NONLINEAR H* METHOD FOR CONTROL OF UNCERTAIN WING ROCK MOTIONS
NONLINEAR H* METHOD FOR CONTROL OF UNCERTAIN WING ROCK MOTIONS
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发表时间：
1998
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通讯作者：
S. Shue;Peng Shit;R. Agarwal;M. E. Sawan
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作者：
S. Shue;Peng Shit;R. Agarwal;M. E. Sawan
提出了一种基于非线性H_∞鲁棒控制的细长三角翼非线性摇摆运动控制方法。机翼摇摆运动的数学描述是一个非线性常微分方程的系数随迎角变化。在时域方法中，状态反馈的非线性Ha鲁棒控制问题被转化为Hamilton-Jacobi-Bellman不等式（HJBI）。假设机翼摇摆运动非线性方程中的系数满足范数有界的非线性准则，HJBI可以写成矩阵形式。状态向量被表示为一系列闭环李雅普诺夫函数（CLLF），其结果在减少HJBI代数Riccati不等式沿着与其他几个代数不等式。这些不等式可以在HJB方程的状态向量的级数表示中逐次求解到期望的幂。将非线性H_n状态反馈控制的结果与线性H_n状态反馈控制的结果进行了比较，指出了对非线性动力学采用非线性反馈控制的必要性。L引言在大迎角下，细长三角翼的流场的特征是从其强前缘发出的强有组织的涡流。从前缘发出的涡面滚成一对涡。随着迎角的增加，这些涡流相互作用，
Control of nonlinear wing rock motion of slender delta wings using nonlinear H^ robust method is presented in this paper. The wing rock motion is mathematically described by a nonlinear ordinary differential equation with coefficients varying with angle of attack. In the time domain approach, the nonlinear Ha robust control problem with state feedback is cast in terms of a Hamilton-Jacobi-Bellman inequality (HJBI). Assuming that the coefficients in nonlinear equation of wing rock motion satisfy a norm bounded nonlinear criterion, the HJBI can be written in a matrix form. The state vector is represented as a series of closed loop Lyapunov functions (CLLF) which result in reducing the HJBI to an algebraic Riccati inequality along with several other algebraic inequalities. These inequalities can be successively solved to a desired power in the series representation of the state vector in the HJB equation. The results of the nonlinear H^ state feedback control are compared with these obtained with the linear H „ state feedback control indicating the necessity of employing nonlinear feedback control for nonlinear dynamics. L INTRODUCTION At high angle of attack, flowfield of a slender delta wing is characterized by a strongly organized vortical flow emanating from its strong leading edges. The vortex sheets emanating from the leading edges roll into a pair of vortices. As the angle of attack increases, these vortices interact with each other and