非仿射参数依赖LPV模型的变体飞行器H∞控制

变体飞行器可以在不同的飞行环境及飞行任务下自适应地进行结构变形,从而确保飞行过程中具有最优的气动性能。以一类翼展可变的飞行器模型为对象,研究了一种针对非仿射参数依赖结构的线性变参数(LPV)系统的控制问题。在Jacobian线性化基础上,将变体过程中的非线性模型精确拟合为以翼展变形率为时变参数的LPV系统。与大多数LPV控制不同的是,此系统为多项式参数依赖结构,不具有仿射参数依赖形式。利用线性分式表示(LFR)将具有非仿射参数依赖结构的LPV模型转换为等价的线性时不变(LTI)系统。为保证变体过程的稳定,针对此LFR形式的变体模型,在满足二次Lyapunov稳定的线性矩阵不等式(LMI)条件基础上,设计了一类基于状态反馈的H∞控制器。仿真结果表明,上述控制器在外部存在干扰的情况下,能够保证变体过程的全局稳定性。因此基于LFR转换的控制器设计方法不再局限于仿射参数依赖形式,对于广泛LPV系统具有普遍适用性。

H∞ control for morphing aircraft via non-affine parameter dependent LPV model

Morphing aircraft can adaptively alter configuration according to the different flight conditions or a variety of missions to ensure the optimal aerodynamic performance in flight.A class of variable-span morphing aircraft were considered,and the controller design synthesis for linear parameter varying (LPV) systems with non-affine parameter dependent configuration was researched.Jacobian linearization approach,as well as exact fitting method,was used on multiple balance points to transform the nonlinear model of morphing process into the LPV structure which regards the ratio of variable-span as the varying parameter.In contrast to most LPV systems,the obtained structure was polynomial instead of affine parameter dependent.An equivalent linear time-invariant (LTI) system for the non-affine LPV structure can be obtained by linear fractional representation (LFR).On basis of the sufficient condition of linear matrix inequality(LMI) for quadratic Lyapunov stability,a design methodology of the state feedback H∞ controller was presented to guarantee the stability of morphing process.Its effectiveness for the globally stable performance was illustrated with simulation results,even when the external disturbance was taken into account.Therefore,the controller synthesis based on LFR transformation is no longer limited to the affine parameter dependent form,and can be widely applied to universal LPV system.