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The problem of robust stability in linear systems with parametric uncertainties is considered. Explicit stability bounds on uncertain parameters are derived and expressed in terms of linear inequalities for continuous systems, and inequalities with quadratic terms for discrete-times systems. Cases where system parameters are nonlinear functions of an uncertainty are also examined.
An experimental investigation was made of a preloaded spring-tab flutter model to determine the effects on flutter speed of aspect ratio, tab frequency, and preloaded spring constant. The rudder was mass-balanced, and the flutter mode studied was essentially one of three degrees of freedom (fin bending coupled with rudder and tab oscillations). Inasmuch as the spring was preloaded, the tab-spring system was a nonlinear one. Frequency of the tab was the most significant parameter in this study, and an increase in flutter speed with increasing frequency is indicated. At a given frequency, the tab of high aspect ratio is shown to have a slightly lower flutter speed than the one of low aspect ratio. Because the frequency of the preloaded spring tab was found to vary radically with amplitude, the flutter speed decreased with increase in initial displacement of the tab.
Fluid whirl and fluid whip are rotor self-excited, lateral vibrations which occur due to rotor interactions with the surrounding fluid. There exist various modes of fluid whirl and fluid whip. These modes are close to rotor modes corresponding to free vibrations (based on the linear model). Small differences are due to nonlinearities in the system. This paper presents experimental and analytical results on the lowest modes of fluid whirls and fluid whip. Examples of rotors supported in fluid lubricated bearings show the variations of rotor deflection amplitudes and phases in the whirl and whip modes with changes of rotative speeds and/or changes in lumped mass locations along the shaft.
Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.
This document presents an approach for modeling and simulating landing gear systems. Specifically, a nonlinear model of an A-6 Intruder Main Gear is developed, simulated, and validated against static and dynamic test data. This model includes nonlinear effects such as a polytropic gas model, velocity squared damping, a geometry governed model for the discharge coefficients, stick-slip friction effects and a nonlinear tire spring and damping model. An Adams-Moulton predictor corrector was used to integrate the equations of motion until a discontinuity caused by a stick-slip friction model was reached, at which point, a Runga-Kutta routine integrated past the discontinuity and returned the problem solution back to the predictor corrector. Run times of this software are around 2 mins. per 1 sec. of simulation under dynamic circumstances. To validate the model, engineers at the Aircraft Landing Dynamics facilities at NASA Langley Research Center installed one A-6 main gear on a drop carriage and used a hydraulic shaker table to provide simulated runway inputs to the gear. Model parameters were tuned to produce excellent agreement for many cases.
A space bound storage device has many special requirements. In addition to large storage capacity, fas read/ write time, and high reliability, it also needs to have small volume, light weight, low power consumption, radiation hardening, ability to operate in extreme temperature ranges, etc. Holographic optical recording technology, which has been making major advancements in recent years, is an extremely promising candidate. The goal of this pilot project is to demonstrate a laboratory bench-top holographic optical recording storage system (HORSS) based on nonlinear polymer films 1 and/or other advanced photo-refractive materials. This system will be used as a research vehicle to study relevant optical properties of novel holographic optical materials, to explore massive optical storage technologies based on the photo-refractive effect and to evaluate the feasibility of developing a massive storage system, based on holographic optical recording technology, for a space bound experiment in the near future.
This paper addresses some modeling and control issues for a mixing chamber used in rocket engine testing at NASA Stennis Space Center. The mixer must combine high pressure liquid hydrogen (LH2) and gaseous hydrogen (GH2) to produce and output flow that meets certain thermodynamic properties before it is fed into a test article. More precisely, this paper considers that the quantities to be tracked and/or regulated are mixer internal pressure, exit mass flow, and exit temperature. The available control inputs are given by three value positions, namely those of the GH2, LH2 and exit valves. The mixer is modelled by a system of two nonlinear ordinary differential equations having density and internal energy as states. The model must be simple enough to lend itself to subsequent feedback controller design, yet its accuracy must be tested against real data. For this reason, the model includes function calls to thermodynamic property data. Some structural properties of the resulting model that pertain to controller design, such as controllability and uniqueness of the equilibrium point are shown to hold. Validation of the model against real data is also provided. As a first control approach, a small-signal (linear) model is developed based on the nonlinear model and simulated as well. Pulse disturbances are introduced to the valve positions and the quality of the linear model is ascertained by comparing its behavior against the nonlinear model simulations. Valve control strategies that simulate an operator-in-the-loop scenario are then explored demonstrating the need for automatic feedback control. Classical optimal single-output and multi-output Proportional/Integral controllers are designed based on the linear model and applied to the nonlinear model with excellent results to track simultaneous, constant setpoint changes in desired exit flow, exit temperature, and mixer pressure, as well as to reject unmeasurable but bounded additive step perturbations in the valve positions. A feedback linearization controller is designed and used to achieve tracking and regulation of the outputs over an extended range of the variables of interest.
A mixing chamber used in rocket engine testing at the NASA Stennis Space Center is modelled by a system of two nonlinear ordinary differential equations. The mixer is used to condition the thermodynamic properties of cryogenic liquid propellant by controlled injection of the same substance in the gaseous phase. The three inputs of the mixer are the positions of the valves regulating the liquid and gas flows at the inlets, and the position of the exit valve regulating the flow of conditioned propellant. Mixer operation during a test requires the regulation of its internal pressure, exit mass flow, and exit temperature. A mathematical model is developed to facilitate subsequent controller designs. The model must be simple enough to lend itself to subsequent feedback controller design, yet its accuracy must be tested against real data. For this reason, the model includes function calls to thermodynamic property data. Some structural properties of the resulting model that pertain to controller design, such as uniqueness of the equilibrium point, feedback linearizability and local stability are shown to hold under conditions having direct physical interpretation. The existence of fixed valve positions that attain a desired operating condition is also shown. Validation of the model against real data is likewise provided.
We present the formulation and testing of a mathematical model for the kinetics of homotypic cellular aggregation. The model considers cellular aggregation under no-flow conditions as a two-step process. Individual cells and cell aggregates 1) move on the tissue culture surface and 2) collide with other cells (or aggregates). These collisions lead to the formation of intercellular bonds. The aggregation kinetics are described by a system of coupled, nonlinear ordinary differential equations, and the collision frequency kernel is derived by extending Smoluchowski's colloidal flocculation theory to cell migration and aggregation on a two-dimensional surface. Our results indicate that aggregation rates strongly depend upon the motility of cells and cell aggregates, the frequency of cell-cell collisions, and the strength of intercellular bonds. Model predictions agree well with data from homotypic lymphocyte aggregation experiments using Jurkat cells activated by 33B6, an antibody to the beta 1 integrin. Since cell migration speeds and all the other model parameters can be independently measured, the aggregation model provides a quantitative methodology by which we can accurately evaluate the adhesivity and aggregation behavior of cells.
The Platform Precision Autopilot is an instrument landing system interfaced autopilot system, developed to enable an aircraft to repeatedly fly nearly the same trajectory hours, days, or weeks later. The Platform Precision Autopilot uses a novel design to interface with a NASA Gulfstream III jet by imitating the output of an instrument landing system approach. This technique minimizes, as much as possible, modifications to the baseline Gulfstream III jet and retains the safety features of the aircraft autopilot. The Platform Precision Autopilot requirement is to fly within a 5-m (16.4-ft) radius tube for distances to 200 km (108 nmi) in the presence of light turbulence for at least 90 percent of the time. This capability allows precise repeat-pass interferometry for the Uninhabited Aerial Vehicle Synthetic Aperture Radar program, whose primary objective is to develop a miniaturized, polarimetric, L-band synthetic aperture radar. Precise navigation is achieved using an accurate differential global positioning system developed by the Jet Propulsion Laboratory. Flight-testing has demonstrated the ability of the Platform Precision Autopilot to control the aircraft within the specified tolerance greater than 90 percent of the time in the presence of aircraft system noise and nonlinearities, constant pilot throttle adjustments, and light turbulence.
The Platform Precision Autopilot is an instrument landing system-interfaced autopilot system, developed to enable an aircraft to repeatedly fly nearly the same trajectory hours, days, or weeks later. The Platform Precision Autopilot uses a novel design to interface with a NASA Gulfstream III jet by imitating the output of an instrument landing system approach. This technique minimizes, as much as possible, modifications to the baseline Gulfstream III jet and retains the safety features of the aircraft autopilot. The Platform Precision Autopilot requirement is to fly within a 5-m (16.4-ft) radius tube for distances to 200 km (108 nmi) in the presence of light turbulence for at least 90 percent of the time. This capability allows precise repeat-pass interferometry for the Unmanned Aerial Vehicle Synthetic Aperture Radar program, whose primary objective is to develop a miniaturized, polarimetric, L-band synthetic aperture radar. Precise navigation is achieved using an accurate differential global positioning system developed by the Jet Propulsion Laboratory. Flight-testing has demonstrated the ability of the Platform Precision Autopilot to control the aircraft within the specified tolerance greater than 90 percent of the time in the presence of aircraft system noise and nonlinearities, constant pilot throttle adjustments, and light turbulence.
The PLANS system is described which is a finite element program for nonlinear analysis. The system represents a collection of special purpose computer programs each associated with a distinct physical problem class. Modules of PLANS specifically referenced and described in detail include: (1) REVBY, for the plastic analysis of bodies of revolution; (2) OUT-OF-PLANE, for the plastic analysis of 3-D built-up structures where membrane effects are predominant; (3) BEND, for the plastic analysis of built-up structures where bending and membrane effects are significant; (4) HEX, for the 3-D elastic-plastic analysis of general solids; and (5) OUT-OF-PLANE-MG, for material and geometrically nonlinear analysis of built-up structures. The SATELLITE program for data debugging and plotting of input geometries is also described. The theoretical foundations upon which the analysis is based are presented. Discussed are the form of the governing equations, the methods of solution, plasticity theories available, a general system description and flow of the programs, and the elements available for use.
A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.
The parameter identification problem of general discrete time, nonlinear, multiple input/multiple output dynamic systems with Gaussian white distributed measurement errors is considered. The knowledge of the system parameterization was assumed to be known. Concepts of local parameter identifiability and local constrained maximum likelihood parameter identifiability were established. A set of sufficient conditions for the existence of a region of parameter identifiability was derived. A computation procedure employing interval arithmetic was provided for finding the regions of parameter identifiability. If the vector of the true parameters is locally constrained maximum likelihood (CML) identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the constrained maximum likelihood estimation sequence will converge to the vector of true parameters.
The research progress for FY-91 is presented. Wintertime and springtime stratocumulus observations for a number of 5-day periods were collected. Close correlations between the mean 850 and 500 mb trough positions and cloud cover over marine areas were found. A linear study of the radiatively-driven interaction between stratocumulus and synoptic-scale waves was completed. Shallow surface-bound traveling waves are created that are strongly dependent on the phase relation between cloud and low-level flow. A nonlinear model is now under development that will permit a more detailed investigation of these interactions. Finally, a nonlinear study of the modifications of the background flow by boundary layer roll vortices was revised for submission for publication. The research plans for FY-92 are included.
An integrated autopilot/autothrottle was designed for flight test on the NASA TSRV B-737 aircraft. The system was designed using a total energy concept and is attended to achieve the following: (1) fuel efficiency by minimizing throttle activity; (2) low development and implementation costs by designing the control modes around a fixed inner loop design; and (3) maximum safety by preventing stall and engine overboost. The control law was designed initially using linear analysis; the system was developed using nonlinear simulations. All primary design requirements were satisfied.
We characterize both nonlinear and high order linear responses of fiber-optic and optoelectronic components using spread spectrum temperature cycling methods. This Thermal Signature Identification System (TheSIS) provides much more detail than conventional narrowband or quasi-static temperature profiling methods. This detail allows us to match components more thoroughly, detect subtle reversible shifts in performance, and investigate the cause of instabilities or irreversible changes. In particular, we create parameterized models of athermal fiber Bragg gratings (FBGs), delay line interferometers (DLIs), and distributed feedback (DFB) lasers, then subject the alternative models to selection via the Akaike Information Criterion (AIC). Detailed pairing of components, e.g. FBGs, is accomplished by means of weighted distance metrics or norms, rather than on the basis of a single parameter, such as center wavelength.
In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.