Optimizing Flight Trajectories for Space Vehicles with an Additional Fuel Tank. II

We solve the optimization problem for space trajectories of spacecraft flights with an auxiliary fuel tank from a low round orbit of a man-made Earth satellite to a geotransitional orbit. Control over the spacecraft motion is performed with a jet engine of bounded thrust. To discard the auxiliary tank, one has to turn off the engine, which takes some known time. The mass of the discarded tank is assumed to be proportional to the mass of fuel spent, and the mass of the engine and additional constructions is proportional to the thrust-to-weight ratio. We minimize the value of injection impulse needed to transfer to the geostationary orbit for a given useful mass.In the second part of the paper the problem at hand is formalized as an optimal control problem for a collection of dynamical systems and is solved based on the corresponding maximum principle. In this work we solve boundary problems of the maximum principle numerically with the shooting method. As a result of solving the problem, we construct one- and two-revolution Pontryagin extremals. We perform a series of parametric computations that are used to determine optimal parameters of the spacecraft construction: the best thrust-to-weight ratio and the best distribution of fuel among the tanks.     

Optimizing flight trajectories for space vehicles with an additional fuel tank. I

We consider optimization problems for spatial trajectories of space flights for space vehicles with an additional fuel tank from a low circular orbit of a man-made Earth satellite to a geotransitional orbit. The motion of the space vehicle is controlled through a jet engine with bounded thrust. To discard the additional tank, the vehicle needs to switch off its engine and spend a certain time. The mass of the discarded tank is assumed to be proportional to the mass of the expended fuel, and the mass of the engine and additional constructions is proportional to the thrust. We minimize the value of the impulse needed to transfer to the geostationary orbit for a given useful mass, or, which is the same, maximize the useful mass for a given value of this impulse. In the first part of the paper, we consider in detail the history of this problem and computational schemes that can be used to solve this kind of problems.     

Autonomous implementation of dynamic operations in a geostationary orbit. II. Synthesis of control algorithms

This study continues the series of papers devoted to the problems of autonomous operation of spacecraft in a geostationary orbit. The solution of the problem considered here assumes the formation of a set of algorithms for control processes in a closed autonomous spacecraft control and navigation system in a geostationary orbit. The paper is aimed at the formalization and solution of the new technical task of autonomous control during the spacecraft’s ascent to the given orbital position and remaining in this position. An important requirement is to provide the safe separation of several spacecraft in one orbital position. The control problem is solved using the combined optimization method developed by us; in this method, the control vector is divided into the synthesized and the programmed components taking into account the principle of the separation of the navigation and control problem in the stochastic approach. The motion’s models proposed in the previous paper are used to develop the control algorithms for a spacecraft’s ascent to the working position in a geostationary orbit and remaining in this position. The results of the algorithms simulating the ascent and maintaining for the exactly known state vector taking into account the random spread of the initial conditions and thrust are presented.     

Nonlinear dynamics and control of space vehicles with multiple fuel slosh modes

This paper studies the modeling and control problem for planar maneuvering of space vehicles with fuel slosh dynamics. A multi-mass–spring model is considered for the characterization of the most prominent sloshing modes. The control inputs are defined by the gimbal deflection angle of a non-throttable thrust engine and a pitching moment about the center of mass of the spacecraft. The control objective, as is typical in a thrust vector control design for a liquid upper stage spacecraft during orbital maneuvers, is to control the translational velocity vector and the attitude of the spacecraft, while attenuating the sloshing modes characterizing the internal dynamics. Subsequently, a nonlinear mathematical model that reflects these specifications is derived. Finally, Lyapunov-based nonlinear feedback control laws are designed to achieve the control objective. A simulation example is included to illustrate the effectiveness of the control laws.     

Guidance in the main deceleration section during a lunar landing of a spacecraft with an integrated propulsion system

An algorithm is developed for terminal guidance during the main deceleration section of the lunar landing trajectory of a spacecraft with an integrated propulsion system, which has a main engine with variable thrust and four auxiliary nonthrottleable engines. A method of guidance adaptation to the actual motion conditions by measuring the thrust acceleration with jumps in time is proposed.     

COOPT — a software package for optimal control of large-scale differential–algebraic equation systems

This paper describes the functionality and implementation of COOPT. This software package implements a direct method with modified multiple shooting type techniques for solving optimal control problems of large-scale differential–algebraic equation (DAE) systems. The basic approach in COOPT is to divide the original time interval into multiple shooting intervals, with the DAEs solved numerically on the subintervals at each optimization iteration. Continuity constraints are imposed across the subintervals. The resulting optimization problem is solved by sparse sequential quadratic programming (SQP) methods. Partial derivative matrices needed for the optimization are generated by DAE sensitivity software. The sensitivity equations to be solved are generated via automatic differentiation.COOPT has been successfully used in solving optimal control problems arising from a wide variety of applications, such as chemical vapor deposition of superconducting thin films, spacecraft trajectory design and contingency/recovery problems, and computation of cell traction forces in tissue engineering.     

航天器任意椭圆轨道最优转移问题研究

目前航天器最优转移轨道研究中,常忽略摄动力影响,仅考虑能量最优,且采用常值推力控制量,得到的转移轨道精度低,转移时间长,非理论最优。本文考虑地球非球形摄动力J2的影响,建立时间-能量综合最优性能指标,基于变推力控制量,研究了任意椭圆轨道最优转移问题。建立高斯拉格朗日状态方程,应用Pontryagin极小值原理和共轭梯度法求解最优转移问题;研究了J2摄动力对转移轨道根数、推力加速度和最优转移轨道的影响。结果表明:J2摄动力对转移轨道根数和推力加速度都有影响,不能忽略;时间-能量综合最优转移同时考虑轨道转移时间和能量消耗,优化结果更利于工程应用;最优推力加速度不是常值,即采用常值推力控制量得到的并非理论最优转移轨道。     

优化模型在挤出吹塑工艺模拟中的运用

为减轻汽车塑料燃油箱的总质量,模拟挤出吹塑工艺中燃油箱的壁厚变化。将模拟问题分为3部分,即型坯长度优化、静态柔性变形板优化和垂直厚度分布系统优化。每个优化过程抽象为一个数学模型,在MATLAB中求解数学模型并获得最优解。优化结果与实际试验结果基本一致,产品总质量偏差小于3%,壁厚偏差小于7%,证明模拟方法合理。     

The problem of optimal control of the orientation of an orbit of a spacecraft as a deformable figure

The problem of optimal control of the orbit orientation of a spacecraft regarded as a deformable figure is studied. The problem of optimal re-orientation of an orbit is formulated as a problem of optimal control of the motion of the center of mass of a spacecraft with a movable right end of the trajectory and is solved based on the Pontryagin maximum principle. To describe the orientation of an instantaneous orbit, a new quaternion osculating element that replaces three classical angular elements of the orbit is applied. Necessary optimality conditions are obtained; several first integrals of the system of equations of the boundary-value problem of the maximum principle are found; transformations that reduce the dimension of the system of differential equations of the boundary-value problem (without their complication) are proposed; the proposed approach is analyzed, and an example of numerical solution of the problem is presented     

基于电化学原理的飞机燃油箱氧浓度机载测量技术

飞机燃油箱惰化系统属飞机燃油系统设计中重要的分系统，为了准确评估燃油箱惰化系统的功能与性能，需要根据飞机实际使用剖面和惰化系统设计特点确定适用的飞行测试方法。提出了一种基于电化学原理的飞机燃油箱氧浓度机载测量方法，用于飞行实时测量运输类飞机油箱内无油空间或惰化管路的气体氧浓度，并对飞行中的实际影响因素进行模拟分析。经过分析飞行实际环境影响因素、关键传感器匹配性以及原理样机的试验验证等工作，将燃油箱氧浓度机载测量技术转化为专用的飞机燃油箱氧浓度机载测量系统，并通过了飞行实测考验。试飞结果表明，该项技术能够实时准确测量运输类飞机各种状态下的燃油箱氧浓度，满足飞机燃油箱惰化系统的效能评估要求。     

静压力储罐自动化计量系统

本文介绍了一种新型静压力储罐自动化计量系统,给出了其中质量、液位、容积和密度的实时计量算法。文中还涉及了采用HTG系统原理的一个实际应用,通过特别设计的投入式液位传感器,解决了在役罐的自动化计量难题。     

Minimum fuel lunar trajectories for a low-thrust power-limited spacecraft

Minimum fuel trajectories from a low Earth parking orbit to a low Moon orbit are obtained for a low-thrust power-limited spacecraft with thrust acceleration levels of the order of 10^–3 G. The trajectories are found by matching an Earth spiral to a Moon spiral at some intermediate distance. Results are given for the planar case and for the three dimensional case where the Moon orbit is polar.Received his Ph.D. under Professor John V. Breakwell in 1990. Currently at Rafael, MOD, Israel.     

Optimal control of a fuel-fired auxiliary heater for an improved passenger vehicle warm-up

In order to mitigate the comfort problems during a vehicle warm-up, the vehicles propelled by high-efficiency engines are increasingly equipped with auxiliary heaters. Although the usage of an auxiliary heater improves engine efficiency during warm-up, a higher total fuel consumption results in general. In this paper, an optimal, model-based feedback control law for the optimal operation of a fuel-fired heater with respect to passenger comfort and fuel economy is derived. To this end, a control-oriented mathematical model of the system is established, calibrated, and validated. Based on this model, an optimal control problem is formulated and solved. In simulation studies, the functionality of the resulting optimal controller is demonstrated, and its superiority to the state-of-the-art control laws is assessed.     

A simulation of aircraft fuel management system

Aircrafts usually have several fuel tanks, and there are fuel transfers among these tanks along a flight. These transfers are controlled with valves, and may follow several alternative paths, since structural fuel system redundancies are provided for evident reasons. An on board program for the management and reconfiguration of the fuel system must be developed and tested. The article introduces an aircraft fuel management system simulation, which provides a platform for the study of the fuel system logic and sequencing that the on board program must implement for normal flights and for malfunction cases. The simulation environment can be easily modified and extended, for instance to consider the use of new components. A specific example is considered: an aircraft with six tanks in the wings and a tail tank. The article presents a two-layer model, the use of the model for simulation experiments, and some illustrative examples.     

飞机燃油箱无油空间氧气浓度测量系统研究和发展综述

为了降低飞机燃油箱可燃性,绝大部分民用和军用飞机都安装了油箱惰化系统,来控制油箱无油空间的氧气浓度,但却一直没有适用于机载燃油箱的氧浓度实时监测系统。根据多型机油箱惰化系统试飞经验,总结了基于电化学原理和光谱吸收原理测量系统使用中的问题。依据文献分析,认为基于荧光猝灭原理的传感器将成为下一代机载油箱氧浓度测量系统的核心,并详细介绍了荧光猝灭效应的原理、检测方法、受感部和测量系统框架的研究现状。最后,指出测量系统应该向着轻量化、智能化和高可靠性方向发展。     

基于混合算法的航天器轨道规划方法

空间在轨服务过程中,当目标航天器周围有若干小卫星环绕时,服务航天器要避开小卫星的安全范围,与目标航天器成功交会并进行在轨服务,航天器的机动轨道规划是其重要前提;在路径规划中,遗传算法应用广泛,但是求解实际问题的时间容易受到染色体基因等算子数目的影响,求解效率未得到保证;提出了一种混合遗传算法,将遗传算法全局搜索能力和模拟退火算法较强的局部搜索能力进行整合,以服务航天器机动轨道的路径安全、任务时间、燃料消耗、总路程等为约束条件,并对算子进行特殊设计,规划出最优机动轨道路径;通过场景假设和仿真实验证明,该混合遗传算法能够规划出符合约束条件的最优机动轨道路径,并且极大地提高了求解效率。     

追踪器本体坐标系下航天器姿轨一体化控制律设计

在追踪航天器本体坐标系下, 联合相对轨道动力学模型和四元素姿态动力学模型, 引入推进器配置矩阵, 建立六自由度姿态和轨道一体化模型. 该模型避免了控制输入向追踪器本体坐标系下的转换. 在此基础上, 采用输入-状态(ISS) 稳定性原理, 在干扰输入信息完全未知的情况下, 设计了非线性鲁棒一体化控制律. 该控制律实现了对椭圆轨道上目标航天器的扰动抑制和跟踪, 具有较好的鲁棒性和跟踪性. 最后, 针对运行在椭圆轨道上的目标给出仿真结果, 表明了所提出的一体化控制律的可行性和有效性.

     

An application of an analog computer to solve the two-point boundary-value problem for a fourth-order optimal control problem

The application of Pontryagin's maximum principle to trajectory optimization problems results in a two-point boundary-value problem. Computationally, this problem is solved by various digital techniques which are sometimes inconvenient and costly. An analog computer can be used to solve a large class of two-point boundary-value problems if the accuracy is acceptable. In this paper, an analog computer is used in conjunction with a human operator who has a display of the phase planes of the admissible trajectories. The human operator, having a general knowledge of the behavior of the system, adjusts control law parameters until the boundary conditions of the system are satisfied. Apparently this technique has been avoided previously due to the impression that unacceptable errors would be introduced in solving the problem. This technique was applied to a time-optimal rendezvous with bounds on rocket thrust and fuel available and demonstrated that accurate analog computer solutions are possible. Solutions of the rendezvous problem were compared with an exact solution using MIMIC.     

Two classes of extreme motion trajectories of a point with varying specific impulse

The variational problem to determine the optimal trajectories of the center of mass of a spacecraft moving in the central Newtonian field with limited power and specific momentum was considered. The extremal trajectory was shown to contain elements of zero, intermediate, and maximal power with a constant or variable specific momentum. For the circular and spiral trajectories, extremal analytical solutions were established. These elements can find use in the problems of departure and transfer to the parking orbit, as well as in the problems of orbital transfers. The problem of transfer to the given elliptical orbit was considered as an example.     

Suboptimal on Average Satellite Attitude Control in the Presence of Discrete Inaccurate Measurements

The problem of the active stabilization of the oscillations of an artificial satellite by thrusters is considered. The satellite moves in a circular orbit and oscillates around the center of mass in the plane of the orbit. Relay control is used to minimize fuel consumption. The state of the plant is not known with certainty, but it is refined by discrete inaccurate measurements. Therefore, the problem of the optimal on average control of a bundle of trajectories is investigated. The stability error is characterized by the average value of the energy integral. Taking into account the practical accuracy of executing the thruster firing and shutdown commands, the constrained minimization problem to be solved becomes discrete. The optimal control of one trajectory is used to control the bundle. This approach based on the principle of separation leads to the suboptimal control of the bundle, which, however, proves to be acceptable in practice.