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Control laws for minimum orbital change - The satellite retrieval problem

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2001年第6期24卷 1231-1233页

作者： Cichan, T Melton, RG Spencer, DB Penn State Univ Dept Aeronaut Engn University Pk PA 16802 USA

Satellite retrieval might require expending unused propellant for safety reasons prior to the retrieval. Blended extremal controls that minimize changes in semimajor axis, eccentricity, and inclination during a single, constant-thrust burn can result in modest requirements for thrust seeing. The method is shown to produce acceptable changes in these orbital elements. The optimization program finds solutions that include very little out-of-plane thrusting.

关键词： Satellites Solid Propellants Orbital Elements Periapsis Nonlinear programming Orbital Maneuvering System sequential quadratic programming Apogee Kick Motors Trajectory Optimization Runge Kutta Integration

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Regulation about time-varying trajectories: Precision entry guidance illustrated

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1999年第6期22卷 784-790页

作者： Lu, P Iowa State Univ Dept Aerosp Engn & Engn Mech Ames IA 50011 USA

A new method for regulating nonlinear dynamic systems about time-varying reference trajectories is introduced. The control law is a closed-form approximate receding-horizon control law based on the linearized time-varying dynamics. No on-line integration or explicit gain scheduling is required for implementation. Closed-loop stability can always be achieved with such a control law. The application of this method in entry guidance for the X-33 vehicle leads to very accurately controlled flight in all the state variables in simulations, which was difficult to achieve previously. This application demonstrates the potential of this approach as a powerful guidance and trajectory control method in eases for which high precision is required.

关键词： Lyapunov Stability Theory Mach Numbers Angle of Attack Feedback Control Earth Trajectory Optimization Space Shuttle Heading Angle sequential quadratic programming Control Guidance

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Multidisciplinary Design Optimization: A Survey of Architectures

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AIAA JOURNAL 2013年第9期51卷 2049-2075页

作者： Martins, Joaquim R. R. A. Lambe, Andrew B. Univ Michigan Ann Arbor MI 48109 USA Univ Toronto Toronto ON M3H 5T6 Canada

Multidisciplinary design optimization is a field of research that studies the application of numerical optimization techniques to the design of engineering systems involving multiple disciplines or components. Since the inception of multidisciplinary design optimization, various methods (architectures) have been developed and applied to solve multidisciplinary design-optimization problems. This paper provides a survey of all the architectures that have been presented in the literature so far. All architectures are explained in detail using a unified description that includes optimization problem statements, diagrams, and detailed algorithms. The diagrams show both data and process flow through the multidisciplinary system and computational elements, which facilitate the understanding of the various architectures, and how they relate to each other. A classification of the multidisciplinary design-optimization architectures based on their problem formulations and decomposition strategies is also provided, and the benefits and drawbacks of the architectures are discussed from both theoretical and experimental perspectives. For each architecture, several applications to the solution of engineering-design problems are cited. The result is a comprehensive but straightforward introduction to multidisciplinary design optimization for nonspecialists and a reference detailing all current multidisciplinary design-optimization architectures for specialists.

关键词： MDO Numerical Optimization Lagrange Multipliers sequential quadratic programming Structural Optimization Computing Structural Analysis Aircraft Design Aerodynamic Loads sequential Linear programming

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Optimization of Unpowered Descents of Commercial Aircraft in Altitude-Dependent Winds

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JOURNAL OF AIRCRAFT 2012年第5期49卷 1460-1470页

作者： Franco, Antonio Rivas, Damian Valenzuela, Alfonso Univ Seville Dept Aerosp Engn Sch Engn Seville 41092 Spain

Unpowered descents of commercial transport aircraft are optimized in the presence of altitude-dependent winds with the objective of maximizing range. The optimal problem and an optimized constant calibrated-airspeed procedure are analyzed. The optimal problem is studied using the theory of singular optimal control. The optimal control is of the bang-singular-bang type, and the optimal trajectories are formed by a singular arc and two minimum/maximum-path-angle arcs joining the singular arc with the given initial and final points. The constant calibrated-airspeed procedure is optimized using parametric optimization theory. Results are presented for a model of a Boeing 767-300ER and for linear wind profiles. The effects of both the average wind and the wind shear on the optimal results, as well as the effects of the aircraft weight, are analyzed. The wind shear is shown to have a clear effect on the maximum range. The comparison between the two sets of results shows that the optimized constant calibrated-airspeed descent is very close to optimal. From the operational point of view, the optimum descent calibrated airspeed is defined in terms of the wind profile and the aircraft weight.

关键词： Calibrated Airspeed Wind Shear Legendre Clebsch Condition Commercial Aircraft Aircraft Altitude Terminal Manoeuvring Area sequential quadratic programming Flight Path Angle Flight Testing Drag Coefficient

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Optimal Deployment Control of Spinning Space Webs and Membranes

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2009年第5期32卷 1519-1530页

作者： Gardsback, Mattias Tibert, Gunnar Royal Inst Technol Dept Mech S-10044 Stockholm Sweden

Future solar sail and solar power satellite missions will consider using centrifugal forces for deployment and stabilization. Some of the main advantages with spin deployment are that the significant forces are in the plane of rotation, and a relatively simple control can be used and the tension in the membrane or web can be adjusted by the spin rate. Existing control strategies seem to either consume excessive energy or cause oscillations. In this study, control laws are derived from the solution to relevant optimal control problems and existing controls. The derived control laws are used in deployment simulations with both simple analytical three-degree-of-freedom models and a fully-three-dimensional finite element model. The results indicate that the derived control laws can be used to minimize the energy consumption and oscillations as for an optimal control, yet retain the simplicity of previous control laws.

关键词： Bang Bang Control Finite Element Analysis Nonlinear programming Energy Consumption Elastic Modulus Solar Power Satellite sequential quadratic programming Electric Motors Solar Sail Linear quadratic Regulator

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Design optimization of reinforced concrete structures

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COMPUTERS AND CONCRETE 2006年第5期3卷 313-334页

作者： Guerra, Andres Kiousis, Panos D. Colorado Sch Mines Div Engn Golden CO 80401 USA

A novel formulation aiming to achieve optimal design of reinforced concrete (RC) structures is presented here. Optimal sizing and reinforcing for beam and column members in multi-bay and multistory RC structures incorporates optimal stiffness correlation among all structural members and results in cost savings over typical-practice design solutions. A Nonlinear programming algorithm searches for a minimum cost solution that satisfies ACI 2005 code requirements for axial and flexural loads. Material and labor costs for forming and placing concrete and steel are incorporated as a function of member size using RS Means 2005 cost data. Successful implementation demonstrates the abilities and performance of MATLAB's (The Mathworks, Inc.) sequential quadratic programming algorithm for the design optimization of RC structures. A number of examples are presented that demonstrate the ability of this formulation to achieve optimal designs.

关键词： sequential quadratic programming cost savings reinforced concrete optimal stiffness distribution optimal member sizing RS means nonlinear programming design optimization

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Spectral algorithm for pseudospectral methods in optimal control

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2008年第3期31卷 460-471页

作者： Gong, Qi Fahroo, Fariba Ross, I. Michael Univ Texas San Antonio Dept Elect & Comp Engn San Antonio TX 78249 USA USN Postgrad Sch Dept Appl Math Monterey CA 93943 USA USN Postgrad Sch Dept Mech & Aeronaut Engn Monterey CA 93943 USA

Recent convergence results with pseudospectral methods are exploited to design a robust, multigrid, spectral algorithm for computing optimal controls. The design of the algorithm is based on using the pseudospectral differentiation matrix to locate switches, kinks, corners, and other discontinuities that are typical when solving practical optimal control problems. The concept of pseudospectral knots and Gaussian quadrature rules are used to generate a natural spectral mesh that is dense near the points of interest. Several stopping criteria are developed based on new error-estimation formulas and Jackson's theorem. The sequence is terminated when all of the convergence criteria are satisfied. Numerical examples demonstrate the key concepts proposed in the design of the spectral algorithm. Although a vast number of theoretical and algorithmic issues still remain open, this paper advances pseudospectral methods along several new directions and outlines the current theoretical pitfalls in computation and control.

关键词： Pseudospectral Knotting Method Algorithms Convergence Covector Mapping Principle Gaussian Quadrature Computing Quaternions Earth sequential quadratic programming International Space Station Earth's Magnetic Field

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Surface Mesh Movement Algorithm for Computer-Aided-Design-Based Aerodynamic Shape Optimization

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AIAA JOURNAL 2016年第2期54卷 542-556页

作者： Truong, Anh H. Zingg, David W. Haimes, Robert Univ Toronto Inst Aerosp Studies 4925 Dufferin Street Toronto ON M3H 5T6 Canada Univ Toronto JA Bombardier Fdn Chair Aerosp Flight 4925 Dufferin Street Toronto ON M3H 5T6 Canada Univ Toronto Computat Aerodynam & Environmentally Friendly Air Inst Aerosp Studies 4925 Dufferin Street Toronto ON M3H 5T6 Canada MIT 77 Massachusetts Ave Cambridge MA 02139 USA

This paper focuses on the development of a surface mesh movement algorithm suitable for computer-aided-design-based aerodynamic shape optimization. The algorithm interrogates the computer-aided-design system via the vendor-neutral application programming interface Computational Analysis programming Interface and uses the Computational Analysis programming Interface's watertight triangulation of a modified computer-aided-design geometry to guide the movement of the structured surface mesh as the geometry changes during the optimization process. A mapping procedure is introduced that not only preserves the characteristics of the original surface mesh but also guarantees that the new mesh points are on the computer-aided-design geometry. The deformed surface mesh is then smoothed in the parametric space before it is transformed back into three-dimensional space. The procedure is efficient, in that all the processing is done in the parametric space, incurring minimal computational cost. The mesh movement tool is integrated into a three-dimensional shape-optimization framework, with a linear-elasticity volume-mesh movement algorithm, a Newton-Krylov flow solver for the Euler equations, and a discrete-adjoint gradient-based optimizer. The accuracy of the computed gradients is verified through a number of examples.

关键词： Aerodynamic Shape Optimization Computer Aided Design Application programming Interface Shape Optimization Linear Elasticity Euler Equations Angle of Attack Multidisciplinary Design Optimization sequential quadratic programming Mesh Parameterization

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Optimal Control Framework for a Centralized Approach to Separation Management

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2014年第3期37卷 1033-1037页

作者： Walter, Leif Kostina, Ekaterina French German Inst St Louis F-68301 St Louis France Univ Marburg Fac Math & Comp Sci D-52425 Marburg Germany

A framework based on optimal control theory, for resolving air traffic conflict situations by providing conflict-free and optimal trajectories for all airspace users are presented. Details about numerical experiments for two different traffic scenarios were presented, as well as a discussion on a full set of traffic situations. These scenarios were designed to represent worst-case traffic situations, incorporating conflicts between multiple aircrafts. The numerical results obtained by solution of optimal control problems were compared to real-time simulations performed by human controllers who have solved the same traffic scenarios. Results show that compared to the human average, the optimal control solutions achieved better results. Results of numerical experiments also indicate that the approach must be further adapted to enable a possible application in the real world as a human controller assistance tool.

关键词： Optimal Control Airspace Bank Angle Flight Tracking ATM sequential quadratic programming Air Traffic Controller Predictive Control Method Knots Indicated Airspeed Base of Aircraft Data

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Extended Monte Carlo Simulation for Parametric Global Sensitivity Analysis and Optimization

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AIAA JOURNAL 2014年第4期52卷 867-878页

作者： Wei, Pengfei Lu, Zhenzhou Song, Jingwen Northwestern Polytech Univ Sch Aeronaut Xian 710072 Peoples R China

Estimating the functional relation between the probabilistic response of a computational model and the distribution parameters of the model inputs is especially useful for 1)assessing the contribution of the distribution parameters of model inputs to the uncertainty of model output (parametric global sensitivity analysis), and 2)identifying the optimized distribution parameters of model inputs to efficiently and cheaply reduce the uncertainty of model output (parametric optimization). In this paper, the extended MonteCarlo simulation method is developed for this purpose, which provides four benefits to the parametric global sensitivity analysis and parametric optimization problems. First, the extended MonteCarlo simulation method is able to provide an unbiased or progressive unbiased estimate for the model whose behavior is even mainly governed by high nonlinearity or interaction terms. Second, only one set of model input-output samples is needed for implementing the method;thus, the computational burden is free of input dimensionality. Third, the extended MonteCarlo simulation is a derivative-free method. Fourth, the extended MonteCarlo simulation method enables us to solve problems with dependent and non-normally distributed model inputs. Additionally, the R-indices are introduced for conquering the overparameterized problem in the optimization process. An analytical example and two engineering examples are used to demonstrate the power of the proposed methods.

关键词： Monte Carlo Simulation Sensitivity Analysis Derivative Free Method Wing Box Finite Element Modeling Computing Cumulative Distribution Function sequential quadratic programming Structural System Numerical Integration

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