Modelling of Actuator Dynamics for Spacecraft Attitude Control

Abstract

S PACECRAFT mission success is often highly dependent on the performance and robustness of the attitude control system, which consists of different types of actuators, such as reaction control thrusters, reaction wheels, and magnetic actuators. Solutions to spacecraft attitude control problems often rely on inherent assumptions that the onboard actuators are able to deliver the exact torque desired by the attitude controller at a specified time. The actuators are thus assumed to have no dynamics, or the actuator dynamics are assumed to be fast enough to allow them to be neglected. Although this has shown to be a sufficient approach in the past, it is obvious that attitude actuators, as all electromechanical devices, have dynamics that might impact controller performance. With an increasing demand for high-precision attitude control for purposes such as formation control and optical intersatellite links, the necessity of including actuator dynamics within the control solution is increasingly evident. Mathematical modelling of the complex and nonideal dynamical behavior of actuators and its influence on spacecraft attitude control is a cumbersome task. This dynamical behavior has traditionally been found through laboratory testing, and the subsequent controller design has been influenced by these considerations. One example in this direction is the requirement of reaction thruster response delays being less than the duration of the minimum activation pulse of the actuator. There exist, however, theoretical results from themodelling and analysis of actuator dynamics, such as in [1], in which the effect of unmodelled fast actuator dynamics on the output feedback stabilization of feedback linearizable systems is studied. Similarly, in [2,3], the robust stabilization of a class of nonlinear systems in the presence of unmodelled actuator and sensor dynamics is investigated. More applicable results for our purpose are found in [4,5], in which general multiple-input/multiple-output (MIMO) linear actuator models for underwater vehicle thrusters with dynamics are presented. Because underwater vehicle thrusters are essentially propellers connected to dc motors, analogous to, for example, reaction wheels for spacecraft attitude control, is it possible to describe other actuators with the same model subject to minor changes and tuning. In this paper, we substantiate a unified mathematical model of various attitude control actuators for space applications, in particular, reaction thrusters, reaction wheels, and magnetic torquers. The general actuator dynamical model is based on the marine technology work of [5], appropriately fitted to the aforementioned actuator categories. To describe time delays in the response of actuators such as, for example, thrusters, an expansion of the general actuatormodel is suggested.