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The purpose of this paper is to investigate the pose control of rigid spacecraft subject to dead-zone input, unknown external disturbance and parametric uncertainty in space maneuvering mission.

First, a 6-Degree of Freedom (DOF) dynamic model of rigid spacecraft with dead-zone input, unknown external disturbances and parametric uncertainty is derived. Second, a super-twisting-like fixed-time disturbance observer (FTDO) with strong robustness is developed to estimate the lumped disturbances in fixed time. Based on the proposed observer, a non-singular fixed-time terminal sliding-mode (NFTSM) controller with superior performance is proposed.

Different from the existing sliding-mode controllers, the proposed control scheme can directly avoid the singularity in the controller design and speed up the convergence rate with improved control accuracy. Moreover, no prior knowledge of lumped disturbances’ upper bound and its first derivatives is required. The fixed-time stability of the entire closed-loop system is rigorously proved in the Lyapunov framework. Finally, the effectiveness and superiority of the proposed control scheme are proved by comparison with existing approaches.

The proposed NFTSM controller can merely be applied to a specific type of spacecrafts, as the relevant system states should be measurable.

A NFTSM controller based on a super-twisting-like FTDO can efficiently deal with dead-zone input, unknown external disturbance and parametric uncertainty for spacecraft pose control.

This investigation uses NFTSM control and super-twisting-like FTDO to achieve spacecraft pose control subject to dead-zone input, unknown external disturbance and parametric uncertainty.

The purpose of this paper is to present a method to achieve small satellite formation keeping operations by using the differential lift and drag to control the drift caused by J2 perturbation in circular or near-circular low earth orbits (LEOs).

Each spacecraft is equipped with five large flat plates, which can be controlled to generate differential accelerations. The aerodynamic lift and drag acting on a flat plate is calculated by the kinetic theory. To maintain the formation within tracking error bounds in the presence of J2 perturbation, a nonlinear Lyapunov-based feedback control law is designed.

Simulation results demonstrate that the proposed method is efficient for the satellite formation keeping and better accuracy advantage in comparison with classical approaches via the fixed maximum differential aerodynamic acceleration.

Because the aerodynamic force will reduce drastically as the orbital altitude increases, the formation keeping control strategy for small satellites presented in this paper should be limited to the scenarios when satellites are in LEO.

The formation keeping control method in this paper can be applied to solve satellite formation keeping problem for small satellites in LEO.

This paper proposes a Lyapunov control strategy for satellite formation keeping considering both lift and drag forces, and simulation results show better performance with high accuracy under J2 perturbation.

The purpose of this paper is to propose a new fuel-balanced formation keeping reference trajectories planning method based on selecting the virtual reference center(VRC) in a fuel-balanced sense in terms of relative eccentricity and inclination vectors (E/I vectors).

By using the geometrical intuitive relative E/I vectors theory, the fuel-balanced VRC selection problem is reformulated as the geometrical problem to find the optimal point to equalize the distances between the VRC and the points determined by the relative E/I vectors of satellites in relative E/I vectors plane, which is solved by nonlinear programming method.

Numerical simulations demonstrate that the new proposed fuel-balanced formation keeping strategy is valid, and the new method achieves better fuel-balanced performance than the traditional method, which keeps formation with respect to geometrical formation center.

The new fuel-balanced formation keeping reference trajectories planning method is valid for formation flying mission whose member satellite is in circular or near circular orbit in J2 perturbed orbit environment.

The new fuel-balanced formation keeping reference trajectories planning method can be used to solve formation flying keeping problem, which involves multiple satellites in the formation.

The fuel-balanced reference trajectories planning problem is reformulated as a geometrical problem, which can provide insightful way to understand the dynamic nature of the fuel-balanced reference trajectories planning issue.

This paper aims to innovatively propose to improve the efficiency of satellite observation and avoid the waste of satellite resources, a genetic algorithm with entropy operator (GAE) of synthetic aperture radar (SAR) satellites’ task planning algorithm.

The GAE abbreviated as GAE introduces the entropy value of each orbit task into the fitness calculation of the genetic algorithm, which makes the orbit with higher entropy value more likely to be selected and participate in the remaining process of the genetic algorithm.

The simulation result shows that in a condition of the same calculate ability, 85% of the orbital revisit time is unchanged or decreased and 30% is significantly reduced by using the GAE compared with traditional task planning genetic algorithm, which indicates that the GAE can improve the efficiency of satellites’ task planning.

The GAE is an optimization of the traditional genetic algorithm. It combines entropy in thermodynamics with task planning problems. The algorithm considers the whole lifecycle of task planning and gets the desired results. It can greatly improve the efficiency of task planning in observation satellites and shorten the entire task execution time. Then, using the GAE to complete SAR satellites’ task planning is of great significance in reducing satellite operating costs and emergency rescue, which brings certain economic and social benefits.

The purpose of this paper is to propose a modified fuel-balanced formation keeping strategy based on actively rotating satellites in the formation in the J2 perturbed environment.

Based on the relative orbital elements theory, the J2 perturbed relative motions between different satellites in the formation are analyzed, and then, the method to estimate fuel required to keep the in-plane and out-of-plane relative motions is presented, based on which a modified fuel-balanced formation keeping strategy is derived by considering both in-plane and out-of-plane J2 perturbations.

Numerical simulations demonstrate that the modified fuel-balanced formation keeping strategy is valid, and the modified fuel-balanced formation keeping strategy requires less total fuel consumption than original Vadali and Alfriend’s method.

The modified fuel-balanced formation keeping strategy is valid for formation flying mission whose member satellite is in circular or near-circular orbit.

The modified fuel-balanced formation keeping strategy can be used to solve formation flying keeping problem, which involves multiple satellites in the formation.

The modified fuel-balanced formation keeping strategy is proposed by considering both in-plane and out-of-plane J2 perturbations, which further reduce the fuel consumption than the original Vadali and Alfriend’s method.

The purpose of this paper is to present a novel high-precision relative navigation method for tight formation-keeping based on thrust on-line identification.

Considering that thrust acceleration cannot be measured directly, an on-line identification method of thrust acceleration is explored via the estimated acceleration of major space perturbation and the inter-satellite relative states obtained from space-borne acceleration sensors; then, an effective identification model is designed to reconstruct thrust acceleration. Based on the identified thrust acceleration, relative orbit dynamics for tight formation-keeping is established. Further, using global positioning system (GPS) measurement information, a modified extended Kalman filter (EKF) is suggested to obtain the inter-satellite relative position and relative velocity.

Compared with the normal EKF and the adaptive robust EKF, the proposed modified EKF has better estimation accuracy in radial and along-track directions because of accurate compensation of thrust acceleration. Meanwhile, high-precision relative navigation results depend on high-precision acceleration sensors. Finally, simulation studies on a chief-deputy formation flying control system are performed to verify the effectiveness and superiority of the proposed relative navigation algorithm.

This paper provides a reference in solving the problem of high-precision relative navigation in tight formation-keeping application.

This paper proposes a novel on-line identification method for thrust acceleration and shows that thrust identification-based modified EKF is more efficient in relative navigation for tight formation-keeping.

The purpose of this paper is to present a method to conduct small satellite rendezvous mission by using the differential aerodynamic forces under J2 perturbation in low earth orbit (LEO).

Each spacecraft is assumed to be equipped with two large flat plates, which can be controlled for generating differential accelerations in all three directions. Based on the kinetic theory, the aerodynamic lift and drag generated by a flat plate are calculated. To describe the relative dynamics under J2 perturbation, a modified model is derived from the high-fidelity linearized J2 equations proposed by Schweighart and Sedwick.

Simulation results demonstrate that the proposed method is valid and efficient to solve satellite rendezvous problem, and the modified model considering J2 effect shows better accuracy than the Horsley’s Clohessy–Wiltshire-based model.

Because aerodynamic force will reduce drastically as orbital altitude rises, the rendezvous control strategy for small satellites presented in this paper should be limited to the scenarios when satellites are in LEO.

The rendezvous control method in this paper can be applied to solve satellite rendezvous maneuver problem for small satellites in LEO.

This paper proposes a modified differential aerodynamic control model by considering J2 perturbation, and simulation results show that it can achieve higher rendezvous control accuracy.

This paper aims to investigate the magnetostrictive phenomenon in a single electrical steel sheet, which may cause vibration and noise in the cores of transformers and induction motors. A measurement system of magnetostriction is created and the principal strain of magnetostriction is modeled. Furthermore, the magnetostriction property along arbitrary alternating magnetization directions is modeled.

A measurement system with a triaxial strain gauge is developed to obtain the magnetostrictive waveform, and the principal strain is computed in terms of the in-plane strain formula. A three-layer feed-forward neural network model is proposed to model the measured magnetostriction property of the electrical steel sheet.

The principal strain of magnetostriction of the non-oriented electrical steel has strong anisotropy. The proposed estimation model can be effectively used to model the anisotropic magnetostriction with an acceptable prediction time.

This paper develops the neural network combined with fast Fourier transform (FFT) to model the principal strain property of magnetostriction under alternating magnetizations, and its validation has been verified.

The purpose of this study is to develop a reliable finite element algorithm based on the transmission line method (TLM) to solve the nonlinear problem in electromagnetic field calculation.

In this paper, the TLM has been researched and applied to solve nonlinear iteration in FEM. LU decomposition method and the Jacobi preconditioned conjugate gradient method have been investigated to solve the equations in transmission line finite element method (FEM-TLM). The algorithms have been developed in C++ language. The algorithm is applied to analyze the magnetic field of a long straight current-carrying wire and a single-phase transformer.

FEM-TLM is more effective than traditional FEM in nonlinear iteration. The results of FEM-TLM have been compared and analyzed under different calculation scales. It is found that the LU decomposition method is more suitable for FEM-TLM because there is no need to repeatedly assemble the global coefficient matrix in the iterative solution process and it is not affected by the disturbance of the right-hand vector.

An effective algorithm is provided for solving nonlinear problems in the electromagnetic field, which can save a lot of computing costs. The efficiency of LU decomposition and CG method in FEM-TLM nonlinear iteration is investigated, which also makes a preliminary exploration for the research of FEM-TLM parallel algorithms.

The purpose of this paper is to improve the modeling accuracy of the magnetostrictive hysteretic characteristics by introducing hysteresis energy instead of pinning energy in the assembled domain structure model (ADSM).

First, the magnetostrictive characteristics and the domain movement process in an electrical steel sheet are measured and observed. The reasons for the influence of stress on magnetostriction are discussed on the mesoscopic level. Second, the ADSM model using the hysteresis energy is investigated to estimate the influence of external stress. Finally, the simulation results of the modified ADSM model are compared with the experimental data under the same calculation conditions.

The results show that the improved model not only explains the cause of hysteresis clearly from the perspective of the magnetic moment but also improves the modeling ability of magnetostrictive hysteretic.

The magnetostriction in electrical steel lags behind the external magnetic field, and it is significant for reducing core vibration to estimate the magnetostrictive hysteretic property accurately. This paper proposes an effective approach to model the hysteretic characterization of magnetostriction.