Small-Satellite Attitude Control Using Piecewise-Sinusoidal Controls in the Presence of Disturbance Torques

This paper addresses small-satellite attitude control in the presence of external disturbance torques using internal rotating-mass actuators. Unlike reaction wheels, these rotating-mass actuators cannot perform complete rotations. Instead, their stroke is limited to a radians of total rotation. We present a setpoint tracking control algorithm that uses feedback of the satellite's attitude and angular velocity to determine the control signals, which are the angles of the rotating-mass actuators relative to the satellite's body. This feedback algorithm yields control signals that are continuous but only piecewise-continuously differentiable sinusoids. We analyze the stability and performance of the closed-loop system for the case where no external torque is acting on the satellite. We present three numerical simulations to demonstrate the setpoint tracking attitude controller: i) a satellite in low-Earth orbit neglecting aerodynamic moment; ii) a satellite in low-Earth orbit including aerodynamic moment; and iii) a satellite on an air-bearing on Earth, which results in a moment due to gravity.