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.     

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.     

一种使用RBF网络的自适应滑模控制器

针对实际系统易受未知非线性、外界干扰和参数摄动等不确定因素影响的问题,以高精度模拟转台为例,采用一种基于RBF(Radial Basis Function)网络的自适应滑模控制器.控制器由名义反馈控制器和滑模干扰补偿器两个子系统组成.反馈控制器通过极点配置的方法实现,用来稳定名义系统.干扰补偿器使用一个自适应RBF网络在线辨识不确定性的上界值.计算机仿真结果表明了该法的鲁棒性和有效性.     

Spin deployment of Hub-Spoke tethered satellite formation with sliding mode tether tension control

This work develops a tension control strategy for deploying an underactuated spin-stable tethered satellite formation in the hub-spoke configuration. First, the Lagrange equation is used to model the spin-deployment dynamics of the tethered satellite formation. The central spacecraft is modeled as a rigid body, and the tethered subsatellites are simplified as lumped masses. Second, a pure tension controller has been proposed to suppress the tether libration motion in the deployment without thrusting at the subsatellites. A nonlinear sliding mode control is introduced in the tension controller for the underactuated system to suppress the periodic gravitational perturbations caused by the spinning hub-spoke tethered satellite formation. The unknown upper bounds of the perturbations are estimated by adaptive control law. The bounded stability of the closed-loop tension controller has been proved by the Lyapunov theory. Finally, numerical simulations validate the effectiveness and robustness of the proposed controller, i.e., tethers are fully deployed stably to the desired hub-spoke configuration.     

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.     

直达滑模控制

用传统到达条件综合而成的滑模控制系统不能保证所有出发于滑动模态邻域的相轨线都能直接到达邻近的滑动模态分支,导致状态转移过程超调,这对于某些控制工程是不允许的.为使滑模控制过程单向收敛,提出了直达滑模控制方法.通过对传统到达条件表述中的不足的分析,介绍了直达函数的定义和直达条件的建立.直达条件是用直达滑模控制法综合滑模控制系统的依据.直达滑模控制系统由指令模态及开关型直达滑模控制组成.与传统到达条件不同,满足直达条件的控制,可保证所有出发于滑动模态邻域的相轨线都能直接到达邻近的滑动模态分支,沿滑动模态趋向零态,状态转移过程快速而无超调.将直达滑模控制应用于示例系统并进行仿真,仿真结果符合对直达滑模控制性能的预期.      

Minimum sliding mode error feedback control for fault tolerant small satellite attitude control

This paper proposes a new control strategy (which we call “minimum sliding mode error feedback control, MSMEFC”) for small satellite attitude control. As we know, the attitude control algorithm plays a significant role in the whole performance of the satellite, especially under the existence of uncertain disturbances from the space. Without loss of generality, the MSMEFC is presented based on the sliding mode theory. It is assumed that the equivalent control error is defined to offset the uncertain disturbances to improve the control performance. Hence, in order to estimate the optimal equivalent control error, a cost function is derived on the basis of the principle of minimum sliding mode error. Then, the equivalent control error wills feedback to the conventional sliding mode control to obtain the final MSMEFC. According to the theoretical analyzes, the sliding mode after the MSMEFC will approximate to the ideal sliding mode, resulting in enhancing the control performance. Moreover, an adaptive non-singular terminal sliding mode is employed to compare with the performance of MSMEFC. Several simulations are performed to verify the effectiveness of proposed MSMEFC in the presence of serious perturbations, even in some fault-tolerant scenarios.     

Optimal spacecraft rendezvous using the combination of aerodynamic force and Lorentz force

This paper presents a propellantless spacecraft rendezvous method by using the optimal combination of aerodynamic force and Lorentz force. Aerodynamic force is provided by the rotations of the plates attached to the spacecraft, and Lorentz force is achieved by modulating spacecraft's electrostatic charge. Considering the limitation of the charging level of the spacecraft and physical constraints of the plates system, an optimal open-loop rendezvous trajectory is designed, which aims to minimize the energy consumed to actuate the hybrid system. The rotation rates of the plates and the electrostatic charge are constrained in the optimization problem, which is solved via the Gauss pseudospectral method. To track the open-loop trajectory in the presence of external perturbations, a novel adaptive nonsingular terminal sliding mode controller is designed. The stability of the closed-loop system is proved by the Lyapunov-based method. Several numerical examples are conducted to verify the validity of both the open-loop and closed-loop control strategy.     

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。     

基于多模态滑模的快速非奇异终端滑模控制

根据多模态滑模概念,提出了一种快速非奇异终端滑模控制方法(FNTSM,Fast Nonsingular Terminal Sliding Mode),实现了非奇异终端滑模控制的全局快速收敛.多模态滑模通过设计分段切换函数,实现多个滑动模态.FNTSM的切换函数由线性滑模的切换函数和非奇异终端滑模的切换函数连接而成.当系统状态远离平衡点时,系统运行于线性滑动模态;当系统状态靠近平衡点时,系统运行于非奇异终端滑动模态.设计了切换型控制律,保证了系统的到达时间和滑动时间都是有限的.数值仿真表明:FNTSM控制与非奇异终端滑模控制、线性滑模控制相比具有快速性优点.      

Adaptive sliding mode control of spacecraft attitude-orbit dynamics on SE(3)

In this paper, to solve the problem of parameters uncertainty in spacecraft tracking control, an adaptive controller based on sliding mode is proposed for the relative spacecraft attitude-orbit dynamics on the Lie group SE(3). The dynamic equations of relative attitude orbit error for two spacecraft are established in the framework of Lie group SE(3). Considering the uncertainty of spacecraft parameters, a formal decomposition of known and unknown parameters, the state variables and control variables is firstly made in the original system. An online estimator is designed to evaluate the unknown parameters. A sliding mode controller is developed to actuate the spacecraft to track the target spacecraft. Then a Lyapunov function of tracking error and parameters estimated error is designed to prove the stability of the closed-loop system. Finally, the simulation results and analysis are presented to verify the effectiveness and feasibility of the proposed method.     

基于Terminal滑模的小行星探测器着陆连续控制

针对弱引力场不规则小行星探测器安全下降与着陆,提出了一种基于比例微分(PD,Proportional plus Derivative)及非奇异Terminal滑模的连续控制方法.在着陆点坐标系下推导了探测器的动力学方程,设计了开环燃料次最优多项式标称轨迹制导方法.针对下降和着陆两个不同阶段提出了PD和非奇异Terminal滑模变结构连续控制方法.将PD控制的易操作性与非奇异Terminal滑模控制收敛速度快、调整时间短有效结合,保证了探测器安全着陆.仿真结果表明了提出方法的可行性和有效性.     

Fault tolerant small satellite attitude control using adaptive non-singular terminal sliding mode

The Attitude Control System (ACS) plays a pivotal role in the whole performance of the spacecraft on the orbit; therefore, it is vitally important to design the control system with the performance of rapid response, high control precision and insensitive to external perturbations. In the first place, this paper proposes two adaptive nonlinear control algorithms based on the sliding mode control (SMC), which are designed for small satellite attitude control system. The nonlinear dynamics describing the attitude of small satellite is considered in a circle reference orbit, and the stability of the closed-loop system in the presence of external perturbations is investigated. Then, in order to account for accidental or degradation fault in satellite actuators, the fault-tolerant control schemes are presented. Hence, two adaptive fault-tolerant control laws (continuous sliding mode control and non-singular terminal sliding mode control) are developed by adopting the nonlinear analytical model to describe the system, which can guarantee global asymptotic convergence of the attitude control error with the existence of unknown external perturbations. The nonlinear hyperplane based Terminal sliding mode is introduced into the control law design; therefore, the system convergence performance improves and the control error is convergent in “finite time”. As a result, the study on the non-singular terminal sliding mode control is the emphasis and the continuous sliding mode control is used to compare with the non-singular terminal sliding mode control. Meanwhile, an adaptive fuzzy algorithm has been proposed to suppress the chattering phenomenon. Moreover, several numerical examples are presented to demonstrate the efficacy of the proposed controllers by correcting for the external perturbations. Simulation results confirm that the suggested methodologies yield high control precision in control. In addition, actuator degradation, actuator stuck and actuator failure for a period of time are simulated to demonstrate the fault recovery capability of the fault tolerant controllers. The numerical results clearly demonstrate the good performance of the adaptive non-singular terminal control in the event of actuator fault compare with the continuous sliding mode control.     

仿射非线性系统的二阶滑模控制律研究

分析现有滑模控制算法特别是二阶滑模控制算法在抑制抖动和鲁棒性等方面所存在的问题,以仿射非线性系统为对象,针对近似时间最优的二阶滑模控制律收敛速度慢和抖振较大的问题,提出改进控制算法,通过设计适当的约束条件和修正滑模趋近加速度,提高了二阶滑模的响应速度,并在不损失鲁棒性的前提下削弱了抖振的频率和幅度.以单摆模型为例,分别对该算法和二阶Lyapunov函数法以及一阶指数趋近法进行仿真研究,仿真结果表明该算法适用于具有不确定性的非线性系统,并在削抖和快速响应方面具有相对优势.     

EHA反馈线性化最优滑模面双模糊滑模控制

为提高电静液作动器（EHA）控制性能,提出了一种反馈线性化最优滑模面的双模糊滑模控制方法。该方法在EHA的非线性模型上,利用反馈线性化方法将其线性化,在此基础上建立线性切换函数,并采用最优控制理论对切换函数进行设计。为削弱抖振将模糊控制算法引入滑模控制中,采用一个模糊控制器,根据最优滑模函数运动特性的数值对切换控制增益进行估计;采用另一个模糊控制器,根据滑模控制原理对切换控制项进行调整。仿真结果证明了该方法的有效性。      

基于遗传算法的高速飞行器滑模控制律设计

以高超声速飞行器GHV(Generic Hypersonic Vehicle)的俯仰通道为控制对象,针对其6自由度非线性模型设计了滑模控制律.为了便于应用滑模控制理论,首先对该模型进行了输入输出反馈线性化,将原模型转换成为仿射型.设计好滑模控制律结构以后,基于遗传算法完成了滑模控制律参数设计.该过程利用了随机鲁棒思想,即在随机均匀分布的参数不确定性作用下,通过遗传算法优化滑模控制律参数,使得飞行控制系统失去稳定性和鲁棒性的概率达到最小.仿真表明,该方法可以同时满足飞行控制系统鲁棒性和参数优化过程收敛性的要求.     

直接力/气动力复合控制导弹 自适应模糊滑模控制

针对采用直接力/气动力复合控制导弹所具有的强耦合非线性等特性,提出了一种基于自适应模糊滑模控制的自动驾驶仪设计方法.该方法利用自适应模糊系统所具有的万能逼近特性,对大攻角飞行过程中导弹动力学系统存在的非线性特性进行逼近,并利用变结构控制对外界干扰的强鲁棒性,构造误差系统滑模面,克服了逼近误差和外界干扰对控制系统的影响,实现了对大机动指令的精确跟踪.仿真结果表明,所设计的控制方法对大过载指令有较好的跟踪效果,对模型不确定性和外界干扰也具有较好的鲁棒性.由于采用直接力/气动力复合控制,有效的减小了气动舵偏角,避免了气动舵的饱和.      

MIMO仿射型极值搜索系统的输出反馈滑模控制

针对一类多输入多输出(MIMO)仿射型非线性极值搜索系统的控制问题,提出了一种输出反馈滑模控制方法。将原系统分解为若干个单输入单输出(SISO)极值搜索子系统,并针对每个极值搜索子系统,考虑到系统状态量不可测的特点,以斜坡函数作为新系统输出量的参考跟踪信号,采用输出跟踪误差以及该误差符号函数的积分值建立切换函数,设计得到基于输出反馈的滑模极值搜索控制律。稳定性分析证明:在任意初始条件下,本文方法可使系统的输出量全局收敛至期望极值的任意小邻域内,并且所有状态量均一致范数有界。仿真结果验证了本文方法的有效性。      

柔性卫星大角度机动的自适应模糊变结构控制

针对柔性卫星大角度机动过程中多种模态的强耦合非线性动力学控制问题,提出了一种自适应模糊变结构姿态控制方法.首先利用拉格朗日方程建立了带柔性附件卫星的动力学模型,然后设计变结构控制器使得系统状态能在有限时间内到达滑模面,并采用自适应模糊系统逼近系统所存在的耦合非线性项.为了削弱变结构控制项所带来的抖动,避免激发柔性附件的高频模态,采用边界层方法来代替开关项,并通过模糊规则表的方法确定边界层的厚度.仿真结果表明,所提出的控制方法既实现了柔性卫星高精度姿态控制,也保证了卫星大角度机动过程中柔性附件弹性模态的有效抑制,系统对各种干扰具有一定的鲁棒性.