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.

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.

Application of Ultrasonic Motor to Control of Moment Gyroscope Gimbal Servo System

Attitude control system is one of the most important subsystems in a spacecraft.As a key actuator,the control moment gyroscope(CMG)mainly determines the performance of attitude control system.Whereas,the control accuracy and output torque smoothness of the CMG depends more on its gimbal servo system.Considering the constraints of size,mass and power consumption for a small satellite,here,a mini-CMG is designed,in which the gimbal servo system is driven by an ultrasonic motor.The good performances of the CMG are obtained by both the ultrasonic motor and the rotary inductosyn.The direct drive of gimbal improves its dynamic performance,with the output bandwidth above 20 Hz.The angular and speed closed-loop control obtains the 0.02°/s gimbal rate,and the output torque resolution better than 2×10^(-3) N·m.The ultrasonic motor provides 1.0N·m self-lock torque during power-off,with 12arc-second position accuracy.

陀螺角速度控制下的单辙两轮车自平衡研究

针对单辙两轮车的不稳定的系统,提出通过控制两个单框架控制力矩陀螺(SGCMG)来研究单辙两轮车的自平衡问题,设计了一个基于滑模控制(SMC)的陀螺角速度控制器,控制SGCMG产生进动力矩,并采用一个奇异回避算法避免陀螺发生奇异现象,以实现整车在静止和动态下的自平衡,并通过仿真验证验证在越障和跨壕沟路况时的自平衡能力。仿真结果表明,所采用的控制方法能够以较小的框架角度使整车快速平衡到直立状态,并且在行驶过过程中很好的抵抗外部干扰,以一个距平衡角度2°范围内的侧倾角度行驶,仿真结果对单辙两轮车的平衡行驶有显著意义。

采用SGCMG的两轮单辙平台自平衡控制技术

针对以自行车、摩托车为代表的两轮单辙平台的自然不稳定问题,采用单框架控制力矩陀螺(SGCMG)为平衡控制机构,研究两轮单辙平台不同工况下自平衡控制算法。分析两轮单辙平台横向力矩,推导横滚转动动力学方程,并根据不同状态误差设计了增益调度PID控制器;建立轮-地接触点模型,修正曲线运动时目标横滚角,减小反馈静差,获得更好的动态响应;以前叉转向趋势预估未来时刻转向角度与目标平衡横滚角度,提前调整姿态以重力矩抵消离心力矩,模拟人骑行时的预判压弯行为。相关算法经仿真验证与实车测试,可在静止与曲线运动等工况下保持动态平衡,效果良好,表明了算法的有效性。

CMG框架超低速无电流环矢量控制研究

针对控制力矩陀螺框架在超低速工况下存在转速测量精度低、多源扰动力矩及非线性摩擦等问题,提出了基于无电流环矢量控制的超低速驱动控制方法。首先,建立超低速工况下的框架电机的机电模型,设计了无电流环磁场矢量控制器(field-oriented control,简称FOC);其次,针对转速测量精度的问题,设计了转速观测器作为反馈环节。结果表明,与方波驱动法相比,该方法无换相转矩,提高了转速测量精度,且在面对多源扰动、非线性摩擦时具有鲁棒性。仿真和实验结果验证了该方法的可行性和有效性。

SGCMGs驱动的挠性航天器有限时间自适应鲁棒控制

针对挠性航天器系统中同时存在单框架控制力矩陀螺群(Single gimbaled control moment gyroscopes,SGCMGs)摩擦非线性、电磁干扰力矩、惯量摄动以及外部干扰等问题,提出了一种有限时间自适应鲁棒控制(Finite-time adaptive robust control,FTARC)方法.针对系统中存在未知参数的情况,分别设计自适应更新律,使得控制器的设计不依赖参数信息,同时减小外部干扰对系统的不利影响.应用Lyapunov稳定性理论证明了闭环系统姿态角误差和姿态角速度误差可在有限时间内收敛到原点附近的邻域内.仿真结果表明,所提控制律可实现挠性航天器姿态快速机动,并获得甚高指向精度.

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.

一种变鲁棒系数的SGCMGs伪逆操纵律

针对五棱锥单框架控制力矩陀螺群(Single gimbaled control moment gyroscopes,SGCMGs)中存在的奇异问题,建立五棱锥构型SGCMGs系统动力学模型,基于双曲正弦函数和分段函数设计鲁棒系数,改进鲁棒伪逆操纵律,使SGCMGs系统在处于奇异状态时,保证框架角速度不为零,从而逃离奇异;在接近奇异状态时迅速避开奇异,在远离奇异状态时更精确地输出期望力矩。通过SGCMGs不同类型力矩输出和挠性航天器大角度姿态机动控制的仿真结果表明,所提SGCMGs操纵律既能够较好地规避奇异状态,又能在远离奇异时精确地输出期望力矩。

使用SGCMGs航天器滑模姿态容错控制

基于滑模控制与自适应理论,对使用单框架控制力矩陀螺群(SGCMGs)的刚性航天器的被动姿态容错控制问题进行了研究。首先建立了含有陀螺框架转速故障的系统数学模型。然后将框架转速直接作为控制量并应用滑模控制理论设计了容错控制器,同时控制器中还设计了自适应律对故障信息和干扰进行估计。由此,可在故障和干扰的先验信息未知的情况下,实现对航天器无故障和有故障情况下的姿态稳定控制,且具有较强的鲁棒性。最后,对2种构型单框架控制力矩陀螺群的不同故障模式进行数学仿真,验证了该控制方法的有效性和可行性。

An improved constrained steering law for SGCMGs with DPC

An improved constrained （IC） steering law for single gimbal control moment gyros （SGCMGs） with deformed pyramid configuration （DPC） is proposed, First of all, the original system with five pyramid configuration （FPC） whose two adjacent gyros are in failure state is reconfigured as a degraded system with DPC. Then, the singular angular momentum hypersurfaces of the original and the degraded systems are plotted via the singular angular momentum equa- tion of SGCMGs. Based on singular surfaces, the differences between FPC and DPC in singularity and momentum envelope are obtained directly, which provide an important reference for steering law design of DPC. Finally, an IC steering law is designed and applied to DPC. The simulation results demonstrate that the IC steering law has advantages in simplicity of calculation, avoidance of singularity and exactness of output torque, which endow the degraded system with fine controllability in a restricted workspace.

Steering laws analysis of SGCMGs based on singular value decomposition theory

The steering laws of single gimbal control moment gyros （SGCMGs） are analyzed and compared in this paper for a spacecraft attitude control system based on singular value decomposition （SVD） theory. The mechanism of steering laws escaping singularity, especially how the steering laws affect singularity of gimbal configuration and the output torque error, is studied using SVD theory. Performance of various steering laws are analyzed and compared quantitatively by simulation. The obtained results can be used as a reference for designers.

一种改进的SGCMGs奇异鲁棒伪逆操纵律算法

以单框架控制力矩陀螺(SGCMG)为卫星动量交换机构,基于建立的姿态控制系统与SGCMG系统的动力学模型,设计零动量卫星的PD(比例微分)解耦姿态控制律。为逃避奇异,提出了一种改进的单框架控制力矩陀螺群(SGCMGs)奇异鲁棒伪逆操纵律算法。某航天器姿态控制仿真结果表明:改进算法可避免奇异,算法有效性得以验证。

五棱锥SGCMGs失效时奇异构型几何分析及操纵律设计

单框架控制力矩陀螺群(SGCMGs)的奇异构型几何分析及相应的操纵律设计是其在使用中遇到的主要问题。针对五棱锥SGCMGs构型及其单只失效后的奇异情况进行几何分析,考虑五棱锥构型单只SGCMG失效后显奇异点深入角动量体内部这一特性,设计了一种既能充分利用零空间运动,又能实现显奇异点规避的SGCMGs操纵律。仿真分析结果表明:设计改进后的操纵律能在有效解决五棱锥SGCMGs构型中单只陀螺失效后带来内部复杂奇异问题的同时,实现控制精度的大幅提升。

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.

双框架磁悬浮控制力矩陀螺动框架效应补偿方法

双框架磁悬浮控制力矩陀螺(Double gimbal magnetically suspended control moment gyroscope,DGMSCMG)是由磁悬浮高速转子系统与内框架、外框架速率伺服系统构成的航天器新型姿控执行机构。由于非线性及三个子系统间的强耦合,框架转动时磁悬浮转子位移急剧增大影响稳定性,同时框架系统的响应速度显著下降,称之为动框架效应。该效应严重影响了DGMSCMG的功能,必须加以抑制。建立DGMSCMG的动力学模型,分析三个子系统间的动力学耦合机理,提出一种基于复合控制的补偿方法,引入针对陀螺项的反馈和针对框架角速率给定的前馈消除磁悬浮转子附加位移,提高框架系统响应速度,并对补偿后系统做全局稳定性分析。仿真和试验结果表明,该方法能在保证系统稳定性的前提下有效抑制动框架效应,满足DGMSCMG的功能要求。

基于terminal滑模控制的小卫星机动方法

采用terminal滑模控制方法研究了以单框架控制力矩陀螺(SGCMG)为执行机构的小卫星的姿态机动控制。首先,基于修正罗德里格斯(MRP)参数建立了小卫星数学模型,以terminal滑模控制方法进行控制力矩规划。然后,采用SGCMGs作为小卫星执行机构,以非对角奇异鲁棒操纵律跟踪terminal滑模控制产生的期望力矩;通过仿真分析归纳出terminal滑模控制设计参数的变化规律和选取原则。最后,利用小卫星三轴气浮转台实验验证termianl滑模控制方法的实用性。实验显示:根据参数选取原则设定的参数进行小卫星机动稳定实验得到的姿态角和姿态角速度控制精度和稳态误差分别小于0.1°和0.01(°)/s,满足三轴气浮转台最佳控制精度。结果表明terminal滑模控制方法在小卫星机动稳定任务中具有很高的控制精度和稳定度,能够为小卫星成像任务稳定执行提供良好的基础。

快速机动小卫星执行机构研究

为了验证采用控制力矩陀螺作为小卫星的姿态控制执行部件,大幅提升小卫星机动能力的可行性,根据控制力矩陀螺的工作原理,设计了控制力矩陀螺原理样机,并利用单轴气浮转台进行了控制力矩陀螺半物理仿真实验。实验结果表明,控制力矩陀螺作为小卫星执行机构,可使小卫星在8 s内机动20°,机动速度可达2.5°/s,实现了在短时间内完成小卫星大角度快速机动和入轨后快速定姿,为控制力矩陀螺在小卫星上的实际工程应用提供了依据。

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