面向控制的仿鸽扑翼机纵向动力学建模与分析

鸽子飞行时常采用变频率和变振幅模式来操控翅膀扑动与扭转以达到高效飞行的目的。为了给研究扑翼机控制和分配算法提供通用的设计验证平台，建立包含3个控制输入自由度的仿鸽扑翼机动力学模型，并开展开闭环模型有效性验证。考虑机翼运动惯性力和力矩，基于Kane方程建立仿鸽扑翼机的纵向多刚体非线性模型。选择升降舵偏转角、机翼扑动角振幅和机翼扭转角振幅作为控制输入，定义机翼定周期扑动的操纵机制，估算面向控制模型所需的气动导数和操纵导数，建立面向控制的仿鸽扑翼机线性时变周期系统模型。基于Floquet理论对线性时变周期系统模型进行动稳定性分析，结果与开环时域仿真一致。从闭环角度对模型有效性和适应性进行验证，仿真表明，所建模型能有效反映仿鸽扑翼机时变周期动力学特性，并能支撑控制分配方法的设计研究。 

Control oriented longitudinal modeling and analysis of pigeon-like flapping-wing aircraft

Pigeon usually flaps and twists its wings by changing the frequency or the amplitude to achieve efficient flying. Inspired by this, to provide a generic design and verification platform for the study of flapping-wing aircraft control laws and control allocation algorithms, a dynamic model of a pigeon-like flapping-wing aircraft with three control inputs is established, and then validated through open-loop and closed-loop simulation. Specifically, the longitudinal multi-rigid nonlinear dynamic model of the pigeon-like flapping-wing aircraft is founded based on Kane equation with the inertial forces and moments of the wings considered. The elevator deflection, the varying amplitude of the wing flapping angle and the varying amplitude of the wing torsion angle are selected as the control inputs, and the control mechanism is then given with a fixed wing-flapping time period. The aerodynamic and control derivatives are calculated in a practical way, and the control oriented linear time-varying periodic system model of the pigeon-like flapping-wing aircraft is finally established. The dynamic stability of the linear time-varying periodic system model is then analyzed based on Floquet theory, which indicates the result obtained is consistent with the subsequent open-loop time-domain simulation results. Finally, the closed-loop simulations are performed and show that the model established in this paper can well reflect the time-varying period dynamic characteristics of the pigeon-like flapping-wing aircraft, and lays a foundation for the study of control laws and allocation algorithms on pigeon-like flapping-wing aircraft.