Minimum fuel attitude control of a non-linear satellite system
Nonlinear satellite system attitude control for minimum fuel consumption, deriving linear programming algorithm based on optimal control theory
Wolske, G. D.↗
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Synthesis of a non-linear feedback system with significant plant-ignorance for prescribed time-domain tolerances
The problem considered is the design of a feedback system containing a linear, time invariant, minimum phase plant, whose parameters are known only within given bounds, such that the time response of the system remains within specified limits. A quasi-optimal design, for given design constraints, is one which minimizes the effect of white sensor noise on the input to the plant. An investigation was conducted on the use of the non linear device known as the Clegg integrator in the design of such a system. The describing function of the Clegg integrator has the same magnitude characteristic, apart from a scale factor, as the linear integrator, but has 52 deg less phase-lag, at all frequencies, than the linear integrator; thus, when used in a feedback system, it provides a larger stability margin than the linear integrator. This property allows the nonlinear feedback system to be designed so that the sensor noise is attenuated more than in the linear design.
Krishnan, K. R.↗
Dual characterizations of optimal systems.
The complementary variational principle developed in a Hilbert space setting provides a duality principle in the calculus of variations with dynamic constraints. This concept is adopted in this paper to investigate dual characterizations of optimal control systems. Systems under consideration include those with dynamics governed by linear ordinary differential equations, linear partial differential equations and non-linear ordinary differential equations.
Chan, W. L.↗
Mission analysis flow sequencing optimization
This investigation is an extension of a project dealing with the problem of optimal use of ground resources for future space missions. This problem was formulated as a linear programming problem using an indirect approach. Instead of minimizing the inventory level of needed ground resources, the overlapping periods during which the same types of resources are used by various flights are minimized. The model was built upon the assumption that during the time interval under consideration, the costs of various needed resources remain constant. Under other assumptions concerning costs of resources, the objective function, in general, assumes a non-linear form. In this study, one case where the form of the objective function turns out to be quadratic is considered. Also, disadvantages and limitations of the approach used are briefly discussed.
Scott, M.↗
Position Control for Non-linear, Multiple-Link Robots
Several approaches to complicated control problem examined. Report surveys methods for controlling motion of robot manipulators. Applies to coupled, highly nonlinear multiple-link robots. Presents adaptive control technique based on discrete linear model of robot arm, obtained by linearizing nonlinear dynamical equations about nominal trajectory. Parameters of model calculated with adaptive parameter-identification algorithm. Based on system model, optimal control input computed using position and velocity feedback.
Seraji, H.↗
A study of the use of linear programming techniques to improve the performance in design optimization problems
This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.
Young, Katherine C.↗
A study of equation solvers for linear and non-linear finite element analysis on parallel processing computers
Concurrent computing environments provide the means to achieve very high performance for finite element analysis of systems, provided the algorithms take advantage of multiple processors. The authors have examined several algorithms for both linear and nonlinear finite element analysis. The performance of these algorithms on an Alliant FX/80 parallel supercomputer has been studied. For single load case linear analysis, the optimal solution algorithm is strongly problem dependent. For multiple load cases or nonlinear analysis through a modified Newton-Raphson method, decomposition algorithms are shown to have a decided advantage over element-by-element preconditioned conjugate gradient algorithms.
Watson, Brian C.↗
Mechanically fastened composite laminates subjected to combined bearing-bypass and shear loading
Bolts and rivets provide a means of load transfer in the construction of aircraft. However, they give rise to stress concentrations and are often the source and location of static and fatigue failures. Furthermore, fastener holes are prone to cracks during take-off and landing. These cracks present the most common origin of structural failures in aircraft. Therefore, accurate determination of the contact stresses associated with such loaded holes in mechanically fastened joints is essential to reliable strength evaluation and failure prediction. As the laminate is subjected to loading, the contact region, whose extent is not known, develops between the fastener and the hole boundary through this contact region, which consists of slip and no-slip zones due to friction. The presence of the unknown contact stress distribution over the contact region between the pin and the composite laminate, material anisotropy, friction between the pin and the laminate, pin-hole clearance, combined bearing-bypass and shear loading, and finite geometry of the laminate result in a complex non-linear problem. In the case of bearing-bypass loading in compression, this non-linear problem is further complicated by the presence of dual contact regions. Previous research concerning the analysis of mechanical joints subjected to combined bearing-bypass and shear loading is non-existent. In the case of bearing-bypass loading only, except for the study conducted by Naik and Crews (1991), others employed the concept of superposition which is not valid for this non-linear problem. Naik and Crews applied a linear finite element analysis with conditions along the pin-hole contact region specified as displacement constraint equations. The major shortcoming of this method is that the variation of the contract region as a function of the applied load should be known a priori. Also, their analysis is limited to symmetric geometry and material systems, and frictionless boundary conditions. Since the contact stress distribution and the contact region are not known a priori, they did not directly impose the boundary conditions appropriate for modelling the contact and on-contact regions between the fastener and the hole. Furthermore, finite element analysis is not suitable for iterative design calculations for optimizing laminate construction in the presence of fasteners under complex loading conditions. In this study, the solution method developed by Madenci and Ileri (1992a,b) has been extended to determine the contact stresses in mechanical joints under combined bearing-bypass and shear loading, and bearing-bypass loading in compression resulting in dual contact regions.
Madenci, Erdogan↗
Fluid flow volume measurements using a capacitance/conductance probe system
A probe system has been developed to measure the flow volume of a single fluid passing through an orifice or flow line. The system employs both capacitance and a conductance probe at the orifice, together with phase detection and data acquisition circuitry to measure flow volume and salinity under low or zero gravity conditions. A wide variety of frequencies can be used for the radio frequency (RF) signal source which is chosen primarily by the capacitance of the orifice probe and the fluid passing through the orifice. Rapid measurements are made using the reflected signal from the orifice probe to determine the 'instantaneous' permittivity of the fluid/gas mixture passing through. The 'instantaneous' measurements are integrated over time to determine flow volume. Analysis reveals that a narrow orifice helps to reduce non-linearities caused by differing flow rates. The geometry of 'deflectors' and 'directors' for the flowing fluid are important in obtaining linearity. Measured data shows that a volume measurement accuracy of approximately four percent can be consistently achieved. The prototype hardware system and associated software have been optimized and are available for further applications. The system has immediate application in low or zero gravity environments for measurements of urine or other liquid volumes.
Nguyen, T. X.↗
Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse-Shear Effects
The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. The formulation uses the principle of virtual work. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are then derived after the application of several simplifying assumptions. These equations are then modified to allow the reference surface of the plate to be located at a distance z(sub c) from the centroidal surface. The implementation of the new theory into the VICONOPT exact buckling and vibration analysis and optimum design computer program is described as well. The terms of the plate stiffness matrix using both Classical Plate Theory (CPT) and first-order Shear-Deformation Plate Theory (SDPT) are presented. The necessary steps to include the effects of in-plane transverse and in-plane shear loads in the in-plane stability equations are also outlined. Numerical results are presented using the newly implemented capability. Comparisons of results for several example problems with different loading states are made. Comparisons of analyses using both physical and tensorial strain measures as well as CPT and SDPF are also made. Results comparing the computational effort required by the new analysis to that of the analysis currently in the VICONOPT program are presented. The effects of including terms related to in-plane transverse and in-plane shear loadings in the in-plane stability equations are also examined. Finally, results of a design-optimization study of two different cylindrical shells subject to uniform axial compression are presented.
McGowan, David Michael↗
Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse Shear Effects
The analytical formulation of curved-plate non-linear equilibrium equations that include transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Using several simplifying assumptions, linearized, stability equations are derived that describe the response of the plate just after bifurcation buckling occurs. These equations are then modified to allow the plate reference surface to be located a distance z(c), from the centroid surface which is convenient for modeling stiffened-plate assemblies. The implementation of the new theory into the VICONOPT buckling and vibration analysis and optimum design program code is described. Either classical plate theory (CPT) or first-order shear-deformation plate theory (SDPT) may be selected in VICONOPT. Comparisons of numerical results for several example problems with different loading states are made. Results from the new curved-plate analysis compare well with closed-form solution results and with results from known example problems in the literature. Finally, a design-optimization study of two different cylindrical shells subject to uniform axial compression is presented.
McGowan, David M.↗
Engineering Overview of a Multidisciplinary HSCT Design Framework Using Medium-Fidelity Analysis Codes
An objective of the HPCC Program at NASA Langley has been to promote the use of advanced computing techniques to more rapidly solve the problem of multidisciplinary optimization of a supersonic transport configuration. As a result, a software system has been designed and is being implemented to integrate a set of existing discipline analysis codes, some of them CPU-intensive, into a distributed computational framework for the design of a High Speed Civil Transport (HSCT) configuration. The proposed paper will describe the engineering aspects of integrating these analysis codes and additional interface codes into an automated design system. The objective of the design problem is to optimize the aircraft weight for given mission conditions, range, and payload requirements, subject to aerodynamic, structural, and performance constraints. The design variables include both thicknesses of structural elements and geometric parameters that define the external aircraft shape. An optimization model has been adopted that uses the multidisciplinary analysis results and the derivatives of the solution with respect to the design variables to formulate a linearized model that provides input to the CONMIN optimization code, which outputs new values for the design variables. The analysis process begins by deriving the updated geometries and grids from the baseline geometries and grids using the new values for the design variables. This free-form deformation approach provides internal FEM (finite element method) grids that are consistent with aerodynamic surface grids. The next step involves using the derived FEM and section properties in a weights process to calculate detailed weights and the center of gravity location for specified flight conditions. The weights process computes the as-built weight, weight distribution, and weight sensitivities for given aircraft configurations at various mass cases. Currently, two mass cases are considered: cruise and gross take-off weight (GTOW). Weights information is obtained from correlations of data from three sources: 1) as-built initial structural and non-structural weights from an existing database, 2) theoretical FEM structural weights and sensitivities from Genesis, and 3) empirical as-built weight increments, non-structural weights, and weight sensitivities from FLOPS. For the aeroelastic analysis, a variable-fidelity aerodynamic analysis has been adopted. This approach uses infrequent CPU-intensive non-linear CFD to calculate a non-linear correction relative to a linear aero calculation for the same aerodynamic surface at an angle of attack that results in the same configuration lift. For efficiency, this nonlinear correction is applied after each subsequent linear aero solution during the iterations between the aerodynamic and structural analyses. Convergence is achieved when the vehicle shape being used for the aerodynamic calculations is consistent with the structural deformations caused by the aerodynamic loads. To make the structural analyses more efficient, a linearized structural deformation model has been adopted, in which a single stiffness matrix can be used to solve for the deformations under all the load conditions. Using the converged aerodynamic loads, a final set of structural analyses are performed to determine the stress distributions and the buckling conditions for constraint calculation. Performance constraints are obtained by running FLOPS using drag polars that are computed using results from non-linear corrections to the linear aero code plus several codes to provide drag increments due to skin friction, wave drag, and other miscellaneous drag contributions. The status of the integration effort will be presented in the proposed paper, and results will be provided that illustrate the degree of accuracy in the linearizations that have been employed.
Weston, R. P.↗
Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse-Shear Effects
The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are derived. These equations are then modified to allow the plate reference surface to be located a distance z(sub c) from the centroidal surface. The implementation of the new theory into the VICONOPT exact buckling and vibration analysis and optimum design computer program is described. The terms of the plate stiffness matrix using both classical plate theory (CPT) and first-order shear-deformation plate theory (SDPT) are presented. The effects of in-plane transverse and in-plane shear loads are included in the in-plane stability equations. Numerical results for several example problems with different loading states are presented. Comparisons of analyses using both physical and tensorial strain measures as well as CPT and SDPT are made. The computational effort required by the new analysis is compared to that of the analysis currently in the VICONOPT program. The effects of including terms related to in-plane transverse and in-plane shear loadings in the in-plane stability equations are also examined. Finally, results of a design-optimization study of two different cylindrical shells subject to uniform axial compression are presented.
McGowan, David M.↗
Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm
A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and by appropriate choice of coordinates and simplified measurement modeling is formulated as a linear time-invariant system. Results for improvements to the GSFC algorithm and a multiple satellite formation will be addressed. The goal of this investigation is to progressively relax the assumptions that result in linear time-invariance, ultimately to the point of linearization of the non-linear dynamics about the current state estimate as in the extended Kalman filter. An assessment will then be made about the feasibility of the decentralized approach to the realistic formation flying application of the EO-1/Landsat 7 formation flying experiment.
Folta, David C.↗
Multiple Mode Actuation of a Turbulent Jet
The effects of multiple mode periodic excitation on the evolution of a circular turbulent jet were studied experimentally. A short, wide-angle diffuser was attached to the jet exit. Streamwise and cross-stream excitations were introduced at the junction between the jet exit and the diffuser inlet on opposing sides of the jet. The introduction of high amplitude, periodic excitation in the streamwise direction enhances the mixing and promotes attachment of the jet shear-layer to the diffuser wall. Cross-stream excitation applied over a fraction of the jet circumference can deflect the jet away from the excitation slot. The two modes of excitation were combined using identical frequencies and varying the relative phase between the two actuators in search of an optimal response. It is shown that, for low and moderate periodic momentum input levels, the jet deflection angles depend strongly on the relative phase between the two actuators. Optimum performance is achieved when the phase difference is pi +/- pi/6. The lower effectiveness of the equal phase excitation is attributed to the generation of an azimuthally symmetric mode that does not produce the required non-axisymmetric vectoring. For high excitation levels, identical phase becomes more effective, while phase sensitivity decreases. An important finding was that with proper phase tuning, two unsteady actuators can be combined to obtain a non-linear response greater than the superposition of the individual effects.
Pack, LaTunia G.↗
Planning Paths Through Singularities in the Center of Mass Space
The center of mass space is a convenient space for planning motions that minimize reaction forces at the robot's base or optimize the stability of a mechanism. A unique problem associated with path planning in the center of mass space is the potential existence of multiple center of mass images for a single Cartesian obstacle, since a single center of mass location can correspond to multiple robot joint configurations. The existence of multiple images results in a need to either maintain multiple center of mass obstacle maps or to update obstacle locations when the robot passes through a singularity, such as when it moves from an elbow-up to an elbow-down configuration. To illustrate the concepts presented in this paper, a path is planned for an example task requiring motion through multiple center of mass space maps. The object of the path planning algorithm is to locate the bang- bang acceleration profile that minimizes the robot's base reactions in the presence of a single Cartesian obstacle. To simplify the presentation, only non-redundant robots are considered and joint non-linearities are neglected.
Doggett, William R.↗
Predicting Team Functioning in Long Term Space Missions Using Acoustic and Linguistic Measures
Maintaining optimal team functioning is critical for long-duration space exploration missions, yet traditional monitoring methods, such as self-reports and wearable sensors, often impose operational burdens or suffer from bias. This paper investigates a non-intrusive speech-based artificial intelligence (AI) framework to predict degradations in team functioning using data from the Human Exploration Research Analog (HERA) of the U.S. National Aeronautics and Space Administration (NASA). Using acoustic features, linguistic descriptors, and semantic embeddings, we evaluate static non-linear and temporal machine learning models to predict both objective (task accuracy) and subjective (self-reported efficacy and cohesion) team functioning outcomes. Results indicate that temporal models outperform static approaches, with prediction of objective task accuracy in Team Interaction Battery (TIB) improving from near chance to 71%. Self-reported outcomes, including team efficacy and cohesion, are predicted more reliably than task performance, achieving balanced accuracies of up to 85.56% and 78.12%, respectively, and are found to be most strongly associated with acoustic features. In a second interdependent task, the MMSEV–EVA, accuracies of up to 78% are achieved using temporal models with acoustic features. Furthermore, incorporating just 1–2 days of team-specific historical data systematically improved performance, and acoustic markers from informal pre-task interactions provided modest predictive gains. Finally, while automated preprocessing yielded viable accuracy, humancorrected data provided moderate performance gains, though transcription error rates did not significantly correlate with model performance. These findings highlight the potential of speech as a passive, high-fidelity monitoring tool for autonomous habitats.
Temporal modeling↗
Poisson Log-Normal Process for Count Data Prediction
Modeling count data is important in physics and other scientific disciplines, where measurements often involve discrete, non-negative quantities such as photon or neutrino detection events. Traditional parametric approaches can be trained to generate integer-count predictions but may struggle with capturing complex, non-linear dependencies often observed in the data. Gaussian process (GP) regression provides a robust non-parametric alternative to modeling continuous data; however, it cannot generate integer outputs. We propose the Poisson Log-Normal (PoLoN) process, a framework that employs GP to model Poisson log-rates. As in GP regression, our approach relies on the correlations between data points captured via GP kernel structure rather than explicit functional parameterizations. We demonstrate that the PoLoN predictive distribution is Poisson-LogNormal and provide an algorithm for optimizing kernel hyperparameters. Furthermore, we adapt the PoLoN approach to the problem of detecting weak localized signals superimposed on a smoothly varying background - a task of considerable interest in many areas of science and engineering. Our framework allows us to predict the strength, location and width of the detected signals. We evaluate PoLoN's performance using both synthetic and real-world datasets, including the open dataset from CERN which was used to detect the Higgs boson at the Large Hadron Collider. Our results indicate that the PoLoN process can be used as a non-parametric alternative for analyzing, predicting, and extracting signals from integer-valued data.
Saha, Anushka [Rutgers U., Piscataway]↗