多项式理论在导弹稳定性能评估中的应用

摘要

针对线性参数不确定性系统的鲁棒稳定性问题，提出一种新的分析方法，并对其在导弹自动驾驶仪鲁棒稳定性评估中的可行性进行了研究。首先给出线性参数不确定性系统在其特征多项式系数不相关情况下的鲁棒稳定性的充要条件，并通过自适应网格划分算法将此条件与鲁棒D-稳定性理论结合，得到基于多项式理论的评估算法。将算法用于导弹自动驾驶仪鲁棒稳定性评估，得到了不同攻角下导弹在全包线范围内的稳定区域。和只能在离散点进行评估的传统评估方法比较，结果表明提出的算法可以在全包线范围内连续进行评估，从而发现一些隐蔽的不稳定区域。%A new method for application to robust stability of linear systems subject to uncertain parameters and applica-bility to the robustness stability clearance problem of missile autopilot is proposed. First, the necessary and sufficient con-ditions for robust stability of linear systems subject to uncertain parameters are given for which the characteristic polyno-mial coefficients are not relevant, then the conditions are combined to robust D-stability theory through adaptive grid gen-eration algorithm, and the polynomial clearance algorithm is obtained. The algorithm is applied to missile stability clear-ance, the stability region of the whole flight envelope under different angles of attack is obtained. With respect to classical methods, where the analysis is conducted on simple discrete points, the results show that the polynomial based clearance algorithm allows the flight envelope to be investigated continuously to determine the stable regions and discover hidden unstable regions.