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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.
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This paper is concerned with the problem of designing a controller for a complex dynamical system using output feedback. The system selected for the study is the Boeing-Vertol CH-46 tandem rotor helicopter. Feedback gains are obtained by a least square solution of the nonlinear equations derived from pole-placement theory.
The mechanical and electrical characteristics of the conical arc-chamber driver and the 1450-microfarad capacitor bank are described. The system dynamic performance can be approximated by a second-order nonlinear equation. The discharge of the capacitor bank into the conical arc-chamber was investigated at a variety of initial conditions. Details of the discharge are explained and compared for typical performance with both hydrogen and helium arc-chamber gases. At peak current the hydrogen plasma resistivity is significantly higher than that of the helium plasma and this, in part, accounts for the better shock speed performance with hydrogen. The lower melting and boiling point exploding wires of aluminum, copper, and stainless steel produced higher shock speed performance than the apparently nonexploding tungsten wire.
Description of a variable step incremental procedure for the solution of nonlinear equations in finite element structural analysis. The proposed procedure is effective in improving the accuracy of the basic incremental technique and in providing, in addition, an accurate estimate of the discretization error. The proposed approach is highly appropriate for solving problems for which the user has no a priori estimate of the step size to use.
Description of a model developed to predict the interactions between multiple electrostatic probes separated by distances that are shorter than or comparable to the characteristic plasma shielding length. The computation involves crude approximations accounting for space charge effects, currents due to the emission and exchange of photoelectrons, and currents from the ambient plasma. Floating potentials are calculated by requiring current balance for each probe and solving by iterating the resulting coupled nonlinear equations. Although only qualitative accuracy is claimed, predictions using the model are found to be in good agreement with observations from the Explorer 45 satellite. The Explorer 45 satellite measures the potential difference between a pair of symmetrical spherical floating probes. The Explorer 45 data show that with increasing altitude, first, the sunward sphere will typically assume a more negative potential than the antisunward sphere; second, the polarities of the probes in the region L = 2 to 4 may switch, sometimes several times; and, finally, near the plasmapause the detector output may saturate, the sunward sphere being more negative.
A mathematical model of the helicopter requires appropriate representation of the constituent elements of rotor dynamics. General-purpose programs that model a variety of configurations for a broad range of operating conditions result in varying and incompatible levels of sophistication. Analysis of specific dynamic problems facilitates the identification of configuration parameters which determine system behavior. For the present analysis, the nonlinear equations of a torsionally rigid hingeless rotor are linearized about an equilibrium condition to determine flap-lag stability characteristics in hover. A collocation method was used to obtain the coupled natural frequencies and modes. These modes allow exact treatment of the effect of elastic coupling which more than compensates for the destabilizing inertial coupling. The sensitivity of damping to the number of modes was found to be small, and reasonable accuracy was obtained the first flapwise and edgewise coupled modes. The range of destabilizing precone was found to be small.
A multilevel scheme was proposed for control of Large Space Telescope (LST) modeled by a three-axis-six-order nonlinear equation. Local controllers were used on the subsystem level to stabilize motions corresponding to the three axes. Global controllers were applied to reduce (and sometimes nullify) the interactions among the subsystems. A multilevel optimization method was developed whereby local quadratic optimizations were performed on the subsystem level, and global control was again used to reduce (nullify) the effect of interactions. The multilevel stabilization and optimization methods are presented as general tools for design and then used in the design of the LST Control System. The methods are entirely computerized, so that they can accommodate higher order LST models with both conceptual and numerical advantages over standard straightforward design techniques.
This paper presents a new algorithm for solving systems of nonlinear equations, which combines elements of the method of local variations with a sequential secant method. The new algorithm converges superlinearly and its convergence does not depend upon a good initial guess at a solution.
Explicit second-order upwind difference schemes in combination with spatially symmetric schemes can produce larger stability bounds and better numerical resolution than symmetric schemes alone. However, if conservation form is essential, a special operator is required for transition between schemes. An operational approach has been devised for deriving transition operators so that strict conservation and local consistency are maintained. Various aspects of hybrid schemes are studied numerically for model linear and nonlinear equations. To demonstrate the utility of combining two different algorithms, MacCormack's explicit, noncentered, second-order method is combined with a completely upwind version, and numerical solutions of the Euler equations are obtained for two-dimensional, transonic flows with embedded supersonic regions and shock waves. The general utility of the operational approach for combining schemes is emphasized by deriving a second-order conservative scheme for the steady transonic small-disturbance potential equation.
A dynamic model is presented for the strong zonal circulation within the stratosphere of Venus which was observed by Mariner 10 and Venera. Rotational effects are neglected, a compressible and radiating atmosphere is considered, and diurnal radiative heating is shown to be negligible in the lower stratosphere (below 85 km). Analysis of the model indicates that propagating internal gravity waves generated by solar heating of the upper stratosphere may induce mean zonal velocities within the upper and lower stratosphere which would have a retrograde direction. The nonlinear equations of motion and energy are solved by an approximate analytical method to determine the magnitude of the zonal velocity, which is found to increase from zero at the tropopause to about 200 m/sec at the 85-km level. The calculated velocity near the UV cloud level compares favorably with the observed value of 100 m/sec.
A recently developed method for estimating transonic aircraft aerodynamics to high angles of attack which is especially suited to computerized aircraft design and optimization studies is described. Following theoretical and empirical guidelines, explicit nonlinear equations are formulated for subsonic, transonic, and supersonic speeds; new algorithms are used for assessing compressibility effects and for analyzing transonic, shock-dominated flows which adhere to Laitone's limit Mach-number criterion. Viscous dominated flows are not analyzed. The transonic influence of viscosity is indirectly accommodated by assigning designated inputs rather than extracted solutions for the chordwise locations of shock and separation. The method is extended to complete aircraft configurations by including accounts for nose lift, the wing downwash field, and tail lift. Several comparisons of experiment and estimate are included.
This paper presents an analysis of the attitude dynamics of the Long Duration Exposure Facility (LDEF). LDEF is a large cylindrical gravity gradient stabilized earth satellite which is planned to be delivered to a 270-n mi circular orbit by the space shuttle. The fundamental linear stability, capture requirements, and pitch bias constraints generated by the Garber instability are discussed. Numerical simulations, based on the full nonlinear equations for the coupled orbital and attitude motion of the vehicle and the viscous magnetic damper, show stable behavior of the spacecraft and a damping time constant of 30 to 70 orbits.
Methods of linear systems analysis were applied to mathematical models of aircraft flying at high angle of attack and maneuver rate. First order longitudinal and lateral directional coupling is obtained by linearizing the complete nonlinear equations of motion about a generalized (quasi steady) trim point. Open loop stability boundaries are defined using the linear dynamic equations, and pilot in the loop effects are presented. Stability augmentation structures for maneuvering flight conditions are shown to be defined readily using optimal control theory.
The effects of gravity gradient torques during boom deployment maneuvers of a spinning spacecraft are examined. Configurations where the booms extended only along the hub principal axes and where one or two booms are offset from the principal axes were considered. For the special case of symmetric deployment (principal axes booms) the stability boundaries are determined, and a stability chart is used to study the system behavior. Possible cases of instability during this type of maneuver are identified. In the second configuration an expression for gravity torque about the hub center of mass was developed. The nonlinear equations of motion are solved numerically, and the substantial influence of the gravity torque during asymmetric deployment maneuvers is indicated.
Simple mechanical linkages have not solved the many control problems associated with high performance aircraft maneuvering throughout a wide flight envelope. One procedure for retaining uniform handling qualities over such an envelope is to implement a digital adaptive controller. Towards such an implementation an explicit adaptive controller which makes direct use of on-line parameter identification, has been developed and applied to both linearized and nonlinear equations of motion for a typical fighter aircraft. This controller is composed of an on-line weighted least squares parameter identifier, a Kalman state filter, and a model following control law designed using single stage performance indices. Simulation experiments with realistic measurement noise indicate that the proposed adaptive system has the potential for on-board implementation.
The motion of a two-dimensional packet of capillary-gravity waves on water of finite depth is studied. The evolution of a packet is described by two partial differential equations: the nonlinear Schroedinger equation with a forcing term and a linear equation, which is of either elliptic or hyperbolic type depending on whether the group velocity of the capillary-gravity wave is less than or greater than the velocity of long gravity waves. These equations are used to examine the stability of the Stokes capillary-gravity wave train. The analysis reveals the existence of a resonant interaction between a capillary-gravity wave and a long gravity wave. The interaction requires that the liquid depth be small in comparison with the wavelength of the (long) gravity waves and the evolution equations describing the dynamics of this interaction are derived.
The problem to be solved is formulated precisely and the introduction of quasi-Newton methods is motivated by considering the classical Newton and secant methods and their properties. Three highly successful quasi-Newton methods are surveyed: Broyden's method for the solution of general nonlinear equations, and the Davidon-Fletcher-Powell and Broyden-Fletcher-Goldfarb-Shanno procedures for unconstrained minimization. Finally, the properties of these methods are compared to those of Newton's method and UHMLE in potential applications to maximum-likelihood estimation of parameters in mixture distributions.
A computer program for the application of parameter identification on the structural dynamic models of space shuttle and other large models with hundreds of degrees of freedom is described. Finite element, dynamic, analytic, and modal models are used to represent the structural system. The interface with math models is such that output from any structural analysis program applied to any structural configuration can be used directly. Processed data from either sine-sweep tests or resonant dwell tests are directly usable. The program uses measured modal data to condition the prior analystic model so as to improve the frequency match between model and test. A Bayesian estimator generates an improved analytical model and a linear estimator is used in an iterative fashion on highly nonlinear equations. Mass and stiffness scaling parameters are generated for an improved finite element model, and the optimum set of parameters is obtained in one step.
The effects of wind shear on aircraft flying through thunderstorm gust fronts were investigated. A computer program was developed to solve the two dimensional, nonlinear equations of aircraft motion, including wind shear. The procedure described and documented accounts for spatial and temporal variations of the aircraft within the flow regime. Analysis of flight paths and control inputs necessary to maintain specified trajectories for aircraft having characteristics of DC-8, B-747, augmentor wing STOL, and DHC-6 aircraft was recorded. From the analysis an attempt was made to find criteria for reduction of the hazards associated with landing through thunderstorm gust fronts.