如何建立实际问题的数学模型

通过对一例实际问题的物理分析，结合高等数学知识，阐述建立相应数学模型的方法。     

航空发动机百年回顾

本系统回顾了航空发动机的百年发展，可供航空史研究参考。     

飞机液压系统柱塞泵热分析

随着飞机液压系统向高压化、大功率化方向发展，液压系统的发热及温升问题受到了广泛关注。柱塞泵作为液压系统中重要的能量转换装置，对液压系统的功率损失和温度有重大的影响，良好的柱塞泵的热分析对液压系统的热设计和温度控制有重要的意义。然而传统的柱塞泵热分析方法，如平均油温法、软件仿真法和热节点网络法，因不够准确、高效和简洁而不能满足现代飞机液压系统热分析和热设计的相关需求。本文针对飞机液压系统柱塞泵发热的相关问题，采用基于集总参数的热网络分析方法，建立了柱塞泵热网络模型，通过对柱塞泵不同工况下的仿真，验证了模型的有效性和准确性，为柱塞泵及液压系统的热分析提供了参考。     

Evasion guidance algorithms for air-breathing hypersonic vehicles in three-player pursuit-evasion games

In practical combat scenario, the cooperative intercept strategies are often carefully designed, and it is challenging for the hypersonic vehicles to achieve successful evasion. Based on the analysis, it can be found that if several Successive Pursuers come from the Same Direction (SPSD) and flight with a proper spacing, the evasion difficulty may increase greatly. To address this problem, we focus on the evasion guidance strategy design for the Air-breathing Hypersonic Vehicles (AHVs) under the SPSD combat scenario. In order to avoid the induced influence on the scramjet, altitude and speed of the vehicle, the lateral maneuver and evasion are employed. To guarantee the remnant maneuver ability, the concept of specified miss distance is introduced and utilized to generate the guidance command for the AHV. In the framework of constrained optimal control, the analytical expression of the evasion command is derived, and the constraints of the overload can be ensured to be never violated. In fact, by analyzing the spacing of the pursers, it can be classified whether the cooperative pursuit is formed. For the coordination-unformed multiple pursers, the evasion can be achieved lightly by the proposed strategy. If the coordination is formed, the proposed method will generate a large reverse direction maneuver, and the successful evasion can be maintained as a result. The performance of the proposed algorithms is tested in numerical simulations.     

失效航天器姿态接管的SDRE微分博弈控制

针对燃料耗尽的失效航天器姿态接管控制问题，提出多颗微卫星协同实现姿态稳定的状态相关黎卡提方程(SDRE)微分博弈控制方法。首先，将姿态接管问题转化为多颗微卫星的微分博弈问题，基于组合航天器的姿态模型和微卫星的性能指标函数建立多颗微卫星的非线性微分博弈模型，微卫星通过独立优化各自的性能指标函数得到控制策略。其次，引入状态相关系数矩阵，将非线性博弈转化为状态相关线性二次型博弈，采用SDRE方法更方便地逼近微卫星的博弈均衡策略。最终通过李雅普诺夫迭代法求解耦合状态相关黎卡提方程组得到微卫星的状态反馈控制器，实现微卫星的自主决策。数值仿真验证了多颗微卫星采用微分博弈控制方法实现姿态接管的有效性和容错性。     

Load distribution strategy for multi-lift system with helicopters based on power consumption and robust adaptive game control

It is of great significance to reasonably distribute the slung load to each helicopter while considering difference in power consumption, relative position and interaction comprehensively. Therefore, the load distribution strategy based on power consumption and robust adaptive game control is proposed in this paper. The study is on a “2-lead” multi-lift system of four tandem helicopters carrying a load cooperatively. First, based on the hierarchical control, the load distribution problem is divided into two parts: the calculation of expected cable force and the calculation of the anti-disturbance cable force. Then, aimed at minimizing the maximum equivalent power of helicopter, an optimization problem is set up to calculate the expected cable force. Specially, the agent power model is trained by BP neural network, the safe distance constraint between helicopters is set to 2.5 rotor diameters to reduce aerodynamic interference, and the helicopters with different performance can be considered by introducing the equivalent power factor into the objective function. Next, considering the difference and interaction between helicopters, the robust adaptive differential game control is proposed to calculate the anti-disturbance cable force. Particularly, to solve the coupled Hamiltonian equations, an adaptive solving method for value function is proposed, and its stability is proved in the sense of Lyapunov. The simulation results indicate that the proposed load distribution method based on power consumption is applicable to the entire flight trajectory even there are differences between helicopters. The game control can consider interaction between helicopters, can deal with different objective functions, and has strong robustness and small steady-state error. Based on the entire strategy, the cable force can be reasonably allocated so as to resist disturbance and improve the flight performance of the whole system.     

空间坐标转换技术的分析与研究(一)

系统分析了空间坐标转换的不同形式及其相互关系,运用旋转矩阵理论作了较为深入的探讨,指出了使用中应注意的问题。提出了齐次矩阵,微分算子及雅可比阵矩等有用概念,作为例子,讨论了这些概念在机器人学中的应用。     

风对探空火箭飞行弹道影响的分析

本文导出探空火箭速度方向角(俯仰角)和方位角(偏航角)满足的一组微分方程,并在一些近似假定下分析了风对探空火箭飞行弹道的影响。     

压电复合材料壁板颤振的控制

针对考虑热效应的壁板颤振问题,利用von Karman大变形应变-位移关系、气动力活塞理论和准定常热应力理论建立了埋入压电材料的复合材料板颤振的气动弹性力学模型,使用Bogner-Fox-Schmit单元推导出壁板颤振的非线性有限元方程.将该动力学方程转换到状态空间模型,给出了基于这个非线性模型的最优控制.应用Runge-Kutta方法在时域内对一个四边简支的含压电材料的复合材料壁板颤振的控制进行了仿真,数值结果证明了该方法的有效性.     

变循环发动机模态转换建模及控制规律设计方法研究

为了实现变循环发动机快速可靠的模态转换,本文发展了变循环发动机模态转换过渡态模型及控制规律设计方法。在变循环发动机动态数值仿真程序的基础上,针对模态选择阀与涵道引射器这两个模态转换过程中的关键变几何部件,建立了高精度的气流突扩局部损失模型。首次提出了可考虑模态选择阀堵塞对发动机性能影响的模态选择阀堵塞模型,消除了由于模型不精确造成的模态转换参数波动。在建立的变循环发动机数学模型的基础上,提出了基于直接推力控制技术的模态转换控制规律设计方法,考虑了变循环发动机的8个可调参数,采用差分进化算法对模态转换过程进行了优化。结果表明,本文提出的模态转换控制规律设计方法可以实现变循环发动机快速平稳的模态转换,双外涵转单外涵的参数变化规律与单外涵转双外涵的参数变化规律基本类似,推力在0.6秒就稳定在目标推力值,其余参数大多在1.4秒之后才趋于稳定。本文提出的变循环发动机模态转换控制规律设计方法还可应用于常规航空发动机的加/减速过渡态控制规律设计中。