多自由度混合动力系统运动流状态边界切换奇异动力学分析

It is different to study the switching behavior of the motion flow for hybrid dynamical system on state boundary comparing with that for traditional system switching problems. When the motion flow comes to the state boundary, the switchability for such a flow becomes a problem. With the increase of the degrees of freedom for the hybrid dynamical system, the state space becomes more complicated such that it will be more difficult to analyze such a problem. In this project, morphing aircraft will be selected to be a typical multi-degree-of-freedom hybrid dynamical system. In order to deal with the nonlinearity, singularity and switchability problems for motion flow switching on the state boundary for morphing aircraft, the mechanism of switchability, sliding and grazing for motion flow of morphing aircraft will be studied based on switching complexity of flows. The methodology for analyzing the singular dynamic of morphing aircraft will be developed based on discrete mapping technique. The effects of system parameters, switching criteria and external excitation on the dynamic behavior and stability of periodic motions for morphing aircraft will be revealed. Then it will be extended to investigate other multi-degree-of-freedom hybrid dynamic systems, and it will give a different theoretical approach for dynamics analysis and control for multi-degree-of-freedom hybrid dynamic system switching on state boundary.

研究混合动力系统运动流状态边界的切换行为不同于关于时间的切换，其运动流在切换过程中存在是否能够切换、如何进行切换的问题。随着混合动力系统自由度的提高，增加了状态空间的复杂程度，更加大了其研究难度。本项目选取变体飞行器作为一种典型的多自由度混合动力系统，针对变体飞行器运动流在状态边界切换中存在的非线性、奇异性和可切换性问题，基于流转换复杂性理论，研究变体飞行器运动流切换、滑动和擦边机理，提出基于离散映射的变体飞行器奇异动力学分析方法，揭示系统参数、切换准则、外部载荷对变体飞行器动力学行为与稳定性的影响规律，并推广至一类多自由度混合动力系统，为状态边界切换的多自由度混合动力系统奇异动力学分析与无人控制提供一种新的理论方法。

研究混合动力系统运动流状态边界的切换行为不同于时间的切换，其运动流在切换过程中存在是否能够切换、如何进行切换的问题。随着混合动力系统自由度的提高，增加了状态空间的复杂程度，更加大了其研究难度。本项目主要研究内容包含：基于流转换的变体飞行器运动流可切换性机理、基于离散映射的变体飞行器奇异动力学分析。本项目选取变体飞行器作为一种典型的多自由度混合动力系统，定义了变体飞行器的子空间域、状态边界。基于流转换复杂性理论，给出了变体飞行器运动流切换、滑动和擦边的充分必要条件。讨论了变体飞行器运动流的八种基本映射，并给出了其数学表达式，提出了采用映射结构表达变体飞行器周期运动的方法。分析了发动机推力激励变化作用下变体飞行器出现的复杂非线性动力学规律，得出如下重要结论：.（1）变体飞行器周期运动的映射结构会随着激励频率的改变而变化；.（2）变体飞行器的气动效率和发动机推力的改变会导致变体飞行器运动流在状态边界产生滑动运动；.（3）当变体飞行器运动流在状态边界出现滑动运动时，若变体飞行器直接变换构型，会导致运动颤振的产生。.本项目提出的变体飞行器奇异动力学分析方法，可以推广至一类多自由混合动力系统，为状态边界切换的多自由度混合动力系统奇异动力学分析与无人控制提供一种新的理论方法。