Analysis of Minimum-Fuel Low-Thrust Orbit Transfer by Using Parametric Optimization with Piecewise Continuous Control Models PDF Download

Author: 陳育民
Publisher:
ISBN:
Category :
Languages : en
Pages : 194

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Author: Eugene A. Smith
Publisher:
ISBN:
Category :
Languages : en
Pages : 93

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Book Description
Minimum fuel continuous low thrust orbit transfer is an optimal control problem which requires the application of iterative numerical methods to solve the resulting two point boundary value problem. A combination gradient- neighboring extremal algorithm gives accurate results when both the initial and terminal orbits are coplanar. These results are then used to extend the problem to include out-of-plane transfers between orbits of widely varying inclination. Control histories, in terms of thrust direction, are plotted as a function of time for both coplanar and non-coplanar transfers. Steering programs for coplanar transfers are characterized by a rapid thrust reversal which is dependent on eccentricity for the time of its occurrence. In the latter case, out-of-plane thrusting is primarily a function of the inclination change between orbits. On the basis of these results, the particular numerical approach used provides an effective method for generating optimal low thrust orbital transfer guidance.

Author: Eugene A. Smith (CAPT, USAF.)
Publisher:
ISBN:
Category : Orbital transfer (Space flight)
Languages : en
Pages : 160

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Author: Peter Alexander Bidian
Publisher:
ISBN:
Category :
Languages : en
Pages : 310

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Author: Christopher Rampersad
Publisher: Library and Archives Canada = Bibliothèque et Archives Canada
ISBN: 9780612951822
Category : Artificial satellites
Languages : en
Pages : 188

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The direct approach for trajectory optimization was found to be very robust. For most problems, solutions were obtained even with poor initial guesses for the controls. The direct approach was also found to be only slightly less accurate than the indirect methods found in the literature (within 0.7%). The present study investigates minimum-time and minimum-fuel low-thrust trajectory problems via a single shooting direct method. Various Earth-based and interplanetary case studies have been examined and have yielded good agreement with similar cases in the literature. Furthermore, new near-optimal trajectory problems have been successfully solved. A multiple-orbit thrust parameterization strategy was also developed to solve near-optimal very-low-thrust Earth-based transfers. Lastly, this thesis examines the use of the high-accuracy complex-step derivative approximation method for solving low-thrust transfer problems. For certain very nonlinear transfer problems, the complex-step derivative approximation was found to increase the robustness of the single shooting direct method.

Author: Lawrence E. Halbach
Publisher:
ISBN: 9781423532118
Category :
Languages : en
Pages : 92

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This thesis studies the fuel optimal periodic reboost profile required to maintain a spacecraft experiencing drag in low-earth-orbit (LEO). Recent advances in computational optimal control theory are employed, along with a Legendre-Gauss-Lobatto Pseudospectral collocation code developed at the Naval Postgraduate School, to solve the problem. Solutions obtained by this method are compared against a previous study. Key issues were checking the optimality of the solutions by way of the necessary conditions and the behavior of the solution to changes in the thruster size. The results confirmed Jensen's findings of propellant savings of one to five percent when compared against a middle altitude Forced Keplerian Trajectory (FKT). Larger savings are predicted if compared against a finite-burn Hohmann transfer with drag. The costates estimates compared favorably against necessary conditions of Pontryagin's Minimum Principle. Analysis of the switching flinction yielded periods of thrust-modulated arcs. The optimal thrust profile appears to be a thrust- modulated burn to raise the orbit followed by an orbital decay and a terminating thrust-modulated arc. For a sufficiently low thrust-control authority, the switching structure includes a maximum thrust arc. Indirect optimization techniques to confirm these findings were unsuccessful.

Author: Zahi Bassem Tarzi
Publisher:
ISBN:
Category :
Languages : en
Pages : 119

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Low-thrust electric propulsion is increasingly being used for spacecraft missions primarily due to its high propellant efficiency. Since analytical solutions for general low-thrust transfers are not available, a simple and fast method for low-thrust trajectory optimization is of great value for preliminary mission planning. However, few low-thrust trajectory tools are appropriate for preliminary mission design studies. The method presented in this paper provides quick and accurate solutions for a wide range of transfers by using numerical orbital averaging to improve solution convergence and include orbital perturbations. Thus allowing preliminary trajectories to be obtained for transfers which involve many revolutions about the primary body. This method considers minimum fuel transfers using first order averaging to obtain the fuel optimum rates of change of the equinoctial orbital elements in terms of each other and the Lagrange multipliers. Constraints on thrust and power, as well as minimum periapsis, are implemented and the equations are averaged numerically using a Gaussian quadrature. The use of numerical averaging allows for more complex orbital perturbations to be added without great difficulty. Orbital perturbations due to solar radiation pressure, atmospheric drag, a non-spherical central body, and third body gravitational effects have been included. These perturbations have not ben considered by previous methods using analytical averaging. Thrust limitations due to shadowing have also been considered in this study. To allow for faster convergence of a wider range of problems, the solution to a transfer which minimizes the square of the thrust magnitude is used as a preliminary guess for the minimum fuel problem. Thus, this method can be quickly applied to many different types of transfers which may include various perturbations. Results from this model are shown to provide a reduction in propellant mass required over previous minimum fuel solutions. Minimum time transfers are also solved and compared to minimum fuel.

Author: James M Longuski
Publisher: Springer Science & Business Media
ISBN: 1461489458
Category : Technology & Engineering
Languages : en
Pages : 286

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Want to know not just what makes rockets go up but how to do it optimally? Optimal control theory has become such an important field in aerospace engineering that no graduate student or practicing engineer can afford to be without a working knowledge of it. This is the first book that begins from scratch to teach the reader the basic principles of the calculus of variations, develop the necessary conditions step-by-step, and introduce the elementary computational techniques of optimal control. This book, with problems and an online solution manual, provides the graduate-level reader with enough introductory knowledge so that he or she can not only read the literature and study the next level textbook but can also apply the theory to find optimal solutions in practice. No more is needed than the usual background of an undergraduate engineering, science, or mathematics program: namely calculus, differential equations, and numerical integration. Although finding optimal solutions for these problems is a complex process involving the calculus of variations, the authors carefully lay out step-by-step the most important theorems and concepts. Numerous examples are worked to demonstrate how to apply the theories to everything from classical problems (e.g., crossing a river in minimum time) to engineering problems (e.g., minimum-fuel launch of a satellite). Throughout the book use is made of the time-optimal launch of a satellite into orbit as an important case study with detailed analysis of two examples: launch from the Moon and launch from Earth. For launching into the field of optimal solutions, look no further!

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 45

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The object of this study is to derive a set of equations which predict the results of orbital maneuvers of vehicles using constant low thrust. These equations are developed by simplifying the problem to circular orbits in a two-body dynamic system. The results are presented in three parts. The first part solves for the equation of the coplanar radius change problem. The second finds the equation for the minimum fuel inclination change problem. The third part of this study puts the equations from the first two parts together to solve a minimum fuel transfer problem involving both radius and inclination changes. The solution of the minimum fuel transfer problem is not to perform the total radius change and then perform the total inclination change. Instead, the solution is to perform both radius and inclination changes on a per orbit basis.

Author: Giorgio Fasano
Publisher: Springer Science & Business Media
ISBN: 1461444691
Category : Mathematics
Languages : en
Pages : 409

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Book Description
This volume presents a selection of advanced case studies that address a substantial range of issues and challenges arising in space engineering. The contributing authors are well-recognized researchers and practitioners in space engineering and in applied optimization. The key mathematical modeling and numerical solution aspects of each application case study are presented in sufficient detail. Classic and more recent space engineering problems – including cargo accommodation and object placement, flight control of satellites, integrated design and trajectory optimization, interplanetary transfers with deep space manoeuvres, low energy transfers, magnetic cleanliness modeling, propulsion system design, sensor system placement, systems engineering, space traffic logistics, and trajectory optimization – are discussed. Novel points of view related to computational global optimization and optimal control, and to multidisciplinary design optimization are also given proper emphasis. A particular attention is paid also to scenarios expected in the context of future interplanetary explorations. Modeling and Optimization in Space Engineering will benefit researchers and practitioners working on space engineering applications. Academics, graduate and post-graduate students in the fields of aerospace and other engineering, applied mathematics, operations research and optimal control will also find the book useful, since it discusses a range of advanced model development and solution techniques and tools in the context of real-world applications and new challenges.