基于T-H方程的卫星轨迹模型参考输出跟踪控制方法

当目标卫星沿椭圆轨道运行时,描述追踪星与目标星相对运动的线性化方程为T-H方程。将描述航天器相对运动的T-H方程变换为周期系统的状态空间形式,并给出卫星轨迹跟踪控制问题的数学描述。基于周期系统的参量Lyapunov方法和模型参考跟踪控制理论,提出了卫星轨迹跟踪控制器的设计方法。利用该方法设计了带有收敛速率保障的反馈镇定控制器和具有自由参数的前馈控制器。对追踪星相对目标星悬停任务进行了数值仿真,仿真结果表明提出的控制方案是有效的。     

A fault-tolerant magnetic spin stabilizing controller for the JC2Sat-FF mission

This paper presents a spin-stabilization algorithm for the Japan Canada Joint Collaboration Satellite-Formation Flying (JC2Sat-FF) mission using magnetic actuation only. It is shown that under a reasonable assumption on the Earth’s magnetic field, the resulting control law is asymptotically stabilizing for an axisymmetric spacecraft, even under the failure of up to two magnetic torque rods and magnetic torque rod saturation. It is also stabilizing under quantization. The satellite motion remains stable under control outages, meaning that the error can be reduced by implementing the control intermittently. The effectiveness of the control law is demonstrated using a high fidelity attitude control system simulator for the JC2Sat-FF satellite.     

A heuristic design method for attitude stabilization of magnetic actuated satellites

In this paper a heuristic design strategy for stabilizing the satellite attitude has been proposed. It is assumed that the satellite is actuated by a set of mutually perpendicular magnetic coils. Using well-known Lyapunov direct stability method it is shown that the proposed controller causes to a global asymptotic stable system for all near polar orbits. The design procedure is based on analyzing of the conceptual effects of magnetic coils on the satellite attitude motion. Considering these effects lead to some intuitive results which determine the global stabilizing control law. The performance and robustness of the designed controller against actuators saturation and quantization error have been verified using a real-time-hardware–software in-loop (RTHSIL) simulation results. These results show that the global stability can be achieved although some disturbances and restrictions exist. This stabilizing controller can be simply combined with a linear explicit model predictive controller (EMPC) to achieve a full three-axis control law.     

Variable structure control for satellite attitude stabilization in elliptic orbits using solar radiation pressure

The paper proposes the use of solar radiation pressure for satellite attitude control in elliptic orbits based on variable structure control. The system comprises of a satellite with two-oppositely placed solar flaps. Sliding mode control and terminal sliding mode control techniques have been adopted to develop nonlinear control laws for suitably rotating the control solar flaps to neutralize the adverse effect of eccentricity normally responsible for a considerable deterioration in the attitude control performance. The detailed numerical simulation of the governing nonlinear equation of the motion including the effects of various system parameters on the controller performance, establishes the feasibility of the proposed control strategy. The proposed controller is found to be robust against parameter uncertainties and external disturbances and thereby, the control strategy presented in the paper may be applicable to future satellite missions.     

Model development and adaptive imbalance vibration control of magnetic suspended system

A system model is developed to describe the translational and rotational motion of an active-magnetic-bearing-suspended rigid rotor of a single-gimbal control moment gyro (SCMG) onboard a rigid satellite. This model closely reflects the motion characteristics of the rotor by considering the dynamic and static imbalance as well as the coupling between the gimbal's and the rotor's motion on a satellite platform. Adaptive autocentering control is strictly constructed for the preceding rotor with unknown dynamic imbalance. The rotor achieves its rotation about the principal axis of inertia by identifying the little rotational angles from the geometric axis to the principal axis and then using the results to tune a stabilizing controller, which is composed of a decentralized PD controller with cross-axis proportional gains and high-pass and low-pass filters. The main disturbance in the wheel spinning can thereby be completely removed and the vibration acting on the satellite can be attenuated.     

A heuristic design method for attitude stabilization of magnetic actuated satellites

In this paper a heuristic design strategy for stabilizing the satellite attitude has been proposed. It is assumed that the satellite is actuated by a set of mutually perpendicular magnetic coils. Using well-known Lyapunov direct stability method it is shown that the proposed controller causes to a global asymptotic stable system for all near polar orbits. The design procedure is based on analyzing of the conceptual effects of magnetic coils on the satellite attitude motion. Considering these effects lead to some intuitive results which determine the global stabilizing control law. The performance and robustness of the designed controller against actuators saturation and quantization error have been verified using a real-time-hardware–software in-loop (RTHSIL) simulation results. These results show that the global stability can be achieved although some disturbances and restrictions exist. This stabilizing controller can be simply combined with a linear explicit model predictive controller (EMPC) to achieve a full three-axis control law.     

绳系卫星系统中的周期运动

在椭圆轨道上飞行的绳系卫星系统的重要特征是系绳的方向角具有周期性运动，称为驻环。不稳定的驻环导致全系统的不稳定性。本文给出系统运动的数学模型、距离速率控制方法、求解驻环的数值迭代算法、驻环的稳定性和吸引域以及控制参数平面上驻环存在的区界和计算机仿真结果     

Attractive manifold-based adaptive solar attitude control of satellites in elliptic orbits

The paper presents a novel noncertainty-equivalent adaptive (NCEA) control system for the pitch attitude control of satellites in elliptic orbits using solar radiation pressure (SRP). The satellite is equipped with two identical solar flaps to produce control moments. The adaptive law is based on the attractive manifold design using filtered signals for synthesis, which is a modification of the immersion and invariance (I&I) method. The control system has a modular controller–estimator structure and has separate tunable gains. A special feature of this NCEA law is that the trajectories of the satellite converge to a manifold in an extended state space, and the adaptive law recovers the performance of a deterministic controller. This recovery of performance cannot be obtained with certainty-equivalent adaptive (CEA) laws. Simulation results are presented which show that the NCEA law accomplishes precise attitude control of the satellite in an elliptic orbit, despite large parameter uncertainties.     

考虑执行器动态补偿的动中通系统非线性鲁棒控制

研究用于移动载体卫星通信的动中通系统的稳定跟踪问题。选取动中通系统的三轴非线性模型为被控对象,较单轴模型更能准确地描述子系统之间的运动学与动力学特性。在执行器动态特性的基础上,设计了一种具有执行器动态补偿的非线性鲁棒控制器。该控制器不仅能够使系统在载体移动过程中隔离载体扰动的影响,精确跟踪目标卫星,而且还进一步解决了执行器动态特性对系统的影响,更符合实际动中通控制系统设计的需要。最后通过三组对比仿真结果验证了所设计控制器在不同扰动条件下的稳定跟踪性能。     

Analysis of a double gimbaled reaction wheel spacecraft attitude stabilization system

Three axis attitude stabilization of a satellite using a single spinning reaction wheel mounted on a two degree-of-freedom passively and actively torqued gimbal system is investigated. The passive control is assumed to be provided by a spring-loaded damper mounted on each of the gimbal axes, while active control results from both the wheel acceleration and the torque applied about the gimbal axes. The stability of the uncontrolled and passively controlled systems is investigated analytically. For constant wheel speed the pitch motion is decoupled from the roll-yaw and gimbal motions. Control laws for the roll-yaw motion are developed based on pole clustering and linear optimal control theory. For the pitch motion control laws are obtained based on classical second order system theory. Estimation techniques are applied to the roll-yaw system for the case when the complete state may not be directly observable (in the absence of a fine yaw position sensor).     

Asymptotic study of a complete magnetic attitude control cycle providing a single-axis orientation

The angular motion of an axisymmetrical satellite equipped with the active magnetic attitude control system is examined. Attitude control system has to ensure necessary orientation of the axis of symmetry in the inertial space. It implements the following strategy: coarse reorientation of the axis of symmetry with nutation damping or “-Bdot” without initial detumbling; spinning-up about the axis of symmetry to achieve the property of a gyro; fine reorientation of the axis in the inertial space. Dynamics of the satellite is analytically studied using averaging technique on the complete control loop consisting of five algorithms. Solutions of the equations of motion are obtained in terms of quadratures for most cases or even in closed-form. The latter allowed to study the dependence of motion parameters including time-response with respect to the orbit inclination and other parameters for all algorithms.     

Study of a bunch of three algorithms for magnetic control of attitude and spin rate of a spin-stabilized satellite

We consider the angular motion of an axi-symmetrical satellite equipped with an active magnetic attitude control system. Dynamics of the satellite is studied on the entire control loop, consisting of a bunch of three successively used algorithms. The control cycle includes the stages of nutation damping, spinning up the satellite about its symmetry axis, and reorienting the symmetry axis into a preset direction in the inertial space. The results are confirmed by numerical simulations.     

Rotational motion of <Emphasis Type="Italic">Foton M-4</Emphasis>

The actual controlled rotational motion of the Foton M-4 satellite is reconstructed for the mode of single-axis solar orientation. The reconstruction was carried out using data of onboard measurements of vectors of angular velocity and the strength of the Earth’s magnetic field. The reconstruction method is based on the reconstruction of the kinematic equations of the rotational motion of a solid body. According to the method, measurement data of both types collected at a certain time interval are processed together. Measurements of the angular velocity are interpolated by piecewise-linear functions, which are substituted in kinematic differential equations for a quaternion that defines the transition from the satellite instrument coordinate system to the inertial coordinate system. The obtained equations represent the kinematic model of the satellite rotational motion. A solution of these equations that approximates the actual motion is derived from the condition of the best (in the sense of the least squares method) match between the measurement data of the strength vector of the Earth’s magnetic field and its calculated values. The described method makes it possible to reconstruct the actual rotational satellite motion using one solution of kinematic equations over time intervals longer than 10 h. The found reconstructions have been used to calculate the residual microaccelerations.     

Realization of modes of satellite attitude motion with a small level of microaccelerations using electromechanical executive devices

Quasi-static microaccelerations are estimated for a satellite specially designed to perform space experiments in the field of microgravity. Three modes of attitude motion of the spacecraft are considered: passive gravitational orientation, orbital orientation, and semi-passive gravitational orientation. In these modes the lengthwise axis of the satellite is directed along the local vertical, while solar arrays lie in the orbit plane. The second and third modes are maintained using electromechanical executive devices: flywheel engines or gyrodynes. Estimations of residual microaccelerations are performed with the help of mathematical modeling of satellite’s attitude motion under the action of gravitational and aerodynamic moments, as well as the moment produced by the gyro system. It is demonstrated that all modes ensure rather low level of quasi-static microaccelerations on the satellite and provide for a fairly narrow region of variation for the vector of residual microacceleration. The semi-passive gravitational orientation ensures also a limited proper angular momentum of the gyro system.     

Nanosatellite <Emphasis Type="Italic">REFLECTOR</Emphasis>: Choice of parameters of the attitude control system

We consider methodological and applied problems of choosing parameters and developing a passive gravity-gradient attitude control system for the REFLECTOR nanosatellite. The attitude control system consists of appropriately distributed satellite mass and additional masses forming the required tensor of inertia, as well as of a set of hysteresis rods manufactured from a magnetically soft material. The combination of these elements allows one, independent of the satellite’s initial angular motion, to maintain its three-axial orientation in the orbital coordinate system with preset performance in precision and fast response. The satellite’s dynamics is investigated using asymptotic and numerical methods. The problems of arrangement of the additional masses and hysteresis rods are discussed, as well as their interaction with magnetizable elements.     

Attitude dynamics of a pendulum-shaped charged satellite

In this paper, we investigate the possibility of the use of the Lorentz force, which acts on charged satellite when it is moving through the magnetic field, as a means of satellite attitude control. We first derive the equations of attitude motion of charged satellite and then investigate the stability of the motion. Finally we propose an attitude control method using the Lorentz force. Our method requires moderate charge level for future Lorentz-augmented satellite.     

Modifying the atlas of low lunar orbits using inert tethers

For long enough tethers, the coupling of the attitude and orbital dynamics may show non-negligible effects in the orbital motion of a tethered satellite about a central body. In the case of fast rotating tethers the attitude remains constant, on average, up to second order effects. Besides, for a tether rotating in a plane parallel to the equatorial plane of the central body, the attitude–orbit coupling effect is formally equal to the perturbation of the Keplerian motion produced by the oblateness of the central body and, therefore, may have a stabilizing effect in the orbital dynamics. In the case of a tethered satellite in a low lunar orbit, it is demonstrated that feasible tether lengths can help in modifying the actual map of lunar frozen orbits.     

Periodic motions of a satellite-gyrostat relative to its center of mass under the action of gravitational torque

We investigated periodic motions of the axis of symmetry of a model satellite of the Earth, which are similar to the motions of the longitudinal axes of the Mir orbital station in 1999–2001 and the Foton-M3 satellite in 2007. The motions of these spacecraft represented weakly disturbed regular Euler precession with the angular momentum vector of motion relative to the center of mass close to the orbital plane. The direction of this vector during the motion was not practically changed. The model satellite represents an axisymmetric gyrostat with gyrostatic moment directed along the axis of symmetry. The satellite moves in a circular orbit and undergoes the action of the gravitational torque. The motion of the axis of symmetry of this satellite relative to the absolute space is described by fourth-order differential equations with periodic coefficients. The periodic solutions to this system with special symmetry properties are constructed using analytical and numerical methods.     

Estimation of residual microaccelerations on board an artificial earth satellite in the monoaxial solar orientation mode

The mode of monoaxial solar orientation of a designed artificial Earth satellite (AES), intended for microgravitational investigations, is studied. In this mode the normal line to the plane of satellite’s solar batteries is permanently directed at the Sun, the absolute angular velocity of a satellite is virtually equal to zero. The mode is implemented by means of an electromechanical system of powered flywheels or gyrodynes. The calculation of the level of microaccelerations arising on board in such a mode, was carried out by mathematical modeling of satellite motion with respect to the center of masses under an effect of gravitational and restoring aerodynamic moments, as well as of the moment produced by the gyrosystem. Two versions of a law for controlling the characteristic angular momentum of a gyrosystem are considered. The first version provides only attenuation of satellite’s perturbed motion in the vicinity of the position of rest with the required velocity. The second version restricts, in addition, the increase in the accumulated angular momentum of a gyrosystem by controlling the angle of rotation of the satellite around the normal to the light-sensitive side of the solar batteries. Both control law versions are shown to maintain the monoaxial orientation mode to a required accuracy and provide a very low level of quasistatic microaccelerations on board the satellite.     

TETHERED SATELLITE SYSTEM ANALYSIS (1) — TWO-DIMENSIONAL CASE AND REGULAR DYNAMICS

The study on tethered satellite system (TSS) in two-dimensional in-planar motion is restricted in that the tether is assumed to be massless. The equations of motion are given in a spherical coordinate system to describe the magnitude (tether length) and direction angle of the position vector between the satellites. A length rate control algorithm is adopted, and the controlled motion of the directional angle by the algorithm will have a stable equilibrium state. The equilibrium state is a fixed point if the orbit of the base-satellite is circular, and a limit cycle if the orbit is elliptic. The value and stability of the equilibrium state are determined by the parameters of the control algorithm, and the bifurcation analysis is also given. Two typical TSS missions have been simulated.