High precision dynamic model and control considering J2 perturbation for spacecraft hovering in low orbit

For spacecraft hovering in low orbit, a high precision spacecraft relative dynamics model without any simplification and considering J₂ perturbation is established in this paper. Using the derived model, open-loop control and closed-loop control are proposed respectively. Gauss's variation equations and the coordinate transformation method are combined to deal with the relative J₂ perturbation between the two spacecraft. The sliding mode controller is adopted as the closed-loop controller for spacecraft hovering. To improve the control accuracy, the relative J₂ perturbation is regarded as a known parameter term in the closed-loop controller. The external uncertainty perturbations except J₂ perturbation are estimated by numerical difference method, and the boundary layer method is used to weaken the impact of chattering on the sliding mode controller. The open-loop control of spacecraft hovering with the relative J₂ perturbation and without the relative J₂ perturbation are simulated and compared, and the results prove that the accuracy of open-loop control with relative J₂ perturbation has been significantly improved. Similarly, the simulation of the closed-loop control are presented to validate the effectiveness of the designed sliding mode controller, and the results demonstrate that the designed sliding mode controller including the derived relative J₂ perturbation can guarantee the high accuracy and robustness of spacecraft hovering in long-term mission.     

航天器非奇异自适应终端滑模姿轨联合控制

为了实现航天器姿态与轨道的同步控制，提出了一种航天器姿态与轨道联合控制的非奇异自适应终端滑模控制律。首先，建立了航天器姿轨耦合运动的对偶四元数模型；其次，提出了一种姿轨联合跟踪控制的非奇异终端滑模控制律，并设计了自适应控制律以改善质量特性不确定性的影响，利用李雅普诺夫函数证明了所提控制律的稳定性；最后，绕飞小行星的跟踪控制仿真算例表明了控制律的有效性。结果表明:所提控制律具有较高的控制精度，能够在有限时间内收敛，仿真过程中不存在奇异点，抑制了质量特性的不确定性对控制的影响，且对滑模的抖振特性有抑制效果。      

Space-based line-of-sight tracking control of GEO target using nonsingular terminal sliding mode

This paper addresses the issue of high-precision line-of-sight (LOS) tracking of geosynchronous earth orbit target in highly dynamic conditions via spacecraft attitude maneuver. First, characteristics of the LOS motion are analyzed by a simplified linear relative motion model. Second, after transforming the quaternion-based attitude model into a double integrator system, a new nonsingular terminal sliding mode controller is proposed for spacecraft attitude tracking in a nominal case without parametric uncertainties and external disturbances. Third, an adaptive new nonsingular terminal mode controller is proposed for spacecraft attitude tracking in an uncertain case, which is done via constructing a pair of adaptive laws to estimate the parametric uncertainties and external disturbances online. The robust stability and finite time convergence property of the closed-loop system are demonstrated by Lyapunov theorem. Under control of the proposed controller, zero steady state error tracking of LOS with a smooth transition phase can be achieved in scheduled time, regardless of parametric uncertainties and external disturbances online. Finally, detailed numerical simulation results are presented to illustrate the effectiveness and performance of the proposed controllers. Contrasting simulation results shows that proposed controllers can track the desired trajectories effectively and have better performance against the controllers based on linear sliding mode and the existing fast nonsingular terminal sliding mode.     

Robust fault-tolerant saturated control for spacecraft proximity operations with actuator saturation and faults

In this paper, the motion control problem of autonomous spacecraft rendezvous and docking with a tumbling target in the presence of unknown model parameters, external disturbances, actuator saturation and faults is investigated. Firstly, a nonlinear six degree-of-freedom dynamics model is established to describe the relative motion of the chaser spacecraft with respect to the tumbling target. Subsequently, a robust fault-tolerant saturated control strategy with no precise knowledge of model parameters and external disturbances is proposed by combining the sliding mode control technique with an adaptive methodology. Then, within the Lyapunov framework, it is proved that the designed robust fault-tolerant controller can guarantee the relative position and attitude errors converge into small regions containing the origin. Finally, numerical simulations are performed to demonstrate the effectiveness and robustness of the proposed control strategy.     

CMGs驱动空间机械臂的自适应终端滑模控制

摘要： 针对V构型控制力矩陀螺（CMGs）驱动的空间机械臂的轨迹跟踪控制问题,研究一种自适应非奇异终端滑模（ANTSM）控制方法.利用基于Kane方程的递推组集算法建立了系统的动力学模型.以跟踪误差为变量,构造非奇异滑动面,以保证跟踪误差在滑动面上有限时间收敛.针对系统质量特性参数与关节处干扰力矩的不确定性,设计自适应控制器用以调节控制增益.该控制方法无需不确定性的上界,且闭环系统具有最终一致有界性.仿真结果表明,该控制器可使系统准确跟踪期望轨迹,并对质量特性参数不确定性和关节干扰力矩具有良好的鲁棒性.     

基于ESO的电液位置伺服系统反步滑模控制

针对阀控电液位置伺服系统未建模摩擦力、参数不确定性和外部随机干扰造成的复合扰动问题, 提出一种基于扩张状态观测器(ESO)的反步滑模控制方法。ESO的设计可以对作动器速度、加速度和复合扰动进行在线估计, 解决工程应用中对以上信号难以测定的问题;基于ESO估计值和位移反馈信号进行反步滑模控制器设计, 通过构造包含反步设计误差、滑模函数和观测器误差的Lyapunov函数, 对所提控制方法进行稳定性证明;为验证所提方法的有效性, 进行了AMESim和MATLAB/Simulink联合仿真, 与PID控制器、传统的反步滑模控制器和基于ESO的滑模控制器的控制效果进行对比, 并对仿真数据进行了分析。研究结果表明:所提方法可以有效抑制系统复合扰动, 位移跟踪精度高, 鲁棒性强。      

变结构航天器模糊神经网络滑模控制器设计

变结构航天器是目前航天领域的重要发展方向，航天器结构的变化将导致质量分布发生明显变化，这对航天器动力学建模和控制器设计都提出新的问题。针对这种情况，采用混合坐标法和拉格朗日方程建立了航天器刚柔耦合动力学模型，利用几种典型工况的参数近似得到变结构过程中动力学参数的变化规律。设计滑模控制器对航天器变结构过程进行姿态控制，为提高滑模控制器的适应性，设计模糊神经网络（FNN）自适应调节滑模控制器参数，并利用径向基函数（RBF）神经网络逼近动力学模型，得到控制力矩与姿态变化之间的近似关系，用于FNN的优化。通过仿真得到航天器变结构期间无控、滑模控制和模糊神经网络滑模控制的姿态变化，仿真结果对比验证了模糊神经网络滑模控制对于滑模控制的优势，证明了其在变结构航天器姿态控制方面的有效性。     

时间与燃料约束的参数自主寻优变轨滑模控制

航天器相对运动轨控采用滑模控制具有较好的抗扰能力，但参数设置复杂。为贴近工程实际，引入燃料最优约束和寻优算法，提出一种综合考虑时间、燃耗以及误差的参数自主寻优滑模控制。首先，基于线性相对运动方程与指数趋近的滑模控制，建立相对运动滑模控制器模型，并由能量最优的轨迹规划器给出收敛约束时间，实现高效机动；然后，分析滑模控制器中可调参数与时间、误差的约束条件，制定了参数量级寻优规则；最后，通过惯性权值改进的粒子群算法，将误差允许范围内的最少燃料消耗作为寻优评价标准，输出最优量级与系数组合的控制参数，实现滑模的最优控制。仿真表明，使用粒子寻优器得到的参数组合，可使滑模偏差控制器在规定时间内通过最小燃料消耗令位置与速度误差稳定收敛，增加航天器在轨寿命。     

事件触发机制下的充液航天器姿态控制

针对液体大幅晃动、通信资源受限的充液航天器姿态控制系统，提出一种自适应滑模控制与事件触发机制相结合的控制策略。首先，针对固-液耦合的充液航天器姿态控制系统，选用滑模变结构控制来削弱液体大幅晃动的非线性影响，并设计自适应更新律在线估计不确定参数来提高系统的鲁棒性。然后，考虑星载计算机资源的限制，设计相对阈值的事件触发机制来决定控制输入信号的更新，从而减少控制器与执行器之间的信号更新对通信网络的占用。最后，仿真结果表明，在液体大幅晃动下，所提控制策略不但可以使航天器姿态控制系统最终收敛到任意小的界内，而且可以减少96%的控制信号传输，减轻航天器的通信负载。      

Command filtered sliding mode trajectory tracking control for unmanned airships based on RBFNN approximation

This paper presents two sliding mode controllers to address the trajectory tracking problem of unmanned airships in the presence of unknown wind disturbance. The sliding mode controller proposed first is designed by a fast power rate reaching law(FPRRL). The disturbance is compensated by a radial basis function neural network (RBFNN). To avoid the aggressive adaptation, the controller is augmented by a command filter. The controller provides good robustness and tracking performance with no chattering under the hypothesis of ideal wind field. However, serious chattering occurs when simulation is performed under discontinuous wind field. To simulate the wind in practice, the wind field employed in the simulation is generated by the combination of a constant field and white noise. The controller is improved subsequently with an extended model to suppress the chattering induced by the white noise. The enhanced controller manipulates the derivation of system input, thus attenuating the chattering. Stability analysis shows that both controllers drive the tracking error into a controllable small region near zero. Simulations are provided to validate the performance of the proposed controllers under different wind hypothesis.     

火星大气进入滑模自抗扰制导方法

针对火星探测器大气进入制导阶段存在着模型参数误差等不确定性,基于直接反馈线性化理论设计了一种滑模自抗扰进入制导方法。首先利用反馈线性化方法对跟踪系统模型进行线性化处理;在此基础上设计了滑模控制律,并利用线性扩张状态观测器估计系统的未知不确定量,在控制律中进行补偿;此外还给出了大气进入段的横向制导律。仿真结果表明,与反馈线性化方法相比,该方法设计的制导律有效地降低了模型参数误差对制导精度的影响,实现了对参考轨迹的良好跟踪,提高了探测器开伞点的精度。     

Finite-time relative orbit-attitude tracking control for multi-spacecraft with collision avoidance and changing network topologies

This paper addresses the relative position tracking and attitude synchronization control problem for spacecraft formation flying (SFF). Based on the derived relative coupled six-degree-of-freedom dynamics, a robust adaptive finite-time fast terminal sliding mode controller is proposed to achieve the desired formation in the presence of model uncertainties and external disturbances. It is shown that the designed controller is effective for changing information exchange topology making it robust to node failure. Then, the artificial potential function method is employed to generate collision avoidance schemes to modify the controller such that inter-agent collision avoidance can be ensured during the formation maneuver, which is critical for practical missions. The stability of the overall closed-loop system is proved by using Lyapunov theory. Finally, numerical examples for a given SFF scenario are presented to illustrate the performance of the controller.     

航天器相对姿态跟踪的非线性前馈控制

针对航天器相对姿态跟踪过程中严重的非线性及控制器设计的复杂性,建立了基于修正罗德里格斯参数的航天器相对姿态运动学和动力学方程并根据Lyapunov直接法设计了非线性前馈控制律.设计的控制律不仅保证闭环系统稳定,还使得航天器相对姿态跟踪误差快速收敛到零点邻域内.通过在Matlab/Simulink环境下对航天器相对姿态跟踪进行数值仿真,验证了建立模型和设计控制律的有效性.     

Optimal spacecraft formation establishment and reconfiguration propelled by the geomagnetic Lorentz force

The Lorentz force acting on an electrostatically charged spacecraft as it moves through the planetary magnetic field could be utilized as propellantless electromagnetic propulsion for orbital maneuvering, such as spacecraft formation establishment and formation reconfiguration. By assuming that the Earth’s magnetic field could be modeled as a tilted dipole located at the center of Earth that corotates with Earth, a dynamical model that describes the relative orbital motion of Lorentz spacecraft is developed. Based on the proposed dynamical model, the energy-optimal open-loop trajectories of control inputs, namely, the required specific charges of Lorentz spacecraft, for Lorentz-propelled spacecraft formation establishment or reconfiguration problems with both fixed and free final conditions constraints are derived via Gauss pseudospectral method. The effect of the magnetic dipole tilt angle on the optimal control inputs and the relative transfer trajectories for formation establishment or reconfiguration is also investigated by comparisons with the results derived from a nontilted dipole model. Furthermore, a closed-loop integral sliding mode controller is designed to guarantee the trajectory tracking in the presence of external disturbances and modeling errors. The stability of the closed-loop system is proved by a Lyapunov-based approach. Numerical simulations are presented to verify the validity of the proposed open-loop control methods and demonstrate the performance of the closed-loop controller. Also, the results indicate the dipole tilt angle should be considered when designing control strategies for Lorentz-propelled spacecraft formation establishment or reconfiguration.     

Robust optimal sliding mode control for the deployment of Coulomb spacecraft formation flying

Inter-spacecraft electrostatic force (Coulomb force) is desirable for close formation flying control because of its propellant-less and free contaminate characteristics attributed to the propellant exhaust emission. This paper presents robust optimal sliding mode control to deal with the problem of thruster saturation in tracking the formation trajectory for Coulomb spacecraft formation flying. The robust controller design is based on optimal control theory as a linear quadratic system, and it is augmented with an integral sliding mode control technique. The stability of the closed-loop system is guaranteed using the second Lyapunov method. The developed controller outperforms the existing ones, because it has a higher degree of fine-tuning to cope with the uncertainty. Numerical simulations are employed to confirm the efficiency of the developed controller.     

基于模糊神经网络干扰观测器的组合体航天器姿态控制

针对非合作目标存在对抗性力矩输出情况下的组合体航天器姿态控制系统,提出了一种基于模糊神经网络干扰观测器（Fuzzy Neural Network Disturbance Observer,FNNDO）的非奇异终端滑模（Nonsingular Terminal Sliding Mode,NTSM）有限时间控制策略。首先以服务航天器为基准,建立组合体航天器姿态数学模型,然后针对包含惯量不确定性、目标对抗性力矩等的等效干扰力矩,设计了一种具有自适应能力的FNNDO,可以实现对等效干扰的有效跟踪。在FNNDO的基础上,设计NTSM控制器,利用Lyapunov理论证明闭环系统的有限时间稳定性。最后,仿真实验结果表明了控制策略的有效性和观测器在观测性能上的优越性。     

基于观测器的平台无陀螺姿态复合控制

针对超静卫星星体平台无陀螺、载荷敏感器与星体平台执行机构非共基准安装时整星存在姿态异位控制问题,提出了一种基于观测器估计星体平台姿态的复合控制方法。首先,建立星体平台/Stewart平台/载荷的动力学模型,并获得Stewart平台作动器关节空间的等效动力学模型。针对关节空间等效模型,设计super twisting观测器,以作动器平动位移为输入,以载荷和星体平台之间的相对姿态和角速度为输出,实现星体平台姿态和角速度估计。其次,以载荷测量姿态信息为输入,设计Stewart作动器的积分滑模控制律,实现载荷高精度指向控制。以观测器估计的星体平台姿态信息为输入,设计星体平台控制器实现星体平台的稳定控制。Lyapunov稳定性分析表明所设计的观测器和控制器能够保证闭环系统渐近稳定。数学仿真结果表明：在星体平台有陀螺时,载荷能够实现0.1″指向精度;在星体平台无陀螺时,采用观测器估计星体平台姿态并进行控制,载荷亦可实现0.1″指向精度。     

Guaranteed performance based adaptive attitude tracking of spacecraft with control constraints

The guaranteed performance control problem of spacecraft attitude tracking with control constraint, disturbance and time-varying inertia parameters is investigated. A new saturation function is designed to satisfy different magnitude constraints by introducing a piecewise smooth asymmetric Gauss error function. Based on the mean-value theorem, the constrained problem is transformed into an unconstrained control design subject to an unknown bounded coefficient matrix. To satisfy the constraints by performance functions, a tracking error constrained control is developed based on a hyperbolic arc-tangent asymmetric barrier Lyapunov function (BLF). In the backstepping framework, an adaptive robust control law is proposed by employing a smooth robust term simultaneously counteracting the parametric and non-parametric uncertainties, where the unknown coefficient matrix resulting from the control constraint is compensated by a Nussbaum function matrix. Rigorous stability analysis indicates that the proposed control law realizes the asymptotically tracking of spacecraft attitude and that the tracking error remains in a prescribed set which implies the achievement of the guaranteed transient performance. Numerical simulations validate the proposed theoretical results.     

Adaptive sliding mode fault-tolerant control for satellite attitude tracking system

In this paper, an adaptive modified sliding mode control approach is developed for attitude tracking of a nano-satellite with three magnetorquers and one reaction wheel. A sliding variable is chosen based on finite-time convergence of the nano-satellite attitude tracking error and avoiding the singularity of the control signal. The control gain of the proposed method is developed adaptively to reduce the tracking error and improve the closed-loop control performance. The sliding variable and adaptive parameter are also employed in the reaching phase of the control law to decrease the chattering phenomenon. In addition, the finite-time convergence of attitude variables in the presence of actuator faults, inertia uncertainty, and external disturbances is proved using the extended Lyapunov theorem. The simulations are conducted to evaluate the performance of the proposed method according to different evaluation criteria. Monte Carlo simulations are also used to survey the reliability of the system in the presence of the mentioned condition.