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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5

Aeroassisted orbital maneuvering using Lyapunov optimal feedback control

A Liapunov optimal feedback controller incorporating a preferred direction of motion at each state of the system which is opposite to the gradient of a specified descent function is developed for aeroassisted orbital transfer from high-earth orbit to LEO. The performances of the Liapunov controller and a calculus-of-variations open-loop minimum-fuel controller, both of which are based on the 1962 U.S. Standard Atmosphere, are simulated using both the 1962 U.S. Standard Atmosphere and an atmosphere corresponding to the STS-6 Space Shuttle flight. In the STS-6 atmosphere, the calculus-of-variations open-loop controller fails to exit the atmosphere, while the Liapunov controller achieves the optimal minimum-fuel conditions, despite the + or - 40 percent fluctuations in the STS-6 atmosphere.

Grantham, Walter J.↗

Control optimization of a lifting body entry problem by an improved and a modified method of perturbation function

A study of the solution problem of a complex entry optimization was studied. The problem was transformed into a two-point boundary value problem by using classical calculus of variation methods. Two perturbation methods were devised. These methods attempted to desensitize the contingency of the solution of this type of problem on the required initial co-state estimates. Also numerical results are presented for the optimal solution resulting from a number of different initial co-states estimates. The perturbation methods were compared. It is found that they are an improvement over existing methods.

Garcia, F., Jr.↗

A Transformation Approach to Optimal Control Problems with Bounded State Variables

A technique is described and utilized in the study of the solutions to various general problems in optimal control theory, which are converted in to Lagrange problems in the calculus of variations. This is accomplished by mapping certain properties in Euclidean space onto closed control and state regions. Nonlinear control problems with a unit m cube as control region and unit n cube as state region are considered.

Hanafy, Lawrence Hanafy↗

Preliminary Design of Low-Thrust Interplanetary Missions

For interplanetary missions, highly efficient electric propulsion systems can be used to increase the mass delivered to the destination and/or reduce the trip time over typical chemical propulsion systems. This technology is being demonstrated on the Deep Space 1 mission - part of NASA's New Millennium Program validating technologies which can lower the cost and risk and enhance the performance of future missions. With the successful demonstration on Deep Space 1, future missions can consider electric propulsion as a viable propulsion option. Electric propulsion systems, while highly efficient, produce only a small amount of thrust. As a result, the engines operate during a significant fraction of the trajectory. This characteristic makes it much more difficult to find optimal trajectories. The methods for optimizing low-thrust trajectories are typically categorized as either indirect, or direct. Indirect methods are based on calculus of variations, resulting in a two-point boundary value problem that is solved by satisfying terminal constraints and targeting conditions. These methods are subject to extreme sensitivity to the initial guess of the variables - some of which are not physically intuitive. Adding a gravity assist to the trajectory compounds the sensitivity. Direct methods parameterize the problem and use nonlinear programming techniques to optimize an objective function by adjusting a set of variables. A variety of methods of this type have been examined with varying results. These methods are subject to the limitations of the nonlinear programming techniques. In this paper we present a direct method intended to be used primarily for preliminary design of low-thrust interplanetary trajectories, including those with multiple gravity assists. Preliminary design implies a willingness to accept limited accuracy to achieve an efficient algorithm that executes quickly.

Sims, Jon A.↗

Discrete approximations to optimal trajectories using direct transcription and nonlinear programming

A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculus-of-variations problem with a nonlinear-programming problem, which is solved numerically. This paper identifies this method as a direct transcription method and proceeds to investigate the relationship between the original optimal-control problem and the nonlinear-programming problem. The discretized adjoint equation of the collocation method is found to have deficient accuracy, and an alternate scheme which discretizes the equations of motion using an explicit Runge-Kutta parallel-shooting approach is developed. Both methods are applied to finite-thrust spacecraft trajectory problems, including a low-thrust escape spiral, a three-burn rendezvous, and a low-thrust transfer to the moon.

Enright, Paul J.↗

Estimation in nonlinear systems with transport delay.

The problem of estimation of state in nonlinear dynamical systems containing time delays is studied. The plant is specified by a set of nonlinear differential-difference equations. Observations are a nonlinear function of current and/or delayed states. Both contain additive disturbances. The criterion used for the optimal estimates is the integral of the weighted squared error. Using the theory of the calculus of variations, equations are developed for the estimation. They are first expressed in the form of a split boundary value problem, which is then converted to an initial value problem for on-line estimation. The result yields a sequential estimation scheme in which filtered and smoothed estimates are computed in a sequential manner. The applicability of the procedure is demonstrated by a practical example.

Stoller, R. L.↗

A simple analytical aerodynamic model of Langley Winged-Cone Aerospace Plane concept

A simple three DOF analytical aerodynamic model of the Langley Winged-Coned Aerospace Plane concept is presented in a form suitable for simulation, trajectory optimization, and guidance and control studies. The analytical model is especially suitable for methods based on variational calculus. Analytical expressions are presented for lift, drag, and pitching moment coefficients from subsonic to hypersonic Mach numbers and angles of attack up to +/- 20 deg. This analytical model has break points at Mach numbers of 1.0, 1.4, 4.0, and 6.0. Across these Mach number break points, the lift, drag, and pitching moment coefficients are made continuous but their derivatives are not. There are no break points in angle of attack. The effect of control surface deflection is not considered. The present analytical model compares well with the APAS calculations and wind tunnel test data for most angles of attack and Mach numbers.

Pamadi, Bandu N.↗

Nonprincipal plane scattering of flat plates and pattern control of horn antennas

Using the geometrical theory of diffraction, the traditional method of high frequency scattering analysis, the prediction of the radar cross section of a perfectly conducting, flat, rectangular plate is limited to principal planes. Part A of this report predicts the radar cross section in nonprincipal planes using the method of equivalent currents. This technique is based on an asymptotic end-point reduction of the surface radiation integrals for an infinite wedge and enables nonprincipal plane prediction. The predicted radar cross sections for both horizontal and vertical polarizations are compared to moment method results and experimental data from Arizona State University's anechoic chamber. In part B, a variational calculus approach to the pattern control of the horn antenna is outlined. The approach starts with the optimization of the aperture field distribution so that the control of the radiation pattern in a range of directions can be realized. A control functional is thus formulated. Next, a spectral analysis method is introduced to solve for the eigenfunctions from the extremal condition of the formulated functional. Solutions to the optimized aperture field distribution are then obtained.

Balanis, Constantine A.↗

(abstract) Optimal Low Thrust Trajectories Using Differential Inclusion Concepts

Low thrust propulsion systems typically have their greatest benefit for high energy missions or missions with large post-launch maneuver requirements. Missions which have been examined include main belt asteroid rendezvous, comet rendezvous, outer planet and Mercury orbiters, Pluto flyby, and solar probe missions. Low thrust mission design software used to determine these trajectories is based on two distinct formulations of the optimal control problem: the indirect and direct methods. The traditional approach (indirect) is to use the calculus of variations to obtain first order necessary conditions on the states and costates. In contrast, direct methods are conceptually different in that no explicit integration takes place. A direct method based on differential inclusion concepts has been developed and successfully used to compute low thrust trajectories. This new approach removes explicit control dependence from the problem thereby reducing the dimension of the parameter space for the nonlinear programming problem. Also when compared to other direct methods, fewer nonlinear constraints are required to represent the dynamics of the problem.

low↗

Optimum Interplanetary Rendezvous Trajectories With Powerlimited Vehicles

The optimum-thrust equations for both variable and constant thrust are presented. These thrust programs are used to generate rendezvous trajectories from the Earth to Mars for various flight times and launch dates during the years 1968-71. The manner in which the propulsion requirements vary with flight time and launch date are considered, and a comparison of vehicle performance using the variable- and constant-thrust programs is presented. The optimization of the pro- pulsion system parameters is discussed, and the existence of optimum launch dates is interpreted in terms of certain transversality conditions derivable from the calculus of variations. A brief comparison of the advanced propulsion vehicle and the ballistic vehicle propulsion requirements is made for Earth-Mars rendezvous trajectories. An appendix considering the analytical basis for this work is included.

INTERPLANETARY TRAJECTORY↗

Optimal control of a variable spin speed CMG system for space vehicles

Many future NASA programs require very high accurate pointing stability. These pointing requirements are well beyond anything attempted to date. This paper suggests a control system which has the capability of meeting these requirements. An optimal control law for the suggested system is specified. However, since no direct method of solution is known for this complicated system, a computation technique using successive approximations is used to develop the required solution. The method of calculus of variations is applied for estimating the changes of index of performance as well as those constraints of inequality of state variables and terminal conditions. Thus, an algorithm is obtained by the steepest descent method and/or conjugate gradient method. Numerical examples are given to show the optimal controls.

Liu, T. C.↗