Exact Modal Decomposition of Non-linear Second-Order Systems

Abstract

Generation of control torque for highly agile satellite missions is generally achieved with momentum exchange devices, such as reaction wheels and control moment gyros (CMGs) with high slew maneuverability. However, the generation of a high control torque from the respective actuators requires high power and thus a large mass. This paper proposes a novel type of control actuator that will generate torques in all three principal axes of a rigid satellite using only a spinning wheel and a simple tilt mechanism. The tilt mechanism will rotate the spin axis of the wheel (tilt the generated angular momentum vector) about two additional axes thereby generating high control torque about the axes orthogonal to the wheel spin axis. Torque will also be generated about the wheel spin axis through the increase or decrease of the wheel angular speed. This newly proposed actuator generates control torque through controlled precession of the spinning wheel while the tilt angle and the tilt rates are computed without the use of the popular pseudo-inverse calculation obtained with CMGs leading to no singularities being experienced during nominal wheel operation. This paper describes the fundamental mathematical dynamic model of the system and numerical simulations are used to demonstrate the agile three-axis attitude control capability that guarantees a highly efficient trade-off between torque capability, mass, and power consumption. The system actuator sizing is based on slew rates of up to two degrees per second.