A technique for optimum final value control of powered flight trajectories /revision no. 1/
Least squares optimum final value control method for determining steering angle program of rocket vehicle until thrust termination
FLIGHT PATH↗
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Technique for calculating optimum noise-abatement take-off profiles
Optimal noise reduction analysis for jet aircraft take-off and climbing flight paths
Drinkwater, F. J., III↗
Space Launch System Implementation of Adaptive Augmenting Control
Given the complex structural dynamics, challenging ascent performance requirements, and rigorous flight certification constraints owing to its manned capability, the NASA Space Launch System (SLS) launch vehicle requires a proven thrust vector control algorithm design with highly optimized parameters to robustly demonstrate stable and high performance flight. On its development path to preliminary design review (PDR), the stability of the SLS flight control system has been challenged by significant vehicle flexibility, aerodynamics, and sloshing propellant dynamics. While the design has been able to meet all robust stability criteria, it has done so with little excess margin. Through significant development work, an adaptive augmenting control (AAC) algorithm previously presented by Orr and VanZwieten, has been shown to extend the envelope of failures and flight anomalies for which the SLS control system can accommodate while maintaining a direct link to flight control stability criteria (e.g. gain & phase margin). In this paper, the work performed to mature the AAC algorithm as a baseline component of the SLS flight control system is presented. The progress to date has brought the algorithm design to the PDR level of maturity. The algorithm has been extended to augment the SLS digital 3-axis autopilot, including existing load-relief elements, and necessary steps for integration with the production flight software prototype have been implemented. Several updates to the adaptive algorithm to increase its performance, decrease its sensitivity to expected external commands, and safeguard against limitations in the digital implementation are discussed with illustrating results. Monte Carlo simulations and selected stressing case results are shown to demonstrate the algorithm's ability to increase the robustness of the integrated SLS flight control system.
VanZwieten, Tannen S.↗
Space Launch System Implementation of Adaptive Augmenting Control
Given the complex structural dynamics, challenging ascent performance requirements, and rigorous flight certification constraints owing to its manned capability, the NASA Space Launch System (SLS) launch vehicle requires a proven thrust vector control algorithm design with highly optimized parameters to provide stable and high-performance flight. On its development path to Preliminary Design Review (PDR), the SLS flight control system has been challenged by significant vehicle flexibility, aerodynamics, and sloshing propellant. While the design has been able to meet all robust stability criteria, it has done so with little excess margin. Through significant development work, an Adaptive Augmenting Control (AAC) algorithm has been shown to extend the envelope of failures and flight anomalies the SLS control system can accommodate while maintaining a direct link to flight control stability criteria such as classical gain and phase margin. In this paper, the work performed to mature the AAC algorithm as a baseline component of the SLS flight control system is presented. The progress to date has brought the algorithm design to the PDR level of maturity. The algorithm has been extended to augment the full SLS digital 3-axis autopilot, including existing load-relief elements, and the necessary steps for integration with the production flight software prototype have been implemented. Several updates which have been made to the adaptive algorithm to increase its performance, decrease its sensitivity to expected external commands, and safeguard against limitations in the digital implementation are discussed with illustrating results. Monte Carlo simulations and selected stressing case results are also shown to demonstrate the algorithm's ability to increase the robustness of the integrated SLS flight control system.
Wall, John H.↗
Approximate optimal atmospheric entry trajectories.
For a reentry glider, approximate solutions are found in closed form for the problem of maximizing a function of the terminal velocity, altitude, flight-path angle and heading angle subject to, at most, three terminal nonlinear constraints. The results given here extend the previous results in two important ways: (1) the second-order approximation of the entry dynamics of Loh is used instead of the first-order approximation of Allen and Eggers. This approximation is found to compare extremely well with an exact numerical optimal path. (2) A three-dimensional optimization problem is solved which includes Loh's second-order approximation where the roll angle as well as the lift coefficient are determined subject to constraints which include the terminal heading angle. Furthermore, closed-form solutions can also be obtained subject to in-flight constraints on the lift coefficient and roll angle.
Speyer, J. L.↗
Optimum VTOL flight paths under constraint
Minimum fuel takeoff and landing paths for VTOL aircraft with constraints on state and control, determining optimal trajectories
Hollister, W. M.↗
Fundamental limitations on V/STOL terminal guidance due to aircraft characteristics
A review is given of limitations on approach flight paths of V/STOL aircraft, including limits on descent angle due to maximum drag/lift ratio. A method of calculating maximum drag/lift ratio of tilt-wing and deflected slipstream aircraft is presented. Derivatives and transfer functions for the CL-84 tilt-wing and X-22A tilt-duct aircraft are presented. For the unaugmented CL-84 in steep descents the transfer function relating descent angle to thrust contains a right-half plane zero. Using optimal control theory, it is shown that this zero causes a serious degradation in the accuracy with which steep flight paths can be followed in the presence of gusts.
Wolkovitch, J.↗
Computationally-Efficient Minimum-Time Aircraft Routes in the Presence of Winds
A computationally efficient algorithm for minimizing the flight time of an aircraft in a variable wind field has been invented. The algorithm, referred to as Neighboring Optimal Wind Routing (NOWR), is based upon neighboring-optimal-control (NOC) concepts and achieves minimum-time paths by adjusting aircraft heading according to wind conditions at an arbitrary number of wind measurement points along the flight route. The NOWR algorithm may either be used in a fast-time mode to compute minimum- time routes prior to flight, or may be used in a feedback mode to adjust aircraft heading in real-time. By traveling minimum-time routes instead of direct great-circle (direct) routes, flights across the United States can save an average of about 7 minutes, and as much as one hour of flight time during periods of strong jet-stream winds. The neighboring optimal routes computed via the NOWR technique have been shown to be within 1.5 percent of the absolute minimum-time routes for flights across the continental United States. On a typical 450-MHz Sun Ultra workstation, the NOWR algorithm produces complete minimum-time routes in less than 40 milliseconds. This corresponds to a rate of 25 optimal routes per second. The closest comparable optimization technique runs approximately 10 times slower. Airlines currently use various trial-and-error search techniques to determine which of a set of commonly traveled routes will minimize flight time. These algorithms are too computationally expensive for use in real-time systems, or in systems where many optimal routes need to be computed in a short amount of time. Instead of operating in real-time, airlines will typically plan a trajectory several hours in advance using wind forecasts. If winds change significantly from forecasts, the resulting flights will no longer be minimum-time. The need for a computationally efficient wind-optimal routing algorithm is even greater in the case of new air-traffic-control automation concepts. For air-traffic-control automation, thousands of wind-optimal routes may need to be computed and checked for conflicts in just a few minutes. These factors motivated the need for a more efficient wind-optimal routing algorithm.
Jardin, Matthew R.↗
Conjugate gradient optimization programs for shuttle reentry
Two computer programs for shuttle reentry trajectory optimization are listed and described. Both programs use the conjugate gradient method as the optimization procedure. The Phase 1 Program is developed in cartesian coordinates for a rotating spherical earth, and crossrange, downrange, maximum deceleration, total heating, and terminal speed, altitude, and flight path angle are included in the performance index. The programs make extensive use of subroutines so that they may be easily adapted to other atmospheric trajectory optimization problems.
Powers, W. F.↗
Flight Test Design and Implementation for Airspace Independent Surveillance Through a Distributed Ground Based Sensor Network
The paper presents a system architecture for distributed sensing, networking and computing, its hardware implementation, and execution of initial flight experiments to validate theoretical findings. It induces development of distributed sensing requirements, framework, and architecture, development of distributed ground node hardware prototypes, integration of all nodes and testing of baseline functionalities, integration of in-house developed perception, migration and tracking software packages, establishing flight scenario and flyable path for a selected UAS, flying the air vehicle along the path, recording sensors measurements, pre-processing them and transferring the resulting data to an optimal computing center. It also addresses the challenges related to pre-flight hardware calibration, clock synchronization, sensor registration and establishing a communication network. Sensors data processing results demonstrate the functionality of the presented distributed architecture and satisfactory performance of the applied technologies.
Target tracking↗
Flight Test Design and Implementation for Independent Surveillance of an Airspace Through a Distributed Ground Sensing Network
The paper presents a system architecture for distributed sensing, networking and computing, its hardware implementation, and execution of initial flight experiments to validate theoretical findings. It induces development of distributed sensing requirements, framework, and architecture, development of distributed ground node hardware prototypes, integration of all nodes and testing of baseline functionalities, integration of in-house developed perception, migration and tracking software packages, establishing flight scenario and flyable path for a selected UAS, flying the air vehicle along the path, recording sensors measurements, pre-processing them and transferring the resulting data to an optimal computing center. It also addresses the challenges related to pre-flight hardware calibration, clock synchronization, sensor registration and establishing a communication network. Sensors data processing results demonstrate the functionality of the presented distributed architecture and satisfactory performance of the applied technologies.
Distributed sensing↗
Classical and neo-classical cruise-dash optimization
Cruise-dash flight performance is analyzed in the context of singular perturbations. Attention is given to the problem of determining an atmospheric flight path between given end points which minimizes a linear combination of time and fuel. It is shown that nonconvexity in the fuel-flow vs. airspeed graph has important consequences in optimum-cruise problems with time restrictions. Certain velocity regions are nonoptimal for cruise-dash and optimal cruise-dash sometimes requires time-shared operation between two altitude-airspeed points. Calculations are presented illustrating the occurrence of time-shared operation between two altitude-airspeed combinations for optimal cruise-dash.
Cliff, E. M.↗
Generation and evoluation of near-optimum vertical flight profiles
The overall objectives of this research effort have been to develop and evaluate algorithms and flight management concepts for minimization of fuel or direct operating costs. These concepts are to be used for flight planning or for on-board computation and steering of turbojet transport aircraft in the vertical path. Within this research context, a computer program, called OPTIM, has been developed to use these algorithms to generate near-optimum vertical reference profiles. OPTIM contains control options to examine effects of various flight constraints on cost performance. A companion program, called TRAGEN, was developed to simulate an aircraft flying along a given vertical reference profile. TRAGEN is used to verify OPTIM's output , to examine the effects of parameter value uncertainty (such as prevailing wind), and to compare cost performance of profiles generated by different techniques. This paper describes OPTIM and TRAGEN and presents examples of the programs utility.
Sorensen, J. A.↗
Optimal trajectories for hypervelocity flight
Optimal trajectories for hypervelocity flight of interest in aeroassisted orbital transfer are discussed. Both coplanar and noncoplanar transfer are studied. More precisely, the geosynchronous-earth-orbit-, high-earth orbit- and low-earth-orbit-to-low earth-orbit transfers are considered in connection with a spacecraft that is controlled during the atmospheric pass by the angle of attack (coplanar case) or by the angle of attack and the angle of bank (noncoplanar case). Within the framework of classical optimal control, the following problems are studied: minimize the energy required for orbital transfer; maximize the time of flight during the atmospheric portion of the trajectory; and minimize the time integral of the square of the path inclination. Within the framework of minimax optimal control, the problem studied is to minimize the peak rate. Numerical solutions for the problems are obtained by means of the sequential gradient-restoration algorithm. The engineering implications of the results are discussed.
Miele, A.↗
Decomposition technique and optimal trajectories for the aeroassisted flight experiment
An actual geosynchronous Earth orbit-to-low Earth orbit (GEO-to-LEO) transfer is considered with reference to the aeroassisted flight experiment (AFE) spacecraft, and optimal trajectories are determined by minimizing the total characteristic velocity. The optimization is performed with respect to the time history of the controls (angle of attack and angle of bank), the entry path inclination and the flight time being free. Two transfer maneuvers are considered: direct ascent (DA) to LEO and indirect ascent (IA) to LEO via parking Earth orbit (PEO). By taking into account certain assumptions, the complete system can be decoupled into two subsystems: one describing the longitudinal motion and one describing the lateral motion. The angle of attack history, the entry path inclination, and the flight time are determined via the longitudinal motion subsystem. In this subsystem, the difference between the instantaneous bank angle and a constant bank angle is minimized in the least square sense subject to the specified orbital inclination requirement. Both the angles of attack and the angle of bank are shown to be constant. This result has considerable importance in the design of nominal trajectories to be used in the guidance of AFE and aeroassisted orbital transfer (AOT) vehicles.
Miele, A.↗
Decomposition technique and optimal trajectories for the aeroassisted flight experiment
An actual geosynchronous earth orbit-to-low earth orbit (GEO-to-LEO) transfer is considered with reference to the aeroassisted flight experiment (AFE) spacecraft, and optimal trajectories are determined by minimizing the total characteristic velocity. The optimization is performed with respect to the time history of the controls (angle of attack and angle of bank), the entry path inclination and the flight time being free. Two transfer maneuvers are considered: direct ascent (DA) to LEO and indirect ascent (IA) to LEO via parking earth orbit (PEO). By taking into account certain assumptions, the complete system can be decoupled into two subsystems: one describing the longitudinal motion and one describing the lateral motion. The angle of attack history, the entry path inclination, and the flight time are determined via the longitudinal motion subsystem. In this subsystem, the difference between the instantaneous bank angle and a constant bank angle is minimized in the least square sense subject to the specified orbital inclination requirement. Both the angles of attack and the angle of bank are shown to be constant. This result has considerable importance in the design of nominal trajectories to be used in the guidance of AFE and aeroassisted orbital transfer (AOT) vehicles.
Miele, A.↗
Flight guidance research for recovery from microburst wind shear
Research is in progress to develop flight strategy concepts for avoidance and recovery from microburst wind shears. The objectives of this study are to evaluate the performance of various strategies for recovery from wind shear encountered during the approach-to-landing, examine the associated piloting factors, and evaluate the payoff of forward-look sensing. Both batch and piloted simulations are utilized. The industry-recommended manual recovery technique is used as a baseline strategy. Two advanced strategies were selected for the piloted tests. The first strategy emulates the recovery characteristics shown by prior optimal trajectory analysis, by initially tracking the glideslope, then commanding a shallow climb. The second strategy generates a flight path angle schedule that is a function of airplane energy state and the instantaneous shear strength. All three strategies are tested with reactive sensing only and with forward-look sensing. Piloted simulation tests are in progress. Tentative results indicate that, using only reactive alerts, there appears to be little difference in performance between the various strategies. With forward-look alerts, the advanced guidance strategies appear to have advantages over the baseline strategy. Relatively short forward-look alert times, on the order of 10 or 15 seconds, produce a far greater recovery benefit than optimizing a recovery from a reactive alert.
Hinton, David A.↗
Rapid near-optimal trajectory generation and guidance law development for single-stage-to-orbit airbreathing vehicles
General problems associated with on-board trajectory optimization, propulsion system cycle selection, and with the synthesis of guidance laws were addressed for an ascent to low-earth-orbit of an air-breathing single-stage-to-orbit vehicle. The NASA Generic Hypersonic Aerodynamic Model Example and the Langley Accelerator aerodynamic sets were acquired and implemented. Work related to the development of purely analytic aerodynamic models was also performed at a low level. A generic model of a multi-mode propulsion system was developed that includes turbojet, ramjet, scramjet, and rocket engine cycles. Provisions were made in the dynamic model for a component of thrust normal to the flight path. Computational results, which characterize the nonlinear sensitivity of scramjet performance to changes in vehicle angle of attack, were obtained and incorporated into the engine model. Additional trajectory constraints were introduced: maximum dynamic pressure; maximum aerodynamic heating rate per unit area; angle of attack and lift limits; and limits on acceleration both along and normal to the flight path. The remainder of the effort focused on required modifications to a previously derived algorithm when the model complexity cited above was added. In particular, analytic switching conditions were derived which, under appropriate assumptions, govern optimal transition from one propulsion mode to another for two cases: the case in which engine cycle operations can overlap, and the case in which engine cycle operations are mutually exclusive. The resulting guidance algorithm was implemented in software and exercised extensively. It was found that the approximations associated with the assumed time scale separation employed in this work are reasonable except over the Mach range from roughly 5 to 8. This phenomenon is due to the very large thrust capability of scramjets in this Mach regime when sized to meet the requirement for ascent to orbit. By accounting for flight path angle and flight path angle rate in construction of the flight path over this Mach range, the resulting algorithm provides the means for rapid near-optimal trajectory generation and propulsion cycle selection over the entire Mach range from take-off to orbit.
Calise, A. J.↗