This paper proposes a novel strategy to design a suboptimal attitude tracking control law for a near-space hypersonic vehicle (NSHV) based on the Koopman operator and stable manifold theory. The nonlinear vector field of the NSHV attitude model is locally Lipschitz continuous and can be approximated by a high-dimensional linear system over a compact set. Linear and nonlinear parts of the attitude dynamics are determined based on this system. Subsequently, the stable manifold theory is applied to determine the unconstrained approximated optimal control law that is used to further consider the control input constraints of the NSHV attitude model. The suboptimality of the control law is analyzed, and the local exponential stability of the closed-loop system with input constraints is proven. Furthermore, the eigenvalues for the closed-loop nonlinear attitude error dynamics are analyzed. After the control input saturation, the nonlinear closed-loop error dynamics of the NSHV can be approximated by a high-dimensional linear system with a minimal dimension. The eigenvalues of this linear system indicate the stability and time response characteristics of the attitude error dynamics of the NSHV. The numerical simulation results demonstrate the effectiveness and suboptimality of the proposed attitude tracking control law and workflow of the eigenvalue analysis.

高超声速飞行器是结合了“空”和“天”的优势,是目前世界各军事大国积极投入研究的重要技术领域之一。但由于其飞行环境严峻,非线性特性复杂,且其内部变量存在着严重的非线性耦合,大大增加了飞行控制的难度,甚至威胁到飞行安全。因此,为提高高超声速飞行器飞行品质,研究高超声速飞行器各变量之间的耦合特性,并在此基础上设计协调控制系统应对耦合问题成为研究的热点和难点。本文立足于高超声速飞行器的动态耦合分析,设计协调控制器,为最终解决飞行器的协调一体化控制提供有价值的参考。本文的主要研究内容如下:首先,基于国内外已公开的关于高超声速飞行器的研究报告、飞行数据,建立了高超声速飞行器较完备的气动模型,动力学模型和推进系统模型。立足于飞行器的模型,定义了动态耦合分析方法,基于该分析方法研究了高超声速飞行器姿态三通道与轨迹之间的动态耦合特性、三通道变量之间的动态耦合特性、操纵舵面偏角与三通道变量之间的动态耦合特性、推进系统与三通道变量之间的动态耦合特性,结合仿真数据对系统中的主要耦合进行分析,为动态协调控制器的设计奠定基础。其次,针对高超声速飞行器姿态数学模型,利用以上提出的动态耦合分析方法,得出姿态三通道与操纵舵面偏角间的动态耦合矩阵,分析耦合的变化特点,采用分层滑模控制的思想,有针对性的设计三通道与舵面间的协调控制器,协调控制器可根据耦合的变化实时地改变控制策略,利用通道间的强耦合,有效地解决耦合对于系统的影响。然后,在实现姿态三通道协调控制的基础上,对姿态系统进行更全面的动态耦合分析,得出相应的动态耦合矩阵。按照时标分离的原则,将姿态系统分为快回路和慢回路,分别考虑两个回路的参数不确定和复合干扰,并对两个回路中的不确定进行自适应在线估计,为保证系统的动态性能,采用一种新型的终端滑模控制方法,设计了快回路和慢回路的鲁棒协调控制器,有效应对高超声速飞行器姿态系统的非线性、强耦合和不确定等问题。最后,针对高超声速飞行器纵向数学模型,利用以上提出的动态耦合分析方法,得出纵向系统中姿态、轨迹与操纵舵面偏角和油门开度的动态耦合矩阵,分析耦合的变化特点。根据轨迹系统和姿态系统中变量的变化特点,分别采用普通滑模和新型终端滑模与协调控制项结合的协调控制方法,设计纵向系统的协调控制器。实现了操纵舵面和推进系统对飞行器轨迹的高效控制。在实现纵向系统协调控制的基础上,考虑了纵向系统的参数不确定和复合干扰,并对系统中的不确定部分进行自适应在线估计,设计了纵向系统鲁棒协调控制器,并通过仿真验证了控制的有效性。

Purpose To suppress fatigue damage and ensure structural safety, this paper aims to analyze the effect of the damage accumulation on the aeroelastic model of an air-breathing hypersonic flight vehicle (AHFV). Design/methodology/approach Initially, by constructing the modified longitudinal elastic model of an AHFV, the stress condition of the fuselage is analyzed, and the model differences with the rigid body are studied. Then, a new damage dynamic model is presented to describe the damage dynamic evolution. Finally, combining the damage model and the longitudinal model of the AHFV, the key variables affecting the damage accumulation are determined. Findings It is demonstrated that the elastic deformation must be considered when analyzing the damage characteristics of the fuselage and to determine the key variables that affect the damage accumulation, which provides a more accurate reference for improving the structural reliability and lifespan of AHFVs. Originality/value The novelty of this paper comes from the application of the force and stress models for the damage evolution of the AHFV and the development of a new damage model for the entire body with the elastic dynamics of AHFVs.