A robust and high precision optimal explicit guidance scheme for solid motor propelled launch vehicles with thrust and drag uncertainty

A new nonlinear optimal and explicit guidance law is presented in this paper for launch vehicles propelled by solid motors. It can ensure very high terminal precision despite not having the exact knowledge of the thrust–time curve apriori. This was motivated from using it for a carrier launch vehicle in a hypersonic mission, which demands an extremely narrow terminal accuracy window for the launch vehicle for successful initiation of operation of the hypersonic vehicle. The proposed explicit guidance scheme, which computes the optimal guidance command online, ensures the required stringent final conditions with high precision at the injection point. A key feature of the proposed guidance law is an innovative extension of the recently developed model predictive static programming guidance with flexible final time. A penalty function approach is also followed to meet the input and output inequality constraints throughout the vehicle trajectory. In this paper, the guidance law has been successfully validated from nonlinear six degree-of-freedom simulation studies by designing an inner-loop autopilot as well, which enhances confidence of its usefulness significantly. In addition to excellent nominal results, the proposed guidance has been found to have good robustness for perturbed cases as well.     

Time-varying control via nominal trajectory linearization for an air-breathing hypersonic vehicle

A time-varying control law via nominal trajectory linearization for an air-breathing hypersonic vehicle (ABHV) model is applied. Feasible guidance command signal serials are generated by nonlinear dynamic inverse (NDI) method considering interactions between aerodynamic effects and propulsion systems. Multiple-time-scale continuous time-varying control, which meets the requirement with accurate, robust, and decoupled tracking of both the commanded trajectory and angular rate profiles in the presence of modeling uncertainties and external disturbances are applied. The simulations for an ABHV model with modeling uncertainties, wind gust, and measuring noises are presented to demonstrate the capacity and reliability of this proposed method.     

组合大视场星敏感器自主定轨方法

在卫星自主轨道确定中,敏感仪器和其使用方法是很关键的问题。如何利用低成本的设备实现高精度自主定轨,足一个值得研究的重要课题。该文提出了一种组合大视场星敏感器自主定轨方法,在该方法中,整个地球在敏感仪器视场范围内,且每个星敏感器能至少观测到星光穿过地球边缘周围附近的一颗恒星。这样既可利用星敏感器的高精度,又可得到观测整个地球边缘附近恒星所需要的大视场;叙述了利用组合大视场星敏感器确定地心的方法;最后运用广义号尔曼滤波算法进行了仿真。考虑到星表、敏感仪器和仪器标定精度,星光大气折射改正以及地球非球形几何改正,其定轨精度估计可达100m～150m．     

面向控制的弹性体高超声速飞行器建模与分析

针对高超声速飞行器建模中气动-推进-弹性结构之间的耦合问题, 给出飞行器综合建模方法. 利用空气动力学相关理论估算气动力、推力及弹性模态, 建立了高超声速飞行器弹性体机理模型和面向控制模型, 分析了气动加热和质量变化对飞行器弹性模态的影响及纵向气动特性. 实验结果表明, 气动加热和质量变化对弹性模态影响显著, 面向控制模型能降低模型的复杂度, 保留机理模型的耦合特性, 并为控制器设计提供模型依据.

     

Flatness-based hypersonic reentry guidance of a lifting-body vehicle

This paper deals with the design of a guidance algorithm for the hypersonic phase of a lifting-body vehicle. The guidance strategy is based on a particular kind of nonlinear dynamic inversion, the so-called flatness approach. The main advantage of this approach is that the longitudinal guidance law is in-flight self-adaptive to any feasible hypersonic trajectory and can be written in analytical form with a small set of design parameters. Therefore, the required on-board computational resources are limited, and a reduced off-line design effort is needed for the change of vehicle parameters. Moreover, the closed-loop longitudinal guidance commands are computed on-board in a coupled way without relying on an explicit deceleration profile. Consequently, the approach leads to an efficient management of the degree of freedom associated with the angle-of-attack. PID controllers are then designed based on the longitudinal flat model in order to circumvent uncertainties and parameters dispersions. The crossrange is controlled by a series of bank reversals determined by an azimuth error deadband. The robustness and performance of the proposed guidance law are assessed by performing Monte Carlo runs with various sets of dispersions.     

基于信息几何的高超声速飞行器搜索方法

由于地面雷达受视距限制无法对高超声速飞行器进行连续观测, 针对高超声速飞行器飞出雷达视距盲区后难以搜索的问题, 提出了一种基于信息几何的雷达搜索方法. 本文利用非参数概率密度估计法对高超声速飞行器的出现位置的概率密度进行估计, 并将估计的位置概率密度作为雷达搜索的引导信息; 根据引导信息确定搜索区域, 以区域覆盖率最大化作为优化目标在搜索区域内进行波位编排; 基于信息几何理论, 将搜索策略建模为统计流形, 利用KL (Kullback-Leibler)散度来度量搜索策略与引导信息之间的差异, 通过最小化KL散度获得最优搜索策略. 通过仿真实验验证了本文所提方法的有效性和可行性, 并验证了相比其他搜索方法具有较明显的优势.     

Modeling and robust decoupling control for hypersonic scramjet vehicle

In this paper, the modeling and the robust decoupling control for a generic hypersonic scramjet vehicle are studied. Firstly, the dynamics of the hypersonic vehicle are modeled by applying the Lagrangian approach, which captures the most primary characteristics such as elastic deformation, aerodynamics, aero-heating, variable mass, effect of spherical rotating earth and their inherent interactions. Then, a robust output decoupling controller is designed by using nonlinear dynamic inversion plus the desired proportional integral dynamics, and natural time-scale separation theorem between fast and slow variables. Finally, the nonlinear simulations confirm the effectiveness of the robust decoupling controller.     

Nonlinear programming control using differential aerodynamic drag for CubeSat formation flying

Because of their volume and power limitation, it is difficult for CubeSats to configure a traditional propulsion system. Atmospheric drag is one of the space environmental forces that low-orbit satellites can use to realize orbit adjustment. This paper presents an integrated control strategy to achieve the desired in-track formation through the atmospheric drag difference, which will be used on ZJUCubeSat, the next pico-satellite of Zhejiang University and one of the participants of the international QB50 project. The primary mission of the QB50 project is to explore the near-Earth thermosphere and ionosphere at the orbital height of 90–300 km. Atmospheric drag cannot be ignored and has a major impact on both attitude and orbit of the satellite at this low orbital height. We conduct aerodynamics analysis and design a multidimensional nonlinear constraint programming (MNLP) strategy to calculate different desired area–mass ratios and corresponding hold times for orbit adjustment, taking both the semimajor axis and eccentricity into account. In addition, area–mass ratio adjustment is achieved by pitch attitude maneuver without any deployable mechanism or corresponding control. Numerical simulation based on ZJUCubeSat verifies the feasibility and advantage of this design.     

一种基于零脱靶量的最优制导律设计

基于导弹和目标的三维相对运动关系,提出了一种三维非线性的最优制导律.在导弹和目标的三维相对运动方程的基础上,区别于以往的以视线角和视线角速率作为状态变量的方法,而采用以相对距离和相对速度作为状态变量的方法建立了一种新的状态方程,然后基于零脱靶量的思想,利用最优控制相关理论,设计了一种三维非线性的最优制导律.分别针对匀速运动的目标和大机动目标,用所设计的制导律和比例导引律分别进行了数学仿真,结果表明,所设计的最优制导律能有效地拦截机动目标,其性能优于比例导引律.     

基于解析控制律的太阳帆星际转移轨道控制

太阳帆航天器可依靠反射太阳光子提供动力,因此较适用于远距离的星际转移任务.针对太阳帆航天器星际转移轨道控制问题,提出一种新的解析最优控制律,通过设定混合权重对各轨道根数进行联合控制.引入改进春分点轨道根数对解析控制律进行了优化推导,并以水星探测任务为背景进行了相应的仿真分析.仿真结果表明,该控制律计算速度较快,可对各个轨道根数进行联合控制,从而得到满足工程要求的太阳帆航天器星际转移轨道.     

Optimal design of an Australian medium launch vehicle

Conceptual design of a satellite launch vehicle is a multidisciplinary task which must take into account interactions of disciplines such as propulsion, aerodynamics, structures, guidance and orbital mechanics. We discuss the initial modelling of a clean sheet design for a putative Australian medium launch vehicle capable of placing an Ariane-44L equivalent payload into geostationary transfer orbit. While the Ariane-44L vehicle design is a three and a half stage vehicle, the alternative design is for a straight three stage vehicle. The “ideal velocity” or delta-V capability of the AR44L is first derived from published data. The proposed design is then modeled using a spreadsheet. The gross lift-off weight of the vehicle is then minimised while still providing the same delta-V as Ariane. Various differences between the two vehicles are discussed. The initial design of a launch vehicle as presented here is based on a simple stack model optimised automatically using an evolutionary algorithm. The efficiency of the proposed approach and the reasons for using evolutionary algorithms is discussed along with future developments in the areas of multi-objective formulations of the design optimisation problem as well as the vehicle model from the standpoint of a number of system considerations.     

基于加幂积分方法的制导控制一体化设计

针对高超声速飞行器纵向制导控制一体化设计问题展开研究.首先建立纵向制导与控制系统一体化设计模型;然后结合非线性干扰观测器与加幂积分方法设计制导与控制一体化算法,并借助相关基础理论证明级联系统是全局有限时间稳定的.所提出的方法可以使制导与控制系统协调配合,更充分地利用飞行器控制能力.通过与反步滑模制导控制一体化设计方法进行对比仿真,验证了该方法有效且更具优势,并通过模拟外扰及参数拉偏情况下的仿真验证了所提出方法亦具备较强的鲁棒性.     

Differential evolution based 3-D guidance law for a realistic interceptor model

This paper presents a novel, soft computing based solution to a complex optimal control or dynamic optimization problem that requires the solution to be available in real-time. The complexities in this problem of optimal guidance of interceptors launched with high initial heading errors include the more involved physics of a three dimensional missile–target engagement, and those posed by the assumption of a realistic dynamic model such as time-varying missile speed, thrust, drag and mass, besides gravity, and upper bound on the lateral acceleration. The classic, pure proportional navigation law is augmented with a polynomial function of the heading error, and the values of the coefficients of the polynomial are determined using differential evolution (DE). The performance of the proposed DE enhanced guidance law is compared against the existing conventional laws in the literature, on the criteria of time and energy optimality, peak lateral acceleration demanded, terminal speed and robustness to unanticipated target maneuvers, to illustrate the superiority of the proposed law.     

Apollo lunar descent guidance

Apollo Lunar-descent Guidance transfers the Lunar Module from a near-circular orbit to touchdown, traversing 17° central angle and 15 km altitude in 11 min.A group of interactive programs in an onboard computer guide the descent, controlling altitude and the descent propulsion system throttle. A ground-based program precomputes guidance targets.This paper describes the concepts involved. Explicit and implicit guidance are discussed, guidance equations are derived, and the earlier Apollo explicit equation is shown to be an inferior special case of the later implicit equation. The paper describes interactive guidance by which the two-man crew selects a landing site in favorable terrain and directs the trajectory there. Interactive terminal-descent guidance enables the crew to control the essentially vertical descent rate in order to land in minimum time with safe contact speed. The attitude maneuver routine uses concepts that make gimbal lock inherently impossible. The throttle routine yields zero steady-state thrust-acceleration error or avoids operation within a thrust region forbidden because of hardware limitations. The ground-based program precomputes guidance targets which shape the trajectory to produce an efficient descent with adequate visibility and no transients at the final phasic interface.     

Development of guidance laws for a variable-speed missile

The most used guidance law for short-range homing missiles is proportional navigation (PN). In PN, the acceleration command is proportional to the line-of-sight (LOS) angular velocity. Indeed, if a missile and a target move on a collision course with constant speeds, the LOS rate is zero. The speed of a highly maneuverable modem missile varies considerably during flight. The performance of PN is far from being satisfactory in that case.In this article we analyze the collision course for a variable-speed missile and define a guidance law that steers the heading of the missile to the collision course. We develop guidance laws based on optimal control and differential game formulations, and note that both optimal laws coincide with the Guidance to Collision law at impact. The performance improvement of the missile using the new guidance law as compared to PN is demonstrated.Recommended by A.W. Merz     

Closed-loop magnetic control of a spin-stabilized satellite

Autonomous closed-loop magnetic control is achievable for a spinning satellite in a near magnetically polar orbit for maintaining a programmed spin rate and a spin pointing-axis normal to the orbit plane. The system requires a spin-pointing coil to generate magnetic moments parallel to the spin axis, a spin rate coil with an axis normal to the spin vector, an earth sensor, a magnetometer measuring the earth field components normal to the spin, and electronic logic and circuitry to perform timing measurements between the earth sensor pulses and detect errors in spin rate and pointing elevation angles between the spin axis and the horizontal (roll). Programmed altitude corrections to these timing measurements are required for non-circular orbits. In addition, the electronics make sequenced samples of the magnetometer signals, perform the control law logic, and command the electrical connections to energize the magnetic coils. The spin control generates magnetic torque when the field is detected in the appropriate direction to provide spin torque in the direction to correct spin rate.     

基于hp-自适应伪谱法的高超声速飞行器上升段闭环制导研究

对于高超声速飞行器的上升段而言,希望其能够在短时间内飞行较远的距离,并且达到理想的速度和高度;最重要的就是如何优化其轨迹,规避上升过程中的各种干扰因素,自主完成整个飞行任务。文章以X-33飞行器模型作为研究对象,提出一种基于hp-自适应伪谱方法的轨迹优化方法和闭环制导策略,实时修正飞行路径,使其最终以理想速度到达目标位置。通过仿真验证了该方法的可靠性。结果表明,该方法具有较高的精度,收敛时间快,为闭环制导实时性研究提供了方向。     

航天器交会对接的模型预测与反演制导控制

面向空间交会对接和停靠的任务需求,将航天器相对制导控制系统视为离散时间控制系统.利用系统状态转移模型外推预测相对运动状态偏差,在每个控制周期中推力恒定的假设下,根据轨控作用对系统状态的影响规律,采用广义逆方法反演得到交会对接制导控制序列.对时间约束下的基于空间相对运动状态转移预测与反演的相对制导控制律进行设计,讨论该方法在实际应用中的一些特点.预测与反演制导控制中的控制输出直接表示为轨控加速度,更符合工程实际情况.近圆轨道的交会对接仿真结果表明,所提出的方法能够实现精度更高、更为柔顺平滑的交会对接,在轨控速度增量和推力器输出上也具有更好的工程适用性.     

The stochastic sliding mode variable structure guidance laws based on optimal control theory

A stochastic sliding-mode variable structure guidance law involving optimal control theory is presented for the missile target intercept model, in which state noise, uncertain system parameters, target movement and measured noise are considered. This guidance law synthesizes the merits of optimal guidance law with line-of-sight rate convergence and sliding-mode guidance law with strong robustness. Through theoretic analysis, it is proved that the sliding mode hyperplane is sub-achievable in the closed loop system. The numerical results show the effectiveness of the proposed control algorithm.     

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.