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Inhaltsangabe:Abstract: This thesis presents improvements to FLOAT, a hybrid analytical/numerical algorithm for rapid generation of three dimensional, optimal launch vehicle ascent trajectories. Improvements have been made to the terminal constraints, which are now available in a more general form to allow for an optimal attachment point to the target orbit.The existing algorithm also has been extended with logic that allows for vehicles with low thrust to weight ratios in the upper stage and successful convergence of problems with path constraints for normal force and angle of attack Another major extension made to the code is the introduction of coasting arcs. Coasting arcs are implemented using a completely analytical solution for the prediction of states and costates as well as for the required sensitivity matrix. This allows for a very fast and accurate calculation even with long coasting arcs. Finally, an approach for the optimization of start and end time of coast arcs is presented.This approach was implemented and the results of a test case compare very well with results generated with OTIS for the same case. At the end, suggestions for future development are made. Inhaltsverzeichnis:Table of Contents: Summaryi Acknowledgementsii Contentsiii Nomenclaturev Figuresviii Introduction1 1.Problem description3 1.1Describing the final orbit3 1.2Coordinate frame5 1.3Dynamic system6 1.4Initial conditions7 1.5Path constraints7 1.6Performance index7 1.7Terminal constraints8 1.8Solution method8 1.9Non-dimensionalization of the variables9 2.Solving the two-point boundary value problem10 2.1Vacuumsolution10 2.1.1Simplified model equations10 2.1.2Optimal control for vacuum solution11 2.1.3Thrust integrals and closed form solution for ascent in vacuum12 2.2Atmospheric solution13 2.2.1Dynamic system and collocation variables13 2.2.2Optimality condition to solve for 1b14 2.2.3Differential equations for the costate variables16 2.3Terminal constraints16 2.3.1Attaching at perigee17 2.3.2Free attachment point17 2.4Transversality conditions18 2.4.1Final costates for attaching at perigee18 2.4.2Final costates for free attachment point19 2.4.3Equatorial orbits22 2.5Adjusting final time22 2.6Computation procedure23 2.7Numerical results24 3.Low thrust upper stages27 3.1Typical low thrust case27 3.2Problems with low thrust upper stages28 3.3Upper stage modification30 3.4Advantage of free attachment point for low thrust [...]
The objective of this research effort was to develop a real-time guidance approach for launch vehicles ascent to orbit injection. Various analytical approaches combined with a variety of model order and model complexity reduction have been investigated. Singular perturbation methods were first attempted and found to be unsatisfactory. The second approach based on regular perturbation analysis was subsequently investigated. It also fails because the aerodynamic effects (ignored in the zero order solution) are too large to be treated as perturbations. Therefore, the study demonstrates that perturbation methods alone (both regular and singular perturbations) are inadequate for use in developing a guidance algorithm for the atmospheric flight phase of a launch vehicle. During a second phase of the research effort, a hybrid analytic/numerical approach was developed and evaluated. The approach combines the numerical methods of collocation and the analytical method of regular perturbations. The concept of choosing intelligent interpolating functions is also introduced. Regular perturbation analysis allows the use of a crude representation for the collocation solution, and intelligent interpolating functions further reduce the number of elements without sacrificing the approximation accuracy. As a result, the combined method forms a powerful tool for solving real-time optimal control problems. Details of the approach are illustrated in a fourth order nonlinear example. The hybrid approach is then applied to the launch vehicle problem. The collocation solution is derived from a bilinear tangent steering law, and results in a guidance solution for the entire flight regime that includes both atmospheric and exoatmospheric flight phases. Calise, Anthony J. and Leung, Martin S. K. Unspecified Center ADVANCED LAUNCH SYSTEM (STS); ALGORITHMS; ASCENT TRAJECTORIES; INJECTION GUIDANCE; LAUNCH VEHICLES; OPTIMAL CONTROL; PERTURBATION THEORY; PROBLEM SOLVING; REAL TIME OPERATION; SPACEC...
Recent, interests in responsive launch have highlighted the need for rapid and fully automated ascent guidance planning and guidance parameter generation for launch vehicles. This dissertation aims at developing methodology and algorithms for on-demand generation of optimal launch vehicle ascent trajectories from lift-off to achieving targeting conditions outside the atmosphere. The entire ascent trajectory from lift-off to final target point is divided into two parts: atmospheric ascent portion and vacuum ascent portion. The two portions are integrated via a fixed-point iteration based on the continuity condition at the switch point between atmospheric ascent portion and vacuum ascent portion. The previous research works on closed-loop endo-atmospheric ascent guidance shows that the classical finite difference method is well suited for fast solution of the constrained optimal three-dimensional ascent problem. The exploitation of certain unique features in the integration procedure between the atmospheric portion and vacuum portion and the finite difference method, allows us to cast the atmospheric ascent problem into a nested fixed-point iteration problem. Therefore a novel Fixed-Point Iteration algorithm is presented for solving the endo-atmospheric ascent guidance problem. Several approaches are also provided for facilitating the convergence of the fixed-point iteration. The exo-atmospheric ascent portion allows an optimal coast in between the two vacuum powered stages. The optimal coast enables more efficient usage of the propellant. The Analytical Multiple-Shooting algorithm is developed to find the optimal trajectory for this portion. A generic launch vehicle model is adopted in the numerical simulation. A series of open-loop and closed-loop simulations are performed. The results verify the effectiveness, robustness and reliability of the Fixed-Point Iteration (FPI) algorithm and Analytical Multiple-Shooting (AMS) algorithm developed in this research. In comparison to Finite Difference (FD) algorithm, the Fixed-Point Iteration algorithm is more adaptive to the "cold start" case for endo-atmospheric ascent guidance. The simulations also validate the feasibility of the methodology presented in this research in rapid panning and guidance for ascent through atmosphere.
This open access book highlights the autonomous and intelligent flight control of future launch vehicles for improving flight autonomy to plan ascent and descent trajectories onboard, and autonomously handle unexpected events or failures during the flight. Since the beginning of the twenty-first century, space launch activities worldwide have grown vigorously. Meanwhile, commercial launches also account for the booming trend. Unfortunately, the risk of space launches still exists and is gradually increasing in line with the rapidly rising launch activities and commercial rockets. In the history of space launches, propulsion and control systems are the two main contributors to launch failures. With the development of information technologies, the increase of the functional density of hardware products, the application of redundant or fault-tolerant solutions, and the improvement of the testability of avionics, the launch losses caused by control systems exhibit a downward trend, and the failures induced by propulsion systems become the focus of attention. Under these failures, the autonomous planning and guidance control may save the missions. This book focuses on the latest progress of relevant projects and academic studies of autonomous guidance, especially on some advanced methods which can be potentially real-time implemented in the future control system of launch vehicles. In Chapter 1, the prospect and technical challenges are summarized by reviewing the development of launch vehicles. Chapters 2 to 4 mainly focus on the flight in the ascent phase, in which the autonomous guidance is mainly reflected in the online planning. Chapters 5 and 6 mainly discuss the powered descent guidance technologies. Finally, since aerodynamic uncertainties exert a significant impact on the performance of the ascent / landing guidance control systems, the estimation of aerodynamic parameters, which are helpful to improve flight autonomy, is discussed in Chapter 7. The book serves as a valuable reference for researchers and engineers working on launch vehicles. It is also a timely source of information for graduate students interested in the subject.
Launch ascent guidance is an area that routinely involves applications of optimization tools and optimal control theory. The vacuum ascent trajectory problem has been formulated as a two-point boundary-value problem with an interior-point state constraint and is solved with a method of direct parameter optimization. The direct method simplifies the more complicated full costate problem and an off-line trajectory optimization routine for the Ares V Cargo Launch Vehicle (CaLV) shows optimal performance as compared to trajectory simulations performed in the industry standard software, Optimal Trajectories by Implicit Simulation (OTIS). The guidance solution may also be determined through an analytic method, developed by assuming polynomial approximations for the steering profiles and flight-path angle profiles. The analytic solutions prove to be useful when applied to the Shuttle-based Powered Explicit Guidance (PEG) routine, where the results have been shown to converge to near a near optimal trajectory.
An advanced ascent guidance algorithm for rocket-powered launch vehicles is developed. The ascent guidance function is responsible for commanding attitude, throttle and setting during the powered ascent phase of flight so that the vehicle attains target cutoff conditions in a near-optimal manner while satisfying path constraints such as maximum allowed bending moment and maximum allowed axial acceleration. This algorithm cyclically solves the calculus-of-variations two-point boundary-value problem starting at vertical rise completion through orbit insertion. This is different from traditional ascent guidance algorithms which operate in an open-loop mode until the high dynamic pressure portion of the trajectory is over, at which time there is a switch to a closed loop guidance mode that operates under the assumption of negligible aerodynamic forces. The main contribution of this research is an algorithm of the predictor-corrector type wherein the state/costate system is propagated with known (navigated) initial state and guessed initial costate to predict the state/costate at engine cutoff. The initial costate guess is corrected, using a multi-dimensional Newton?s method, based on errors in the terminal state constraints and the transversality conditions. Path constraints are enforced within the propagation process. A modified multiple shooting method is shown to be a very effective numerical technique for this application. Results for a single stage to orbit launch vehicle are given. In addition, the formulation for the free final time multi-arc trajectory optimization problem is given. Results for a two-stage launch vehicle burn-coast-burn ascent to orbit in a closed-loop guidance mode are shown. An abort to landing site formulation of the algorithm and numerical results are presented. A technique for numerically treating the transversality conditions is discussed that eliminates part of the analytical and coding burden associated with optimal control theory.
Realizing a reusable launch vehicle (RLV) that is low cost with highly effective launch capability has become the "Holy Grail" within the aerospace community world-wide. Clear understanding of the vehicle's operational limitations and flight characteristics in all phases of the flight are preponderant components in developing such a launch system. This dissertation focuses on characterizing and designing the RLV optimal trajectories in order to aid in strategic decision making during mission planning in four areas: 1) nominal ascent phase, 2) abort scenarios and trajectories during ascent phase including abort-to-orbit (ATO), transoceanic-abort-landing (TAL) and return-to-launch-site (RTLS), 3) entry phase (including footprint), and 4) systems engineering aspects of such flight trajectory design. The vehicle chosen for this study is the Lockheed Martin X-33 lifting-body design that lifts off vertically with two linear aerospike rocket engines and lands horizontally. An in-depth investigation of the optimal endo-atmospheric ascent guidance parameters such as earliest abort time, engine throttle setting, number of flight phases, flight characteristics and structural design limitations will be performed and analyzed to establish a set of benchmarks for making better trade-off decisions. Parametric analysis of the entry guidance will also be investigated to allow the trajectory designer to pinpoint relevant parameters and to generate optimal constrained trajectories. Optimal ascent and entry trajectories will be generated using a direct transcription method to cast the optimal control problem as a nonlinear programming problem. The solution to the sparse nonlinear programming problem is then solved using sequential quadratic programming. Finally, guidance system hierarchy studies such as work breakdown structure, functional analysis, fault-tree analysis, and configuration management will be developed to ensure that the guidance system meets the definition of vehicle design requirements and constraints.
This book presents advanced case studies that address a range of important issues arising in space engineering. An overview of challenging operational scenarios is presented, with an in-depth exposition of related mathematical modeling, algorithmic and numerical solution aspects. The model development and optimization approaches discussed in the book can be extended also towards other application areas. The topics discussed illustrate current research trends and challenges in space engineering as summarized by the following list: • Next Generation Gravity Missions • Continuous-Thrust Trajectories by Evolutionary Neurocontrol • Nonparametric Importance Sampling for Launcher Stage Fallout • Dynamic System Control Dispatch • Optimal Launch Date of Interplanetary Missions • Optimal Topological Design • Evidence-Based Robust Optimization • Interplanetary Trajectory Design by Machine Learning • Real-Time Optimal Control • Optimal Finite Thrust Orbital Transfers • Planning and Scheduling of Multiple Satellite Missions • Trajectory Performance Analysis • Ascent Trajectory and Guidance Optimization • Small Satellite Attitude Determination and Control • Optimized Packings in Space Engineering • Time-Optimal Transfers of All-Electric GEO Satellites Researchers working on space engineering applications will find this work a valuable, practical source of information. Academics, graduate and post-graduate students working in aerospace, engineering, applied mathematics, operations research, and optimal control will find useful information regarding model development and solution techniques, in conjunction with real-world applications.