Angular Velocity Estimation of a Reaction Sphere Actuator for Attitude Satellite Control

Abstract

In different types of spacecraft, such as stabilised satellites, the Attitude Determination and Control System (ADCS) is responsible for stabilisation and achieving the desired rotational movement of the spacecraft. Depending on its application, many satellites may require a threeaxis stabilisation system, thus a device or set of devices capable of applying three-axis rotational motion is needed. These torques are commonly applied by a set of minimum three Reaction Wheels (RW), but commonly four of them are used for redundancy and optimization purposes.
An alternative device to this set of RWs was proposed more than 60 years ago: Reaction Spheres (RSs), but the performance of these designs was not comparable to the one obtained with RWs.
The main idea behind Reaction Spheres is substituting the three or four rotating masses by a single mass in the shape of a hollow sphere that can be accelerated, and thus apply torque, about any given axis.
More recently, a novel concept of Reaction Sphere was proposed and manufactured, in which the spherical actuator is magnetically levitated and can be torqued about any desired axis electronically. The design consists of an eight-pole Permanent Magnet spherical rotor and a twenty-pole stator with electromagnets. Magnetic flux model, required for optimization of the design and for deriving force and torque models, was developed and validated by using a hybrid analytical-FEM approach, and taking advantage of Spherical Harmonic decomposition, which allowed to model and control the system by means of magnetic information, called magnetic state or magnetic orientation, without explicitly knowing the physical orientation of the rotor.
This design, developed at CSEM SA, is able to magnetically levitate and acquire angular velocities up to 300 rpm about any given axis, but it faced some limitations. In order to manage the stored angular momentum, and for closed-loop control purposes, measurement of the angular velocity of the rotor inside the stator is required. As there is no direct measure of this magnitude, a technique based on determining the back-EMF voltage induced in the stator coils was developed and experimentally validated. Nevertheless, this direct method is specially susceptible to magnetic flux density distortions of the rotor. Alternatively, some work on implementing an Extended Kalman Filter by using rotor orientation instead of the magnetic state has been done, but the algorithm was too heavy to be implemented in real-time.
In this thesis, a novel approach based on a Linear Parameter-Varying Kalman Filter observer has been proposed. This method tries to combine the main advantages of the previous approaches for angular velocity estimation, such as fast computations and execution time obtained by making use of the aforementioned Spherical Harmonic decomposition and back-EMF voltage estimation, and the noise filtering and optimality of estimations, under specific circumstances and conditions, obtained with Kalman Filter.
A state-space model of the available system is derived, by making use of the magnetic state and sensor measurements as parameters and input respectively, yielding a Linear Parameter-Varying model, in which the proposed Kalman Filter observer is based, and obtaining this way the novel LPV KF estimator.
This estimator is validated and analysed both in simulation and experimentally with the real prototype, obtaining promising results when used in the angular velocity closed-loop control system, specially for high angular velocities, in which the oscillations around the desired value are reduced by a factor of two or three in amplitude, and these noisy oscillations are substituted by sinusoidal deviations. However, it is believed that the obtained performance could be further improved by improving the control technique used in the closed-loop system to be better adapted to the proposed observer, as the whole system (sphere, estimator and controller) should be taken into account.
We believe that the work developed in this thesis continues with the baseline marked at the Centre Suisse d'Electronique et de Microtechnique SA for the available Reaction Sphere prototype, improving and proposing a promising alternative to one of the critical problems: angular velocity estimation. Nonetheless, the system is still not fully prepared, requiring to study some of the issues shown in this thesis.