固定鸭舵双旋弹动态稳定性分析

针对一种固定鸭舵双旋弹，研究了滚转角控制量任意时变条件下的动态稳定性问题。在弹体固定面坐标系中给出固定鸭舵双旋弹的力方程组和力矩方程组，建立了角运动状态空间模型。运用Lyapunov方法研究了固定鸭舵双旋弹的动态稳定性问题，证明可以通过求解一个Riccati形式的线性矩阵不等式来判断其动态稳定性。利用复数平方根计算方法得出稳定因子表达式，基于界实引理定义了绝对稳定H_∞范数。提出固定鸭舵双旋弹的绝对稳定性判据，包括稳定因子约束和绝对稳定H_∞范数约束,外弹道仿真结果验证了该稳定性判据的正确性。

Analysis of Dynamic Stability of Fixed Canard Dual-spin Projectile

Dynamic stability of a fixed canard dual-spin projectile under the condition of arbitrary time-varying roll angle input is investigated. Force equations and moment equations are presented in body fixed plane frame for fixed canard dual-spin projectile, and a state space model for angular motion is established. Dynamic stability is addressed by using Lyapunov method. The dynamic stability of projectile can be determined by solving a Riccati-type linear matrix inequality. The stability factor equation is derived by using complex square root calculation method, and the H_∞ norm of absolute stability is defined based on the bounded real lemma. Absolute stability criteria for fixed canard dual-spin projectile is proposed，including stability factor constraint and H_∞ norm constraint of absolute stability, and the correctness of stability criteria is validated by using exterior ballistic simulation results.