Showing papers on "Linearization published in 1978"

An Efficient Method to Solve the Minimax Problem Directly

Abstract: Over the past few years the circuit and system designers have shown great interest in minimax algorithms. The purpose of this paper is to present a new algorithm to solve the nonlinear minimax problem. The minimax optimization problem can be stated as" where minimize Mr(x) Mr(x) max /)(x) li;m andx=(xl, x2," ,x,)r. The above objective function has discontinuous first partial derivatives at points where two or more of the functions/ are equal toM even if/(x), 1 _<-i-

Field matter interactions in thermoelastic solids

Abstract: Basic concepts- A survey of electromechanical interaction models- Equivalence of the models- Material description- Linearization

Linearized vertically-integrated equations for residual circulation in coastal seas

Abstract: The non-linear vertically-integrated hydrodynamic equations for tides and storm surges are formulated and their linearization to yield a set of equations for longerterm residual motion is described. Particular attention is paid to the reduction of quadratic friction to yield a linear law of bottom stress. The use of both the nonlinear and the linearized equations for residual flow computations is discussed.

The Operational Approach to Physical Geodesy.

Abstract: : The operational approach to physical geodesy starts from the measurements and asks how they can be used in the best way to determine the earth's figure and gravitational field. All measurements can be represented as nonlinear functionals of the potential and of systematic parameters such as station coordinates. After linearization we obtain an improperly posed problem, to which three standard methods of solving such problems are applied: a change in the solution space, a variational principle according to Tichonov, and a statistical approach. All three approaches seem to converge on collocation with kernel functions and least-squares collocation. Some alternatives are also discussed. (Author)

On the Stochastic Maximum Principle

Abstract: A representation of the adjoint process, which appears in a general version of the maximum principle for control systems described by Girsanov solutions of stochastic differential equations, is given in terms of the linearization of the state equation. The result is only valid when the optimal control and the coefficiencies in the state equation are smooth; however two examples show that the result can nevertheless be applied to the nonsmooth case, solving in particular the linear regulator and the “predicted miss” problems.

Linearization technique for closed-loop acousto-optic modulators

Abstract: Linearization of a closed-loop acousto-optic modulation system is maintained over a uniform closed-loop bandwidth that is independent of the output light intensity level through the use of a compensating square-root function generator which employs the third quadrant characteristic of a MOSFET. The MOSFET may be connected as the feedback impedance of an operational amplifier which provides the square-root gain control function for complementing the non-linearity of the acousto-optic modulator. By utilizing the third quadrant characteristics of the source-to-drain voltage relative to the drain current of the MOSFET, the square-root function generator has a transfer function which insures that a linear relationship between modulator output light intensity and input signal current can be obtained irrespective of light intensity. In accordance with a preferred embodiment of the present invention, the operational amplifier of the square-root function generator may be supplied with an offset voltage in order to insure that the desired square-root transfer function can be attained regardless of differences in the manufactured characteristics of the field effect transistors that may be used. Temperature compensation circuitry may also be adopted as part of the square-root gain control component of the system to counteract the temperature sensitivity of the MOSFET's square-root current-voltage characteristic.

Linearization of operator functions on arbitrary open sets

Abstract: In this paper it is shown that after a suitable extension an operator function A, which is holomorphic on an open set Ω in ℂ, is equivalent on Ω to a linear pencil S-λV. If Ω is bounded, then V turns out to be right invertible, and in that case a further extension is equivalent on Ω to a linear pencil T-λI.

Two wire current transmitter with adjustable current control linearization

Abstract: A two wire current transmitter for controlling the total current in the two wires in accordance with a value of a parameter to be sensed, which provides for substantial linearization of the electrical characteristic representative of the value of the parameter to be sensed by adjusting the current from an adjustable current control to substantially compensate for the nonlinear relationship of the parameter to be sensed versus the electrical output of the sensor of said parameter. The circuit also provides for substantial compensation for sensor lead wire effects.

Stability Analysis of a Second-Order Thyristor Device Control System

Abstract: In this paper, a new method is presented for the study of the stability of a second-order thyristor device control system; the current loop of a separately excited dc motor is considered in particular. Nonlinear discrete mathematical models are proposed for continuous and discontinuous operations. For local analysis, exact analytical formulas are given by linearization of the equations around the considered operating point. Graphical methods are proposed for the global behavior of the system which allow us to study the nonlinear effects, for example, the subharmonics appearing when the system becomes unstable. For accurate results, these graphical methods are transposed to simple digital computer programs.

Linearization of holomorphic operator functions. I

Abstract: This paper is a continuation of [2]. It contains the proof of the main linearization theorem announced in [2], some modifications of the construction and some unsolved problems for the case of several variables. Without further explanation we shall use the notations of [2], and we shall continue the numbering of formulae, sections, theorems and lemmas as begun in [2].

Response of a pendulum spar to 2-dimensional random waves and a uniform current

Abstract: A linearized theory for the response of a circular pendulum spar in 2-dimensional waves and a uniform current is developed. The linear forces on the cylinder are predicted using an approximate potential flow theory for slender bodies. The dynamic equations are then amended to account for the wake effects of viscous bluff body flow by including a quadratic drag law and neglecting wave damping. A spectral model for the forces on a cylinder due to an oscillating wake, modeling the force as a frequency modulation process, is proposed. The non-linear equations of motion which result are then solved, assuming constant force coefficients, by linearization for use with a Gaussian random sea. The method of equivalent linearization is extended to include mean flow effects and a spatially distributed process. Some numerical experiments are then used to test the performance of the linearization. For a variety of environments, the linearization predicts the standard deviation of the simulation response to within 10% and the mean angle of inclination to within 30%. Results of the numerical experiments indicate that there is significant variation (order of magnitude changes) in both response and mean angle of inclination. Thus, significant changes are followed by the linearization. A laboratory experiment was carried out to test the linearized spar model in a realistic fluid environment. Only the low Keulegan Carpenter number regime was investigated. With some minimal manipulations, good agreement is obtained between the experiment and the linearized estimates. It appears that the drag coefficients for vortex induced in-line forces may be an order of magnitude larger than those reported in the literature, .5 instead of .06, and that the shedding of vortices due to steady flow may reduce the added mass coefficient significantly, as observed in oscillating flows with significant vortex shedding.

Stochastic seismic stability prediction of earth dams

Abstract: A method, based on stochastic principles, is presented for seismic stability prediction of earth dams. The problem of nonlinearity due to strain dependent soil properties is solved through the stochastic linearization technique; the formulation for applying this technique to a finite element discretization of a dam is developed. The method is iterative and step-wise linear. Stochastic description of seismic input in terms of spectral density function can be conveniently used in this method. The method can also be used directly with the ground response spectra curves usually prescribed in seismic designs. The concept of linear cumulative damage is used to define failure. Zero crossing the peak statistics of the stress response are used to define the statistics of cumulative damage. The damage is related to the factor of safety which is conventionally used with civil engineering structures. The application of the method is demonstrated with an example of an earth dam. /Author/

Landau Damping for Students

Abstract: By using the linearized equations of motion for particle streams, and by properly including the initial conditions, Landau's equations for electrostatic wave propagation with the correct damping decrement are easily obtained. No Vlasov equation, Laplace transform, contour integration, evaluation of residues at singularities, or analytical continuation is required. A discussion of the validity of the linearization is included.

An abstract quasi-linearization algorithm for estimating parameters in hereditary systems

Abstract: A parameter estimation problem for class of linear hereditary systems is recast in a state space setting. A quasi-linearization type algorithm is developed, based on the state space formulation. The resulting algorithm requires the solution of initial value problems for hereditary systems. A numerical example is given to illustrate the technique.

The application of quasi-linearization techniques to rail vehicle dynamic analyses

Abstract: The objective of the work reported here was to define methods for applying the describing function technique to realistic models of nonlinear rail cars. The describing function method offers a compromise between the accuracy of nonlinear digital simulation and the computational efficiency of linear methods. This work entailed the development of realistic describing function representations for nonlinearities such as the wheel/rail contact interaction and the development of algorithms for using these describing functions to predict the occurrence and stability of hunting and the forced response of rail vehicles to sinusoidal and statistical track irregularities. This report explains the describing function technique, demonstrates how it can be applied to nonlinear rail vehicle dynamics problems, describes algorithms that can be used for such problems, and presents results for typical nonlinear problems, including wheel profile and suspension nonlinearities.

Linearization of the Transfer Characteristic of a Phase- Controlled Converter Under Discontinuous Conduction

Abstract: An open-loop control circuit is described which, in conjunction with a cosine wave crossing technique, provides a linear transfer characteristics of a phase-controlled converter under both continuous and discontinuous conduction, regardless of ?L/R values of the load. The nonlinear transfer characteristic between the signal and the output voltage at discontinuous conduction has been counteracted by an inversely nonlinear control function for different ?L/R values. The control functions have been approximated by piecewise linear segments, synthesized by analog circuits, and identified by digital addresses. A complete control circuit has been designed and tested with a single-phase center-tap converter. The experimental results agree well with the theory. The principle can be extended to polyphase and multiquadrant converters.