航天器有限时间自适应容错姿态控制

针对存在执行器故障、转动惯量偏差以及外部扰动等系统不确定性的航天器姿态跟踪问题,提出一种有限时间自适应容错姿态控制方法。建立基于四元数的航天器姿态动力学模型、执行器故障模型和系统不确定性模型,并将执行器故障分为乘性故障和加性故障两大类;利用滑模控制和有限时间控制理论设计有限时间姿态控制器,并通过设计自适应变量及更新方法对执行器故障以及系统不确定性引起的控制偏差上界进行估计和补偿,使姿态控制器对故障和扰动具有良好的适应性和鲁棒性。得到的新型有限时间自适应容错姿态控制器能够保证航天器在执行器故障以及系统不确定性条件下在有限时间内精确收敛到期望值。利用Lyapunov稳定性理论证明了系统的渐进稳定性和有限时间稳定性,数值仿真验证了所提出方法的可行性和有效性。     

基于四元数自适应卡尔曼滤波的快速对准算法

针对捷联惯导初始对准问题,提出了一种具有干扰抑制能力的四元数自适应卡尔曼滤波初始对准算法。通过将初始对准问题转化为Wahba姿态确定问题,直接建立四元数的滤波模型,并采用自适应卡尔曼滤波对初始时刻姿态四元数进行估计,利用姿态四元数更新求出当前姿态来实时地反映载体的姿态变化。针对直接构建量测模型导致收敛速度慢的问题,提出一种基于最优四元数估计法构造K矩阵原理的改进算法。利用三轴转台模拟不同的摇摆环境进行实验,转台实验表明了改进算法具有较快的收敛速度和良好的稳定性及精度,中等精度的惯导系统在150s至200s的对准时间内,航向角均值误差小于2'。     

基于输入成型的挠性航天器自适应姿态控制（英文）

针对快速调姿挠性航天器的姿态控制问题,提出一种基于输入成型的自适应姿态控制方法,解决俯仰、偏航、滚转三通道的控制耦合问题,抑制航天器挠性振动、提高姿态控制精度。首先,建立了考虑弹性振动、执行器故障及惯量不确定性的挠性航天器姿态动力学模型。基于欧拉轴角提出一种姿态机动参考轨迹设计方法,避免了俯仰、偏航、滚转三通道的耦合问题。通过多模输入成型方法对姿态机动参考轨迹进行修正,以抑制航天器弹性振动。采用自适应容错控制方法对修正后的参考轨迹进行跟踪,以实现挠性航天器快速姿态机动任务。数值仿真结果表明,与传统PD姿态控制方法相比,所提出的基于输入成型的挠性航天器自适应姿态控制方法可将残余弹性振动幅值和姿态控制偏差降低两个数量级,验证了该方法的有效性。     

大角度范围内欧拉角到四元数的变换（英文）

由于非合作目标的不规则运动,航天器参考系与非合作目标坐标系之间往往存在大角度变换。针对这一问题,提出一种基于牛顿插值的算法实现四元数与欧拉角的变换。与其它文献中提出的算法相比,新的欧拉角表示方法将欧拉角的变换范围扩展至(-∞,+∞)。为了验证该方法的有效性,也研究了非合作目标相对于航天器的相对姿态信息,并作为仿真实验的数据。实验结果显示,该方法能够有效实现欧拉角到四元数的变换,且转换精度能达到10~(-15)。     

欠驱动航天器姿态机动时间-能量最优控制研究

针对由动量飞轮作为执行机构的欠驱动航天器,研究以飞轮角加速度作为控制输入的航天器大角度姿态机动问题。利用四元数描述欠驱动航天器的姿态运动学模型,分别以时间最优控制、时间-能量最优控制作为目标函数进行了基于Chebyshev-Gauss(CG)伪谱法的优化设计和讨论。采用Clenshaw-Curtis积分近似得到了性能指标函数中的积分项,应用重心拉格朗日插值逼近状态变量和控制变量,将连续最优控制问题进行离散,转变为一个非线性规划(NLP)的问题,NLP问题则可应用序列二次规划方法计算。两种目标函数优化的结果均使系统从初始姿态机动到终端姿态,终端角速度也都达到了预定值,对比发现时间-能量最优结果的能耗值比时间最优的能耗值小,但其机动耗时较长。     

基于Gauss伪谱法的3D刚体摆姿态最优控制

研究Gauss伪谱法求解3D刚体摆姿态最优控制问题．针对其最优姿态控制问题,既要满足由任意位置运动到平衡位置姿态运动规划问题,又要满足系统含有动力学约束的力学模型问题,提出基于四元数来描述3D刚体摆的数学模型,建立3D刚体摆姿态的动力学和运动学方程,为了解决3D刚体摆在平衡位置处的姿态最优控制问题,设计基于Gauss伪谱算法的最优姿态开环控制器,得到了3D刚体摆的姿态最优控制轨迹,得到满足的可行解,通过仿真实验验证了其开环解在平衡位置的控制姿态最优性．     

星敏感器辅助的临近空间飞行器姿态匹配传递对准方法

为解决临近空间飞行器的精确、快速传递对准问题,提出了发射点惯性坐标系下基于星敏感器信息辅助的传递对准方案。根据星敏感器输出的不同形式的姿态信息,如利用TRIAD算法获得的姿态角信息或利用QUEST算法获得的姿态四元数信息,分别建立了基于平台失准角和基于加性四元数的非线性传递对准模型。针对非线性特性模型,采用UKF滤波算法进行了数学仿真。仿真结果表明,在2 s内,两种方案的姿态角误差均可以收敛到20"。仿真验证了两种算法的有效性,为临近空间飞行器的传递对准提供了参考。     

基于加性四元数误差方程的惯性/天文姿态组合算法

针对采用旋转四元数误差进行的组合导航误差建模中状态方程的非线性化问题,提出一种新的惯性/天文组合姿态组合算法,以姿态加性四元数误差和陀螺漂移为状态变量,推导系统线性化状态方程,并以天文导航和惯导姿态四元数之差为量测量,建立系统量测方程,然后利用卡尔曼滤波实现对该组合模式的信息融合,仿真分析表明,所设计的基于姿态四元数误差和陀螺漂移的组合模式能够有效估计系统状态误差,姿态误差0.02°左右,验证了其有效性,可避免较为复杂的非线性滤波器的使用,为工程实践提供了理论支持.     

飞轮控制航天器的自适应姿态跟踪

本文讨论飞轮控制航天器的姿态控制问题。由于航天器在运行过程中受各种复杂环境因素的影响，难以确定其动力学参数的准确值，因此姿态控制系统必须具有自适应能力，以适应不可预计的干扰和航天器自身参数的改变。文中基于滑模控制方法提出一种改进的自适应姿态控制规律，适用于有内扰动力短存在的航天器。此控制规律可在不须提供动力学参数的情况下，使飞轮控制航天器跟踪期望的姿态变化规律以实现姿态机动。利用Lyapunov直接方法证明了控制系统的渐近稳定性。对于受随机扰动力短作用的航天器姿态跟踪的时间历程进行了数值仿真，计算结果证实上述方法的有效性。     

基于对偶四元数的双星编队相对位姿测量

为了描述编队卫星中主从星的相对位置和姿态信息,提出了基于对偶四元数的编队卫星相对位姿测量算法。以双星编队飞行的位姿运动为主线,运用对偶四元数工具,充分发挥其能以最简洁的形式表示一般性刚体运动的优点,对卫星轨道和姿态进行分析并建立了对偶四元数位姿模型。同时设计类GPS测量技术来测量编队卫星的相对位置和姿态,该技术载波相位波长和伪码码元比GPS的更短,可获得更高精度的相对测量信号。由于状态方程和观测方程的非线性特征,使用UKF滤波来消除随机噪声对量测过程的干扰。实验结果表明,所设计的算法能够有效估计系统误差,卫星的位置误差和四元数误差收敛于零,验证了该算法的有效性。     

小肠内药物分布与吸收模型的解析解

Y.Miyamoto等人根据小肠的生理和解剖特点,忽略小肠的固有运动对药物分布与吸收的影响,提出了肠内药物分布与吸收的二维层流、可渗壁多孔圆管模型。他们应用数值方法进行了计算。本文给出了包括灭活作用在内的上述模型的稳态解析解。所得结果与他们的数值解是一致的。解析解揭示了模型中各生理参数之间的相互关系,刻划了药物和营养物通过肠壁吸收规律,为在体实验测定肠壁对药物和营养物的渗透和反射系数提供了理论分析基础。同时从理论上证明了一些极为重要的结论。     

Piezomagnetic and piezoelectric poling effects on mode I and II crack initiation behavior of magnetoelectroelastic materials

The ferrite and ferroelectric phase of magnetoelectroelastic (MEE) material can be selected and processed to control the macroscopic behavior of electron devices using continuum mechanics models. Once macro- and/or microdefects appear, the highly intensified magnetic and electric energy localization could alter the response significantly to change the design performance. Alignment of poling directions of piezomagnetic and piezoelectric materials can add to the complexity of the MEE material behavior to which this study will be concerned with.Appropriate balance of distortional and dilatational energy density is no longer obvious when a material possesses anisotropy and/or nonhomogeneity. An excess of the former could result in unwanted geometric change while the latter may lead to unexpected fracture initiation. Such information can be evaluated quantitatively from the stationary values of the energy density function dW/dV. The maxima and minima have been known to coincide, respectively, with possible locations of permanent shape change and crack initiation regardless of material and loading type. The direction of poling with respect to a line crack and the material microstructure described by the constitutive coefficients will be specified explicitly with reference to the applied magnetic field, electric field and mechanical stress, both normal and shear. The crack initiation load and direction could be predicted by finding the direction for which the volume change is the largest. In contrast to intuition, change in poling directions can influence the cracking behavior of MEE dramatically. This will be demonstrated by the numerical results for the BaTiO₃–CoFe₂O₄ composite having different volume fractions where BaTiO₃ and CoFe₂O₄ are, respectively, the inclusion and matrix.To be emphasized is that mode I and II crack behavior will not have the same definition as that in classical fracture mechanics where load and crack extension symmetry would coincide. A striking result is found for a mode II crack. By keeping the magnetic poling fixed, a reversal of electric poling changed the crack initiation angle from θ₀=+80° to θ₀=−80° using the line extending ahead of the crack as the reference. This effect is also sensitive to the distance from the crack tip. Displayed and discussed are results for r/a=10⁻⁴ and 10⁻¹. Because the theory of magnetoelectroelasticity used in the analysis is based on the assumption of equilibrium where the influence of material microstructure is homogenized, the local space and temporal effects must be interpreted accordingly. Among them are the maximum values of (dW/dV)_max and (dW/dV)_min which refer to as possible sites of yielding and fracture. Since time and size are homogenized, it is implicitly understood that there is more time for yielding as compared to fracture being a more sudden process. This renders a higher dW/dV in contrast to that for fracture. Put it differently, a lower dW/dV with a shorter time for release could be more detrimental.     

An analytical solution for the model of drug distribution and absorption in small intestine

According to the physiological and anatomical characteristics of small intestine, neglecting the effect of its motility on the distribution and absorption of drug and nutrient, Y. Miyamoto et al.^[1] proposed a model of two-dimensional laminar flow in a circular porous tube with permeable wall and calculated the concentration profile of drug by numerical analysis. In this paper, we give a steady state analytical solution of the above model including deactivation term. The obtained results are in agreement with the results of their numerical analysis. Moreover the analytical solution presented in this paper reveals the relation among the physiological parameters of the model and describes the basic absorption rule of drug and nutrient through the intestinal wall and hence provides a theoretical basis for determining the permeability and reflection coefficient through in situ experiments. The project supported by NSF of Shandong Province     

Impact phenomena of rotor-casing dynamical systems

Rubbing and impacting between a rotor and adjacent motion-constraining structures is a serious malfunction in rotating machinery. A shaver rotor-casing system with clearance and mass imbalance is modelled with two second-order ordinary differential equations and inelastic impact conditions. The dynamics is investigated analytically, as well as by numerical simulation. A Lyapunov exponent technique is developed to characterize the topologically different behavior as the parameters are varied. The dry friction coefficient and the eccentricity of the rotor imbalance were chosen to be the two variable parameters, the effect of which on the system dynamics is illustrated through phase plots, bifurcation diagrams, as well as Poincaré maps. The results demonstrate the existence of both rubbing and impacting behavior. Depending on values of the parameters, rubbing motion in both the clockwise and counter-clockwise directions may occur. Within the impact regime, the impact behavior could be periodic, quasi-periodic or chaotic, as confirmed by the calculation of Lyapunov exponents.     

Deterministic and Stochastic Oscillations of a Flexible Cylinder in Arrays of Static Tubes

This study concentrates on vortex-induced vibrations of one flexiblecylinder in an array of fixed tubes. To describe approximately thedynamics of this system we generalize a previously developed linearsemi-empirical model that includes memory effects. We choose a cubicdamping term to model adequately vortex-induced oscillations and weobtain thus a nonlinear integro-differential equation governing thedisplacement of the cylinder. We use a two-variable expansion to derivecriteria for the appearance of stable, periodic, nonlinear oscillations.This approach predicts the appearance of a limit cycle and gives acriterion for the stability of the oscillations. In a stochasticoscillation model we apply additive white noise to the otherwisedeterministic oscillator model. For small values of the noise intensitywe can approximately solve the Fokker–Planck equation. A comparison ofthis approximation with numerical simulations shows a satisfactorydegree of agreement.     

Bending and buckling of a class of nonlinear fiber composite rods

An investigation of the mechanics of bending and buckling is carried out for a class of nonlinear fiber composite rods composed of embedded unidirectional fibers parallel to the rod axis. The specific class of composite considered is one in which the fibers interact with the matrix through a nonlinear Needleman-type cohesive zone [Needleman, A., 1987. A continuum model for void nucleation by inclusion debonding. ASME J. Appl. Mech. 54, 525-531; Needleman, A., 1992. Micromechanical modelling of interfacial decohesion. Ultramicroscopy 40, 203-214]. The primary decohesive mechanism active in bending and buckling of these composite rods is shear slip along the fiber-matrix interfaces allowing the use of a previously developed constitutive relation for antiplane shear response [Levy, A.J., 2000b. The fiber composite with nonlinear interface—part II: antiplane shear. ASME J. Appl. Mech. 67, 733-739]. The formulation requires the specification of a potential interface force-slip law that is assumed to permit interface failure in shear.Four cases of the bending and shearing of beams (concentrated or uniform load on a cantilever or a simply supported beam) are analyzed, each of which exhibits qualitatively distinct response. For certain values of interface parameters, the beam deflection or its gradient at a fixed location can change discontinuously with load. Furthermore, for interface parameter values within a certain range, singular surfaces will exist in uniformly loaded beams where there is a non-uniform distribution of shear stress along the beam length. These singular surfaces divide the beam into regions of maximal and minimal fiber slip and propagate with a rate that varies inversely as the square of the applied load. For other parameter values, singular surfaces will not exist and fiber slip will be diffuse.For the class of nonlinear composite considered, bifurcation and imperfection buckling of pinned-pinned columns is analyzed. For bifurcation buckling, a nonlinear eigenvalue problem is derived and the solution is obtained by Galerkin's method. It is demonstrated that critical loads are influenced by the initial slope, and hence the linear portion, of the interface force-slip relation but the post-buckling response, which in some sense resembles that of plastic buckling, is affected by the entire interface constitutive relation. Imperfection buckling is analyzed in a similar manner by assuming a slight initial curvature of the rod. Sensitivity of the response to imperfection magnitude is discussed as well.     

Numerical and geometrical analysis of bifurcation and chaos for an asymmetric elastic nonlinear oscillator

An asymmetric nonlinear oscillator representative of the finite forced dynamics of a structural system with initial curvature is used as a model system to show how the combined use of numerical and geometrical analysis allows deep insight into bifurcation phenomena and chaotic behaviour in the light of the system global dynamics.Numerical techniques are used to calculate fixed points of the response and bifurcation diagrams, to identify chaotic attractors, and to obtain basins of attraction of coexisting solutions. Geometrical analysis in control-phase portraits of the invariant manifolds of the direct and inverse saddles corresponding to unstable periodic motions is performed systematically in order to understand the global attractor structure and the attractor and basin bifurcations.     

A method to compute ship exhaust plumes with waves and wind

Thermal and concentration transport models are implemented in CFDShip‐Iowa version 4.5, a semi‐coupled solver for air/water free surface flow (Int. J. Numer. Meth. Fluids 2008; 58 (6):591–624), to investigate the exhaust plume around ship superstructures. An incompressible, variable density approximation is implemented where the density can change in all governing equations due to temperature variations only. The thermal and concentration models are tested for the cases of steady and unsteady flow with thermal and solution transport in a 2D square cavity, and for a 3D thermal plume in an open environment, showing good agreement between computational results and experimental data. To test the method in an extreme motions condition, the exhaust plume of the ONR Tumblehome model DTMB 5613 is studied, showing complicated vortical structures in air including a pair of counter‐rotating vortices downstream of the stack for cross‐flow, and bended bird‐plume shape in the symmetry plane and varying arc‐shape in axial sections both for temperature and NO_x concentration fields. Effects of smoke exhaust speed and wind speed on the temperature and concentration distributions are studied. Finally, a smoke downwash computation is performed for a ship free to move in 6 degrees of freedom in a sea state 8 condition. Copyright © 2010 John Wiley & Sons, Ltd.     

Nonlinear delay difference equations for housing dynamics assuming heterogeneous backward-looking expectations

China's first interest rate hike during the last decade, aiming to cool down the seemingly overheated real estate market, had aroused more caution on housing market. This paper aims to analyze the housing price dynamics after an unanticipated economic shock, which was believed to have similar properties with the back ward- looking expectation models. The analysis of the housing price dynamics is based on the cobweb model with a simple user cost affected demand and a stock-flow supply assumption. Several nth-order delay rational difference equations are set up to illustrate the properties of housing dynamics phenomena, such as the equilibrium or oscillations, overshoot or undershoot and convergent or divergent, for a kind of heterogeneous backward-looking expectation models. The results show that demand elasticity is less than supply elasticity is not a necessary condition for the occurrence of oscillation. The housing price dynamics will vary substantially with the heterogeneous backward-looking expectation assumption and some other endogenous factors.