Nonlinear Feed Forward Control of a Perturbed Satellite using Extended Least Squares Adaptation and a Luenberger Observer

Abstract

Three adaptive approaches for a non-linear feed-forward controller are combined with two physics-inspired sinusoidal trajectory planners in a spacecraft attitude control model for large slew maneuvers. The basis of the model is a space based satellite sensor which has suffered an unwanted collision where the inertial matrix of the craft is no longer similar to the originally measured inertial matrix. This causes a large inherent error in the feedforward control needed for system maneuvers due to the mismatch of expected dynamics. Trajectory generation, feedforward control, feedback control, filters, observers, and system stability are discussed in relation to the non-linear dynamics under simulation. The adaptive feed-forward controllers discussed include a proportional-derivative (PD) adaptive controller, a Recursive Least Square (RLS) Method, and an Extended Least Squares (ELS) Method. Mean control effort stayed relatively constant between configurations. The controller configuration with ELS feedforward, PID feed-back, and an extended sinusoidal trajectory outperformed the baseline adaptive controller. Mean error was decreased by 23.4%, error standard deviation by 34.0%, and maximum error by 33.0% from a similar case using RLS adaptation. This improvement is entirely based on a need to correct for un-modeled or mis-modeled dynamics. This scenario occurs in actual operation during spacecraft launch, collisions with debris, or can be caused by fuel slosh or loose components.

State of research and development of small spacecraft with optical communication

“…Luenberger observer gives the focus on the predictor-corrector structure. Feedforward control of nonlinear controller with Leunberger observer using least square estimation described in [18] used for attitude control for large slew maneuvers.…”

An Overview of Evolutionary Algorithms toward Spacecraft Attitude Control

“…The objective function is entirely user defined for the specific application. The objective function could be described with respect to minimizing the control effort needed to achieve a specified trajectory such as described in [51], or in minimizing the error between the actual and the desired trajectory in an attitude control scenario as presented in [52]. The objective function is the key component of any optimization and it is crucial to define it in such away as to minimize (or maximize) said function efficiently and precisely.…”

Deterministic Approaches to Transient Trajectory Generation

“…An example of taking the general formulation above and applying it to a specific system is illustrated in Figure 4 for a spacecraft, more specifically a satellite. Here the system dynamics will also include control moment gyros, and other physical restraints/limitations of a real-world plant [12][13][14][15][16][17][18][19][20]. Additionally, the control variables here are in angle, angular rate, and angular acceleration in order to apply the correct torque on the motors to affect the desired outcome.…”