基于数值微分计算的SERF原子自旋惯性测量动态仿真

基于量子调控技术的SERF原子自旋惯性测量仪表与传统惯性测量仪表相比,具有精度高、无活动部件、对加速度不敏感等优点,被公认是下一代高精度惯性测量的发展方向。分析了SERF原子自旋惯性装置Bloch微分方程组模型下磁场、激光、角速度输入对碱金属电子极化率和惰性气体核子极化率的影响。针对实验条件下原子系综Bloch微分方程组难以解析求解的问题,基于可变阶次数值微分计算,建立了相应的Simulink模型对实验条件下的原子系综进行数值求解,并分析了极化率对光场、磁场、角速度输入的瞬态响应与稳态响应。仿真结果与理论计算结果相吻合,验证了Bloch方程数值求解的可行性与准确性。该方法可得到惯性测量系统的动态响应,可用于模拟复杂输入下的SERF原子自旋惯性测量系统的输出响应。     

Performance analysis of the vectorized high order expansions method in the accurate landing problem of reusable boosters

This paper addresses the design of the terminal phase maneuver of the booster landing in the presence of initial deviations and uncertainties. The primary purpose of this study is to evaluate the effectiveness of the vectorized high order expansions method to extract commands and near-optimal trajectory, while the accurate satisfaction of the terminal conditions is of great importance. After reviewing high order expansions methods, the Vectorized High Order Expansions method is briefly discussed. Then, the solution for the booster landing problem is extracted up to the third order. To study the solution quality in the presence of uncertainties, mass, density, and gravity are assumed to be constant in extracting the 3rd order solution. The assumptions however are eliminated in the simulations, and the effectiveness of high order expansions solution is studied subjectively and numerically in the presence of initial deviations and uncertainties. After implementing simulations and considering different assumptions, it will be shown that the 3rd order solution holds a desirable quality in accurately satisfying final conditions in presence of uncertainties and initial deviations and provides far better results than the 1st order solution. Moreover, in this paper, a novel method is proposed for online updating, and the performance and effect of this modification are studied using simulations. Reviewing the results of the 3rd order solution combined with the online update strategy, it becomes clear that the implementation of the online update significantly reduces landing point errors and improves the performance of the high order method. Furthermore, the study compares the performance of this strategy with the well-known state-dependent Riccati equation method to better evaluate the effectiveness of the proposed approach.