Caratheodory-Hamilton-Jacobi theory in optimal control.
Caratheodory unified approach to Hamilton-Jacobi theory in variational calculus problems of optimal control
HAMILTON-JACOBI EQUATION↗
SEARCH · Search NASA
Results for “control variates”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Guidance and control analysis and integration
Automation of variational methods for solution of optimum control problems, optical data sources for Mars-encounter earth-based orbit determination, and operational support equipment
Source record↗
Singular optimal control and the identically non-regular problem in the calculus of variations
A small but interesting class of optimal control problems featuring a scalar control appearing linearly is equivalent to the class of identically nonregular problems in the Calculus of Variations. It is shown that a condition due to Mancill (1950) is equivalent to the generalized Legendre-Clebsch condition for this narrow class of problems.
Menon, P. K. A.↗
Variable Emissivity Through MEMS Technology
This paper discusses a new technology for variable emissivity (vari-e) radiator surfaces, which has significant advantages over traditional radiators and promises an alternative design technique for future spacecraft thermal control systems. All spacecraft rely on radiative surfaces to dissipate waste heat. These radiators have special coatings, typically with a low solar absorptivity and a high infrared-red emissivity, that are intended to optimize performance under the expected heat load and thermal sink environment. The dynamics of the heat loads and thermal environment make it a challenge to properly size the radiator and often require some means of regulating the heat rejection rate of the radiators in order to achieve proper thermal balance. Specialized thermal control coatings, which can passively or actively adjust their emissivity offer an attractive solution to these design challenges. Such systems would allow intelligent control of the rate of heat loss from a radiator in response to heat load and thermal environmental variations. Intelligent thermal control through variable emissivity systems is well suited for nano and pico spacecraft applications where large thermal fluctuations are expected due to the small thermal mass and limited electric resources. Presently there are three different types of vari-e technologies under development: Micro ElectroMechanical Systems (MEMS) louvers, Electrochromic devices, and Electrophoretic devices. This paper will describe several prototypes of micromachined (MEMS) louvers and experimental results for the emissivity variations measured on theses prototypes. It will further discuss possible actuation mechanisms and space reliability aspects for different designs. Finally, for comparison parametric evaluations of the thermal performances of the new vari-e technology and standard thermal control systems are presented in this paper.
Darrin, Ann Garrison↗
Impact of mismodeled idle engine performance on calculation and tracking of optimal 4-D descent trajectories
Advanced flight management systems are being developed which are capable of calculating optimal 3-D and 4-D flight trajectories for arbitrary fuel and time costs. These systems require mathematical models of airplane performance in order to compute the optimal profiles. Mismodeled idle engine characteristics can result in descent trajectories requiring excessive throttle and/or speedbrake activity in order to achieve the desired end conditions. This paper evaluates the cost and fuel penalties, trajectory variations, and flight control requirements associated with typical idle engine modeling errors for a twin-jet transport airplane. Variations in idle power setting, thrust, fuel flow, and surge bleed operation were evaluated for a cruise/descent flight segment. The results of this analysis provide insight into the penalties associated with uncertainties in idle engine performance and suggest methods of modeling which minimize these penalties.
Williams, D. H.↗
FM oscillator uses tetrode transistor
Tetrode-driven crystal oscillator achieves large frequency variations for a given input signal. Frequency control is obtained by variation of the second base current of the tetrode.
Boensel, D. W.↗
Set-point control of nonlinear systems
A method of nonlinear stochastic control is applied to the problem of providing set-point control. The procedure is illustrated for a nonlinear second-order plant. The controller design uses a variation of the 'multiple-model adaptive control' approach. Specific problems related to the design are investigated, including learning time and set-point accuracy dependence on the number of approximating models, chord versus tangent approximations, and the a priori Markov switching parameter values. Simulations are provided for different situations under various levels of measurement noise.
Vanlandingham, H. F.↗
Environmental parameters of the Tennessee River in Alabama. 2: Physical, chemical, and biological parameters
Physical, chemical and biological water quality data from five sites in the Tennessee River, two in Guntersville Reservoir and three in Wheeler Reservoir were correlated with climatological data for three annual cycles. Two of the annual cycles are for the years prior to the Browns Ferry Nuclear Power Plant operations and one is for the first 14 months of Plant operations. A comparison of the results of the annual cycles indicates that two distinct physical conditions in the reservoirs occur, one during the warm months when the reservoirs are at capacity and one during the colder winter months when the reservoirs have been drawn-down for water storage during the rainy months and for weed control. The wide variations of physical and chemical parameters to which the biological organisms are subjected on an annual basis control the biological organisms and their population levels. A comparison of the parameters of the site below the Power plant indicates that the heated effluent from the plant operating with two of the three reactors has not had any effect on the organisms at this site. Recommendations given include the development of prediction mathematical models (statistical analysis) for the physical and chemical parameters under specific climatological conditions which affect biological organisms. Tabulated data of chemical analysis of water and organism populations studied is given.
Rosing, L. M.↗
Nonlinear control of the minimum safety factor in tokamaks by optimal allocation of spatially moving electron cyclotron current drive
The minimum value of the safety factor profile is related to the magnetohydrodynamic (MHD) stability of the plasma confined in a tokamak. Therefore, active control of the minimum safety factor may mitigate MHD instabilities that can degrade or even terminate plasma confinement. Typically, in most tokamak scenarios, the minimum safety factor evolves spatially with time, i.e., the location at which the safety factor achieves the minimum value changes with time. In addition to the inherent nonlinearities in the minimum safety factor evolution, its spatial variation makes the control design challenging. In particular, complexity in control design may arise from the need for time-dependent nonlinear models that account for spatial variation of the minimum safety factor. Furthermore, the minimum safety factor may drift to locations where the actuator authority is low. The problem of minimum safety factor control with target location tracking and moving electron cyclotron current drive (ECCD) is addressed in this work. A nonlinear time-dependent model that incorporates the spatial variation of the minimum safety factor is presented. A nonlinear controller based on optimal feedback linearization is developed to track a target minimum safety factor. The proposed controller treats the ECCD position as a controllable variable. In other words, the controller prescribes the ECCD position (in addition to the non-inductive powers) in real time based on an optimal criterion that is defined a priori. This work also presents the steps necessary to integrate the minimum safety factor controller with a total energy controller to achieve multiple control objectives simultaneously. In conclusion, the proposed integrated control algorithm is tested using nonlinear simulations in the Control Oriented Transport SIMulator (COTSIM) for a DIII-D tokamak scenario.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Adaptive stochastic control for a class of linear systems.
The problem considered in this paper deals with the control of linear discrete-time stochastic systems with unknown (possibly time-varying and random) gain parameters. The philosophy of control is based on the use of an open-loop feedback optimal (OLFO) control using a quadratic index of performance. It is shown that the OLFO system consists of (1) an identifier that estimates the system state variables and gain parameters and (2) a controller described by an 'adaptive' gain and correction term. Several qualitative properties and asymptotic properties of the OLFO adaptive system are discussed. Simulation results dealing with the control of stable and unstable third-order plants are presented. The key quantitative result is the precise variation of the control system adaptive gains as a function of the future expected uncertainty of the parameters; thus, in this problem the ordinary 'separation theorem' does not hold.
Tse, E.↗
Control law parameterization for an aeroelastic wind-tunnel model equipped with an active roll control system and comparison with experiment
Nominal roll control laws were designed, implemented, and tested on an aeroelastically-scaled free-to-roll wind-tunnel model of an advanced fighter configuration. The tests were performed in the NASA Langley Transonic Dynamics Tunnel. A parametric study of the nominal roll control system was conducted. This parametric study determined possible control system gain variations which yielded identical closed-loop stability (roll mode pole location) and identical roll response but different maximum control-surface deflections. Comparison of analytical predictions with wind-tunnel results was generally very good.
Perry, Boyd, III↗
Control law parameterization for an aeroelastic wind-tunnel model equipped with an active roll control system and comparison with experiment
Nominal roll control laws were designed, implemented, and tested on an aeroelastically-scaled free-to-roll wind-tunnel model of an advanced fighter configuration. The tests were performed in the NASA Langley Transonic Dynamics Tunnel. A parametric study of the nominal roll control system was conducted. This parametric study determined possible control system gain variations which yielded identical closed-loop stability (roll mode pole location) and identical roll response but different maximum control-surface deflections. Comparison of analytical predictions with wind-tunnel results was generally very good.
Perry, Boyd, III↗
The development of a pseudo-nyquist analysis technique for hybrid sampled-data control systems
The stability characteristics of a launch vehicle, as a function of gain and phase variations at the thrust vector controller, cannot be obtained using classical sampled-data control theory if the launch vehicle attitude control system contains both sampled-data and continuous feedback control loops. A method was developed which can be used to generate a sampled-data pseudo-Nyquist plot for gain and phase variations at the controller. This method was developed and used to determine the stability characteristics of the Saturn 1B launch vehicle in the backup guidance mode.
Burnitt, M. G.↗
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.↗
Analysis and design of space vehicle flight control systems. Volume IX - Optimization methods
Variational calculus, gradient methods, maximum principle, and dynamic programing methods of optimal control theory of space vehicles
DYNAMIC PROGRAMMING↗
Self-regulating proportionally controlled heating apparatus and technique
A self-regulating proportionally controlled heating apparatus and technique is provided wherein a single electrical resistance heating element having a temperature coefficient of resistance serves simultaneously as a heater and temperature sensor. The heating element is current-driven and the voltage drop across the heating element is monitored and a component extracted which is attributable to a change in actual temperature of the heating element from a desired reference temperature, so as to produce a resulting error signal. The error signal is utilized to control the level of the heater drive current and the actual heater temperature in a direction to reduce the noted temperature difference. The continuous nature of the process for deriving the error signal feedback information results in true proportional control of the heating element without the necessity for current-switching which may interfere with nearby sensitive circuits, and with no cyclical variation in the controlled temperature.
Strange, M. G.↗
A learning flight control system for the F8-DFBW aircraft
This report contains a complete description of a learning control system designed for the F8-DFBW aircraft. The system is parameter-adaptive with the additional feature that it 'learns' the variation of the control system gains needed over the flight envelope. It, thus, generates and modifies its gain schedule when suitable data are available. The report emphasizes the novel learning features of the system: the forms of representation of the flight envelope and the process by which identified parameters are used to modify the gain schedule. It contains data taken during piloted real-time 6 degree-of-freedom simulations that were used to develop and evaluate the system.
Montgomery, R. C.↗
Temperature effect on turbulent burning velocity of lean premixed hydrogen/air flames
Hydrogen has drawn great attention in recent years as a carbon-free fuel. The turbulent burning velocity (S T ) is an important parameter for the design and modeling of hydrogen-fueled engines given the high propagation speed of hydrogen flames. It has been well documented that S T of hydrogen flames can be dramatically increased by thermo-diffusive effects which are sensitive to thermodynamic conditions. Previous studies have mainly focused on the pressure effect on S T of lean hydrogen flames, while the temperature effect has been largely ignored. Here, in the present study, the turbulent burning velocity for a lean hydrogen/air mixture over a wide range of temperatures (300–641 K) and pressures (1–15 atm) is investigated through direct numerical simulations of statistically planar turbulent premixed flames. Results show that the variation of normalized turbulent burning velocity (S T /S L , where S L is the laminar flame speed) with temperature and pressure is mainly controlled by the variation of the stretching factor I 0 . While S T /S L is only marginally dependent on temperature at the atmospheric pressure, it exhibits a decreasing trend with temperature at an elevated pressure (10 atm). This is associated with different temperature dependencies of flame surface area enlargement at the two different pressures, despite the monotonically decreasing trends of I 0 with temperature at both pressures. In addition, under engine-relevant conditions where the temperature and pressure increase simultaneously, the promotion effect of pressure is found to be largely canceled out by the suppression effect of temperature, leading to only a slight increase in I 0 and S T /S L . The observed trends are further explained through detailed flame dynamic analysis. Furthermore, I 0 at different temperatures and pressures is found to correlate very well with the enhancement of fuel consumption rate in the critically strained laminar flames. The present study elucidates the strong impact of temperature on S T of lean premixed hydrogen/air flames at elevated pressures and provides new insights into the modeling of S T , especially for engine-relevant conditions.
Wang, Yiqing [Argonne National Laboratory (ANL), A↗