Moment Perturbation Research Articles

Fault-tolerant control of flexible satellite with magnetic actuation and reaction wheel

The attitude fault-tolerant control of a flexible satellite actuated by reaction wheels and magnetic torquer bars is investigated in this article. A low earth orbit is considered for moment perturbations such as drag and gravity gradient. Furthermore, the flexible panels attached to a rigid central body are modeled through the assumed mode approach by a finite set of bending modal motion. The ordinary differential equations of their generalized coordinates are found using Lagrange’s equation, and the resulting dynamical model is validated by comparing its simulation results to the NX Siemens software results. Finally, a fault-tolerant controller based on sliding mode control is suggested and tested in different scenarios. It is showed that the proposed control method tolerates the actuators’ faults and controls the satellite’s attitude while desaturating the reaction wheels.

Stability of a uniform attractor for a second-order evolution equation with discontinuous trajectories

The work is devoted to the study of the qualitative behavior of solutions of the wave equation, whose trajectories have impulsive perturbations in moments when they reach a fixed (impulsive) subset of the phase space. Using the general constructing scheme of the infinite-dimensional impulsive dynamical system and using the concept of a uniform attractor — a minimal compact uniformly attracting set, we obtained the result about the existence and the explicit form of a uniform attractor for the corresponding impulsive dynamical system. Trajectories of such system can have an infinite number of impulsive points when they encounter an impulsive subset of the phase space. Thus, a uniform attractor may have a non-empty intersection with the impulsive set and, as a result, may not have the stability property. However, due to the additional conditions on the impulsive parameters of the problem, we managed to prove the stability property for the non-impulsive part of the uniform attractor.

Signal Conditioning for the Kalman Filter: Application to Satellite Attitude Estimation with Magnetometer and Sun Sensors.

Most satellites use an on-board attitude estimation system, based on available sensors. In the case of low-cost satellites, which are of increasing interest, it is usual to use magnetometers and Sun sensors. A Kalman filter is commonly recommended for the estimation, to simultaneously exploit the information from sensors and from a mathematical model of the satellite motion. It would be also convenient to adhere to a quaternion representation. This article focuses on some problems linked to this context. The state of the system should be represented in observable form. Singularities due to alignment of measured vectors cause estimation problems. Accommodation of the Kalman filter originates convergence difficulties. The article includes a new proposal that solves these problems, not needing changes in the Kalman filter algorithm. In addition, the article includes assessment of different errors, initialization values for the Kalman filter; and considers the influence of the magnetic dipole moment perturbation, showing how to handle it as part of the Kalman filter framework.

Effects of Initial Perturbations in the Early Moments of an Explosive Dispersal of Particles

Recent experiments have shown that when a dense layer of solid particles surrounding a high-energy reactive material is explosively dispersed, the particles cluster locally leading to jetlike patterns. The formation of these coherent structures has yet to be fully understood and is believed to have its origin in the early moments of the explosive dispersal. This paper focuses on the early moments of an explosive dispersal of particles. In particular, the effect of initial perturbations on both the gas and particulate phase is investigated, considering heavy particles with a low initial particle volume fraction. Two-dimensional simulations are carried out, and results suggest that a distinctive heterogeneity in the form of a single wavelength perturbation in the rapidly expanding detonation products does not have a significant impact on the early evolution of neither the gas phase nor the cloud of particles. In contrast, the equivalent distinctive heterogeneity in the initial particle volume fraction distribution lingers for the duration of our simulations. Developing instabilities in the gas phase and at the inner- and outer-most front of the particle bed display a dominant wavelength equal to the wavelength of the initial perturbation in the particle volume fraction.

Inglés

Given a sequence of moments $\{c_{n}\}_{n\in\ze}$ associated with an Hermitian linear functional $\mathcal{L}$ defined in the space of Laurent polynomials, we study a new functional $\mathcal{L}_{\Omega}$ which is a perturbation of $\mathcal{L}$ in such a way that a finite number of moments are perturbed. Necessary and sufficient conditions are given for the regularity of $\mathcal{L}_{\Omega}$, and a connection formula between the corresponding families of orthogonal polynomials is obtained. On the other hand, assuming $\mathcal{L}_{\Omega}$ is positive definite, the perturbation is analyzed through the inverse Szego transformation. Keywords: Orthogonal polynomials on the unit circle, perturbation of moments, inverse Szego transformation. To cite this article: E. Fuentes, L.E. Garza, On a finite moment perturbation of linear functionals and the inverse Szego transformation, Rev. Integr. Temas Mat. 34 (2016), No. 1, 39–58.

Composition-dependent structural and magnetic properties of Ni–Mn–Ga alloys studied by ab initio calculations

We have revealed the influence of composition doping (Ni2+x Mn1−x Ga, Ni2+x MnGa1−x , and Ni2Mn1+x Ga1−x ) on lattice constants and atomic magnetic moments of austenite, 7 M and NM martensite, by ab initio calculations. It is demonstrated that Ni-doping decreases the volume, whereas Mn-doping increases it. The total magnetic moment of the three series of alloys is mainly dominated by their Mn content with little phase-state dependence. The perturbation of the magnetic moments by atom substitution is mainly dominated by the Mn environment. This study is expected to provide information on composition-related structure and magnetic properties of Ni–Mn–Ga alloys that could not be obtained by experiments.

Moment perturbation of matrix polynomials

We consider a sequence of perturbed matrix orthogonal polynomials caused by some perturbation on the moments. We find an explicit relation between the perturbed polynomials and the original ones. We also analyse the perturbed second kind polynomials via its associated orthogonal polynomials and the non-perturbed second kind polynomials.

Individual responses to alignment perturbations in socket reaction moments while walking in transtibial prostheses

BackgroundThe alignment of transtibial prostheses has a systematic effect on the mean socket reaction moments in amputees. However, understanding their individual differences in response to alignment perturbations is also important for prosthetists to fully utilize the socket reaction moments for dynamic alignment in each unique patient. The aim of this study was to investigate individual responses to alignment perturbations in transtibial prostheses with solid-ankle-cushion-heel feet. MethodsA custom instrumented prosthesis alignment component was used to measure the socket reaction moments while walking in 11 amputees with transtibial prostheses under 17 alignment conditions, including 3° and 6° of flexion, extension, abduction, and adduction of the socket, 5mm and 10mm of anterior, posterior, lateral, and medial translation of the socket, and an initial baseline alignment. Coronal moments at 30% of stance and maximum sagittal moments were extracted for comparisons from each amputee. FindingsIn the coronal plane, varus moment at 30% of stance was generally reduced by adduction or medial translation of the socket in all the amputees. In the sagittal plane, extension moment was generally increased by posterior translation or flexion of the socket; however, this was not necessarily the case for all the amputees. InterpretationsIndividual responses to alignment perturbations are not always consistent, and prosthetists would need to be aware of this variance when addressing individual socket reaction moments during dynamic alignment in clinical setting.

Analysis of Asymmetric Warpage of Thin Wafers on Flat Plate Considering Bifurcation and Gravitational Force

Large deformation of thin silicon wafer on flat plate induced by film stress was analyzed by analytic method and finite element analysis (FEA) method considering bifurcation and gravitation. Bifurcation criterion was obtained by energy method, and resulting warpage was calculated from obtained curvature. Anisotropy of substrate and film material was considered. For simple cases where mismatch strain was isotropic but the silicon substrate was anisotropic, explicit expression of the bifurcation criterion was obtained. Material anisotropy made great effect on the criterion for (100) wafer. It was almost always in the bifurcation state when the wafer was thinned for packaging process. FEA models to analyze bifurcation were investigated. Gravitational force accompanying with the contact between the flat plate and the silicon wafer were applied. A carefully chosen quarter-model rotated by 45 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> was sufficient to analyze the warpage behavior. Bending down by gravitational force and nonuniform curvature over the wafer were observed. Two FEA schemes were proposed. One was combination of buckling and postbuckling analysis. The other was the force or moment perturbation method. Both methods well described the warpage considering bifurcation and gravitation, and reached the same result.

First principles density functional calculation of magnetic moment and hyperfine fields of dilute transition metal impurities in Gd host

We present first principles calculations of electronic structure and magnetic properties of dilute transition metal (3d, 4d and 5d) impurities in a Gd host. The calculations have been performed within the density functional theory using the full potential linearized augmented plane wave technique and the GGA+U method. The spin and orbital contributions to the magnetic moment and the hyperfine fields have been computed. We find large magnetic moments for 3d (Ti–Co), 4d (Nb–Ru) and 5d (Ta–Os) impurities with magnitudes significantly different from the values estimated from earlier mean field calculation [J. Magn. Magn. Mater. 320 (2008) e446–e449]. The exchange interaction between the impurity and host Gd moments is found to be positive for early 3d elements (Sc–V) while in all other cases an anti-ferromagnetic coupling is observed. The trends for the magnetic moment and hyperfine field of d-impurities in Gd show qualitative difference with respect to their behavior in Fe, Co and Ni. The calculated total hyperfine field, in most cases, shows excellent agreement with the experimental results. A detailed analysis of the Fermi contact hyperfine field has been made, revealing striking differences for impurities having less or more than half filled d-shell. The impurity induced perturbations in host moments and the change in the global magnetization of the unit cell have also been computed. The variation within each of the d-series is found to correlate with the d–d hybridization strength between the impurity and host atoms.

Abstract 435: The Integrity of Central Blood Pressure Regulation in Conscious Patients With Hypertension and Normal Healthy Control

Blood pressure (BP) is centrally regulated by baroreflex mechanism where a change in BP would provoke vagal and sympathetic responses to counteract the moment by moment perturbations in BP. This study investigated the integrity of central regulation of BP in patients with hypertension (HTN) in response to known and standard autonomic tests. Beat-by-beat measurement of arterial BPs (mmHg);systolic, diastolic and mean (M), heart rate (HR) (beats/min) and indices of brainstem responses; cardiac vagal tone (CVT; arbitrary units) and cardiac sensitivity to baroreflex (CSB; ms/mmHg) were continuously monitored and recorded using the Neuroscope system (Medifit instruments Ltd, UK). Statistical analysis was performed using two tail student’s t test. The study included total of 23 subjects; 12 hypertensive males (mean±SD; 45±14.4 years) and 11 (3 females, 8 males) controls (35.6±9.7 y). Their age difference was not significant. The table describes the cardiovascular and brainstem responses during: baseline, supine, before and to the following autonomic tests: deep breathing (DB), sitting up, standing up, isometric handgrip (IHG) and phase IIe of valsalva’s maneouvre (Val-IIe), in addition to P values for control subjects. In conclusion, brainstem mechanism is intact in patients with HTN, however, there were variable responses during deep breathing and sitting up tests. The baseline measurement showed improper BP control and hence continuous measurement showed more reliability than office discrete readings to ensure effective BP monitoring. The adjustment of brainstem responses to antihypertensive therapy is suggested to be used as an index to monitor treatment effect.

A perturbation method for estimation of dynamic systems

A novel framework called the Perturbed Jth Moment Extended Kalman Filter (PJMEKF), based on a classical perturbation technique is proposed for estimating the states of a nonlinear dynamical system from sensor measurements. This method falls under a class of architectures under investigation primarily to study the interplay of major issues in nonlinear estimation such as nonlinearity, measurement sparsity, and initial condition uncertainty in an environment with low levels of process noise. Taylor series expansion of the departure motion dynamics about the best estimate is used to derive a series representation of the unforced motion. It is found that such series representation evolves as a set of differential equations that force each other in a cascade manner, adding up to give the unforced motion (in a so-called “triangular” structure). This formal perturbation solution for the departure motion dynamics is used in deriving the differential equations governing the time evolution of the high order statistical moments of the estimation error. These tensor differential equations are found to possess a similar high order triangular structure in addition to being symmetric (in N tensorial dimensions and we appropriately term the evolution equations as Tensor Lyapunov Equations of statistical moment perturbations). Elegance of the tensor differential equations thus derived is accompanied by the computational advantages due to symmetry in all tensorial dimensions. A vector matrix representation of tensors is proposed with which the representation and solution of the tensor differential equations can be carried out effectively. Approximations are introduced to incorporate low levels of process noise forcing function in the propagation phase of the moment equations. The statistics thus propagated are used in a filtering framework to estimate the state vector of a nonlinear system from noisy measurements, within the traditional Kalman update paradigm. The Kalman gain thus determined is utilized in updating all high order moments in preparation for the subsequent propagation phase leading to improved estimation accuracy. The filter developed is applied to an orbit estimation problem and comparisons are presented with classical extended Kalman filter.

Secular dynamics of a coplanar, non-resonant planetary system under the general relativity and quadrupole moment perturbations

We construct a secular theory of a coplanar system of N planets not involved in strong mean motion resonances, and which are far from collision zones. Besides the point-to-point Newtonian mutual interactions, we consider the general relativistic corrections to the gravitational potential of the star and the innermost planet, and also a modification of this potential by the quadrupole moment and tidal distortion of the star. We focus on hierarchical planetary systems. After averaging the model Hamiltonian with a simple algorithm making use of very basic properties of the Keplerian motion, we obtain analytical secular theory of high order in the semimajor axes ratio. A great precision of the analytic approximation is demonstrated with the numerical integrations of the equations of motion. A survey regarding model parameters (the masses, semimajor axes, spin rate of the star) reveals a rich and non-trivial dynamics of the secular system. Our study is focused on its equilibria. Such solutions predicted by the classic secular theory, which correspond to aligned (mode I) or anti-aligned (mode II) apsides, may be strongly affected by the gravitational corrections. The so-called true secular resonance, which is a new feature of the classic two-planet problem discovered by Michtchenko & Malhotra, may appear in other, different regions of the phase space of the generalized model. We found bifurcations of mode II from which emerge new, yet unknown in the literature, secularly unstable equilibria and a complex structure of the phase space. These equilibria may imply secularly unstable orbital configurations even for initially moderate eccentricities. The point mass gravity corrections can affect the long-term stability in the secular time-scale, which may directly depend on the age of the host star through its spin rate. We also analyse the secular dynamics of the υ Andromedae system in the realm of the generalized model. Also in this case of the three-planet system, new secular equilibria may appear.

Dynamic Reliability Sensitivity Analysis of Torsion Bar

In this paper, the variation rules of strength, load, reliability and failure rate of mechanical components are studied with time, and a state equation model for dynamic reliability of mechanical components is established under random load. Meanwhile, reliability index is obtained by using Second moment method and perturbation method. Based on the reliability design theory and sensitivity analysis method, torsion-bar is taken as an example, and the dynamic reliability sensitivity of torsion-bar is extensively discussed and a computing method is presented for dynamic reliability sensitivity design. The variation rules of dynamic reliability sensitivity are obtained and the effects of design parameters on reliability of torsion-bar are studied. As a result, the proposed method provides theoretical basis for reliability design of torsion bar.

Modeling initial contact dynamics during ambulation with dynamic simulation

Ankle-foot orthoses are frequently used interventions to correct pathological gait. Their effects on the kinematics and kinetics of the proximal joints are of great interest when prescribing ankle-foot orthoses to specific patient groups. Mathematical Dynamic Model (MADYMO) is developed to simulate motor vehicle crash situations and analyze tissue injuries of the occupants based multibody dynamic theories. Joint kinetics output from an inverse model were perturbed and input to the forward model to examine the effects of changes in the internal sagittal ankle moment on knee and hip kinematics following heel strike. Increasing the internal ankle moment (augmentation, equivalent to gastroc-soleus contraction) produced less pronounced changes in kinematic results at the hip, knee and ankle than decreasing the moment (attenuation, equivalent to gastroc-soleus relaxation). Altering the internal ankle moment produced two distinctly different kinematic curve morphologies at the hip. Decreased internal ankle moments increased hip flexion, peaking at roughly 8% of the gait cycle. Increasing internal ankle moments decreased hip flexion to a lesser degree, and approached normal at the same point in the gait cycle. Increasing the internal ankle moment produced relatively small, well-behaved extension-biased kinematic results at the knee. Decreasing the internal ankle moment produced more substantial changes in knee kinematics towards flexion that increased with perturbation magnitude. Curve morphologies were similar to those at the hip. Immediately following heel strike, kinematic results at the ankle showed movement in the direction of the internal moment perturbation. Increased internal moments resulted in kinematic patterns that rapidly approach normal after initial differences. When the internal ankle moment was decreased, differences from normal were much greater and did not rapidly decrease. This study shows that MADYMO can be successfully applied to accomplish forward dynamic simulations, given kinetic inputs. Future applications include predicting muscle forces and decomposing external kinetics.

Paramagnetic susceptibility of ferrite and cementite obtained from ab initio calculations

Paramagnetic susceptibility of BCC ferrite ( α -Fe) and of cementite (Fe 3C), was calculated in a temperature range above the Curie point, using a density functional-based method in conjunction with statistical approximations. The electronic structure and the magnetic energy of both systems were calculated using the full potential linear augmented plane wave (FPLAPW) method as implemented in the Wien2k Code. The temperature effect was captured by introducing the Boltzmann statistical distribution to describe the orientation perturbation of the magnetic moments caused by thermal agitation. The magnetic moment was calculated in the temperature range from 1045 to 1175 K for alpha-iron and from 540 to 640 K for cementite. The modeling was performed for applied magnetic fields ranging from 1–2 T. The main assumption was that the effect of temperature and that of the applied magnetic field can be decoupled and, consequently, be treated separately. The calculated moments were used to estimate the paramagnetic susceptibility according to the linear relation χ = M / B well established for paramagnetic systems. The calculated values were compared with published experimental measurements for iron and with values obtained from the Curie–Weiss law for cementite.

OPTIMAL PERTURBATION OF UNCERTAIN SYSTEMS

In studies of perturbation dynamics in physical systems, certain specification of the governing perturbation dynamical system is generally lacking, either because the perturbation system is imperfectly known or because its specification is intrinsically uncertain, while a statistical characterization of the perturbation dynamical system is often available. In this report exact and asymptotically valid equations are derived for the ensemble mean and moment dynamics of uncertain systems. These results are used to extend the concept of optimal deterministic perturbation of certain systems to uncertain systems. Remarkably, the optimal perturbation problem has a simple solution: In uncertain systems there is a sure initial condition producing the greatest expected second moment perturbation growth.

Stochastic second-order BEM perturbation formulation

This paper presents the stochastic second order moment perturbation approach to the classical deterministic Boundary Element Method (BEM) formulation. Numerous applications of such a formulation in different problems of stochastic mechanics, especially in the field of computational modeling of structural defects in homogeneous and composite materials occurring randomly in solids and engineering structures, were the main reasons to introduce the proposed model. The stochastic boundary element method (SBEM) formulation of the general linear elasticity boundary value has been provided together with an appropriate discretization. The equations describing the expected values and the covariances of stress and strain tensors for points lying on the boundary and inside the region are considered. This set of equations constitutes a formal mathematical statement of the problem and is suitable for computational implementation.

Spatial and temperature dependence of magnetic moment perturbations near the (1-10) Fe/Co interface

The spatial dependence of the magnetic moment perturbation near the (1-10)-Fe/Co interface was derived from hyperfine fields determined by perturbed angular correlation. The amplitude of the moment perturbation decays exponentially with the distance to the interface. The moment perturbation itself is modulated by a sine function of the distance d to the interface Δμ=A*exp(−p*|d|)*sin(−k*d). Between 90 K and 570 K, we observe that the amplitude and the penetration depth of the perturbation as well as the wave vector of the modulation are essentially constant within the accuracy of the values. In this temperature region the average values for the parameters determining the exact moment perturbation are A=1.03μB, p=2.25×109 m and k=1.45×1010 m−1 when d is defined positive at the Co side of the interface.

Bulk and surface magnetic properties of dilute FeCr alloys

The electronic and magnetic structures of dilute FeCr alloys have been investigated in the framework of the periodic Anderson model. The theory involves only a few phenomenological parameters, which can be determined via magnetic properties of pure Fe and Cr samples. Some examples are considered: the perturbation of magnetic moments of Fe atoms due to Cr impurities both in the bulk and near the surface; the electronic structure of the Cr protective monolayer covering the Fe surface; and the properties of Fe/Cr superlattices.