Nonlinear Control Design Techniques For Precision Formation Flying At Lagrange Points
Luquette, Richard J.
Sanner, Robert M.
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Precision spacecraft formation flying is an enabling technology for a variety of proposed space-based observatories, such as NASA's Terrestrial Planet Finder (TPF), the Micro-Arcsecond X-Ray Imaging Mission (MAXIM), and Stellar Imager (SI). This research specifically examines the precision formation flying control architecture, characterizing the relative performance of linear and nonlinear controllers. Controller design is based on a 6DOF control architecture, characteristic of precision formation flying control. In an effort to minimize the influence of design parameters in the comparison, analysis employs "equivalent" controller gains, and incorporates an integrator in the linear control design. Controller performance is evaluated through various simulations designed to reflect a realistic space environment. The simulation architecture includes a full gravitational model and solar pressure effects. Spacecraft model properties are based on realistic mission design parameters. Control actuators are modeled as a fixed set of thrusters for both translation and attitude control. Analysis includes impact on controller performance due to omitted dynamics in the model (gravitational sources and solar pressure) and model uncertainty (mass properties, thruster placement and thruster alignment). Linearized equations of relative motion are derived for spacecraft operating in the context of the Restricted Three Body Problem. Linearization is performed with respect to a reference spacecraft within the formation. Analysis demonstrates robust stability for the Linear Quadratic Regulator controller design based on the linearized dynamics. Nonlinear controllers are developed based on Lyapunov analysis, including both non-adaptive and adaptive designs. While the linear controller demonstrates greater robustness to model uncertainty, both nonlinear controllers exhibit superior performance. The adaptive controller provides the best performance. As a key feature, the adaptive controller design requires only relative navigation knowledge. Analysis demonstrates the ability of the nonlinear controller to compensate for unknown dynamics and model uncertainty. Results exhibit the potential of a nonlinear adaptive architecture for improving controller performance. Nonlinear adaptive control is a viable strategy for meeting the extreme control requirements associated with formation flying missions like MAXIM and Stellar Imager. Mission specific analysis from a systems perspective is required to determine the best controller design.