A Time-Varying Subspace Method for Shape Estimation of a Flexible Spacecraft Membrane

Open Access
- Author:
- Brownell, Matthew
- Graduate Program:
- Aerospace Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- December 02, 2022
- Committee Members:
- Amy Pritchett, Program Head/Chair
Puneet Singla, Thesis Advisor/Co-Advisor
Robert G. Melton, Committee Member
George A Lesieutre, Committee Member
Roshan Thomas Eapen, Committee Member
Andrew Sinclair, Special Signatory - Keywords:
- subspace
spacecraft
flexible
solar
solar power
ERA
reduced-order modeling
analytical modeling
dynamics
structures
space structure
large - Abstract:
- The focus of this work is twofold: i) to derive an accurate rigid-elastic motion model for a large space structure by exploiting the fundamentals of Lagrangian mechanics and ii) to develop a reduced-order model to capture flexible motion of the spacecraft from distributed sensor measurements. The spacecraft structure is motivated by a concept for capturing solar energy and accurately directing it to desired locations on the Earth’s surface. A Lagrangian approach is used to derive an analytical model of the coupled rigid-elastic motion of the spacecraft. This analytical model is then used to simulate data of the fully-coupled attitude-orbital-flexible dynamics of a large spacecraft in orbit. This simulation provides insight into the vibrational modes excited during the spacecraft’s mission, and can be utilized by engineers when designing the structure and orbit of a spacecraft. Utilizing this simulation in place of an experimental test-bed, local acceleration sensor measurements, distributed across the surface of the spacecraft, are obtained. This data is then used to find a reduced-order model to estimate the shape of the spacecraft in real-time. Rather than finding a global model between input and output space, system theory concepts are utilized to find a subspace over which the unknown dynamics evolve. This thesis utilizes the Eigensystem Realization Algorithm (ERA) to obtain said reduced-order model. The derived reduced-order model is guaranteed to capture controllable and observable modes of the spacecraft motion. The reduced-order model’s validity is tested by attempting to replicate the analytical model’s output data and dynamic characteristics such as modal frequency and damping. In both the time-invariant and time-varying model cases, the resultant reduced-order model accurately reproduced the output data and dynamic characteristics of the analytical model. This provides a basis for optimism in identifying flexible-body dynamics from input-output data while in an orbit.