火星固体上升器最优推力条件及制导方法

doi:10.7527/S1000-6893.2022.28155

Abstract

Abstract:

The two-stage solid ascent vehicle is an important part of the large-scale Mars sample recovery program. To address the problems of the optimal thrust design and the depleted shutdown guidance with multi-constraints for solid Mars ascent vehicles in sample return missions， an analytical-numerical fusion method for optimization of the orbit entry phase is proposed， in which the analytical optimization method provides the theoretical basis for the optimal design of the solid thrust， and the numerical optimization method further solves the problem of depleted shutdown guidance faced in the actual flight in the proximity of the theoretically optimal solution. Firstly， to analyze and optimize the thrust parameters of the solid ascent vehicles under the maximum load mass， the problem of optimal control of the thrust direction is constructed based on the Pontryagin maximum principle. A new necessary condition of the optimal thrust parameters is derived to eliminate the costate multiplier vector， so that the analytical expression of the optimal control commands is obtained. Secondly， considering the parameter deviation and uncertainty interference of the ascent vehicles under actual flight conditions， a quadratic numerical optimization method combining the optimal analytical solution sequence is proposed to guide the Mars ascent vehicle to the predetermined target orbit with high accuracy in the depleted shutdown mode， which can quickly calculate the flight commands online by the efficient inverse recursive sensitivity matrix. Finally， a comparison with the GPOPS optimization method verifies the optimality and correctness of the proposed analytical expression. The optimal thrust scheme of Mars ascent vehicles is also given. The numerical simulation results demonstrate that the Mars ascent vehicle can enter the target orbit with high accuracy in the depleted shutdown mode with the interference of deviation and uncertainties by the proposed method.

Key words: Mars ascent vehicle, optimal thrust design, analytical method of optimal control, real-time numerical optimization method, depleted shutdown guidance, analytical-numerical online optimization

CLC Number:

V448

Qian ZHANG, Yuanxin YANG, Shuo TANG, Xianghang YUE, Zhi XU. Optimal thrust conditions and guidance for Mars solid ascent vehicles[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(17): 328155.

Figures/Tables 14

Fig.1

Fig.2

Table 1

Initial states of secondary glide of the SPAV and orbital elements of the target orbit in Mars-centered inertial reference frame

初始参数	数值
位置矢量 $r$ /km	［3 021.427 87.327 1 635.249］
速度矢量 $v$ /（m·s^-1）	［965.873 2 396.260 373.439］
半长轴/km	3 747
偏心率	0
轨道倾角/（°）	28.659 1
升交点赤经/（°）	263.503 2

Table 1

Table 2

Implementation logic of guidance algorithm

名称	编号	操作内容	算法输出
最优推力设计 OCP1方法	Step 1	输入二级初始状态 $r 0$ 、 $v 0$ 和 $m 0$ ，以及终端约束式（7）参数	Out 1优化设计值： $T $ 、 $t s $ Out 2最优条件： $t i g $ 、 $I b (t n)$
	Step 2	根据闭环解析式（36）计算俯仰角 $φ (r, v, θ)$
	Step 3	在每个 $t i g$ 时刻下，采用NLP求解器对非线性方程组式（37）求解
	Step 4	在时间区间［ $t 0$ ， $t a p$ ］（ $t a p$ 为过远地点时间），根据最大载荷质量输出 $t i g *$
	Step 5	计算 $t i g $ 时刻对应的，输出最优值 $T $ 、 $t s $ 以及控制指令 $I b (t n)$
耗尽关机制导 OCP2方法	Step 6	根据Y₁=0或Y₂=0由非线性方程组式（37）计算 $t i g $ ，并将姿态角调整至 $I b (t i g *)$	Out 3制导修正： $d I b$ 箭体执行： $I b = I b * + d I b$
	Step 7	根据OCP1的 $I b * (t n)$ 初始化OCP2离散系统，计算终端偏差 $Δ Y N$
	Step 8	计算离散轨迹上状态量及控制量的敏感度矩阵式（50）~式（52）
	Step 9	采用数值迭代计算方法式（53），计算最优修正指令序列 $d I b (t n)$
	Step 10	判断 $d I b (t n)$ 是否收敛，是则进入下一步，否则转入Step 8
	Step 11	判断 $t ≥ t i g * + t s *$ ，是则制导结束准备星箭分离，否则转入Step 7

Table 2

Fig.3

Fig.4

Fig.5

Table 3

Fig.6

Fig.7

Table 4

Fig.8

Table 5

Table 6

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名称	推力大小/N	工作时间/s
推力配置1	14 982.5	5.924
推力配置2	6 982.5	12.713
推力配置3	12 982.003 8	6.837

偏差参数	均值	标准差
发动机排气速度/（m·s^-1）	2 850	1%
秒流量/（kg·s^-1）	4.555 1	5%
燃料质量/kg	31.143 1	1%
推力/kN	12.982	6%
初值位置矢量/km	3 021.427	0.05%
	87.327	0.05%
	1 635.249	0.05%
初值速度矢量/（m·s^-1）	965.873	1.5%
	2 396.260	1.5%
	373.439	1.5%

统计量	均值差	标准差
半长轴/m	145.855 2	156.378 1
偏心率/10^-4	3.085 2	2.497 2
轨道倾角/（10^-5（°））	3.401 6	3.808 1
升交点赤经/（10^-3（°））	6.732 1	3.519 6

优化制导方法	离散节点数	迭代收敛耗时	迭代收敛次数
OCP2	3 000		发散
	6 837	8.2 ms	5
	11 000	14.7 ms	5
	15 000	18.6 ms	4
GPOPS	hp自适应	862 ms	11

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Optimal thrust conditions and guidance for Mars solid ascent vehicles

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