Geometric Analysis of Singularity for Single-Gimbal Control Moment Gyro Systems

This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.

Underactuated spacecraft angular velocity stabilization and three-axis attitude stabilization using two single gimbal control moment gyros

Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.

Attitude control of a rigid spacecraft with one variable-speed control moment gyro

Nonlinear controllability and attitude stabilization are studied for the underactuated nonholonomic dynamics of a rigid spacecraft with one variable-speed control moment gyro （VSCMG）, which supplies only two internal torques. Nonlinear controllability theory is used to show that the dynamics are locally controllable from the equilibrium point and thus can be asymptotically stabilized to the equilibrium point via time-invariant piecewise continuous feedback laws or time-periodic continuous feedback laws. Specifically, when the total angular momentum of the spacecraft-VSCMG system is zero, any orientation can be a controllable equilib- rium attitude. In this case, the attitude stabilization problem is addressed by designing a kinematic stabilizing law, which is implemented through a nonlinear proportional and deriva- tive controller, using the generalized dynamic inverse （GDI） method. The steady-state instability inherent in the GDI con- troller is elegantly avoided by appropriately choosing control gains. In order to obtain the command gimbal rate and wheel acceleration from control torques, a simple steering logic is constructed to accommodate the requirements of attitude sta- bilization and singularity avoidance of the VSCMG. Illustrative numerical examples verify the efficacy of the proposed control strategy.

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 in a single-gimbal control moment gyro onboard a rigid satellite. This model strictly 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 auto-centering control is carefully constructed for the rotor with unknown dynamic and static imbalance. The rotor makes its rotation about the principal axis of inertia through identifying the small rotational angles between the geometric axis and the principal axis as well as the displacements from the geometric center to the mass center so as to tune a stabilizing controller composed of a decentralized PD controller with cross-axis proportional gains and high- and low-pass filters. The main disturbance in the wheel spinning can thereby be completely removed and the vibration acting on the satellite attenuated.

Error analysis and a new steering law design for spacecraft control system using SGCMGs

Based on the singular value decomposition theory,this paper analyzed the mechanism of escaping/avoiding singularity using generalized and weighted singularity-robust steering laws for a spacecraft that uses single gimbal control moment gyros （SGCMGs） as the actuator for the attitude control system.The expression of output-torque error is given at the point of singularity,proving the incompatible relationship between the gimbal rate and the output-torque error.The method of establishing a balance between the gimbal rate and the output-torque error is discussed,and a new steering law is designed.Simulation results show that the proposed steering law can effectively drive SGCMGs to escape away from singularities.

Attitude control for part actuator failure of agile small satellite

The stability and singularity problem of agile small satellite （ASS） with actuator failure is discussed in this paper. Firstly, the three-axis stabilized controller of an ASS is designed, where micro control moment gyros （MCMG＇s） in pyramid configuration （PC） is used as the actuator. By using the same controller and steering law, the control results before and after one gyro fails are compared by simulation. The variation of singular momentum envelope before and after one gyro fails is also compared. The simulation results show that the failure intensively decreases the capacity of output torque, which leads to the emergence of more singular points and the rapid saturation of MCMG＇s. Finally, the parameters of system controller are changed to compare the control effect.

Local controllability and stabilization of spacecraft attitude by two single-gimbal control moment gyros

The attitude control problem of a spacecraft underactuated by two single-gimbal control moment gyros （SGCMGs） is investigated. Small-time local controllability （STLC） of the attitude dynamics of the spacecraft-SGCMGs system is analyzed via nonlinear controllability theory. The conditions that guarantee STLC of the spacecraft attitude by two non-coaxial SGCMGs are obtained with the momentum of the SGCMGs as inputs, implying that the spacecraft attitude is STLC when the total angular momentum of the whole system is zero. Moreover, our results indi- cate that under the zero-momentum restriction, full attitude stabilization is possible for a spacecraft using two non-coaxial SGCMGs. For the case of two coaxial SGCMGs, the STLC property of the spacecraft cannot be determined. In this case, an improvement to the previous full attitude stabilizing control law, which requires zero-momentum presumption, is proposed to account for the singu- larity of SGCMGs and enhance the steady state performance. Numerical simulation results demonstrate the effectiveness and advantages of the new control law.

Singularity analysis for single gimbal control moment gyroscope system using space expansion method

Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in using CMG is the inherent geometric singularity problem, where there＇s no torque output along a particular direction. Space expansion method has been proposed in this work for the singularity analysis. Based on inverse mapping transformation, an expanded Jacobian matrix which is a full rank square matrix is obtained. The singular angle sets of the 3-parallel cluster and pyramid cluster are distinguished using space expansion method. An effective hybrid steering strategy, able to deal with the elliptic singularity, is further proposed. Simulation results demonstrate the excellent performance of the proposed steering logic compared to the generalized singular robust logic and pseudo inverse logic in terms of energy consumption and torque error.

Neural network-based fault diagnosis for spacecraft with single-gimbal control moment gyros

This paper proposes a neural network-based fault diagnosis scheme to address the problem of fault isolation and estimation for the Single-Gimbal Control Moment Gyroscopes(SGCMGs)of spacecraft in a periodic orbit.To this end,a disturbance observer based on neural network is developed for active anti-disturbance,so as to improve the accuracy of fault diagnosis.The periodic disturbance on orbit can be decoupled with fault by resorting to the fitting and memory ability of neural network.Subsequently,the fault diagnosis scheme is established based on the idea of information fusion.The data of spacecraft attitude and gimbals position are combined to implement fault isolation and estimation based on adaptive estimator and neural network.Then,an adaptive sliding mode controller incorporating the disturbance and fault estimation results is designed to achieve active fault-tolerant control.In addition,the paper gives the proof of the stability of the proposed schemes,and the simulation results show that the proposed scheme achieves better diagnosis and control results than compared algorithm.

Mixture steering law design for control moment gyroscopes

Focusing on the singularities of a spacecraft using control moment gyros(CMGs)to do the large angle maneuvers,a new mixture steering law is proposed to avoid the singularities.According to this method,if the CMGs are far away from the singularity,the Moore-Penrose pseudo-inverse steering law(MP)is used directly.If the CMGs are close to the singularity,instead of solving the inverse matrix,a set of optimal gimbal angles are sought for the singular measurement to reach the maximum,which can avoid the singularities.Simulations show that the designed steering law enables the spacecraft to carry out the large angle maneuver and avoid the singularities simultaneously.

敏捷卫星姿态机动的非线性模型预测控制

针对以金字塔构型控制力矩陀螺(CMG)为执行机构的敏捷小卫星开展了先进机动控制算法的研究。在考虑控制力矩陀螺力矩约束及增量约束情况下,设计了基于非线性模型预测控制(NMPC)方法的卫星姿态快速机动控制律及操纵律。通过多种仿真分析了控制器设计参数变化对卫星姿态机动的影响,并与终端滑模控制方法进行了比较。实验结果表明,增大跟踪性能加权矩阵或延长预测时域均可以提高卫星姿态机动速度,缩短卫星姿态机动时间。设计的控制方法能够使卫星姿态在18s内实现40°的大角度快速机动,姿态指向精度和稳定度分别为0.01°和0.04(°)/s,与终端滑模控制方法相比,机动速度及稳态性均得到提高。本文方法为敏捷小卫星的在轨应用方式提供了理论支撑。

大型航天器SGCMG系统的奇异性分析研究

应用单框架控制力矩陀螺系统 (SGCMG)是大型航天器姿控系统较为理想的选择 ,但是该系统存在严重的奇异现象 ,增加了操纵律的设计与开发的难度。文章从奇异性分析的角度对单框架控制力矩陀螺系统的奇异状态进行了研究 ,提出了奇异可回避性的判别方法 ,并据此对 SGCMG系统奇异状态进行了系统的分类 ,针对常用的各种构形的

使用单框架控制力矩陀螺的空间站姿态控制系统建模与仿真

研究使用单框架控制力矩陀螺群 (SGCMGs)的空间站的姿态控制。完成空间站在轨三轴稳定飞行模式下的动力学和执行机构的建模。基于最小二乘意义下的伪逆原理设计了 SGCMGs的控制律。对于框架构形的隐奇异 ,采用零运动躲避的算法。同时建立了框架电机的动力学、干扰和控制器的仿真模型。提出了适合工程应用的SGCMGs构形显奇异和饱和奇异的工程性的判断条件及卸载方法。为了探讨伺服机构对系统响应特性的影响 ,进行了分系统级的仿真。仿真模型中包括了空间环境力矩、敏感器及姿态确定模型。仿真中使用了五棱锥构形的SGCMGs,这种构形具有好的冗余度和大的角动量包络。仿真结果验证了五棱锥构形

谐波减速器的非线性摩擦建模及补偿

针对带有谐波减速器的双框架控制力矩陀螺框架伺服系统中的非线性摩擦问题,提出了非线性摩擦建模及补偿方法。首先,根据框架伺服系统数学模型导出摩擦力矩与角加速度和电机电流的关系;然后,通过光电码盘测得的角位置计算角速率并设计估计器来估计电机端和负载端的角加速度,利用采样电流和估计的角加速度计算摩擦力矩,建立库伦+粘滞+Stribeck摩擦模型;最后,设计基于摩擦模型的前馈补偿控制器抑制非线性摩擦以提高系统控制精度。实验结果显示,与传统PID控制方法相比,伺服系统加入基于摩擦模型的前馈补偿之后,角速率误差曲线峰峰值减小28.2%,角速率误差均方值减小25.7%;表明通过基于摩擦模型的前馈补偿可以有效抑制非线性摩擦引起的角速率误差,提高伺服系统的控制精度。

控制力矩陀螺框架系统的谐振抑制与精度控制

控制力矩陀螺(CMG)框架系统的速率控制精度是影响其输出力矩精度的重要因素,系统中谐波减速器提高了框架系统的动态响应能力,但其产生的机械谐振大幅降低了系统的控制精度。为抑制框架系统的谐振并满足系统的控制精度,本文建立了框架系统的动力学模型,根据系统动态性能要求选取合适的阻尼系数来设计系统主导极点,使控制器产生的零点与机械谐振对应的极点重合形成偶极子,从而抑制系统的机械谐振。仿真和实验结果显示:提出的方法有效地抑制了控制力矩陀螺框架系统的谐振,0.175rad/s恒速控制精度为0.002,0.175sin(2πt)rad/s正弦随动控制的幅值相对误差为3.28%,相位差为0.13rad。结果很好地满足了控制力矩陀螺的高精度输出力矩需求。

SGCMG框架伺服系统扰动力矩分析与控制

单框架控制力矩陀螺框架伺服系统对扰动力矩抑制能力的不足限制了其控制精度的进一步提高。文章对框架伺服系统受到的扰动力矩及其对框架伺服系统控制性能的影响进行了分析;设计了基于终端滑模变结构控制策略和扰动观测器的框架转速控制器;利用变结构控制对系统干扰的不变性和对滑动模态控制的快速响应特性,实现了框架伺服系统在扰动力矩波动,尤其是高频扰动力矩波动条件下的高精度控制。仿真结果表明,相比传统的比例-积分-微分控制策略,提出的控制方法可行有效,将框架转速波动量缩小了2/3。

具有SGCMG系统的挠性卫星姿态机动控制及验证

针对挠性卫星在轨姿态快速机动的需求,开展了星体姿态机动控制方法及控制实现研究。基于建立的挠性卫星姿态跟踪控制误差方程,给出了PD控制与补偿控制相结合的姿态跟踪控制器形式;考虑系统实现的时延影响,利用经典频率分析方法选择了兼顾系统稳定性及宽带控制的控制参数;在控制具体实现中,采用一种新型的基于力矩矢量调节奇异规避操纵策略,克服常规鲁棒奇异规避操纵存在的框架"锁死"现象,在解决奇异规避的同时避免激发挠性振动。所提出方法的有效性通过了在轨验证。

基于路径规划的敏捷卫星姿态机动反馈控制方法

为了避免奇异状态,单框架控制力矩陀螺(SGCMG)操纵律要求框架角进行快速转动,需要消耗较多的能量,并会对SGCMG和卫星系统带来一系列潜在危害。针对该问题,提出基于路径规划和反馈控制相结合的姿态机动控制方法。根据固定时间姿态机动的任务需求,以能量为优化指标,采用伪谱法优化机动路径并回避奇异状态;将最优控制量作为参考数输入,并利用基于系统限制状态的反馈控制方法消除不确定性和扰动的影响。反馈控制基于名义输入进行数值积分得到的预测状态量,并与期望终端状态比较形成控制误差信号。该方法将卫星和SGCMG作为整体规划姿态运动,能够有效避免奇异状态。结合工程实际,在闭环控制仿真中考虑了卫星角速度和SGCMG框架角的初始偏差。仿真结果表明:本文算法能够有限避免奇异状态,且能消除初始姿态角速度和框架角不确定的影响。

一种双框架磁悬浮控制力矩陀螺框架伺服系统扰动抑制方法研究

为了抑制谐波减速器运动误差对双框架控制力矩陀螺伺服系统速率平稳性的影响,提出一种角加速度反馈的控制方法。建立了带有谐波减速机构的陀螺框架系统的数学模型,对谐波减速器的运动误差进行了分析。通过设计非线性微分跟踪器得到加速度信号构成加速度反馈,对谐波减速器运动误差所造成的速率波动进行抑制。对框架伺服系统进行仿真,仿真结果证明了该控制方法的有效性,在双框架磁悬浮控制力矩陀螺原理样机上进行了实验验证,实验结果表明,在5度/秒的转速情况下,使框架转速波动量减小了59%,显著提高了转速精度。

控制力矩陀螺在天宫一号目标飞行器姿态控制上的应用

根据天宫一号目标飞行器的特点及交会对接任务需求,天宫一号目标飞行器选择单框架控制力矩陀螺作为姿态控制执行机构,这是控制力矩陀螺首次在国内航天器上应用.阐述了单框架控制力矩陀螺在天宫一号目标飞行器姿态控制上的应用,主要包括四个方面:构形选择、操纵律设计、角动量卸载、故障诊断与重构.天宫一号目标飞行器控制力矩陀螺系统采用五棱锥构形,其操纵律设计为带零运动的伪逆操纵律,控制力矩陀螺系统具备故障诊断和重构功能.