含弱阻尼空间结构的耦合动力学保结构分析

大型空间结构的平面运动、姿态变化和结构振动影响着其在轨运行的工作精度、效率和寿命.针对太阳帆塔空间太阳能电站,根据其设计方案的结构特征,简化得到轨道平面内的梁 弹簧 梁模型.考虑系统中存在的弱阻尼作用,建立了耦合系统的动力学控制方程,采用辛Runge Kutta和广义多辛结合的复合保结构方法,对系统的耦合动力学行为和阻尼作用进行了分析.研究发现,弱阻尼作用对空间结构轨道变化存在微小影响,其值与轨道半径的比值在10-8量级.姿态角的变化会导致系统非刚性构件的形变变化.研究工作拓展了保结构方法在复杂空间结构动力学问题中的应用,为复杂系统结构的设计和主动控制提供了理论参考.     

热辐射及重力梯度对大型空间柔性梁结构振动影响分析

鉴于大型航天器在轨服役期间会受到万有引力梯度、热辐射等复杂载荷作用,致使结构诱发热-结构耦合振动现象.因此,本文将研究万有引力梯度和热辐射载荷作用下大型空间柔性梁的动力学行为.首先,基于绝对节点坐标方法和热-结构耦合理论,建立柔性梁的数学模型;其次,通过Legendre变换,推导出Hamilton 体系下柔性梁结构的对偶方程;然后通过数值仿真,研究了无地球阴影时柔性梁的热致振动,发现柔性梁结构的位移响应包括万有引力梯度引起的振动和热致振动,其运动较为稳定;进一步的,数值结果表明地球阴影对柔性梁的热致振动幅值以及稳定性有着非常显著的影响.同时,针对地球静止轨道上的柔性梁,发现热致振动影响大于万有引力梯度,并比较了柱形阴影和锥形阴影的影响.     

航天器姿轨耦合非线性同步控制

研究航天器飞行稳定控制建模问题。航天器动力学模型的精确建立,要求采用单独建立轨道或姿态的模型无法满足任务高精度要求,从非线性相对轨道动力学方程和修正罗德里格斯参数(MRP)表示的姿态运动学方程出发,建立了航天器六自由度的相对耦合动力学方程。为了给出姿轨运动的基准,分别设计了航天器理想姿态和椭圆加指数接近轨道。针对耦合非线性动力学方程设计了非线性同步控制律,并通过Lyapunov证明闭环系统的全局渐近稳定性。通过仿真结果可以看出,非线性同步控制算法能使轨道和姿态误差逐步趋于零,为航天器姿轨耦合设计提供了依据。     

磁浮列车车轨耦合振动仿真研究

为了分析车轨道耦合振动过程中各因素的影响,建立了车体-悬浮架-轨道的简化动力学模型和动力学方程,利用数值方法研究了一节列车在静态悬浮过程中,整个车体与轨道耦合振动的垂向动力学行为.分析了轨道和车辆主要参数对振动的影响,并给出了仿真结果.仿真结果表明,轨道的抗弯刚度,长度,车轨质量比,以及车辆的悬浮刚度对于耦合振动影响较大;同时经过二系悬挂的衰减,车厢的振动较小.结论可供车辆悬浮控制器设计和轨道梁设计参考.     

一种在轨可展开天线的多柔体动力学建模与计算

研究了一种考虑重力梯度的大型空间可展开天线桁架的动力学建模与计算问题.使用绝对节点坐标法和绝对节点坐标参考节点法建立了可展开结构的刚柔耦合动力学模型.利用离散方向导数构建了动力学方程的保能量动量时间积分算法,通过计算获得了含有多个模块的大型空间可展开天线在轨展开以及展开后轨道机动过程轨道-姿态-变形耦合动响应.通过数值计算结果与经典算例结果、商业软件ADAMS计算结果的对比分析验证了提出方法的正确性.     

外部激励对齿轮箱系统振动能量传递特性的影响

针对齿轮箱的振动噪声控制问题,分析了外部激励对齿轮箱非线性系统振动能量传递特性的影响。采用子结构综合法,建立了齿轮箱非线性耦合系统的动力学模型,计算了耦合系统振动能量传递函数;采用数值求解方法,对齿轮箱非线性系统动力学模型进行求解,建立了系统的状态空间方程,并利用MATLAB对该状态空间方程进行了数值仿真。基于MATLAB,对具有对称结构的齿轮箱系统进行了数值仿真,研究了外部激励对系统振动能量传递特性的影响。该系统为齿轮箱振动噪声控制提供了新的理论依据。     

弹塑性梁系统的动力学特性研究

研究了弹塑性梁系统的动力学特性.从弹塑性梁的非线性本构关系出发,同时考虑几何非线性,用虚功原理建立单个梁的动力学变分方程,利用假设模态法离散.在此基础上引入运动学约束关系,建立了弹塑性梁系统的刚-柔耦合动力学方程.对重力作用下的柔性单摆和双摆数值仿真结果表明,塑性应变引起横向变形绝对值增大和横向振动振幅衰减,在角加速度突变时塑性效应最为显著.     

两档输电线路间的非线性耦合振动特性研究

考虑几何非线性的影响,推导了两档输电导线与悬垂绝缘子串耦合振动的非线性动力学方程,并运用数值分析软件对不同工况下的振动响应进行了数值求解.基于输电导线振动的位移时程曲线,得到了两档输电导线的非线性耦合振动特性和共振特性,在小传输角度情况下,角度对输电导线的振动幅度没有明显影响,但振动系统的静平衡位置会发生偏移.     

非合作目标绕飞任务的航天器鲁棒姿轨耦合控制

本文研究了非合作目标强迫绕飞过程中存在外部干扰和参数不确定性以及控制输入饱和约束下的航天器鲁棒姿轨耦合控制问题.首先,根据视线坐标系下的轨道动力学方程和本体坐标系下的姿态动力学方程,建立了满足视线指向要求的航天器相对姿轨耦合动力学模型.其次,针对姿轨耦合模型,基于反步法设计了具有抗饱和能力的鲁棒自适应姿轨耦合控制律,其中利用抗饱和技术设计了饱和补偿器,并结合自适应方法对未知参数和扰动上界进行估计,并基于Lyapunov方法给出了闭环系统的稳定性证明.最后,将提出的控制方案进行了数值仿真和比较,验证了其有效性.     

梁摆系统耦合振动分析

分析了梁摆系统的耦合振动,梁和摆均考虑为线性.研究发现该系统含有非线性动力行为,在某些条件下会发生叉形分叉.用结构动力学理论建立了梁摆系统的耦合振动方程,用摄动法求出了系统的近似解,分析了该系统的动力响应及分叉.最后用MATHMATIC软件对分叉点前后动力响应进行分析.     

Analysis of optimal motion control for a material point in a central field with application of quaternions

This work is devoted to a survey and generalization of results obtained in the theory of optimal motion control for a material point in the central Newtonian gravitational field using the Pontryagin’s maximum principle and quaternion models of orbital motion. This theory is very important in space flight mechanics, being the background of the solution of optimal control problems of the motion of the center of mass of a space vehicle. In the first part of this work, a survey of quaternion models of the motion of a material point in a central Newtonian gravitational field is given, their advantages and disadvantages are analyzed. The formulation of the optimal control problem of the motion of a material point in the central Newtonian gravitational field and its correlation with the optimal control problem of the motion of the center of mass of a space vehicle is considered. The main problems arising in the solution of optimal control problems of the motion of a material point using the maximum principle, including instability in the Lyapunov’s sense of solutions to adjoint equations, are studied. It is shown that efficiency of analytical investigation and numerical solution of the corresponding boundary-value problems can be increased by the application of quaternion models of orbital motion.     

一类磁性刚体航天器的混沌控制研究

采用基于误差线性系统稳定性准则的混沌控制方法,控制具有结构内阻尼的磁性刚体航天器在重力场与磁场共同作用下在圆形轨道的混沌姿态运动.讨论了航天器姿态运动方程中部分参数的取值对于运动姿态的影响,给出了这些参数通过倍周期分岔或逆倍周期分岔通往混沌的途径.当参数使系统做混沌姿态运动时,采用上述方法将混沌运动控制至周期-4轨道,并实现周期-1、2、4轨道之间转换的灵活控制.此外,分析了控制参数的变化对于控制效果的影响,并分别给出了控制至不同轨道时的输入扰动范围及控制参数范围.仿真结果表明,该方法能够实现混沌姿态运动在预定周期轨道间的灵活控制,且输入扰动量小、控制速度快、具有高精度,从而验证了该方法在航天器混沌姿态运动控制方面的有效性.     

Controllability of spacecraft systems in a central gravitationalfield

The configuration space for rigid spacecraft systems in a central gravitational field can be modeled by SO(3)× IR³, where the special orthogonal group SO(3) represents the attitude dynamics and IR³ is for the orbital motion. The attitude dynamics of the spacecraft system is affected by the orbital elements through the well-known gravity-gradient torque. On the other hand, the effects of attitude-orbit coupling can also possibly be used to alter orbital motions by controlling the attitude. This controllability property is the primary issue of this paper. The control systems for spacecraft with either reaction wheels or gas jets being used as attitude controllers are proven in this study to be controllable. Rigorously establishing these results necessitates starting with the formal definitions of controllability and Poisson stability. It is then shown that if the drift vector field of the system is weakly positively Poisson stable and the Lie algebra rank condition is satisfied, controllability can be concluded. The Hamiltonian structure of the spacecraft model provides a natural route of verifying the property of weakly positive Poisson stability. Accordingly, the controllability is obtained after confirming the Lie algebra rank condition. Developing a methodology in deriving Lie brackets in the tangent space of T(SO(3)×IR³), i.e., the second tangent bundle is thus deemed necessary. A general formula is offered for the computation of Lie brackets of second tangent vector fields in TT(SO(3)^m×IRⁿ), in light of its importance in the fields of mechanics, robotics, optimal control, and nonlinear control, among others. With these tools, the controllability results can be proved. The analysis in this paper gives some insight into the attitude-orbit coupling effects and may potentially lead towards new techniques in designing controllers for large spacecraft systems     

Satellite attitude stabilization using solar radiation pressure and magnetotorquer

The paper presents three-dimensional (3-D) attitude stabilization of a geosynchronous satellite. The solar radiation pressure is considered for the satellite pitch and roll stabilization while the yaw attitude is stabilized by a magnetotorquer. The general formulation of the system comprised of a satellite body, two solar flaps, and a magnetotorquer is obtained through Euler's equations. The linearized system model is derived and then the control laws are developed for suitable rotations of solar flaps and variations in magnetic moment. The numerical simulation of the governing nonlinear system equations of motion establishes the feasibility of achieving the desired 3-D satellite attitude. The controllers are successful in stabilizing the satellite attitude even in the presence of orbital eccentricity and variations in system parameters.     

粘弹性传动带的分岔特性和混沌振动分析

研究了粘弹性传动带横向振动的分岔特性和混沌动力学行为．将传动带视为沿轴向运动的抗弯刚度较 小的粘弹性梁模型,同时考虑变形的几何非线性和材料的非线性因素,运用弹性力学方法建立了其横向振动 的偏微分方程,利用 Galerkin 方法得到了时空坐标解耦的二阶非线性动力学方程,重点探讨了带速波动对系统 动态特性的影响．采用数值方法对系统的运动响应进行仿真,分岔图和 Poincaré图表明：随着平均带速和波动 幅值的变化,系统出现周期振动和混沌振动,倍周期分岔是产生混沌振动的途径．     

Entangled spin states in geodesic motion around massive body

We discuss the effect of the gravitational field of a massive body on the spin entanglement of a two-qubit system in the singlet and triplet spin states in circular geodesic motion. We study the entanglement transport using Wootters concurrence, which depends on the momentum state of the system. We describe the behavior of the concurrence as a function of the orbital radius and show that the spin entanglement is more robust against changes caused by motion in the singlet state than in the triplet state. Furthermore, for the singlet (triplet) state, momentum correlation increases (decreases) the concurrence.     

Momentum unloading excessive reaction-wheel system of a spacecraft

Wide use of electromechanical actuators in attitude control systems of spacecraft is intimately connected with improvement of these actuators using unloading methods—relieving excessive momentum. As applied to electromechanical actuators of the type of reaction wheels, the problem of unloading momentum for the case of excessive flywheel system is studied. The key feature of the work is the use of arbitrary parameters in the general solution of the undefined system of linear algebraic equations as additional control parameters. For the minimum excessive flywheel system and magnetorquers of the unloading system creating the additional external moment, control algorithms are synthesized which guarantee asymptotic stability of the zero solution to model equations describing the flywheel motion. The performance of the proposed algorithms and specific features of the process of unloading momentums of the flywheels are studied, as exemplified by the controlled motion of the spacecraft in stabilization of the regime of three-axial orbital orientation.     

弹性基和弹性关节空间机器人的自适应鲁棒抗扰控制及振动抑制

研究不确定弹性基和弹性关节空间机器人的抗扰运动控制及基座和关节弹性振动同步抑制问题.在对基座和关节弹性进行等效线性弹簧假设的基础上,建立了弹性基和弹性关节空间机器人的动力学方程,并推导了基于等效刚度思想的奇异摄动慢、快变子系统.对传统参数自适应控制律进行σ修正并与鲁棒抗扰控制相结合,对不确定参数和有界外部扰动影响下的慢变子系统提出了基座姿态和臂杆关节刚性运动轨迹跟踪的改进自适应鲁棒抗扰控制方案.使用高增益线性状态观测器对快变高阶量进行实时观测,针对快变子系统设计了基座和关节弹性振动同步抑制的改进最优控制方案.仿真示例分析,表明了所提混合控制方案在空间机器人抗扰运动控制及振动抑制上的有效性.     

Analytical development of dynamic equations of motion for a three-dimensional flexible link manipulator with revolute and prismatic joints

In this paper, a mathematical model capable of handling a three-dimensional (3D) flexible n-degree of freedom manipulator having both revolute and prismatic joints is considered. This model is used to study the longitudinal, transversal, and torsional vibration characteristics of the robot manipulator and obtain kinematic and dynamic equations of motion. The presence of prismatic joints makes the mathematical derivation complex. In this paper, for the first time, prismatic joints as well as revolute joints have been considered in the structure of a 3D flexible n-degree of freedom manipulator. The kinematic and dynamic equations of motion representing longitudinal, transversal, and torsional vibration characteristics have been solved in parametric form with no discretization. In this investigation, in order to obtain an analytical solution of the vibrational equations, a novel approach is presented using the perturbation method. By solving the equations of motion, it is shown that mode shapes of the link with prismatic joints can be modeled as the equivalent clamped beam at each time instant. As an example, this method is applied to a three degrees of freedom robot with revolute and prismatic joints. The obtained equations are solved using the perturbation method and the results are used to simulate vibrational behavior of the manipulator.