A control design procedure for plants with random initial conditions and constraints on the mean square actuator rates

1995 ◽  
Vol 26 (3) ◽  
pp. 515-524
Author(s):  
C. FRANGOS ◽  
Y. YAVTN
Keyword(s):  
Initial Conditions ◽  
Design Procedure ◽  
Control Design ◽  
Mean Square ◽  
Random Initial Conditions ◽  
The Mean

scholarly journals Diffusion and Superdiffusion in Lattice Models for Colliding Particles with Stored Momentum

2019 ◽  
Vol 177 (6) ◽  
pp. 1240-1262
Author(s):  
Edward Crane ◽  
Sean Ledger ◽  
Bálint Tóth
Keyword(s):  
Initial Conditions ◽  
Mean Square Displacement ◽  
Lattice Models ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Discrete Models ◽  
One Dimension ◽  
Logarithmic Correction ◽  
Mean Square ◽  
The Mean

Abstract We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension (with power law correction) and diffusive in three and higher dimensions. In two dimensions we demonstrate superdiffusivity (with logarithmic correction) for certain anisotropic initial conditions.

scholarly journals On the decay of inhomogeneous turbulence

1997 ◽  
Vol 342 ◽  
pp. 335-354 ◽  
Author(s):  
J. R. CHASNOV
Keyword(s):  
Scaling Laws ◽  
Initial Conditions ◽  
Homogeneous Turbulence ◽  
Mean Square ◽  
Asymptotic Decay ◽  
Inhomogeneous Turbulence ◽  
Spectral Coefficients ◽  
The Mean ◽  
Decaying Turbulence ◽  
High Reynolds

The decay of high-Reynolds-number inhomogeneous turbulence in an unbounded domain is considered. The turbulence may be initially localized in one to three spatial directions and the fluid is assumed to be at rest at infinity in those directions. Previous arguments used to determine the decay laws of homogeneous turbulence are extended to the decay of inhomogeneous turbulence by integrating the turbulence statistics over the inhomogeneous directions. Dimensional arguments based on the invariance or near-invariance of low-wavenumber spectral coefficients associated with the integrated mean-square velocity are used to determine asymptotic decay laws for inhomogeneous turbulence. These decay laws depend on the number of inhomogeneous directions of the flow field and reduce to the well-known decay laws of homogeneous turbulence when this number is zero. Different decay laws are determined depending on the spectral behaviour at low wavenumbers. Asymptotic similarity states of the spectrum during the decay and of the distribution of the mean-square velocity along the inhomogeneous directions are also determined. An analytical result for the decay of the mean-square velocity at the centre of the initial disturbance is found, and the decay proceeds more rapidly with increasing number of inhomogeneous directions due to the transport of energy along those directions.Large-eddy simulations of decaying turbulence homogeneous in a plane and localized in a single direction are performed to test the theoretical scaling laws. The numerically determined asymptotic decay laws of the integrated mean-square velocity agree well with the theoretical predictions. A self-similar decay of the spectra and mean-square velocity distributions is also observed. The simulation results suggest that when the low-wavenumber spectral coefficient is an exact invariant, a unique similarity state depending only on the initial value of this invariant and independent of all other aspects of the initial conditions is attained asymptotically.

Velocity and displacement correlation functions for fractional generalized Langevin equations

2012 ◽  
Vol 15 (3) ◽  
Author(s):  
Trifce Sandev ◽  
Ralf Metzler ◽  
Živorad Tomovski
Keyword(s):  
Initial Conditions ◽  
Mean Square Displacement ◽  
Langevin Equations ◽  
Average Particle ◽  
Mean Square ◽  
Relaxation Functions ◽  
Long Time ◽  
The Mean ◽  
Diffusive Processes ◽  
Frictional Memory Kernel

AbstractWe study analytically a generalized fractional Langevin equation. General formulas for calculation of variances and the mean square displacement are derived. Cases with a three parameter Mittag-Leffler frictional memory kernel are considered. Exact results in terms of the Mittag-Leffler type functions for the relaxation functions, average velocity and average particle displacement are obtained. The mean square displacement and variances are investigated analytically. Asymptotic behaviors of the particle in the short and long time limit are found. The model considered in this paper may be used for modeling anomalous diffusive processes in complex media including phenomena similar to single file diffusion or possible generalizations thereof. We show the importance of the initial conditions on the anomalous diffusive behavior of the particle.

Control of Oscillations in Electrically Driven Skid Steer Vehicles

2003 ◽  
Author(s):  
Torben Ole Andersen ◽  
Michael Rygaard Hansen ◽  
Henrik Clemmensen Pedersen
Keyword(s):  
Control Strategies ◽  
Tracking Error ◽  
Control Design ◽  
Small Scale ◽  
Mean Square ◽  
Motor Torque ◽  
The Mean ◽  
Objective Being ◽  
Wheeled Vehicles ◽  
Control Of Oscillations

This paper is concerned with the stabilization of skid steer wheeled vehicles. This type of vehicle is often characterized by a short wheelbase and without any suspension other than that of the wheels, and is therefore liable to rotational pitch oscillations. The objective of this paper is twofold. Firstly, the abovementioned oscillation phenomena are examined with a view to improve the understanding of its dependency on weight distribution, and traction characteristics of tire-surface contact. Secondly, a number of control strategies that dampens the oscillatory nature of the vehicle are derived and evaluated. The basic idea of the control strategy is to keep the angular pitch velocity at zero by increasing the motor torque when the vehicle is tilting forward and decreasing the motor torque when the vehicle is tilting backwards. The basic control design objective being to achieve the lowest possible mean square tracking error without letting the mean square input exceed its maximally permissible value. The results are experimentally evaluated by means of a small-scale vehicle.

THE EFFECTS OF QUENCHED DISORDER ON THE CHAOTIC DIFFUSION FOR SIMPLE MAPS

1999 ◽  
Vol 13 (01) ◽  
pp. 83-95 ◽  
Author(s):  
HSEN-CHE TSENG ◽  
HUNG-JUNG CHEN
Keyword(s):  
Initial Conditions ◽  
Mean Square Displacement ◽  
Quenched Disorder ◽  
Mean Square ◽  
Numerical Errors ◽  
Limited Sampling ◽  
Chaotic Diffusion ◽  
Normal Diffusion ◽  
The Mean ◽  
Diffusive Processes

That both normal and anomalous chaotic diffusions are suppressed by the presence of quenched disorder for a large class of maps was established by G. Radons.1 In this paper, we consider simple maps (which exhibit normal diffusion) modified by discrete disorder. By decomposing the mean square displacement (MSD) σ2(t) of the system into three terms, namely, [Formula: see text], we find that the MSD of the random walk which corresponds to disorder, [Formula: see text], enhances that of the original unmodified map, [Formula: see text] and that the term 2σ01(t), which describes the correlation between the diffusion fronts of the previous two diffusive processes, just essentially cancels the sum of [Formula: see text] and [Formula: see text]. In consequence, the trajectories of the system are effectively localized. In this formalism, exact numerical calculations without any round-off error can be achieved, the numerical errors coming only from the limited sampling of the initial conditions.

scholarly journals Spherically Restricted Random Hyperbolic Diffusion

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 217 ◽  
Author(s):  
Philip Broadbridge ◽  
Alexander Kolesnik ◽  
Nikolai Leonenko ◽  
Andriy Olenko ◽  
Dareen Omari
Keyword(s):  
Power Spectrum ◽  
Random Fields ◽  
Spectral Measure ◽  
Convergence Rates ◽  
Initial Conditions ◽  
Angular Power Spectrum ◽  
Numerical Studies ◽  
Random Initial Conditions ◽  
Mean Square Convergence ◽  
The Mean

This paper investigates solutions of hyperbolic diffusion equations in R 3 with random initial conditions. The solutions are given as spatial-temporal random fields. Their restrictions to the unit sphere S 2 are studied. All assumptions are formulated in terms of the angular power spectrum or the spectral measure of the random initial conditions. Approximations to the exact solutions are given. Upper bounds for the mean-square convergence rates of the approximation fields are obtained. The smoothness properties of the exact solution and its approximation are also investigated. It is demonstrated that the Hölder-type continuity of the solution depends on the decay of the angular power spectrum. Conditions on the spectral measure of initial conditions that guarantee short- or long-range dependence of the solutions are given. Numerical studies are presented to verify the theoretical findings.

scholarly journals On the random wave equation within the mean square context

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Julia Calatayud ◽  
Juan Carlos Cortés ◽  
Marc Jornet
Keyword(s):  
Wave Equation ◽  
Initial Conditions ◽  
Classical Method ◽  
Separation Of Variables ◽  
Solution Process ◽  
Random Variable ◽  
Dirichlet Boundary Conditions ◽  
Random Wave ◽  
Mean Square ◽  
The Mean

<p style='text-indent:20px;'>This paper deals with the random wave equation on a bounded domain with Dirichlet boundary conditions. Randomness arises from the velocity wave, which is a positive random variable, and the two initial conditions, which are regular stochastic processes. The aleatory nature of the inputs is mainly justified from data errors when modeling the motion of a vibrating string. Uncertainty is propagated from these inputs to the output, so that the solution becomes a smooth random field. We focus on the mean square contextualization of the problem. Existence and uniqueness of the exact series solution, based upon the classical method of separation of variables, are rigorously established. Exact series for the mean and the variance of the solution process are obtained, which converge at polynomial rate. Some numerical examples illustrate these facts.</p>

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

The mean-square generalized delayed decision feedback sequence detector

2003 ◽  
Vol 14 (3) ◽  
pp. 265-268 ◽  
Author(s):  
Maurizio Magarini ◽  
Arnaldo Spalvieri ◽  
Guido Tartara
Keyword(s):  
Decision Feedback ◽  
Mean Square ◽  
The Mean

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

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