Optimum processes in systems with distributed parameters and some problems of invariance theory
Optimal control processes in systems with distributed parameters, and problems of invariance theory
CONTROL SYSTEM↗
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Entropy and chemical change. 1: Characterization of product (and reactant) energy distributions in reactive molecular collisions: Information and enthropy deficiency
Optimal means of characterizing the distribution of product energy states resulting from reactive collisions of molecules with restricted distributions of initial states are considered, along with those for characterizing the particular reactant state distribution which yields a given set of product states at a specified total energy. It is suggested to represent the energy-dependence of global-type results in the form of square-faced bar plots, and of data for specific-type experiments as triangular-faced prismatic plots. The essential parameters defining the internal state distribution are isolated, and the information content of such a distribution is put on a quantitative basis. The relationship between the information content, the surprisal, and the entropy of the continuous distribution is established. The concept of an entropy deficiency, which characterizes the specificity of product state formation, is suggested as a useful measure of the deviance from statistical behavior. The degradation of information by experimental averaging is considered, leading to bounds on the entropy deficiency.
Bernstein, R. B.↗
Mapping the global distribution of C4 vegetation using observations and optimality theory
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Xiangzhong Luo↗
Computational wing optimization and comparisons with experiment for a semi-span wing model
A computational wing optimization procedure was developed and verified by an experimental investigation of a semi-span variable camber wing model in the NASA Ames Research Center 14 foot transonic wind tunnel. The Bailey-Ballhaus transonic potential flow analysis and Woodward-Carmichael linear theory codes were linked to Vanderplaats constrained minimization routine to optimize model configurations at several subsonic and transonic design points. The 35 deg swept wing is characterized by multi-segmented leading and trailing edge flaps whose hinge lines are swept relative to the leading and trailing edges of the wing. By varying deflection angles of the flap segments, camber and twist distribution can be optimized for different design conditions. Results indicate that numerical optimization can be both an effective and efficient design tool. The optimized configurations had as good or better lift to drag ratios at the design points as the best designs previously tested during an extensive parametric study.
Waggoner, E. G.↗
Development of Variable Camber Continuous Trailing Edge Flap for Performance Adaptive Aeroelastic Wing
This paper summarizes the recent development of an adaptive aeroelastic wing shaping control technology called variable camber continuous trailing edge flap (VCCTEF). As wing flexibility increases, aeroelastic interactions with aerodynamic forces and moments become an increasingly important consideration in aircraft design and aerodynamic performance. Furthermore, aeroelastic interactions with flight dynamics can result in issues with vehicle stability and control. The initial VCCTEF concept was developed in 2010 by NASA under a NASA Innovation Fund study entitled "Elastically Shaped Future Air Vehicle Concept," which showed that highly flexible wing aerodynamic surfaces can be elastically shaped in-flight by active control of wing twist and bending deflection in order to optimize the spanwise lift distribution for drag reduction. A collaboration between NASA and Boeing Research & Technology was subsequently funded by NASA from 2012 to 2014 to further develop the VCCTEF concept. This paper summarizes some of the key research areas conducted by NASA during the collaboration with Boeing Research and Technology. These research areas include VCCTEF design concepts, aerodynamic analysis of VCCTEF camber shapes, aerodynamic optimization of lift distribution for drag minimization, wind tunnel test results for cruise and high-lift configurations, flutter analysis and suppression control of flexible wing aircraft, and multi-objective flight control for adaptive aeroelastic wing shaping control.
Aircraft↗
A minimum principle for smooth first-order distributed systems
Consideration of the problem of characterizing optimal controls for a class of distributed parameter systems. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables. Boundary conditions on the state are in the form of a finite number of algebraic relations between the state and boundary control variables. A few directions are outlined in which the results obtained may be extended further.
Johnson, T. L.↗
Development of Multiobjective Optimization Techniques for Sonic Boom Minimization
A discrete, semi-analytical sensitivity analysis procedure has been developed for calculating aerodynamic design sensitivities. The sensitivities of the flow variables and the grid coordinates are numerically calculated using direct differentiation of the respective discretized governing equations. The sensitivity analysis techniques are adapted within a parabolized Navier Stokes equations solver. Aerodynamic design sensitivities for high speed wing-body configurations are calculated using the semi-analytical sensitivity analysis procedures. Representative results obtained compare well with those obtained using the finite difference approach and establish the computational efficiency and accuracy of the semi-analytical procedures. Multidisciplinary design optimization procedures have been developed for aerospace applications namely, gas turbine blades and high speed wing-body configurations. In complex applications, the coupled optimization problems are decomposed into sublevels using multilevel decomposition techniques. In cases with multiple objective functions, formal multiobjective formulation such as the Kreisselmeier-Steinhauser function approach and the modified global criteria approach have been used. Nonlinear programming techniques for continuous design variables and a hybrid optimization technique, based on a simulated annealing algorithm, for discrete design variables have been used for solving the optimization problems. The optimization procedure for gas turbine blades improves the aerodynamic and heat transfer characteristics of the blades. The two-dimensional, blade-to-blade aerodynamic analysis is performed using a panel code. The blade heat transfer analysis is performed using an in-house developed finite element procedure. The optimization procedure yields blade shapes with significantly improved velocity and temperature distributions. The multidisciplinary design optimization procedures for high speed wing-body configurations simultaneously improve the aerodynamic, the sonic boom and the structural characteristics of the aircraft. The flow solution is obtained using a comprehensive parabolized Navier Stokes solver. Sonic boom analysis is performed using an extrapolation procedure. The aircraft wing load carrying member is modeled as either an isotropic or a composite box beam. The isotropic box beam is analyzed using thin wall theory. The composite box beam is analyzed using a finite element procedure. The developed optimization procedures yield significant improvements in all the performance criteria and provide interesting design trade-offs. The semi-analytical sensitivity analysis techniques offer significant computational savings and allow the use of comprehensive analysis procedures within design optimization studies.
Chattopadhyay, Aditi↗
Coupled Multi-Disciplinary Optimization for Structural Reliability and Affordability
A computational simulation method is presented for Non-Deterministic Multidisciplinary Optimization of engine composite materials and structures. A hypothetical engine duct made with ceramic matrix composites (CMC) is evaluated probabilistically in the presence of combined thermo-mechanical loading. The structure is tailored by quantifying the uncertainties in all relevant design variables such as fabrication, material, and loading parameters. The probabilistic sensitivities are used to select critical design variables for optimization. In this paper, two approaches for non-deterministic optimization are presented. The non-deterministic minimization of combined failure stress criterion is carried out by: (1) performing probabilistic evaluation first and then optimization and (2) performing optimization first and then probabilistic evaluation. The first approach shows that the optimization feasible region can be bounded by a set of prescribed probability limits and that the optimization follows the cumulative distribution function between those limits. The second approach shows that the optimization feasible region is bounded by 0.50 and 0.999 probabilities.
Abumeri, Galib H.↗
Optimal partitioning of random programs across two processors
The optimal partitioning of random-distributed programs is discussed. It is concluded that the optimal partitioning of a homogeneous random program over a homogeneous distributed system either assigns all modules to a single processor, or distributes the modules as evenly as possible among all processors. The analysis rests heavily on the approximation which equates the expected maximum of a set of independent random variables with the set's maximum expectation. The results are strengthened by providing an approximation-free proof of this result for two processors under general conditions on the module execution time distribution. It is also shown that use of this approximation causes two of the previous central results to be false.
Nicol, David M.↗
Electric power processing, distribution and control for advanced aerospace vehicles.
The results of a current study program to develop a rational basis for selection of power processing, distribution, and control configurations for future aerospace vehicles including the Space Station, Space Shuttle, and high-performance aircraft are presented. Within the constraints imposed by the characteristics of power generation subsystems and the load utilization equipment requirements, the power processing, distribution and control subsystem can be optimized by selection of the proper distribution voltage, frequency, and overload/fault protection method. It is shown that, for large space vehicles which rely on static energy conversion to provide electric power, high-voltage dc distribution (above 100 V dc) is preferable to conventional 28 V dc and 115 V ac distribution per MIL-STD-704A. High-voltage dc also has advantages over conventional constant frequency ac systems in many aircraft applications due to the elimination of speed control, wave shaping, and synchronization equipment.
Krausz, A.↗
On modeling performance of open-loop mechanisms
A technique is presented for modeling the performance of open-loop mechanisms or systems, where performance is measured by success or failure as a function of the selected target for movement along a constrained trajectory and without corrective feedback. A modification of signal detection theory is used, which normalizes dissimilar data and indicates two independent parameters of performance: (1) discriminability and (2) optimality of the distribution of selected moves. An illustrative application is made to experimental data.
Sheridan, T. B.↗
High frequency sound attenuation in short flow ducts
A geometrical acoustics approach is proposed as a practical design tool for absorbent liners in such short flow ducts as may be found in turbofan engine nacelles. As an example, a detailed methodology is presented for three different types of sources in a parallel plate duct containing uniform ambient flow. A plane wave whose wavefronts are not normal to the duct walls, an arbitrarily located point source, and a spatially harmonic line source are each considered. Optimal wall admittance distributions are found, and it is shown how to estimate the insertion loss for any admittance distribution. The extension of the methodology to realistic source distributions in variable area cylindrical or annular ducts containing arbitrary flow is shown to be conceptually straightforward and computationally practical on a vector-hardware digital computer.
Posey, J. W.↗
High lift selected concepts
The benefits to high lift system maximum life and, alternatively, to high lift system complexity, of applying analytic design and analysis techniques to the design of high lift sections for flight conditions were determined and two high lift sections were designed to flight conditions. The influence of the high lift section on the sizing and economics of a specific energy efficient transport (EET) was clarified using a computerized sizing technique and an existing advanced airplane design data base. The impact of the best design resulting from the design applications studies on EET sizing and economics were evaluated. Flap technology trade studies, climb and descent studies, and augmented stability studies are included along with a description of the baseline high lift system geometry, a calculation of lift and pitching moment when separation is present, and an inverse boundary layer technique for pressure distribution synthesis and optimization.
Henderson, M. L.↗
Design of helicopter rotor blades for optimum dynamic characteristics
The possibilities and limitations of tailoring blade mass and stiffness distributions to give an optimum blade design in terms of weight, inertia, and dynamic characteristics are discussed. The extent that changes in mass of stiffness distribution can be used to place rotor frequencies at desired locations is determined. Theoretical limits to the amount of frequency shift are established. Realistic constraints on blade properties based on weight, mass, moment of inertia, size, strength, and stability are formulated. The extent that the hub loads can be minimized by proper choice of E1 distribution, and the minimum hub loads which can be approximated by a design for a given set of natural frequencies are determined. Aerodynamic couplings that might affect the optimum blade design, and the relative effectiveness of mass and stiffness distribution on the optimization procedure are investigated.
Peters, D. A.↗
Construction and control of large space structures
Recent NASA research efforts on space construction are reviewed. Preliminary results of the EASE/ACCESS Shuttle experiments are discussed. A 45-foot beam was constructed on orbit in 30 minutes using a manual assembly technique at a work station. A large tetrahedron was constructed several times using a free floating technique. The capability of repair, utilities installation, and handling the structures using a mobile foot restraint on the RMS was also demonstrated. Implications of the experiments for Space Station are presented. Models of 5-meter Space Station structure together with neutral buoyancy simulations suggest manual assembly techniques are feasible. Selected research on control of flexible structures is discussed. To support planned flight experiments, studies of the design and optimal placement of distributed active dampers are underway.
Card, M. F.↗
Cooperative control of two arms in the transport of an inertial load in zero gravity
In designing a robot control system for dual arm configurations, the control engineer is faced with two challenges: to derive the equations of motion for a given situation, and to meet certain desired control requirements (for instance, minimum energy). The former may involve closed kinematic chains, such as the case when the two arms are grasping a common object. The latter usually involves nonlinear optimization. These issues are considered in the context of transporting an inertial load using two planar three-link arms. A generalized 'reduction transformation' is applied to the dynamics to remove the singularity in the system equations. A suboptimal minimum energy method is presented to reduce a difficult 12-state, six-control nonlinear optimization to two independent, nonconflicting suboptimizations. A simulation example is provided to illustrate the degree of energy reduction possible using the optimal arm torque distribution that was developed.
Carignan, Craig R.↗
Application of a Navier-Stokes aeroelastic method to improve fighter wing performance at maneuver flight conditions
An aeroelastic analysis method, based on three-dimensional Navier-Stokes equation aerodynamics, has been applied to improve the performance of fighter wings operating at sustained maneuver flight conditions. The scheme reduces the trimmed pressure drag of wings performing high-g maneuvers through a simultaneous application of control surface deflection and aeroelastic twist. The aerodynamic and structural interactions are decoupled by assuming an aeroelastic twist mode shape and optimizing the aerodynamic performance based on this aeroelastic mode. The wing structural stiffness properties are then determined through an inverse scheme based on the aerodynamic loads and desired twist at the maneuver flight condition. The decoupled technique is verified by performing a fully coupled aeroelastic analysis using the maneuver flight conditions and the optimized structural stiffness distributions.
Schuster, David M.↗
Flight data results of estimate fusion for spacecraft rendezvous navigation from shuttle mission STS-69
A recently developed rendezvous navigation fusion filter that optimally exploits existing distributed filters for rendezvous and GPS navigation to achieve the relative and inertial state accuracies of both in a global solution is utilized here to process actual flight data. Space Shuttle Mission STS-69 was the first mission to date which gathered data from both the rendezvous and Global Positioning System filters allowing, for the first time, a test of the fusion algorithm with real flight data. Furthermore, a precise best estimate of trajectory is available for portions of STS-69, making possible a check on the performance of the fusion filter. In order to successfully carry out this experiment with flight data, two extensions to the existing scheme were necessary: a fusion edit test based on differences between the filter state vectors, and an underweighting scheme to accommodate the suboptimal perfect target assumption made by the Shuttle rendezvous filter. With these innovations, the flight data was successfully fused from playbacks of downlinked and/or recorded measurement data through ground analysis versions of the Shuttle rendezvous filter and a GPS filter developed for another experiment. The fusion results agree with the best estimate of trajectory at approximately the levels of uncertainty expected from the fusion filter's covariance matrix.
Carpenter, J. Russell↗