空-空导弹μ综合控制降阶与算法

Order Reduction and Arithmetic of Air-to-Air Missile μ-Synthesis Controller

针对新型空-空导弹中μ综合方法设计的控制器受到弹载处理器的计算能力等约束,呈现高阶、刚性、病态坏条件等问题,提出了一种收敛性更强的"隐式欧拉加外推"算法。通过对比平衡截断法和Hankel范数逼近法对控制器进行降阶优化处理,对比降阶效果进行偏差估计,分析降阶前后与降阶方法差异导致的闭环系统鲁棒性,证明Hankel范数逼近方法在降阶效果和性能保持能力方面更佳。并根据刚性特征,提出了一种"隐式欧拉加外推"算法。仿真分析和测试数据表明:该算法相对其他ODE差分格式有显著的收敛性,单步运算速度仅2 ms,满足实时性要求。

Controllers designed by μ-synthesis for the next generation air-to-air missile are constraint by the ability of the current CPU. So that these controllers have many problems, i.e. high order stiff and moreover bad condition, a new arithmetic called ＇Implicit Euler and Extrapolate＇ is put forward. Through comparison of declination bound estimation and close-loop robustness after reduction are analyzed between these two reduction means, which validates that Hankel norm approximation performs better reduction effect as well as better performance holding. Due to stiff feature, a new arithmetic called ＇Implicit Euler and Extrapolate＇ for implementing the μ-synthesis controller is introduced which also show better astringency than other arithmetic. At the same time, the running rate reach 2ms per step only, satisfying the real-time requirement.