Developing and implementing a CubeSat's equations of motion

TL;DR

This paper presents the development of a control system for a CubeSat's attitude using newly derived equations of motion, simulations, and hardware testing to ensure accurate ground target tracking during low Earth orbit flyovers.

Contribution

It introduces a novel set of equations of motion for CubeSat attitude control and a gain optimization method, validated through simulations and hardware performance assessments.

Findings

Disturbance torques increase wheel speeds by 12%.

Sensor noise can raise pointing error by 1.9 degrees.

Controller can compensate for gyroscopic torques within system limits.

Abstract

As part of the Bristol PROVE mission, a nano satellite in low Earth orbit will be required to track a ground based target during a 400 second flyover. This requires agile attitude control that will be achieved using a system of flywheels. To calculate the necessary torque from these flywheels, a controller was designed. Using newly derived equations of motion for the system, an expression to optimise the gains was produced. With this controller, simulations were run to evaluate the largest causes of error in target pointing. Disturbance torques were safely handled by the controller, but led to a 12% increase in wheel speeds, reaching 8325 rpm. This higher speed led to an increased gyroscopic torque, reaching 10^-7 Nm in the worst case. However since the flywheels can deliver 10^-5 Nm of torque, the controller could also correct for this. Hardware performance was then varied to assess the effect of each component on pointing accuracy. Attitude sensor noise was found to increase pointing error by 1.9 degrees in the worst case. Minimum performance requirements were then determined for each component in order to maintain an acceptable pointing accuracy.