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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 109 records · Page 6
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NASA NTRSDate not supplied

Optimal Angle of Attack Control for Aerocapture Maneuvers

Recent investigations of aerocapture maneuvers have considered direct force control as a promising alternative to bank angle control. By modulating the angle of attack and sideslip angle independently, the longitudinal and lateral channels can be decoupled and thus solved separately. However, the optimal angle of attack profile for minimizing post-atmospheric propellant expenditure was previously unknown. This research applies principles of optimal control theory to numerically solve for the optimal angle of attack profile for control of the longitudinal channel. Direct methods are first employed to discretize the angle of attack profile and show that an optimal solution follows a nearly bang-bang (full lift up then full lift down) structure under a variety of conditions along the flight path angle corridor. To corroborate these results, indirect methods were also applied to scope the Optimal Control Problem (OCP) as a Two Point Boundary Value Problem (2P-BVP) which could then be solved numerically. The indirect optimization results aligned closely with the direct results, providing further evidence that a bang-bang structure provides a good approximation for the optimal angle of attack profile for aerocapture maneuvers using direct force control.

aerocapture↗
NASA NTRS2011

Cross-Polar Aircraft Trajectory Optimization and Potential Climate Impact

Cross-Polar routes offer new opportunities for air travel markets. Transpolar flights reduce travel times, fuel burns, and associated environmental emissions by flying direct paths between many North American and Asian cities. This study evaluates the potential benefits of flying wind-optimal polar routes and assessed their potential impact on climate change. An optimization algorithm is developed for transpolar flights to generate wind-optimal trajectories that minimize climate impact of aircraft, in terms of global warming potentials (relative to warming by one kg of CO2) of several types of emissions, while avoiding regions of airspace that facilitate persistent contrail formation. Estimations of global warming potential are incorporated into the objective function of the optimization algorithm to assess the climate impact of aircraft emissions discharged at a given location and altitude. The regions of airspace with very low ambient temperature and areas favorable to persistent contrail formation are modeled as undesirable regions that aircraft should avoid and are formulated as soft state constraints. The fuel burn and climate impact of cross-polar air traffic flying various types of trajectory including flightplan, great circle, wind-optimal, and contrail-avoidance are computed for 15 origin-destination pairs between major international airports in the U.S. and Asia. Wind-optimal routes reduce average fuel burn of flight plan routes by 4.4% on December 4, 2010 and 8.0% on August 7, 2010, respectively. The tradeoff between persistent contrail formation and additional global warming potential of aircraft emissions is investigated with and without altitude optimization. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a one percent increase in additional global warming potential, a climate impact equivalent to that of 4070kg and 4220kg CO2 emission, reduces 135 and 105 minutes persistent contrail formation per flight during a day with medium and high contrail formation, respectively.

Sridhar, Banavar↗
NASA NTRS1986

Optimal control of aeroassisted plane change maneuver using feedback expansions

A guidance law for an aeroassisted plane change maneuver is developed by an asymptotic expansion technique using a small parameter which essentially represents the ratio of the inertial forces to the atmospheric forces. This guidance law minimizes the energy loss while meeting terminal constraints on the altitude, flight path angle, and heading angle. By neglecting the inertial forces, the resulting optimization problem is integrable and can be determined in closed form. This zeroth-order solution is the first term in an asymptotic series solution of the Hamilton-Jacobi-Bellman equation. The remaining terms are determined from the solution of a first-order, linear partial differential equation whose solution requires only quadrature integration. Our initial results in using this guidance scheme are encouraging.

Mishne, D.↗
NASA NTRS1998

Minimum Climb to Cruise Noise Trajectories Modeled for the High Speed Civil Transport

The proposed U.S. High Speed Civil Transport (HSCT) will revolutionize commercial air travel by providing economical supersonic passenger service to destinations worldwide. Unlike the high-bypass turbofan engines that propel today's subsonic airliners, HSCT engines will have much higher jet exhaust speeds. Jet noise, caused by the turbulent mixing of high-speed exhaust with the surrounding air, poses a significant challenge for HSCT engine designers. To resolve this challenge, engineers have designed advanced mixer rejector nozzles that reduce HSCT jet noise to airport noise certification levels by entraining and mixing large quantities of ambient air with the engines' jet streams. Although this works well during the first several minutes of flight, far away from the airport, as the HSCT gains speed and climbs, poor ejector inlet recovery and ejector ram drag contribute to poor thrust, making it advantageous to turn off the ejector. Doing so prematurely, however, can cause unacceptable noise levels to propagate to the ground, even when the aircraft is many miles from the airport. This situation lends itself ideally to optimization, where the aircraft trajectory, throttle setting, and ejector setting can be varied (subject to practical aircraft constraints) to minimize the noise propagated to the ground. A method was developed at the NASA Lewis Research Center that employs a variation of the classic energy state approximation: a trajectory analysis technique historically used to minimize climb time or fuel burned in many aircraft problems. To minimize the noise on the ground at any given throttle setting, high aircraft altitudes are desirable; but the HSCT may either climb quickly to high altitudes using a high, noisy throttle setting or climb more slowly at a lower, quieter throttle setting. An optimizer has been programmed into NASA's existing aircraft and noise analysis codes to balance these options by dynamically choosing the best altitude-velocity path and throttle setting history. The noise level standard, or metric, used in the optimizer should be one that accurately reflects the subjective annoyance levels of ground-based observers under the flight path. A variety of noise metrics are available, many of which are practical for airport-vicinity noise certification. Unlike airport noise, however, the HSCT's climb noise will be characterized by relatively low noise levels, long durations, and low-frequency spectra. The noise metrics used in these calculations are based on the recommendations of researchers at the NASA Langley Research Center, who have correlated the flyover noise annoyance levels of actual laboratory subjects with a variety of measurements. Analysis of data from this optimizer has shown that significant reductions in noise may be obtained with trajectory optimization. And since throttling operations are performed in the subsonic portion of the climb path (where thrust is plentiful), only small penalties in HSCT range or fuel performance occur.

Berton, Jeffrey J.↗
NASA NTRS2011

Cross-Polar Aircraft Trajectory Optimization and the Potential Climate Impact

Cross-Polar routes offer new opportunities for air travel markets. Transpolar flights reduce travel times, fuel burns, and associated environmental emissions by flying direct paths between many North American and Asian cities. This study evaluates the potential benefits of flying wind-optimal polar routes and assessed their potential impact on climate change. An optimization algorithm is developed for transpolar flights to generate wind-optimal trajectories that minimize climate impact of aircraft, in terms of global warming potentials (relative to warming by one kg of CO2) of several types of emissions, while avoiding regions of airspace that facilitate persistent contrail formation. Estimations of global warming potential are incorporated into the objective function of the optimization algorithm to assess the climate impact of aircraft emissions discharged at a given location and altitude. The regions of airspace with very low ambient temperature and areas favorable to persistent contrail formation are modeled as undesirable regions that aircraft should avoid and are formulated as soft state constraints. The fuel burn and climate impact of cross-polar air traffic flying various types of trajectory including flight plan, great circle, wind-optimal, and contrail-avoidance are computed for 15 origin-destination pairs between major international airports in the U.S. and Asia. Wind-optimal routes reduce average fuel burn of flight plan routes by 4.4% on December 4, 2010 and 8.0% on August 7, 2010, respectively. The tradeoff between persistent contrail formation and additional global warming potential of aircraft emissions is investigated with and without altitude optimization. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a one percent increase in additional global warming potential, a climate impact equivalent to that of 4070kg and 4220kg CO2 emission, reduces 135 and 105 minutes persistent contrail formation per flight during a day with medium and high contrail formation, respectively.

Ng, Hok K.↗
NASA NTRS1989

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.↗
NASA NTRS1975

Automatic guidance and control of a transport aircraft during a helical landing approach

A linear optimal regulator theory was applied to a nonlinear simulation of a transport aircraft performing a helical landing approach. A closed-form expression for the quasi-steady nominal flight path is presented along with the method for determining the corresponding constant nominal control inputs. The Jacobian matrices and the weighting matrices in the cost functional were time varying. A method of solving for the optimal feedback gains is reviewed. The control system was tested on several alternative landing approaches using both 3 deg and 6 deg flight path angles. On each landing approach, the aircraft was subjected to large random initial-state errors and to randomly directed crosswinds. The system was also tested for sensitivity to changes in the parameters of the aircraft and of the atmosphere. Results indicate that performance of the optimal controller on all the 3 deg approaches is very good. The control system proved to be reasonably insensitive to parametric uncertainties. Performance is not as good on the 6 deg approaches. A modification to the 6 deg flight path was proposed for the purpose of improving performance.

Crawford, D. J.↗
NASA NTRS1974

Curved descending landing approach guidance and control

Linear optimal regulator theory is applied to a nonlinear simulation of a transport aircraft performing a helical landing approach. A closed form expression for the quasi-steady nominal flight path is presented along with the method for determining the corresponding constant nominal control inputs. The Jacobian matrices and the weighting matrices in the cost functional are time varying. A method of solving for the optimal feedback gains is reviewed. The control system is tested on several alternative landing approaches using both three and six degree flight path angles. On each landing approach, the aircraft was subjected to large random initial state errors and to randomly directed crosswinds. The system was also tested for sensitivity to changes in the parameters of the aircraft and of the atmosphere. Performance of the optimal controller on all the three degree approaches was very good, and the control system proved to be reasonably insensitive to parametric uncertainties.

Crawford, D. J.↗
NASA NTRS1983

Optimal symmetric flight with an intermediate vehicle model

Optimal flight in the vertical plane with a vehicle model intermediate in complexity between the point-mass and energy models is studied. Flight-path angle takes on the role of a control variable. Range-open problems feature subarcs of vertical flight and singular subarcs. The class of altitude-speed-range-time optimization problems with fuel expenditure unspecified is investigated and some interesting phenomena uncovered. The maximum-lift-to-drag glide appears as part of the family, final-time-open, with appropriate initial and terminal transient exceeding level-flight drag, some members exhibiting oscillations. Oscillatory paths generally fail the Jacobi test for durations exceeding a period and furnish a minimum only for short-duration problems.

Menon, P. K. A.↗
NASA NTRS1990

Singular perturbation analysis of AOTV-related trajectory optimization problems

The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.

Calise, Anthony J.↗
NASA NTRS1992

Closed form solutions of constrained trajectories - Application in optimal ascent of aerospace plane

The present consideration of the flight trajectory of hypersonic aerospace vehicles subject to a class of path constraints notes the constrained dynamics to constitute a natural two-timescale system, so that problems of trajectory optimization and guidance can be dramatically simplified by means of the asymptotic analytical solutions thus obtained. An illustrative application in ascent trajectory optimization for an aerospace vehicle is presented.

Lu, Ping↗
NASA NTRS2000

The Mathematics of Navigating the Solar System

In navigating spacecraft throughout the solar system, the space navigator relies on three academic disciplines - optimization, estimation, and control - that work on mathematical models of the real world. Thus, the navigator determines the flight path that will consume propellant and other resources in an efficient manner, determines where the craft is and predicts where it will go, and transfers it onto the optimal trajectory that meets operational and mission constraints. Mission requirements, for example, demand that observational measurements be made with sufficient precision that relativity must be modeled in collecting and fitting (the estimation process) the data, and propagating the trajectory. Thousands of parameters are now determined in near real-time to model the gravitational forces acting on a spacecraft in the vicinity of an irregularly shaped body. Completing these tasks requires mathematical models, analyses, and processing techniques. Newton, Gauss, Lambert, Legendre, and others are justly famous for their contributions to the mathematics of these tasks. More recently, graduate students participated in research to update the gravity model of the Saturnian system, including higher order gravity harmonics, tidal effects, and the influence of the rings. This investigation was conducted for the Cassini project to incorporate new trajectory modeling features in the navigation software. The resulting trajectory model will be used in navigating the 4-year tour of the Saturnian satellites. Also, undergraduate students are determining the ephemerides (locations versus time) of asteroids that will be used as reference objects in navigating the New Millennium's Deep Space 1 spacecraft autonomously.

Hintz, Gerald↗
NASA NTRS1997

Dynamic Flow Management Problems in Air Transportation

In 1995, over six hundred thousand licensed pilots flew nearly thirty-five million flights into over eighteen thousand U.S. airports, logging more than 519 billion passenger miles. Since demand for air travel has increased by more than 50% in the last decade while capacity has stagnated, congestion is a problem of undeniable practical significance. In this thesis, we will develop optimization techniques that reduce the impact of congestion on the national airspace. We start by determining the optimal release times for flights into the airspace and the optimal speed adjustment while airborne taking into account the capacitated airspace. This is called the Air Traffic Flow Management Problem (TFMP). We address the complexity, showing that it is NP-hard. We build an integer programming formulation that is quite strong as some of the proposed inequalities are facet defining for the convex hull of solutions. For practical problems, the solutions of the LP relaxation of the TFMP are very often integral. In essence, we reduce the problem to efficiently solving large scale linear programming problems. Thus, the computation times are reasonably small for large scale, practical problems involving thousands of flights. Next, we address the problem of determining how to reroute aircraft in the airspace system when faced with dynamically changing weather conditions. This is called the Air Traffic Flow Management Rerouting Problem (TFMRP) We present an integrated mathematical programming approach for the TFMRP, which utilizes several methodologies, in order to minimize delay costs. In order to address the high dimensionality, we present an aggregate model, in which we formulate the TFMRP as a multicommodity, integer, dynamic network flow problem with certain side constraints. Using Lagrangian relaxation, we generate aggregate flows that are decomposed into a collection of flight paths using a randomized rounding heuristic. This collection of paths is used in a packing integer programming formulation, the solution of which generates feasible and near-optimal routes for individual flights. The algorithm, termed the Lagrangian Generation Algorithm, is used to solve practical problems in the southwestern portion of United States in which the solutions are within 1% of the corresponding lower bounds.

Patterson, Sarah Stock↗
NASA NTRS1971

Approximate optimal atmospheric entry trajectories

Reentry glider approximate optimal atmospheric entry trajectories for maximizing function of terminal velocity, altitude, flight path and heading angle under terminal nonlinear constraints

Speyer, J. L.↗
NASA NTRS1983

Optimal symmetric flight with an intermediate vehicle model

The present investigation is concerned with an examination of optimal symmetry flight on the basis of the intermediate vehicle model. The analysis is partly based upon an exploration of Euler solutions for the path-angle-as-control model carried out by Kelley (1958). The current analysis takes into account higher-order optimality conditions and 'chattering-control' phenomena. Attention is given to details regarding the intermediate vehicle model, the Legendre-Clebsch necessary condition, the conjugate-point test, and the numerical solution of the time-range problem. It is found that the flight path angle takes on the role of control variable in the model. From physical considerations, it can be seen that when a positive margin of thrust over drag exists, the maximum-range climb trajectory without time or fuel constraints has no proper maximum nor an upper bound.

Kelley, H. J.↗
NASA NTRS1983

Optimal symmetric flight with an intermediate vehicle model

The present investigation is concerned with an examination of optimal symmetry flight on the basis of the intermediate vehicle model. The analysis is partly based upon an exploration of Euler solutions for the path-angle-as-control model carried out by Kelley (1958). The current analysis takes into account higher-order optimality conditions and "chattering-control' phenomena. Attention is given to details regarding the intermediate vehicle model, the Legendre-Clebsch necessary condition, the conjugate-point test, and the numerical solution of the time-range problem. It is found that the flight path angle takes on the role of control variable in the model. From physical considerations, it can be seen that when a positive margin of thrust over drag exists, the maximum-range climb trajectory without time or fuel constraints has no proper maximum nor an upper bound.

Menon, P. K. A.↗
NASA NTRSDate not supplied

Reducing the Noise Impact of Small Aircraft through Indirect Trajectory Optimization

This research examined the feasibility of incorporating an acoustic metric into the optimization of an aircraft trajectory to reduce the noise experienced by an observer. The method investigated a perturbed path of an unmanned aerial system with specified boundary conditions on position and velocity while maintaining a nominal flight speed. An acoustic model based on Gutin’s work was developed to estimate propeller noise as a function of flight parameters, propulsion characteristics, and spatial location. A trajectory was then optimized a priori to reduce the noise experienced by an observer. Multiple simulations were performed and results showed that integrating an acoustic metric into the path planning process could be used to reduce the noise impact on an observer with no perturbation to the nominal flight speed.

Matthew B Galles↗