基于离散化思想的吸气式冲压发动机进气道再起动控制问题研究方法

As indicated from recent flight-test accidents, the diversity of hysteresis phenomena has introduced uncertainties to the control of inlet unstart in air-breathing ramjet propulsion systems. A simple perspective on the diversity of hysteresis phenomena is classification， and the novelty of the presented studies lies in the way of how to define the mathematical problem, in which the problem is considered to be a function classification problem. The idea is created that concerns with the description of hysteresis phenomena using hysteresis functions, as well as the mapping of the infinite hysteresis functions in function space into finite discrete qualities in property space. As a result, it is found through discrete mathematics and physical equations that there are finite definite types of hysteresis phenomena in ramjet engines. The finding of this flow law attributes to the definition of function classification problem. Classification is a collection of sets which can be unambiguously defined by a property that all its members share, and it indicates the existence of similarity in control laws for different hysteresis behaviors in one type. Accordingly, the inlet restart control problem is considered to be a double-loop discrete event dynamic system control problem, aiming at avoiding the occurrence of control uncertainties in inlet restart control processes.

吸气式冲压发动机迟滞现象的多样性使得进气道不起动控制过程充满不确定性，多次飞行试验事故不断表明这种不确定性的存在。 面对发动机迟滞现象的多样性，经典研究方法是分类，本研究特别之处在于提炼出了函数分类这一数学问题。基本思路是把物理上的迟滞现象用迟滞函数来表征，然后再设法把函数空间中的无限迟滞函数映射到属性空间中的有限状态（类别）集合之中。沿此思路最终基于离散数学理论和物理方程约束证明：冲压发动机内部流动具有有限个类别可分的迟滞现象。这是基于函数分类问题所发现的发动机内部流动的一个物理规律。 分类定性表达了同类迟滞行为共有属性，也奠定了控制规律相似性基础，为分门别类实施控制创造了条件。在迟滞现象分类的基础上，同样基于离散化思想，把进气道再起动控制问题抽象为双回路离散事件动态系统控制问题。通过引入双控制回路来实施分门别类控制，从方法上解决进气道再起动控制目前所面临的不确定性问题。

吸气式冲压发动机迟滞现象的多样性使得进气道不起动控制过程充满不确定性，多次飞行试验事故不断表明这种不确定性的存在。面对发动机迟滞现象的多样性，本研究提炼出了函数分类这一数学问题。建立了基于离散数学的多稳定性系统突变行为分类方法，建立了描述吸气式发动机燃烧室-进气道相互作用分类问题的无量纲参数及层次分类准则，发现了吸气式冲压发动机燃烧室-进气道相互作用中的复杂临界现象，给出了基于离散化思想的吸气式冲压发动机进气道再起动控制方法。并初步开展了燃烧室-进气道隔离段相互作用迟滞特性和控制的地面实验研究。本项目所获得的研究结果将有助于理解燃烧室-进气道复杂的相互作用，并为地面和飞行试验的进气道再起动控制问题提供较为系统的分析方法。

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