Port-Hamiltonian Mathematical Model of a Fluid Ring Attitude System

Abstract

In this article, we propose a mathematical model using the port-Hamiltonian formalism for a satellite’s three-axis attitude system comprising fluid rings. Fluid rings are an alternative to reaction wheels used for the same purpose, since, for the same mass, they can exert a greater torque than a reaction wheel as the fluid can circulate the periphery of the satellite. The port-Hamiltonian representation lays the foundation for a posterior controller that is feasible, stable, and robust based on the interconnection of the system to energy shaping and/or damping injection components, and by adding energy routing controllers. The torques exerted by the fluid rings are modeled using linear regression analysis on the experimental data got from a prototype of a fluid ring. Since the dynamics of turbulent flows is complex, the torques obtained by the prototype lead to a simpler first approach, leaving its uncertainties to a controller. Thus, the attitude system model could be tested in a future prototype before considering a spatial environment.

Keywords

• Euler’s equations
• attitude system
• fluid rings
• satellite
• port-Hamiltonian system