Leopoldo Rossini

Force and Torque Analytical Models of a Reaction Sphere Actuator Based on Spherical Harmonic Rotation and Decomposition

This paper presents an analytical model for the force and torque developed by a reaction sphere actuator for satellite attitude control. The reaction sphere is an innovative momentum exchange device consisting of a magnetic bearings spherical rotor that can be electronically accelerated in any direction making all the three axes of stabilized spacecrafts controllable by a unique device. The spherical actuator is composed of an 8-pole permanent magnet spherical rotor and of a 20-coil stator. Force and torque analytical models are derived by solving the Laplace equation and applying the Lorentz force law. The novelty consists in exploiting powerful properties of spherical harmonic functions under rotation to derive closed-form linear expressions of forces and torques for all possible orientations of the rotor. Specifically, the orientation of the rotor is parametrized using seven decomposition coefficients that can be determined noniteratively and in a linear fashion by measuring the radial component of the magnetic flux density from at least seven different locations. Therefore, force and torque models for all possible orientations of the rotor are expressed in closed form as linear combination of mutually orthogonal force and torque characteristic matrices, which are computed offline. The proposed analytical models are experimentally validated using a developed laboratory prototype.

Rotor Design Optimization for a Reaction Sphere Actuator

This paper presents the rotor design optimization for a reaction sphere (RS) actuator. The RS is a permanent-magnet synchronous spherical actuator whose rotor is magnetically levitated and can be accelerated about any desired axis. The RS is composed of an 8-pole permanent-magnet (PM) spherical rotor and of a 20-coil stator. Due to the highly complex geometry of the spherical rotor, consisting of eight bulk PM poles with truncated spherical shape adjusted on the back-iron structure with truncated octahedral shape, a pure analytical approach for the optimization problem is not practicable. Therefore, given a set of specifications, the optimization of design parameters is performed using finite-element simulations to minimize the rotor magnetic flux density distortion with respect to the fundamental harmonic. The resulting optimized rotor is fully compliant with design specifications. Finally, experimental measurements on the manufactured rotor are reported showing a strong correspondence with the specified flux density values.

Analytical Model of Eddy Currents in a Reaction Sphere Actuator

A recently proposed technique to control the satellite attitude using a magnetically levitated sphere requires the development of suitable models of its dynamics. One of the phenomena that can affect motion of the system are eddy currents induced in the stator of the actuator due to time variable magnetic field generated by rotational motion of a permanent magnet rotor. We present an analytical model of the eddy currents for the actuator with eight-pole rotor. The model is derived using a second-order vector potential-based approach, and the solution is obtained in terms of spherical harmonic functions. This model allows us to study rotor rotations with constant angular frequency around an axis arbitrarily oriented with respect to both rotor and stator of the reaction sphere actuator.

An open-loop control strategy of a reaction sphere for satellite attitude control

This paper presents an open-loop strategy for the control of the orientation of a reaction sphere actuator. The reaction sphere is a magnetic bearing spherical motor composed of an 8-pole permanent magnet spherical rotor and a 20-pole stator. The control law is based on a rotating magnetic field obtained from a sequence of desired rotor orientations. Hence, the reaction sphere can be accelerated about any desired axis. Force and torque inverse models are developed and employed to derive the control scheme. The proposed method is successfully employed to drive a reaction sphere laboratory prototype up to 480 rpm.

Hybrid FEM-analytical force and torque models of a reaction sphere actuator

This paper presents a hybrid FEM-analytical model for the magnetic flux density, the force and torque of a Reaction Sphere (RS) actuator for satellite attitude control. The RS is a permanent magnet synchronous spherical actuator whose rotor is magnetically levitated and can be accelerated about any desired axis. The spherical actuator is composed of an 8-pole permanent magnet spherical rotor and of a 20-coil stator. Due to the highly complex geometry of the spherical rotor, consisting of 8 bulk permanent magnet poles with truncated spherical shape adjusted on the back-iron structure with truncated octahedral shape, a pure analytical approach is not possible. Therefore, in this article we adopt a hybrid approach in which FEM or measured derived values are combined with other boundary conditions on a known analytical structure to derive expressions for the magnetic flux density, the force, and the torque. The Laplace equation is solved by exploiting powerful properties of spherical harmonic functions under rotation to derive closed-form linear expressions for all possible orientations of the rotor. The proposed models are experimentally validated using a developed laboratory prototype and with finite element simulations.

Analytical and experimental investigation on the force and torque of a Reaction Sphere for satellite attitude control

This paper presents the development of an analytical model for the force and torque developed by a Reaction Sphere for satellite attitude control. The Reaction Sphere is a magnetic bearings spherical motor whose rotation axis can be electronically controlled. The actuator is composed of an 8-pole permanent magnet spherical rotor and a 20-pole stator. Force and torque models are derived by solving the Laplace equation and applying the Lorentz force law. Using the linear superposition principle, the expression of the force and torque is formulated in matrix form. The developed models are validated through an open loop measurement campaign as well as by finite element simulations. Experimental results confirmed the validity of both the force and torque analytical models.

Back-EMF and rotor angular velocity estimation for a reaction sphere actuator

This paper presents a procedure to estimate the back-EMF voltages and the rotor angular velocity of a reaction sphere actuator for satellite attitude control. The reaction sphere is a permanent magnet synchronous spherical actuator whose rotor is magnetically levitated and can be accelerated about any desired axis. The spherical actuator is composed of an 8-pole permanent magnet spherical rotor and of a 20-coil stator. The developed technique to measure the back-EMF voltages is based on Faradays law, in which the magnetic flux density is decomposed on a spherical harmonic basis, whose expansion parameters are derived from measurements of the radial component of the field collected from at least seven locations. Then, given the back-EMF voltages, the rotor angular velocity is derived employing the energy conservation principle. The resulting expressions are linear and are expressed in closed-form. Finally, the proposed method is validated numerically with finite element simulations and experimentally using a developed laboratory prototype.

Linear Parameter-Varying Kalman Filter for angular velocity estimation of a reaction sphere actuator for satellite attitude control

This paper presents a novel angular velocity estimation strategy of a Reaction Sphere (RS) for satellite attitude control based on a Linear Parameter-Varying (LPV) Kalman Filter. The reaction sphere is a permanent magnet synchronous spherical actuator whose rotor is magnetically levitated and can be accelerated about any desired axis. The spherical actuator is composed of an 8-pole permanent magnet spherical rotor and of a 20-coil stator. The proposed technique relies on the implementation of a Kalman Filter observer over a LPV state-space model based on the rotor dynamics and the spherical harmonic decomposition of the magnetic flux density generated by the rotor. First, a theoretical development of the aforementioned estimator will be exposed, followed by a description of simulation and experimental set-ups for the tests. Finally, the proposed estimator is compared with the previous method used for angular velocity estimation based on the estimation of the back-EMF voltages induced in the coils, obtaining a significant reduction in amplitude and frequency of oscillations in the angular velocity control loop.

Novel Type of Inertial Actuator for Satellite Attitude Control System Basis on Concept of Reaction Sphere—ELSA Project

Magnetically levitated reaction sphere systems are considered as a new type of actuator dedicated for satellites ACS system. Inertial Attitude Control Systems used in spacecrafts, traditionally consists of one to four reaction wheels (RW) or control moment gyroscopes (CMG). In a principle, the attitude of the satellite can be changed by the reaction to the acceleration of the appropriate wheel. In practice, for optimization, redundancy purposes and ability to three-axis attitude stabilization, four or five wheels are common. Another approach, which states a general base for this work, assumes use of a single reaction sphere which can be accelerated in any direction instead of set of reaction wheels. The sphere can be accelerated in any direction by a three dimensional (3D) motor. Because of its unparalleled symmetry, a hollow sphere delivers constantly a maximum inertia independently of its current rotation axis. A solution investigated here consists in a rotating permanent magnet spherical rotor enclosed in a multi-coil stator. In opposition to conventional ball bearing momentum exchange devices, rotor in this solution levitates magnetically what results in absence of friction and increase of performance. The sphere can be accelerated in any direction by a three dimensional (3D) motor, making the three axes of the spacecraft controllable by just a single device. Furthermore, a hollow sphere has the natural optimal multi axis inertia-to-mass and-volume ratios.