Generalization of the parameter plane method.
Generalization of parameter plane method for case when characteristic equation coefficients are nonlinear functions of system of adjustable parameters
NONLINEAR SYSTEM↗
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Mean motions and characteristics exponent at the libration points
Solar system planetary mean motions calculation from characteristic equations roots at equilibrium points of restricted three body problem, using Taylor series solution
Cochran, J. E.↗
Generalized characteristics method for elastic wave propagation problems
Elastic wave propagation, deriving characteristic equations in generalized curvilinear coordinates using linear elastic, isotropic and homogeneous constitutive equations
Ziv, M.↗
Synthesis of systems with dominant complex roots
Multiparameter systems with dominant complex roots constrained by degrees of freedom to construct reduced characteristic equation
Cadena, J. E.↗
Parameter plane techniques applied to tactical missile control system design
Stability analysis parameter plane technique for tactical missile control system design, correlating variable parameters with characteristic equation roots location
Seltzer, S. M.↗
A generalized root locus following technique
Feedback control system characteristic equation generalized root locus following technique using straight line approximation
Mcdaniel, W. L., Jr.↗
Hybrid redundancy system for improving reliability - A concept
System combines two concepts - triple modular redundancy (TMR) and spares (replacement system) redundancy. System has triplicated active unit core with associated bank of specifically arranged standby spare units. Curves plotted from characteristic equation show hybrid system is more reliable than conventional TMR systems.
Mathur, F. P.↗
Digital computer program for analyzing chugging instabilities
Program computes combustion delays, gas residence time, characteristic velocity, and other steady-state parameters required for solution of the characteristic equation. Equation is solved for critical values of injector pressure drops and chugging frequency.
Szuch, J. R.↗
A new approach to the design of time varying control systems with application to the space shuttle booster
A general approach toward the analysis and design of closed loop control for slowly time-varying linear systems was investigated. The approach is by the method of generalized multiple scales, in which slow and fast dynamics are systematically separated by employing different clocks which measure time at varying rates. The clocks, which are necessarily nonlinear functions of time, so that the system dynamics are asymptotically invariant with respect to the new time scale. A transfer function relating the output to the input for general linear slowly time-varying systems is developed and represents the actual system under certain conditions. The clock functions are shown to satisfy an algebraic characteristic equation and can be determined in general in terms of the coefficients.
Ramnath, R. V.↗
A problem in micropolar elasticity.
In this paper a three-dimensional analysis for statics and dynamics of a class of simply supported rectangular plates made up of micropolar elastic material is presented. The solution is in the form of series, in which each term is explicitly determined. For free vibrations, the frequencies are obtained by the solution of a closed form characteristic equation.
Srinivas, S.↗
A new approach to the design of time-varying control systems with application to the Space Shuttle Boost
A general approach to the analysis and design of closed-loop control for slowly time-varying linear systems is presented. The approach uses the method of generalized multiple scales in which slow and fast dynamics are systematically separated by employing different 'clocks' which measure time at varying rates. The clocks, which are necessarily nonlinear functions of time, are chosen in such a manner that the system dynamics are asymptotically invariant with respect to the new time scale. A transfer function relating the output to the input for general linear slowly time-varying systems is developed and represents the actual system under certain conditions. The clock function is shown to satisfy an algebraic characteristic equation and can be determined in terms of the coefficients. The approach can be viewed as an extension of time-invariant linear feedback control theory.
Ramanth, R. V.↗
Monte Carlo analysis of inaccuracies in estimated aircraft parameters caused by unmodeled flight instrumentation errors
An output error estimation algorithm was used to evaluate the effects of both static and dynamic instrumentation errors on the estimation of aircraft stability and control parameters. A Monte Carlo error analysis, using simulated cruise flight data, was performed for a high-performance military aircraft, a large commercial transport, and a small general aviation aircraft. The results indicate that unmodeled instrumentation errors can cause inaccuracies in the estimated parameters which are comparable to their nominal values. However, the corresponding perturbations to the estimated output response trajectories and characteristics equation pole locations appear to be relatively small. Control input errors and dynamic lags were found to be in the most significant of the error sources evaluated.
Hodge, W. F.↗
Design implementation and control of MRAS error dynamics
Use is made of linearized error characteristic equation for model-reference adaptive systems to determine a parameter adjustment rule for obtaining time-invariant error dynamics. Theoretical justification of error stability is given and an illustrative example included to demonstrate the utility of the proposed technique.
Colburn, B. K.↗
Effect of axial load on mode shapes and frequencies of beams
An investigation of the effect of axial load on the natural frequencies and mode shapes of uniform beams and of a cantilevered beam with a concentrated mass at the tip is presented. Characteristic equations which yield the frequencies and mode shape functions for the various cases are given. The solutions to these equations are presented by a series of graphs so that frequency as a function of axial load can readily be determined. The effect of axial load on the mode shapes are also depicted by another series of graphs.
Shaker, F. J.↗
Coupling of Helmholtz resonators to improve acoustic liners for turbofan engines at low frequency
An analytical and test program was conducted to evaluate means for increasing the effectiveness of low frequency sound absorbing liners for aircraft turbine engines. Three schemes for coupling low frequency absorber elements were considered. These schemes were analytically modeled and their impedance was predicted over a frequency range of 50 to 1,000 Hz. An optimum and two off-optimum designs of the most promising, a parallel coupled scheme, were fabricated and tested in a flow duct facility. Impedance measurements were in good agreement with predicted values and validated the procedure used to transform modeled parameters to hardware designs. Measurements of attenuation for panels of coupled resonators were consistent with predictions based on measured impedance. All coupled resonator panels tested showed an increase in peak attenuation of about 50% and an increase in attenuation bandwidth of one one-third octave band over that measured for an uncoupled panel. These attenuation characteristics equate to about 35% greater reduction in source perceived noise level (PNL), relative to the uncoupled panel, or a reduction in treatment length of about 24% for constant PNL reduction. The increased effectiveness of the coupled resonator concept for attenuation of low frequency broad spectrum noise is demonstrated.
Dean, L. W.↗
Error magnitude estimation in model-reference adaptive systems
A second order approximation is derived from a linearized error characteristic equation for Lyapunov designed model-reference adaptive systems and is used to estimate the maximum error between the model and plant states, and the time to reach this peak following a plant perturbation. The results are applicable in the analysis of plants containing magnitude-dependent nonlinearities.
Colburn, B. K.↗
Dynamic analysis of a class of mixed lumped-distributed parameter systems via numerical techniques
The modeling via transfer matrices of mixed lumped-distributed parameter systems with feedback control is discussed and novel methods of obtaining information on the controlled system's dynamic response via numerical methods is presented. These methods utilize numerical searches in the complex plane for the roots of the transcendental characteristic equation to determine the closed loop system eigenvalues. The fast Fourier transform (FFT) algorithm is utilized but in the inverse fashion (from frequency domain to time domain). The information obtained is identical to that contained in a model in modal coordinates, and can be used to construct such a model. An interactive computer program to do the required calculation is described, as well as its application to a manipulator arm design problem.
Book, W. J.↗
Application of remotely sensed land-use information to improve estimates of streamflow characteristics, volume 8
The author has identified the following significant results. Land use data derived from high altitude photography and satellite imagery were studied for 49 basins in Delaware, and eastern Maryland and Virginia. Applying multiple regression techniques to a network of gaging stations monitoring runoff from 39 of the basins, demonstrated that land use data from high altitude photography provided an effective means of significantly improving estimates of stream flow. Forty stream flow characteristic equations for incorporating remotely sensed land use information, were compared with a control set of equations using map derived land cover. Significant improvement was detected in six equations where level 1 data was added and in five equations where level 2 information was utilized. Only four equations were improved significantly using land use data derived from LANDSAT imagery. Significant losses in accuracy due to the use of remotely sensed land use information were detected only in estimates of flood peaks. Losses in accuracy for flood peaks were probably due to land cover changes associated with temporal differences among the primary land use data sources.
Pluhowski, E. J.↗