基于分数阶微积分PD^λ比例导引制导规律  

PD^λ guidance law based on fractional calculus

作　　者：王飞[1] 雷虎民[1] 

机构地区：[1]空军工程大学导弹学院,陕西三原713800

出　　处：《控制理论与应用》2010年第1期126-130,共5页Control Theory & Applications

基　　金：总装武器装备预研基金资助项目(9140A04050407JB3201);航天科技创新基金"多导弹协同作战制导研究"资助项目(CASC0209);航空基金资助项目(20090196005)

摘　　要：为了继承和发扬传统PID比例导引的优点,同时弥补其不足,本文在扩展PID比例导引制导律的基础上,提出了分数阶微积分PDλ比例导引律.首先介绍了分数阶微积分的定义、性质及其数值方法,分析了分数阶微积分PDλ比例导引制导系统的静态误差和制导灵敏度,研究了分数阶微积分PDλ比例导引律的弹道特性和控制器特性,最后结合仿真分析得出结论:PDλ控制器对其本身参数和被控对象参数的变化都不敏感,具有更强的鲁棒性,PDλ比例导引律提高了导弹制导系统的性能,提高了导弹的命中精度.To carry forward the advantages of the PID guidance law and avoid its flaws, we employ the fractional PD^λ guidance law. The elementary knowledge of fractional calculus, such as definitions, properties and numerical methods are outlined. Both the static inaccuracy and the sensitivity of the guidance system are analyzed. The performance of the control and the ballistic trajectory are studied theoretically. Numerical simulations results show that the fractional order guidance law are not sensitive to the changes of control parameters and controlled object parameters. At the same time, it has more flexible structure and stronger robustness. The fractional calculus demonstrates prospects of being a useful tool for improving the missile performance.

关 键 词：分数阶微积分 PDλ比例导引律 PID比例导引律 静态误差和制导灵敏度 

分 类 号：TJ765[兵器科学与技术—武器系统与运用工程]