Providing Nanosatellite Triaxial Gravitational Orientation Using Magnetic Actuators

Three-axis gravity stabilization of 3U CubeSat is achieved due to selection of the nanosatellite moments of inertia at the design stage, as well as special modes included in the algorithm to provide stabilization of CubeSat relative to each motion channel separately. In this paper, we propose a modified algorithm based on the magnetic stabilization algorithm B-dot. The modified algorithm provides three modes intended to damp the initial angular velocity to the value of the orbital angular velocity, to keep the angular velocity at a value close to that of the orbital angular velocity, and to provide the nanosatellite gravitational triaxial stabilization by using one magnetic coil located on the axis with the transversal moment of inertia, which is possible due to the small angle between the magnetic field line and the satellite's trajectory. We propose two modifications for forming a control loop for orientation and stabilization of the 3U CubeSat: the first one uses measurements from magnetometers and angular rate sensors as feedback, and the second one, only magnetometers. The efficiency of the two modifications of modifications was studied by means of statistical modeling.

Application of Selected Numerical Methods to Model the Fractional-Order System Behavior of Nonlaminated Magnetic Actuators

The electromagnetic dynamics of nonlaminated magnetic actuators are highly influenced by eddy currents and minor perturbations like core saturation, hysteresis as well as fringing and leakage fluxes. In the literature, analytical high-fidelity models describing these phenomena are known, which lead to complex reluctance networks or transcendental system descriptions with fractional-order characteristics. Therefore, they are not suitable for a direct implementation within the actuator control. Previously, we provided appropriate analytical rational approximations that allow a digital real-time implementation of these models on a microcontroller. However, the inclusion of the minor perturbations, if possible, leads to impractical model orders requiring simplifications, which compromise the model accuracy. This article studies numerical methods to reduce high model orders or directly approximate the transcendental systems or empirical measurement data. The greater degree of freedom allows for a possible higher model accuracy with sufficiently low orders. We review and improve existing approaches like Levy's method and Vector Fitting and apply them to the frequency response of the underlying fractional-order system. Furthermore we propose an order reduction algorithm based on a pole-zero-cancellation with tracking error compensation. Using measurement data, a comparison shows that the numerical approaches match or excel our previously studied analytical approximation.

Application of Selected Numerical Methods to Model the Fractional-Order System Behavior of Nonlaminated Magnetic Actuators

The electromagnetic dynamics of nonlaminated magnetic actuators are highly influenced by eddy currents and minor perturbations like core saturation, hysteresis as well as fringing and leakage fluxes. In the literature, analytical high-fidelity models describing these phenomena are known, which lead to complex reluctance networks or transcendental system descriptions with fractional-order characteristics. Therefore, they are not suitable for a direct implementation within the actuator control. Previously, we provided appropriate analytical rational approximations that allow a digital real-time implementation of these models on a microcontroller. However, the inclusion of the minor perturbations, if possible, leads to impractical model orders requiring simplifications, which compromise the model accuracy. This article studies numerical methods to reduce high model orders or directly approximate the transcendental systems or empirical measurement data. The greater degree of freedom allows for a possible higher model accuracy with sufficiently low orders. We review and improve existing approaches like Levy's method and Vector Fitting and apply them to the frequency response of the underlying fractional-order system. Furthermore we propose an order reduction algorithm based on a pole-zero-cancellation with tracking error compensation. Using measurement data, a comparison shows that the numerical approaches match or excel our previously studied analytical approximation.

Mathematical review of the attitude control mechanism for a spacecraft

The issue of inertial pointing for a spacecraft with magnetic actuators is considered and a practical global response to this problem is obtained by static attitude and speed feedback methods. A local solution dependent on dynamic attitude feedback is additionally introduced. The simulation results show the practical applicability of the proposed approach. The issue of attitude regulation of rigid spacecraft, i.e., spacecraft demonstrated by the Euler's conditions and by an appropriate parameterization of the attitude, has been broadly concentrated as of late. As a matter of first importance, it is beyond the realm of imagination by methods for magnetic actuators to give three autonomous control torques at each time instant. Moreover, the conduct of these actuators is characteristically time-varying, as the control instrument relies on the varieties of the Earth magnetic field along the spacecraft orbit. In any case, demeanor adjustment is conceivable in light of the fact that on normal the framework has solid controllability properties for a wide range of orbit inclinations. A lot of work has been devoted as of late to the issues of examination and structure of attractive control laws in the straight case, i.e., nominal operation of a satellite near its equilibrium attitude. Specifically, ostensible and vigorous solidness and execution have been contemplated, utilizing either devices from occasional control hypothesis misusing the (quasi) intermittent conduct of the framework close to an equilibrium or other techniques aiming at developing suitable time-varying controllers.

Analysis of vector hysteresis models in comparison to anhysteretic magnetization model

The design of electrical machines and magnetic actuators requires accurate models to represent hysteresis effects in ferromagnetic materials. The magnetic nonlinearity of the iron core is usually considered by an anhysteretic magnetization curve. With this assumption, hysteresis’ effects in the field computation are completely neglected. This paper presents a comparative study of different hysteresis models, particularly Pragmatic Algebraic Model (PAM) and vector stop model, with regard to a vector anhysteretic anisotropic model. The PAM turns out to be an efficient model implemented with one mathematical equation. The multi cells stop model relies on a consistent thermodynamic formulation, whose dissipation corresponds to a dry friction-like element. Both models implement a constitutive relationship, in which the magnetic flux density vector as independent input and magnetic field strength as output. With a rotational single sheet tester (RSST), various tests for a sample of material FeSi24-50A (FeSi) with a silicon proportion of 2.4 wt% can be proceeded under the application of relevant field distribution. The obtained measured data are applied to parameterize and validate the models. Following numerical experiments the results are compared with those obtained by means of an anhysteretic anisotropic model.