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.

Model predictive control of rigid spacecraft with two variable speed control moment gyroscopes

In this paper, an attitude maneuver control problem is investigated for a rigid spacecraft using an array of two variable speed control moment gyroscopes （VSCMGs） with gimbal axes skewed to each other. A mathematical model is constructed by taking the spacecraft and the gyroscopes together as an integrated system, with the coupling interaction between them considered. To overcome the singular issues of the VSCMGs due to the conventional torque-based method, the first-order derivative of gimbal rates and the second-order derivative of the rotor spinning velocity, instead of the gyroscope torques, are taken as input variables. Moreover, taking external disturbances into account, a feedback control law is designed for the system based on a method of nonlinear model predictive control （NMPC）. The attitude maneuver can be realized fast and smoothly by using the proposed controller in this paper.

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.

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VSCMG的卫星姿态控制仿真系统

介绍了一种新型卫星姿态控制全物理仿真系统,此仿真系统以长春光机所最新研制的高精度三轴气浮转台为平台,采用变速控制力矩陀螺(VSCMG)为主要控制执行机构,并结合喷气推力机构作为系统的辅助执行机构给控制力矩陀螺进行卸载。此系统应用高精度光纤陀螺、高精度倾角传感器和磁强计等姿态确定器件构成一套完整的姿态控制全物理仿真系统。介绍了整个仿真系统的软硬件构成,并结合传感器和执行机构参数进行建模和误差分析。本仿真系统可以为一般卫星姿态控制,尤其是以VSCMG为主要执行机构的敏捷型小卫星的姿态控制策略和算法提供良好的仿真验证平台。

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.

高姿态稳定度敏捷卫星的VSCMGs操纵律研究

研究采用变速控制力矩陀螺群(VSCMGs)作为姿态控制执行机构的高姿态稳定度敏捷卫星的操纵律设计问题。将VSCMG分为控制力矩陀螺(CMG)和动量轮(MW)两种工作模式,针对每种工作模式进行奇异性分析,并给出逃避奇异的方法。为了获得较好的控制效果,还研究了VSCMGs转子转速向标称转速平衡的方法以及通过调整转子轴构型使转子转速快速返回到标称值的方法。最后通过对算例进行仿真,验证了所设计的操纵律的有效性。

使用VSCMGs的IPACS的奇异性分析与操纵律设计

研究使用变速控制力矩陀螺群(VSCMGs)的能量/姿态一体化控制系统(IPACS)的奇异性分析与操纵律设计问题。提出了VSCMGs的CMG奇异与IPACS奇异两种概念。对于给定的CMG奇异方向,采用优化理论得到了在该方向上VSCMGs的转子达到角动量饱和时的转速表达式,并给出了IPACS奇异的充要条件及其证明。分析了考虑星体角速度影响时的实际IPACS的奇异性质。在此基础上为实现合理的动量管理,采用加权矩阵的方法设计了IPACS的操纵律。最后通过算例验证了所得到的IPACS奇异判据的正确性,并通过数值仿真,验证了所设计的操纵律的正确性及其良好的动量管理性能。

VSCMG簇的操纵律优化设计

变速控制力矩陀螺(variable speed control moment gyro,VSCMG)簇相对于单框架控制力矩陀螺簇仅增加了飞轮转速可调自由度,实现难度不大,但能够缓解奇异问题。基于线性代数理论,从机理上分析了已有的添加零运动的加权伪逆操纵律不能规避VSCMG簇内所有奇异点。针对添加零运动的加权伪逆操纵律不能规避奇异点的问题,采用优化方法,设计出一种新型的VSCMG簇操纵律,能够规避采用传统添加零运动的加权伪逆操纵律不能规避的奇异点。最后搭建整个航天器姿态控制系统,仿真验证了所设计的新型操纵律奇异规避的有效性。

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.

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。

应用变速控制力矩陀螺的卫星姿态机动的非线性控制

研究了以变速控制力矩陀螺(VSCMG)作为执行机构的卫星多目标快速机动的控制问题。首先建立了带有多个变速控制力矩陀螺的航天器姿态动力学模型,采用修正的罗德里格斯参数(MRP)描述姿态运动。在考虑执行机构饱和、机动速率限制、控制带宽限制等情况下,设计了基于Lyapunov理论的非线性姿态反馈控制器。针对外部干扰会使控制力矩陀螺的框架角偏移其标称值的情况,采取磁补偿控制来保持框架角在一定范围变化。以采用VSCMG为执行机构的某卫星为例进行了数值仿真,仿真结果验证了提出的非线性姿态反馈控制器的有效性,采取的磁补偿控制也很好地抑制了变速控制力矩陀螺框架角的偏移。

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

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。