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.

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.

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.

基于聚类变异PSO优化的VSCMGs模糊平滑切换算法

针对变速控制力矩陀螺(variable speed control moment gyro,VSCMG)作为执行机构应用在敏捷遥感卫星上进行姿态机动时末端模式切换的平稳性和快速性冲突问题,在考虑框架转速误差的基础上,设计姿态误差参数作为切换指标,制定误差参数切换区域内的过渡规则,将指令力矩实时分配给控制力矩陀螺(control moment gyro,CMG)和飞轮并分别求解,提出了一种控制力矩陀螺/反作用飞轮工作模式模糊平滑切换操纵律。为了使得姿态机动末端卫星姿态达到姿态稳定度和指向精度要求的时间更短,以该时间为优化指标提出聚类变异改进粒子群算法对该操纵律参数寻优,确定最佳的切换区域和切换参数,并进行了仿真验证。结果表明:改进后粒子群算法在相同的迭代次数中总是表现出比传统粒子群算法更优的适应度,具有更快的收敛速度和更高的收敛精度,参数优化后的模糊平滑切换操纵律相比于现有操纵律能够在较短时间内完成双模式的平滑切换,并在姿态机动末端更迅速地达到姿态稳定度和指向精度要求,提高了遥感卫星敏捷机动与高稳指向的控制性能,有利于高质量完成成像任务。

基于LPV的主动隔振平台单支腿鲁棒控制器设计

利用控制力矩陀螺(CMG)实现敏捷姿态机动控制时,保证机动过程控制输出力矩快速响应的同时,还需要保证机动到位后有效隔离CMG的机械振动以实现高稳定度姿态控制。针对控制CMG主动隔振平台,将控制CMG外框角速度作为变参数,提出单支腿主动隔振平台控制器的一种基于线性变参数(LPV)控制设计实现方法,通过与其他主动隔振控制方法性能比较分析,所提方法在兼顾敏捷姿态机动期间和机动到位后对主动隔振平台不同的力学传递要求方面有更好的性能。

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。

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。

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

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。

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。

控制力矩陀螺框架伺服系统的超低速测速方法

在超低转速下,有限的转速测量分辨率是影响控制力矩陀螺框架伺服系统控制性能的一个重要因素。在分析转速分辨率对超低速控制性能影响的基础上,提出了一种基于多周期后向差分的转速计算方法,可提高测速分辨率并保证测速带宽。针对后向差分带来的相位延迟会限制测速分辨率进一步提高的问题,在选取合适的差分周期基础上,采用Kalman预估器对框架转速进行预估,进一步提高了框架转速的测速分辨率及测速带宽。通过仿真表明,所提出的测速方法将转速分辨率提高了两个数量级,解决了框架伺服系统在超低转速下由于有限的转速测量分辨率造成的爬行现象。