Satellite Attitude Dynamics Research Articles

A fractional-order sliding mode control for nominal and underactuated satellite attitude controls

Sliding mode control (SMC) is widely used in many existing nonlinear control solutions due to its capability against external disturbances and uncertainties, while the fractional order control (FOC) is employed as it can further enhance the control performance due to its robustness. This paper attempts to implement a fractional-order sliding mode control (FOSMC) for a small satellite with reaction wheels (RWs). In this work, a conventional SMC was initially designed to cope with the uncertainties of satellite attitude dynamics. In order to improve the attitude control performance, the FOSMC was designed accordingly and the classical chattering problem was alleviated by using the hyperbolic tangent function. This current work is the maiden work on FOSMC especially for small satellites using RWs. The FOSMC was also tested for a satellite with only two functional RWs, in which the control allocation technique is proposed to solve the underactuated satellite attitude control problem. Since the angular momentum of the reaction wheel will become saturated over time, it will be managed using the momentum unloading technique with the unique fuzzy proportional-integral (FPI) control. All control algorithms were numerically treated and analysed. The results show that the FOSMC is effective in achieving the overall desired attitude control performance for nominal and underactuated satellites.

Simulation of long-term rotational dynamics of large space debris: A TOPEX/Poseidon case study

Accurate knowledge of the rotational dynamics of a large space debris is crucial for space situational awareness (SSA), whether it be for accurate orbital predictions needed for satellite conjunction analyses or for the success of an eventual active debris removal mission charged with stabilization, capture and removal of debris from orbit. In this light, the attitude dynamics of an inoperative satellite of great interest to the space debris community, the joint French and American spacecraft TOPEX/Poseidon, is explored. A comparison of simulation results with observations obtained from high-frequency satellite range measurements is made, showing that the spacecraft is currently spinning about its minor principal axis in a stable manner. Predictions of the evolution of its attitude motion to 2030 are presented, emphasizing the uncertainty on those estimates due to internal energy dissipation, which could cause a change of its spin state in the future. The effect of solar radiation pressure and the eddy-current torque are investigated in detail, and insights into some of the satellite’s missing properties are provided. These results are obtained using a novel, open-source, coupled orbit-attitude propagation software, the Debris SPin/Orbit Simulation Environment (D-SPOSE), whose primary goal is the study of the long-term evolution of the attitude dynamics of large space debris.

Modeling and Simulation of Satellite Attitude Dynamics and Control System using Modelica

The control of attitude of a satellite is difficult to verify since several subsystems of different disciplines, e.g., flexible multibody dynamics, machines, electronics and control, are involved and strongly coupled. A traditional method is to model each single discipline subsystem with a domain specific software, and combine them through interfaces. However, the problems are that lots of interfaces between software have to be developed, and manual decoupling of systems should be considered during modelling process. In this Paper, models of the dynamics and the control system are established in a unified modelling software, MWorks, which is an Integrated Development Environment of Modelica. The model can be used to verify the satellite control strategy, and also provide an effective means for satellite attitude control system design. Moreover, on this basis, the whole satellite was modelled to access state parameters changes under the coupling of the dynamic subsystem, the attitude control subsystem, the power supply subsystem, the propulsion subsystem and the integrated electronic subsystem can be synthetically considered.

Melnikov-based analysis for chaotic dynamics of spin-orbit motion of a gyrostat satellite

Interactions of the orbital motion on attitude dynamics of the gyrostat satellite are considered in this paper. The mathematical model is derived using the Hamiltonian method for the spin-orbit motion of the spacecraft followed by the reduction of the coupled equations of motion using the extended Deprit canonical transformation. The analytical Melnikov method is used innovatively to study chaos on the complex Spin-Orbit dynamics of the gyrostat satellite. Also, the numerical methods such as Lyapunov exponent criterion, Poincaré section, trajectories of phase portrait, and the time–history responses can be proved the heteroclinic bifurcation and chaotic vibrations in the highly nonlinear system. Using the results based on the Melnikov integral, the parameters of the spacecraft including the mass and inertia moment of satellite with respect to the altitude of orbit can be designed in order to control the bifurcation with a view to prevention of chaos in the system in the absence of an active control system.

Stability Analysis of Coupled Orbit–Attitude Dynamics Around Asteroids Using Finite-Time Lyapunov Exponents

This paper investigates coupled orbit–attitude dynamics around asteroids subject to solar radiation pressure and gravity irregularities. The solutions of sun-synchronous orbits with sun-tracking attitude motion are analytically derived, and their stability is evaluated by applying linearization and averaging. To validate the analytical solutions, numerical simulations are performed based on nonlinear coupled orbit–attitude equations of motion. In addition, the nonlinear stability of such coupled motion is analyzed using finite-time Lyapunov exponents. It is demonstrated that the sun-synchronous orbit–attitude coupled motions exhibit long-term stability under certain conditions, and thus, these motions are promising options for asteroid missions.

Defunct Satellites in Nearly Polar Orbits: Long-term Evolution of Attitude Motion

Abstract Low Earth orbits (LEO) are known as a region of high space activity and, consequently, space debris highest density. Launcher upper stages and defunct satellites are the largest space debris objects, whose collisions can result in still greater pollution, rendering further space missions in LEO impossible. Thus, space debris remediation is necessary, and the LEO region is a primary target of active debris removal (ADR) projects. However, ADR planning requires at least an approximate idea of the candidate objects’ attitude dynamics, which is one of the incentives for our study. This paper is mainly focused on modeling and simulating the attitude dynamics of defunct satellites. We consider a “boxwing” configuration satellite with an ellipsoid of inertia close to an oblate ellipsoid of revolution. The dynamical model takes into account the gravity-gradient torque, the torque due to the residual magnetic moment, and the torque due to eddy currents induced by the interaction of conductive materials with the geomagnetic field. A better understanding of the intermediate phase of the exponential deceleration and existing final regimes is achieved owing to a more accurate model of the eddy-current torque than in most prior research.We also show the importance of orbital precession, which contributes to the overall attitude motion evolution.

Relative equilibria and stability of a dumbbell spacecraft about an asteroid

The gravitational orbit-attitude coupling becomes pronounced in spacecraft dynamics about small asteroids, due to the large ratio of the spacecraft's dimension to the orbital radius. In this study, relative equilibria and their stability of the gravitationally coupled orbit-attitude dynamics (full dynamics) of a dumbbell spacecraft about an irregular-shaped asteroid are investigated. The shape of the asteroid is represented by a homogeneous polyhedron, and its non-spherical gravity is calculated accordingly. By using geometric mechanics, the Hamiltonian structure and equations of motion of the full dynamics are derived. Then, the orbit-attitude equilibria about asteroids 4769 Castalia, 433 Eros, and 6489 Golevka are calculated numerically, respectively, and the drift of orbit-attitude equilibria with respect to the dumbbell's varying length is also discussed. By comparing with the equilibria of a point mass, it has been found that a classical point-mass equilibrium can generate three orbit-attitude equilibria located nearby. With the increase of the dumbbell's length, the effects of orbit-attitude coupling become stronger, and the orbit-attitude equilibria diverge further from the classical point-mass equilibria. The spectral stability of the orbit-attitude equilibria is determined numerically and analyzed. It has been found that the gravitational orbit-attitude coupling is likely to make the equilibria unstable in our simulations. The dumbbell is a good approximation of a spacecraft consisting of two modules that are connected by trusses, and its orbit-attitude equilibria have potential applications in asteroid proximity operations, such as body-fixed hovering.

Chaos analysis in attitude dynamics of a flexible satellite

In this paper, we analytically and numerically investigate chaos in attitude dynamics of a flexible satellite composed of a rigid body and two identical rigid panels attached to the main body with springs. Flexibility, viewed as a perturbation, can cause chaos in the satellite. To show this, first, we use a novel approach to define this perturbation. Then, we employ canonical transformation to transform the Hamiltonian of the system from five to three degrees of freedom. Next, we approximate the system by a second-order differential equation with a time quasiperiodic perturbation. Finally, we apply Melnikov–Wiggins’ method near the heteroclinic orbits to prove the existence of chaos. Using the maximum value of Melnikov–Wiggins function and the small perturbation parameter, we find a tool to predict the size of the chaotic layers. Results show that this approach is useful even if the panels are not small. In addition, it is observed that though the satellite attitude dynamics is chaotic, in many cases the width of chaotic layers is very small and therefore negligible.

Stabilization of a programmed rotation mode for a satellite with electrodynamic attitude control system

The paper deals with a dynamically symmetric satellite in a circular near-Earth orbit. The satellite is equipped with an electrodynamic attitude control system based on Lorentz and magnetic torque properties. The programmed satellite attitude motion is such that the satellite slowly rotates around the axis of its dynamical symmetry. Unlike previous publications, we consider more complex and practically more important case where the axis is fixed in the orbital frame in an inclined position with respect to the local vertical axis. The satellite stabilization in the programmed attitude motion is studied. The gravitational disturbing torque acting on the satellite attitude dynamics is taken into account since it is the largest disturbing torque. The novelty of the proposed approach is based on the usage of electrodynamic attitude control system. With the aid of original construction of a Lyapunov function, new conditions under which electrodynamic control solves the problem are obtained. Sufficient conditions for asymptotic stability of the programmed motion are found in terms of inequalities for the values of control parameters. The results of a numerical simulation are presented to demonstrate the effectiveness of the proposed approach.

An effective approach to identify the mass properties of a satellite attitude dynamics simulator

A satellite attitude dynamics simulator (SADS) is a low-cost, ground-based equipment for laboratory simulation of the space environment as satellite weightless, sun and magnetic field simulation as well as implementation of diverse attitude determination and control algorithms. Precise estimation of mass properties plays a significant role in guidance and control algorithms application. The objective of this paper is mass properties identification includes moment of inertia tensor and centre of mass position of a three-degrees-of-freedom SADS at the Space Research Laboratory. This paper investigates the well-known methods to estimate mass properties, i.e. Batch Least Squares and Classical Kalman Filter and presents an innovative approach using the Classical Levenberg–Marquardt (CLM) to solve this major problem. In order to verify the proposed technique, a MATLAB® SIMULINK® model of the SADS is employed. The experimental results indicate that the parameter estimation process using CLM technique is more accurate and reliable than other methods.

Analytical and numerical study of chaos in spatial attitude dynamics of a satellite in an elliptic orbit

In this paper, chaos in spatial attitude dynamics of a triaxial rigid satellite in an elliptic orbit is investigated analytically and numerically. The goal in the analytical part is to prove the existence of chaos and then to find a relation for the width of chaotic layers (i.e. the initial values needed to have a chaotic attitude motion) based on the parameters of the system. The numerical part is aimed at validating the analytical method using the Poincaré maps and the maximum value of the Lyapunov exponents. The rotational–translational Hamiltonian of the system is first derived. This Hamiltonian has six degrees of freedom. Choosing a proper set of coordinates and given the fact that the total angular momentum is constant, the Hamiltonian is then reduced to a four-degree-of-freedom system. Assuming the effect of attitude on the orbital dynamics to be negligible, and assuming a nearly symmetric and fast-spinning satellite, the system is approximated by a second-order differential equation with a time quasi-periodic perturbation. Next, the Melnikov–Wiggins’s method is used to prove the existence of a chaotic behavior followed by the determination of an analytical relation for the width of chaotic layers. Although in the analytical method some restrictive assumptions are enforced, the results show that the analytical relation gives a good estimate for the width of chaotic layers even if these assumptions are not entirely satisfied. The results also show that this method is useful for finding the effects of all the parameters (the orbit and the satellite) and the initial values on the existence of a regular behavior.

Mass properties identification and automatic mass balancing system for satellite attitude dynamics simulator

A Satellite Attitude Dynamics Simulator is a low-cost, ground-based system made to simulate the conditions of a weightless satellite in space. The identification of the mass characteristics is crucial for Satellite Attitude Dynamics Simulator application and so the center of mass place is necessary for balancing the platform and moment of inertia which is a significant factor in designing controllers and selecting actuators. The purposes of this paper are the mass properties identification and design, experimentation, and validation of an automatic mass balancing system, which is assembled on the Satellite Attitude Dynamics Simulator at the Space Research Laboratory. This paper presents a process of mass properties estimation for the Satellite Attitude Dynamics Simulator using classical Levenberg–Marquardt as an optimization method. By employing this technique lack of repeatability and difficulties in implementation will be eliminated. In order to verify this technique, a MATLAB® SIMULINK® model of the Satellite Attitude Dynamics Simulator is established. The gap between the center of mass and center of rotation is decreased by means of the automatic mass balancing system in order to remove gravity disturbance. The results of this identification process are compared to the recursive least square algorithm, which is commonly employed in identification of mass properties. The analytical and experimental results prove that the proposed characteristic estimation process using classical Levenberg–Marquardt algorithm is more effective and appropriate. Proper excitation of the platform will guarantee the accuracy of estimation and compensation of the center of gravity offset utilizing the balancing system.

Exact solutions and adiabatic invariants for equations of satellite attitude motion under Coulomb torque

This paper focuses on the attitude dynamics of a defunct axisymmetric satellite under the action of Coulomb forces to enable active space debris removal. Touchless Coulomb interaction occurs between an active spacecraft and the passive satellite at a fixed separation distance. The recently developed multi-sphere method of Schaub and Stevenson allows providing a simplified electrostatic force and torque model between non-spherical space objects. The existence of torques between charged bodies makes it necessary to study the attitude motion of the passive satellite for ensuring the safety of the space debris removal. The goal is first to deduce the equations of motion in the canonical form which is suitable for analytical analysis and then to construct a phase portrait, and to obtain exact solutions using Jacobi elliptic functions. Finally, for the disturbed motion of the system of two bodies, when the distance between the active spacecraft and the defunct satellite (or) and charge voltage changes slowly over time, adiabatic invariants are found in terms of the complete elliptic integrals. In this case, the adiabatic invariants are approximately first integrals of the disturbed system and they remain approximately constant for long time intervals during which the parameters change considerably. For a plane motion, the adiabatic invariants used to obtain an analytical solution for envelope of a deflection angle of the defunct satellite. This work extends the theory to the three-dimensional tumbling motion of a satellite on an orbit. The obtained results can be applied to study an opportunity of the space debris removal by the Coulomb interaction with the active spacecraft as a pusher.

Stabilization of coupled orbit–attitude dynamics about an asteroid utilizing Hamiltonian structure

The gravitationally coupled orbit–attitude dynamics, also called the full dynamics, in which the spacecraft is modeled as a rigid body, is a high-precision model for the motion in the close proximity of an asteroid. A feedback control law is proposed to stabilize relative equilibria of the coupled orbit–attitude motion in a uniformly rotating second degree and order gravity field by utilizing the Hamiltonian structure. The feedback control law is consisted of potential shaping and energy dissipation. The potential shaping makes the relative equilibrium a minimum of the modified Hamiltonian by modifying the potential artificially. With the energy-Casimir method, it is theoretically proved that an unstable relative equilibrium can always be stabilized in the Lyapunov sense by the potential shaping with sufficiently large feedback gains. Then, the energy dissipation leads the motion to converge to the relative equilibrium. The proposed stabilization control law has a simple form and is easy to implement autonomously, which can be attributed to the utilization of natural dynamical behaviors in the controller design.

Asymptotic stability of a satellite with electrodynamic attitude control in the orbital frame

A satellite in a circular near-Earth orbit is under consideration. The three-axis stabilization of the satellite in the orbital coordinate system with the use of electrodynamic attitude control system is studied. No constraints are imposed on the Earth's magnetic field approximation. The gravity gradient disturbing torque acting on the satellite attitude dynamics is taken into account as the largest disturbing torque. With the use of the Lyapunov direct method, conditions under which electrodynamic control solves the problem are obtained. The restrictions on the control parameter values for which one can guarantee the asymptotic stability of the programmed satellite motion are found and represented in an explicit form. Comparison of the results of numerical simulation and analytical investigation demonstrate effectiveness of the proposed approach.

Preliminary results on the dynamics of large and flexible space structures in Halo orbits

The global exploration roadmap suggests, among other ambitious future space programmes, a possible manned outpost in lunar vicinity, to support surface operations and further astronaut training for longer and deeper space missions and transfers. In particular, a Lagrangian point orbit location - in the Earth- Moon system - is suggested for a manned cis-lunar infrastructure; proposal which opens an interesting field of study from the astrodynamics perspective. Literature offers a wide set of scientific research done on orbital dynamics under the Three-Body Problem modelling approach, while less of it includes the attitude dynamics modelling as well. However, whenever a large space structure (ISS-like) is considered, not only the coupled orbit-attitude dynamics should be modelled to run more accurate analyses, but the structural flexibility should be included too. The paper, starting from the well-known Circular Restricted Three-Body Problem formulation, presents some preliminary results obtained by adding a coupled orbit-attitude dynamical model and the effects due to the large structure flexibility. In addition, the most relevant perturbing phenomena, such as the Solar Radiation Pressure (SRP) and the fourth-body (Sun) gravity, are included in the model as well. A multi-body approach has been preferred to represent possible configurations of the large cis-lunar infrastructure: interconnected simple structural elements - such as beams, rods or lumped masses linked by springs - build up the space segment. To better investigate the relevance of the flexibility effects, the lumped parameters approach is compared with a distributed parameters semi-analytical technique. A sensitivity analysis of system dynamics, with respect to different configurations and mechanical properties of the extended structure, is also presented, in order to highlight drivers for the lunar outpost design. Furthermore, a case study for a large and flexible space structure in Halo orbits around one of the Earth-Moon collinear Lagrangian points, L1 or L2, is discussed to point out some relevant outcomes for the potential implementation of such a mission.

The Coupled Orbit-Attitude Dynamics and Control of Electric Sail in Displaced Solar Orbits

Displaced solar orbits for spacecraft propelled by electric sails are investigated. Since the propulsive thrust is induced by the sail attitude, the orbital and attitude dynamics of electric-sail-based spacecraft are coupled and required to be investigated together. However, the coupled dynamics and control of electric sails have not been discussed in most published literatures. In this paper, the equilibrium point of the coupled dynamical system in displaced orbit is obtained, and its stability is analyzed through a linearization. The results of stability analysis show that only some of the orbits are marginally stable. For unstable displaced orbits, linear quadratic regulator is employed to control the coupled attitude-orbit system. Numerical simulations show that the proposed strategy can control the coupled system and a small torque can stabilize both the attitude and orbit. In order to generate the control force and torque, the voltage distribution problem is studied in an optimal framework. The numerical results show that the control force and torque of electric sail can be realized by adjusting the voltage distribution of charged tethers.

Mixed H<sub>2</sub>/H<sub>∞</sub> Control Approach and its Application in Satellite Attitude Control System

In this paper, we address the mixed H2/H∞ control approach for linear time-invariant system based on linear matrix inequality (LMI). First, the problem to be solved is stated, and the satellite attitude dynamics is established and converted into a corresponding state space form. Then, the mixed H2/H∞ controller based on LMIs is designed in order to attain the state feedback gain matrix. To validate the efficiency and practicability of the proposed controller, simulation results based on satellite attitude system are presented, from which we can observe that under the condition of external disturbances, the system will be stable within 150s, and the maximum of control torque will be no more than 0.025Nm. Expanding the controller gain will affect the stabilizing process, but not the stabilization time, and it will increase the control input which will bring pressure to the actuator.

Stability of Nonclassical Relative Equilibria of a Rigid Body in a J2 Gravity Field

AbstractThe gravitationally coupled orbit–attitude dynamics of a rigid body in a J2 gravity field is a generalization of the traditional point-mass J2 problem to take into account the gravitational orbit–attitude coupling of the considered body. Linear and nonlinear stability of nonclassical relative equilibria in the coupled orbit–attitude dynamics are studied with geometric mechanics in the present paper. Conditions of stability are obtained through the linear system matrix and projected Hessian matrix by using the energy–Casimir method. Linear and nonlinear stability regions are plotted in a wide range of system parameters. It is found that the stability regions are similar to those of classical relative equilibria while, at the same time, some differences do exist. For example, in some cases, the linear stability region contains not only the two regions that are analogues of the Lagrange region and DeBra–Delp region, but also a small irregular region in the third quadrant. Same as the case of classica...

In-orbit magnetometer bias and scale factor calibration

Magnetometers are widely used for LEO small satellites attitude determination and control system. In order to estimate satellite dynamics and control attitude accurately, scale factor and bias of magnetometer must be estimated. In this study a linear Kalman filter (LKF) based algorithm for the estimation of magnetometer biases and scale factors is proposed. Proposed algorithms are simulated through attitude dynamics of a small satellite.