate the control law’s performance for a single panel. This control law is then applied to the flexible appendage to stabilize its shape. Numerical simulations show that this implementation of shape control significantly reduces structural deformations and dampens structural oscillations compared to scenarios without shape control. To perform state estimation of the high-dimensional flexible spacecraft model, dynamic mode decomposition generates a reduced order model that is linear with respect to the evolution of the resulting modes. A Kalman filter estimates the mode amplitudes of the reduced order model from a limited set of measurements, enabling the reconstruction of the entire system state. The optimization of the number and placement of sensors maximizes the observability of the observer. Numerical simulations demonstrate that this framework yields accurate state estimates with reduced computational cost.