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At least 667 records · Page 37

Trajectory optimization and guidance law development for national aerospace plane applications

The problem of onboard trajectory optimization for an airbreathing, single-stage-to-orbit vehicle is examined. A simple model representative of the aerospace plane concept, including a dual-mode propulsion system composed of scramjet and rocket engines, is presented. Consideration is restricted to hypersonic flight within the atmosphere. An energy state approximation is used in a four-state model for flight of a point mass in a vertical plane. Trajectory constraints, including those of dynamic pressure and aerodynamic heating, are initially ignored. Singular perturbation methods are applied in solving the optimal control problem of minimum fuel climb. The resulting reduced solution for the energy state dynamics provides an optimal altitude profile dependent on energy level and control for rocket thrust. A boundary-layer analysis produces an approximate lift control solution in feedback form and accounts for altitude and flight path angle dynamics. The reduced solution optimal climb path is presented for the unconstrained case and the case for which a maximum dynamic pressure constraint is enforced.

Calise, A. J.↗

Experiences with serial and parallel algorithms for channel routing using simulated annealing

Two algorithms for channel routing using simulated annealing are presented. Simulated annealing is an optimization methodology which allows the solution process to back up out of local minima that may be encountered by inappropriate selections. By properly controlling the annealing process, it is very likely that the optimal solution to an NP-complete problem such as channel routing may be found. The algorithm presented proposes very relaxed restrictions on the types of allowable transformations, including overlapping nets. By freeing that restriction and controlling overlap situations with an appropriate cost function, the algorithm becomes very flexible and can be applied to many extensions of channel routing. The selection of the transformation utilizes a number of heuristics, still retaining the pseudorandom nature of simulated annealing. The algorithm was implemented as a serial program for a workstation, and a parallel program designed for a hypercube computer. The details of the serial implementation are presented, including many of the heuristics used and some of the resulting solutions.

Brouwer, Randall Jay↗

H(infinity) and H2 optimal controllers for periodic and multi-rate systems

The solutions to the optimal l2 to l2 disturbance rejection problem H(infinity) as well as to the LQG (linear quadratic Gaussian) H2 problem in periodic systems using the lifting technique are presented. Both problems involve a causality condition on the optimal LTI (linear time invariant) compensator when viewed in the lifted domain. The H(infinity) problem is solved using the Nehari's theorem, whereas in the H2 problem the solution is obtained using the projection theorem in Hilbert spaces. The authors demonstrate that exactly the same method of solution to the H(infinity) and H2 problems in periodic systems applies when considering the same problems in multirate sampled data systems.

Voulgaris, Petros G.↗

Generalized gradient algorithm for trajectory optimization

The generalized gradient algorithm presented and verified as a basis for the solution of trajectory optimization problems improves the performance index while reducing path equality constraints, and terminal equality constraints. The algorithm is conveniently divided into two phases, of which the first, 'feasibility' phase yields a solution satisfying both path and terminal constraints, while the second, 'optimization' phase uses the results of the first phase as initial guesses.

Zhao, Yiyuan↗

Further discrete variable results for a panel flutter optimization problem

Numerical solutions are presented for the problem of minimum weight design of a thin one-dimensional, simply supported, solid panel in compression, with one side exposed to a parallel high supersonic air flow. The flutter speed is held fixed and a minimum thickness constraint is imposed.

Pierson, B. L.↗

Structural optimization with aeroelastic constraints of rotor blades with straight and swept tips

This paper describes a study in which structural optimization techniques are used to minimize the n/rev vertical hub shears in forward flight, subject to aeroelastic stability constraints and frequency placement constraints. A special technique is used to build a sequence of approximate, inexpensive to solve optimization problems, the solutions of which converge to the solution of the exact, expensive to solve optimization problem. Blade configurations with both straight and swept tips, and single- and double-cell cross sections are analyzed. The results show that the approach used in this study is very efficient, and produces improved designs with a very small number of blade aeroelastic analyses.

Celi, R.↗

Update on HCDstruct - A Tool for Hybrid Wing Body Conceptual Design and Structural Optimization

HCDstruct is a Matlab® based software tool to rapidly build a finite element model for structural optimization of hybrid wing body (HWB) aircraft at the conceptual design level. The tool uses outputs from a Flight Optimization System (FLOPS) performance analysis together with a conceptual outer mold line of the vehicle, e.g. created by Vehicle Sketch Pad (VSP), to generate a set of MSC Nastran® bulk data files. These files can readily be used to perform a structural optimization and weight estimation using Nastran’s® Solution 200 multidisciplinary optimization solver. Initially developed at NASA Langley Research Center to perform increased fidelity conceptual level HWB centerbody structural analyses, HCDstruct has grown into a complete HWB structural sizing and weight estimation tool, including a fully flexible aeroelastic loads analysis. Recent upgrades to the tool include the expansion to a full wing tip-to-wing tip model for asymmetric analyses like engine out conditions and dynamic overswings, as well as a fully actuated trailing edge, featuring up to 15 independently actuated control surfaces and twin tails. Several example applications of the HCDstruct tool are presented.

Gern, Frank H.↗

Combined structures-controls optimization of lattice trusses

The role that distributed parameter model can play in CSI is demonstrated, in particular in combined structures controls optimization problems of importance in preliminary design. Closed form solutions can be obtained for performance criteria such as rms attitude error, making possible analytical solutions of the optimization problem. This is in contrast to the need for numerical computer solution involving the inversion of large matrices in traditional finite element model (FEM) use. Another advantage of the analytic solution is that it can provide much needed insight into phenomena that can otherwise be obscured or difficult to discern from numerical computer results. As a compromise in level of complexity between a toy lab model and a real space structure, the lattice truss used in the EPS (Earth Pointing Satellite) was chosen. The optimization problem chosen is a generic one: of minimizing the structure mass subject to a specified stability margin and to a specified upper bond on the rms attitude error, using a co-located controller and sensors. Standard FEM treating each bar as a truss element is used, while the continuum model is anisotropic Timoshenko beam model. Performance criteria are derived for each model, except that for the distributed parameter model, explicit closed form solutions was obtained. Numerical results obtained by the two model show complete agreement.

Balakrishnan, A. V.↗

Minimum deltaV Burn Planning for the International Space Station Using a Hybrid Optimization Technique, Level 1

The International Space Station's (ISS) trajectory is coordinated and executed by the Trajectory Operations and Planning (TOPO) group at NASA's Johnson Space Center. TOPO group personnel routinely generate look-ahead trajectories for the ISS that incorporate translation burns needed to maintain its orbit over the next three to twelve months. The burns are modeled as in-plane, horizontal burns, and must meet operational trajectory constraints imposed by both NASA and the Russian Space Agency. In generating these trajectories, TOPO personnel must determine the number of burns to model, each burn's Time of Ignition (TIG), and magnitude (i.e. deltaV) that meet these constraints. The current process for targeting these burns is manually intensive, and does not take advantage of more modern techniques that can reduce the workload needed to find feasible burn solutions, i.e. solutions that simply meet the constraints, or provide optimal burn solutions that minimize the total DeltaV while simultaneously meeting the constraints. A two-level, hybrid optimization technique is proposed to find both feasible and globally optimal burn solutions for ISS trajectory planning. For optimal solutions, the technique breaks the optimization problem into two distinct sub-problems, one for choosing the optimal number of burns and each burn's optimal TIG, and the other for computing the minimum total deltaV burn solution that satisfies the trajectory constraints. Each of the two aforementioned levels uses a different optimization algorithm to solve one of the sub-problems, giving rise to a hybrid technique. Level 2, or the outer level, uses a genetic algorithm to select the number of burns and each burn's TIG. Level 1, or the inner level, uses the burn TIGs from Level 2 in a sequential quadratic programming (SQP) algorithm to compute a minimum total deltaV burn solution subject to the trajectory constraints. The total deltaV from Level 1 is then used as a fitness function by the genetic algorithm in Level 2 to select the number of burns and their TIGs for the next generation. In this manner, the two levels solve their respective sub-problems separately but collaboratively until a burn solution is found that globally minimizes the deltaV across the entire trajectory. Feasible solutions can also be found by simply using the SQP algorithm in Level 1 with a zero cost function. This paper discusses the formulation of the Level 1 sub-problem and the development of a prototype software tool to solve it. The Level 2 sub-problem will be discussed in a future work. Following the Level 1 formulation and solution, several look-ahead trajectory examples for the ISS are explored. In each case, the burn targeting results using the current process are compared against a feasible solution found using Level 1 in the proposed technique. Level 1 is then used to find a minimum deltaV solution given the fixed number of burns and burn TIGs. The optimal solution is compared with the previously found feasible solution to determine the deltaV (and therefore propellant) savings. The proposed technique seeks to both improve the current process for targeting ISS burns, and to add the capability to optimize ISS burns in a novel fashion. The optimal solutions found using this technique can potentially save hundreds of kilograms of propellant over the course of the ISS mission compared to feasible solutions alone. While the software tool being developed to implement this technique is specific to ISS, the concept is extensible to other long-duration, central-body orbiting missions that must perform orbit maintenance burns to meet operational trajectory constraints.

Brown, Aaron J.↗

Optimal discrete-time dynamic output-feedback design - A w-domain approach

An alternative method for optimal digital control design is described in this paper. The method is based on the usage of the w-transform and has many attractive design features. One of these is its immediate connection with frequency loop-shaping techniques that are now popular and effective for multivariable control synthesis in continuous-time domain. Furthermore, any design algorithms originally developed for continuous-time systems can now be immediately extended to the discrete-time domain. The main results presented in this paper are the exact problem formulation and solution of an optimal discrete-time dynamic output-feedback design in the w-domain involving a quadratic performance index to random disturbances. In addition, necessary conditions for optimality are obtained for the numerical solution of the optimal output-feedback compensator design. A numerical example is presented illustrating its application to the design of a low-order dynamic compensator in a stability augmentation system of a commercial transport.

Ha, Cheolkeun↗

Initial Results of an MDO Method Evaluation Study

The NASA Langley MDO method evaluation study seeks to arrive at a set of guidelines for using promising MDO methods by accumulating and analyzing computational data for such methods. The data are collected by conducting a series of re- producible experiments. In the first phase of the study, three MDO methods were implemented in the SIGHT: framework and used to solve a set of ten relatively simple problems. In this paper, we comment on the general considerations for conducting method evaluation studies and report some initial results obtained to date. In particular, although the results are not conclusive because of the small initial test set, other formulations, optimality conditions, and sensitivity of solutions to various perturbations. Optimization algorithms are used to solve a particular MDO formulation. It is then appropriate to speak of local convergence rates and of global convergence properties of an optimization algorithm applied to a specific formulation. An analogous distinction exists in the field of partial differential equations. On the one hand, equations are analyzed in terms of regularity, well-posedness, and the existence and unique- ness of solutions. On the other, one considers numerous algorithms for solving differential equations. The area of MDO methods studies MDO formulations combined with optimization algorithms, although at times the distinction is blurred. It is important to

Alexandrov, Natalia M.↗

Multiobjective Optimization of Low-Energy Trajectories Using Optimal Control on Dynamical Channels

We introduce a computational method to design efficient low-energy trajectories by extracting initial solutions from dynamical channels formed by invariant manifolds, and improving these solutions through variational optimal control. We consider trajectories connecting two unstable periodic orbits in the circular restricted 3-body problem (CR3BP). Our method leverages dynamical channels to generate a range of solutions, and approximates the areto front for impulse and time of flight through a multiobjective optimization of these solutions based on primer vector theory. We demonstrate the application of our method to a libration orbit transfer in the Earth-Moon system.

trajectory design↗

Optimal aeroassisted guidance using Loh's term approximations

This paper presents three guidance algorithms for aerocapture and/or aeroassisted orbital transfer with plane change. All three algorithms are based on the approximate solution of an optimal control problem at each guidance update. The chief assumption is that Loh's term may be modeled as a function of the independent variable only. The first two algorithms maximize exit speed for fixed exit altitude, flight path angle and heading angle. The third minimizes, in one sense, the control effort for fixed exit altitude, flight path angle, heading angle and speed. Results are presented which indicate the near optimality of the solutions generated by the first two algorithms. Results are also presented which indicate the performance of the third algorithm in a simulation with unmodeled atmospheric density disturbances.

Mceneaney, W. M.↗

Optimal design of a passive vibration absorber for a truss beam

The selection of the design parameters of passive vibration absorbers attached to a long cantilevered beam is studied. This study was motivated by the need for conducting parametric analysis of dynamics and control for Space-Shuttle-attached long beams. An optimization scheme using a quadratic cost function is introduced yielding the optimal sizing of the tip vibration absorber. Analytical solutions for an optimal absorber are presented for the case of one beam vibrational mode coupled with the absorber dynamics, and results are extended to cover the multiple mode case. An algorithm is developed to make an initial estimate of optimal tuning parameters which minimize the quadratic error cost function. Examples are given to illustrate the design concept.

Juang, J.-N.↗

Large-scale structural optimization

Problems encountered by aerospace designers in attempting to optimize whole aircraft are discussed, along with possible solutions. Large scale optimization, as opposed to component-by-component optimization, is hindered by computational costs, software inflexibility, concentration on a single, rather than trade-off, design methodology and the incompatibility of large-scale optimization with single program, single computer methods. The software problem can be approached by placing the full analysis outside of the optimization loop. Full analysis is then performed only periodically. Problem-dependent software can be removed from the generic code using a systems programming technique, and then embody the definitions of design variables, objective function and design constraints. Trade-off algorithms can be used at the design points to obtain quantitative answers. Finally, decomposing the large-scale problem into independent subproblems allows systematic optimization of the problems by an organization of people and machines.

Sobieszczanski-Sobieski, J.↗

Application of Artificial Neural Networks to the Design of Turbomachinery Airfoils

Artificial neural networks are widely used in engineering applications, such as control, pattern recognition, plant modeling and condition monitoring to name just a few. In this seminar we will explore the possibility of applying neural networks to aerodynamic design, in particular, the design of turbomachinery airfoils. The principle idea behind this effort is to represent the design space using a neural network (within some parameter limits), and then to employ an optimization procedure to search this space for a solution that exhibits optimal performance characteristics. Results obtained for design problems in two spatial dimensions will be presented.

Rai, Man Mohan↗

Post-Optimality Analysis In Aerospace Vehicle Design

This analysis pertains to the applicability of optimal sensitivity information to aerospace vehicle design. An optimal sensitivity (or post-optimality) analysis refers to computations performed once the initial optimization problem is solved. These computations may be used to characterize the design space about the present solution and infer changes in this solution as a result of constraint or parameter variations, without reoptimizing the entire system. The present analysis demonstrates that post-optimality information generated through first-order computations can be used to accurately predict the effect of constraint and parameter perturbations on the optimal solution. This assessment is based on the solution of an aircraft design problem in which the post-optimality estimates are shown to be within a few percent of the true solution over the practical range of constraint and parameter variations. Through solution of a reusable, single-stage-to-orbit, launch vehicle design problem, this optimal sensitivity information is also shown to improve the efficiency of the design process, For a hierarchically decomposed problem, this computational efficiency is realized by estimating the main-problem objective gradient through optimal sep&ivity calculations, By reducing the need for finite differentiation of a re-optimized subproblem, a significant decrease in the number of objective function evaluations required to reach the optimal solution is obtained.

Braun, Robert D.↗