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面向随机控制的弹性高超声速飞行器建模
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摘要
针对当前常用的吸气式高超声速飞行器模型中的弹性动态很难直接用于控制器设计,且完全忽略了随机干扰影响的问题。本文提出了弹性动态的简化模型,并据此建立面向随机控制的高超声速飞行器模型。推导过程中将广义力作为弹性系统的输入,分析了弹性力确定输入部分和随机输入部分的响应,建立简化模型来近似这些响应。简化后模型由广义力确定部分的线性函数与Ornstein-Uhlenbeck有色噪声两部分构成,大大简化了原弹性系统的同时也使得控制器的设计更加简单。基于简化后的弹性动态推导了面向随机控制的高超声速飞行器纵向动力学模型。研究结果表明原弹性动态系统与简化等效的弹性动态系统对于随机时变信号的响应是一致的。可以利用简化计算模型来代替原弹性状态二阶动力学方程,大大降低了计算的复杂程度。
The flexible dynamics of commonly used air-breathing hypersonic vehicle model is not tractable for control design and the inevitable stochastic perturbations are neglected. Aiming at these deficiencies, a reduced form flexible dynamics is deducted in this paper and a stochastic control-oriented vehicle model is established in turn. The generalized force is treated as the input of the flexible dynamics system. The responses of the system to the determinate part and the stochastic part of the generalized force are analyzed, respectively. Then the simplified flexible dynamics is deduced to approximate the responses. The reduced flexible dynamics, which greatly reduces the complexity of the former one, is comprised with a simple function of the determined generalized force and an Ornstein-Uhlenbeck colored noise, thus makes it tractable for control design. The longitudinal dynamics in parametric strict feedback form is obtained by substitute the reduced flexible dynamics into the original model. The applicability of the simplified flexible dynamics validates though the numerical simulations.
引文
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