Determinação dos parâmetros do controlador preditivo generalizado com função de pesos variante no tempo através de algoritmos genéticos

The predictive control technique has gotten, on the last years, greater number of adepts in reason of the easiness of adjustment of its parameters, of the exceeding of its concepts for multi-input/multi-output (MIMO) systems, of nonlinear models of processes could be linearised around a operating point, so can clearly be used in the controller, and mainly, as being the only methodology that can take into consideration, during the project of the controller, the limitations of the control signals and output of the process. The time varying weighting generalized predictive control (TGPC), studied in this work, is one more an alternative to the several existing predictive controls, characterizing itself as an modification of the generalized predictive control (GPC), where it is used a reference model, calculated in accordance with parameters of project previously established by the designer, and the application of a new function criterion, that when minimized offers the best parameters to the controller. It is used technique of the genetic algorithms to minimize of the function criterion proposed and searches to demonstrate the robustness of the TGPC through the application of performance, stability and robustness criterions. To compare achieves results of the TGPC controller, the GCP and proportional, integral and derivative (PID) controllers are used, where whole the techniques applied to stable, unstable and of non-minimum phase plants. The simulated examples become fulfilled with the use of MATLAB tool. It is verified that, the alterations implemented in TGPC, allow the evidence of the efficiency of this algorithm

Modelagem e controle de um microveículo aéreo: uma aplicação de estabilidade robusta com a técnica backstepping em uma estrutura hexarrotor

In this Thesis, the development of the dynamic model of multirotor unmanned aerial vehicle with vertical takeoff and landing characteristics, considering input nonlinearities and a full state robust backstepping controller are presented. The dynamic model is expressed using the Newton-Euler laws, aiming to obtain a better mathematical representation of the mechanical system for system analysis and control design, not only when it is hovering, but also when it is taking-off, or landing, or flying to perform a task. The input nonlinearities are the deadzone and saturation, where the gravitational effect and the inherent physical constrains of the rotors are related and addressed. The experimental multirotor aerial vehicle is equipped with an inertial measurement unit and a sonar sensor, which appropriately provides measurements of attitude and altitude. A real-time attitude estimation scheme based on the extended Kalman filter using quaternions was developed. Then, for robustness analysis, sensors were modeled as the ideal value with addition of an unknown bias and unknown white noise. The bounded robust attitude/altitude controller were derived based on globally uniformly practically asymptotically stable for real systems, that remains globally uniformly asymptotically stable if and only if their solutions are globally uniformly bounded, dealing with convergence and stability into a ball of the state space with non-null radius, under some assumptions. The Lyapunov analysis technique was used to prove the stability of the closed-loop system, compute bounds on control gains and guaranteeing desired bounds on attitude dynamics tracking errors in the presence of measurement disturbances. The controller laws were tested in numerical simulations and in an experimental hexarotor, developed at the UFRN Robotics Laboratory

Identificação de uma planta de corrente de um motor de indução utilizando redes de base radial

The present work describes the use of a mathematical tool to solve problems arising from control theory, including the identification, analysis of the phase portrait and stability, as well as the temporal evolution of the plant s current induction motor. The system identification is an area of mathematical modeling that has as its objective the study of techniques which can determine a dynamic model in representing a real system. The tool used in the identification and analysis of nonlinear dynamical system is the Radial Basis Function (RBF). The process or plant that is used has a mathematical model unknown, but belongs to a particular class that contains an internal dynamics that can be modeled.Will be presented as contributions to the analysis of asymptotic stability of the RBF. The identification using radial basis function is demonstrated through computer simulations from a real data set obtained from the plant

Influência da corrente de pulso, do tempo de pulso e diâmetro de gota sobre a estabilidade da transferência metálica no processo MIG-P

To obtain a process stability and a quality weld bead it is necessary an adequate parameters set: base current and time, pulse current and pulse time, because these influence the mode of metal transfer and the weld quality in the MIG-P, sometimes requiring special sources with synergistic modes with external control for this stability. This work aims to analyze and compare the effects of pulse parameters and droplet size in arc stability in MIG-P, four packets of pulse parameters were analysed: Ip = 160 A, tp = 5.7 ms; Ip = 300 A and tp = 2 ms, Ip = 350 A, tp = 1.2 ms and Ip = 350 A, tp = 0.8 ms. Each was analyzed with three different drop diameters: drop with the same diameter of the wire electrode; droplet diameter larger drop smaller than the diameter of the wire electrode. For purposes of comparison the same was determined relation between the average current and welding speed was determined generating a constant (Im / Vs = K) for all parameters. Welding in flat plate by simple deposition for the MIG-P with a distance beak contact number (DBCP) constant was perfomed subsequently making up welding in flat plate by simple deposition with an inclination of 10 degrees to vary the DBCP, where by assessment on how the MIG-P behaved in such a situation was possible, in addition to evaluating the MIG-P with adaptive control, in order to maintain a constant arc stability. Also high speed recording synchronized with acquiring current x voltage (oscillogram) was executed for better interpretation of the transfer mechanism and better evaluation in regard to the study of the stability of the process. It is concluded that parameters 3 and 4 exhibited greater versatility; diameters drop equal to or slightly less than the diameter of the wire exhibited better stability due to their higher frequency of detachment, and the detachment of the drop base does not harm the maintenance the height of the arc

Desenvolvimento de uma unidade laboratorial para quantificação de BTX como poluentes atmosféricos, usando microextração em fase sólida

This dissertation aims the development of an experimental device to determine quantitatively the content of benzene, toluene and xylenes (BTX) in the atmosphere. BTX are extremely volatile solvents, and therefore play an important role in atmospheric chemistry, being precursors in the tropospheric ozone formation. In this work a BTX new standard gas was produced in nitrogen for stagnant systems. The aim of this dissertation is to develop a new method, simple and cheaper, to quantify and monitor BTX in air using solid phase microextraction/ gas chromatography/mass spectrometry (SPME/CG/MS). The features of the calibration method proposed are presented in this dissertation. SPME sampling was carried out under non-equilibrium conditions using a Carboxen/PDMS fiber exposed for 10 min standard gas mixtures. It is observed that the main parameters that affect the extraction process are sampling time and concentration. The results of the BTX multicomponent system studied have shown a linear and a nonlinear range. In the non-linear range, it is remarkable the effect of competition by selective adsorption with the following affinity order p-xylene > toluene > benzene. This behavior represents a limitation of the method, however being in accordance with the literature. Furthermore, this behavior does not prevent the application of the technique out of the non-linear region to quantify the BTX contents in the atmosphere.

Extração de ferro da cera de carnaúba utilizando sistemas microemulsionados

The constant search for biodegradable materials for applications in several fields shows that carnauba wax can be a viable alternative in the manufacturing of biolubricants. Carnauba wax is the unique among the natural waxes to have a combination of properties of great importance. In previous studies it was verified the presence of metals in wax composition that can harm the oxidative stability of lubricants. Considering these factors, it was decided to develop a research to evaluate iron removal from carnauba wax, using microemulsion systems (Me) and perform the optimization of parameters, such as: extraction pH, temperature, extraction time, among others. Iron concentration was determined by atomic absorption and, to perform this analysis, sample digestion in microwave oven was used, showing that this process was very efficient. It was performed some analysis in order to characterize the wax sample, such as: attenuated total reflectance infrared spectroscopy (ATR-IR), thermogravimetry (TG), differential scanning calorimetry (DSC), energy dispersive X-ray fluorescence (EDXRF), scanning electron microscopy (SEM) and melting point (FP). The microemulsion systems were composed by: coconut oil as surfactant, n-butanol as cosurfactant, kerosene and/or heptanes as oil phase, distilled water as water phase. The pH chosen for this study was 4.5 and the metal extraction was performed in finite experiments. To evaluate Me extraction it was performed a factorial design for systems with heptane and kerosene as oil phase, also investigating the influence of temperature time and wax/Me ratio, that showed an statistically significant answer for iron extraction at 95% confidence level. The best result was obtained at 60°C, 10 hours contact time and 1: 10 wax/Me ratio, in both systems with kerosene and heptanes as oil phase. The best extraction occurred with kerosene as oil phase, with 54% iron removal

Estudo do equilíbrio líquido-vapor do sistema água+etanol+líquido iônico visando a separação do álcool anidro

Anhydrous ethanol is used in chemical, pharmaceutical and fuel industries. However, current processes for obtaining it involve high cost, high energy demand and use of toxic and pollutant solvents. This problem occurs due to the formation of an azeotropic mixture of ethanol + water, which does not allow the complete separation by conventional methods such as simple distillation. As an alternative to currently used processes, this study proposes the use of ionic liquids as solvents in extractive distillation. These are organic salts which are liquids at low temperatures (under 373,15 K). They exhibit characteristics such as low volatility (almost zero/ low vapor ), thermal stability and low corrosiveness, which make them interesting for applications such as catalysts and as entrainers. In this work, experimental data for the vapor pressure of pure ethanol and water in the pressure range of 20 to 101 kPa were obtained as well as for vapor-liquid equilibrium (VLE) of the system ethanol + water at atmospheric pressure; and equilibrium data of ethanol + water + 2-HDEAA (2- hydroxydiethanolamine acetate) at strategic points in the diagram. The device used for these experiments was the Fischer ebulliometer, together with density measurements to determine phase compositions. The experimental data were consistent with literature data and presented thermodynamic consistency, thus the methodology was properly validated. The results were favorable, with the increase of ethanol concentration in the vapor phase, but the increase was not shown to be pronounced. The predictive model COSMO-SAC (COnductor-like Screening MOdels Segment Activity Coefficient) proposed by Lin & Sandler (2002) was studied for calculations to predict vapor-liquid equilibrium of systems ethanol + water + ionic liquids at atmospheric pressure. This is an alternative for predicting phase equilibrium, especially for substances of recent interest, such as ionic liquids. This is so because no experimental data nor any parameters of functional groups (as in the UNIFAC method) are needed

Obtenção de emulsões asfálticas modificadas utilizando resíduos industriais

The main objective of this research was the development and characterization of conventional and modified cationic asphalt emulsions. The asphalt emulsions were developed by using the Petroleum Asphalt Cement (CAP 50-70) from Fazenda Belém (Petrobras -Aracati-Ce). The first step in this research was the development of the oil phase (asphalt + solvent) and the aqueous phase (water + emulsifying agent + acid + additives), separately. During the experiments for the obtaining of the conventional asphalt emulsion, the concentration of each constituent was evaluated. For the obtaining of the oil phase, kerosene was used as solvent at 15 and 20 wt.%. For the development of the aqueous phase, the emulsifying agent was used at 0.3 and 3.0 wt.%, whereas the acid and the additive were set at 0.3 wt.%. The percentage of asphalt in the asphalt emulsion was varied in 50, 55, and 60 wt.% and the heating temperature was set at 120 °C. The aqueous phase in the asphalt emulsion was varied from 16.4 to 34.1 wt.% and the heating temperature was set at 60 °C. After the obtaining of the oil and the aqueous phases, they were added at a colloidal mill, remaining under constant stirring and heating during 15 minutes. Each asphalt emulsion was evaluated considering: sieve analysis, Saybolt Furol viscosity, pH determination, settlement and storage stability, residue by evaporation, and penetration of residue. After the characterization of conventional emulsions, it was chosen the one that presented all properties in accordance with Brazilian specifications (DNER-EM 369/97). This emulsion was used for the development of all modified asphalt emulsions. Three polymeric industrial residues were used as modifier agents: one from a clothing button industry (cutouts of clothing buttons) and two from a footwear industry (cutouts of sandals and tennis shoes soles), all industries located at Rio Grande do Norte State (Brazil).The polymeric residues were added into the asphalt emulsion (1 to 6 wt.%) and the same characterization rehearsals were accomplished. After characterization, it were developed the cold-mix asphalts. It was used the Marshall mix design. For cold-mix asphalt using the conventional emulsion, it was used 5, 6 and 7 wt.% asphalt emulsion. The conventional mixtures presented stability values according Brazilian specification (DNER-369/97). For mixtures containing asphalt modified emulsions, it was observed that the best results were obtained with emulsions modified by button residue

Aplicação de tensoativos não iônicos na recuperação de fluidos de perfuração poliméricos

The drilling fluid used to assist in the drilling operation of oil wells, accumulates solids inherent in the formation as it is circulated in the well, interfering in the fluid performance during operation. It is discarded after use. The disposal of these fluids causes one of the most difficult environmental problems in the world. This study aims to promote liquid phase separation of drilling fluids, which have circulated in oil wells, and enable this recovered liquid to formulate a new fluid. For this, non-ionic surfactants were used in order to select the best outcome in phase separation. Five real water-based drilling fluids were utilized, which were collected directly from the fields of drilling oil wells, classified as polymeric fluids. The methodology used consisted in combining the fluid with surfactant and then subjecting it to a process of centrifugation or decantation. The decantating tests were scheduled through experimental planning 23 and 32, using as variables the percentage (%) of surfactant utilized and the stirring time in minutes. The surfactants used were ethoxylated nonylphenol and lauryl alcohol ethoxylated with different degrees of ethoxylation. Phase separation was monitored first by tests of stability, and subsequently by the height of the interface in beakers of 100 mL. The results showed that from the surfactants studied, the lauryl alcohol ethoxylated with 3 ethoxylation units has been the most effective in the phase separation process of the drilling fluids tested. The statistical tool used was of great industrial value regarding the programming phase separation in drilling fluids. In conclusion, the liquid phase separated using surfactant can be reused for a new formulation of drilling fluid with similar properties of a new fluid, assuring its efficiency. And in the resulting analysis it is also suggested that the adsorption is the mechanism that leads the phase separation, with surfactant adsorbing in the active solids

Síntese e caracterização de tensoativos e estudo de equilíbrio de fase dos sistemas CnH2n+2/H2O/CnH2n+1COONa/But-OH

The growing utilization of surfactants in several different areas of industry has led to an increase on the studies involving solutions containing this type of molecules. Due to its amphiphilic nature, its molecule presents one polar part and one nonpolar end, which easily interacts with other molecules, being able to modify the media properties. When the concentration in which its monomers are saturated, the airliquid system interface is reached, causing a decrease in interfacial tension. The surfactants from pure fatty acids containing C8, C12 and C16 carbonic chains were synthesized in an alcoholic media using sodium hydroxide. They were characterized via thermal analysis (DTA and DTG) and via infrared spectroscopy, with the intention of observing their purity. Physical and chemical properties such as superficial tension, critical micelle concentration (c.m.c), surfactant excess on surface and Gibbs free energy of micellization were determined in order to understand the behaviour of these molecules with an aqueous media. Pseudo-ternary phase diagrams were obtained aiming to limit the Windsor equilibria conditions so it could be possible to understand how the surfactants carbonic chain size contributes to the microemulsion region. Solutions with known concentrations were prepared to study how the surfactants can influence the dynamic light scattering spectroscopy (DLS) and how the diffusion coefficient is influenced when the media concentration is altered. The results showed the variation on the chain size of the studied surfactant lipophilic part allows the conception of surfactants with similar interfacial properties, but dependent on the size of the lipophilic part of the surfactant. This variation causes the surfactant to have less tendency of microemulsionate oil in water. Another observed result is that the n-alcanes molecule size promoted a decrease on the microemulsion region on the obtained phase diagrams

Nitrificação de efluentes de reatores anaeróbicos em filtros submersos aerados

Although the good performance in organic matter and suspended solids removal, the anaerobic reactors are unable to remove ammonia nitrogen from sewage, which makes indispensable to include a step of post-treatment for removal of ammonia or nitrate as necessary. This paper presents the performance of a new variant technology, where the nitrification unit, preceded by anaerobic units, is a submerged aerated biological filter, without continuous sludge discharge in their daily operation. The oxygenation system is very simple and inexpensive, consisting of perforated hoses and compressors. The anaerobic reactors are a septic tank with two chambers followed (8.82 m³) and two parallel anaerobic filters (36 m³ each) filled with ceramic bricks and conics plastic parts. Both followed aerated filters were filled with cut corrugated conduit. The study evaluated the behavior of the system with constant domestic sewage flow (10 m³/d) and different aeration conditions, are these: stage 01, when applied air flow of 0.01 m³ air/min in both aerated filter; stage 02, remained in the initial air flow rate in the second aerated filter and increased at the first to 0.05 m³ air/min; at last, at last, in stage 03, the air flow rate of first aerated filter was 0.10 m³ air/min and on the second remained at 0.01 m³ air/min. The filter FA1 received load of 0.41 kg COD/m³.d, 0.37 kg COD/m³.d and 0.26 kg COD/m³.d on phases 01, 02 and 03, respectively. The FA2 received loads of 0.25 kg COD/m³.d, 0.18 kg COD/m³.d and 0.14 kg COD/m³.d on phases 01, 02 and 03, respectively. During stage 01, were found the following results: 98% removals of BODtotal and 92% of CODtotal, with effluent presenting 9 mg/L of BODtotal final average and 53 mg/L of CODtotal average; suspended solids removals of 93%, with a mean concentration of 10 mg/L in the final effluent; 47% reduction of ammonia of FA2 to FAN 's, presenting average of 28 mg NNH3/ L of ammonia in the effluent with; the dissolved oxygen levels always remained around 2.0 mg/L. During stage 02, were found removals of 97% and 95% to BODtotal and suspended solids, respectively, with average final concentrations of 8 and 7 mg/L, respectively; was removed 60% of ammonia, whose final concentration was 16.3 mg NNH3/ L, and nitrate was increased to a final average concentration of 16.55 mg N-NO3/L. Finally, the stage 03 provided 6 mg/L of DBOtotal (98% removal) and 23 mg/L of CODtotal (95% removal) of final effluent concentrations average. At this stage was identified the higher ammonia oxidation (86%), with final effluent showing average concentration of 6.1 mg N-NH3/L, reaching a minimum of 1.70 mg N-NH3/L. In some moments, during stage 03, there was a moderate denitrification process in the last aerated filter. The average turbidity in the effluent showed around 1.5 NTU, proving the good biomass physical stability. Therefore, the results demonstrate the submerged biological filters potential, filled with high void ratio material (98%), and aerated with hoses and compressor adoption, in the carbonaceous and nitrogenous matter oxidation, also generating an effluent with low concentration of solids

Aspectos dinâmicos da água versus álcool e acetona por técnicas de congelamento

Water still represents, on its critical properties and phase transitions, a problem of current scientific interest, as a consequence of the countless open questions and of the inadequacy of the existent theoretical models, mainly related to the different solid and liquid phases that this substance possesses. For example, there are 13 known crystalline forms of water, and also amorphous phases. One of them, the amorphous ice of very high density (VHDA), was just recently observed. Other example is the anomalous behavior in the macroscopic density, which presents a maximum at the temperature of 277 K. In order to experimentally investigate the behavior of one of the liquid-solid phase transitions, the anomaly in its density and also the metastability, we used three different cooling techniques and, as comparison systems, we made use of the solvents: acetone and ethyl alcohol. The first studied cooling system employ a Peltier plate, a device recently developed, which makes use of small cubes made up of semiconductors to change heat among two surfaces; the second system is a commercial refrigerator, similar to the residential ones. Finally, the liquid nitrogen technique, which is used to refrigerate the samples in a container, in two ways: a very fast and other one, almost static. In those three systems, three Beckers of aluminum were used (with a volume of 80 ml, each), containing water, alcohol and acetone. They were closed and maintained at atmospheric pressure. Inside of each Becker were installed three thermocouples, disposed along the vertical axis of the Beckers, one close to the inferior surface, other to the medium level and the last one close the superior surface. A system of data acquisition was built via virtual instrumentation using as a central equipment a Data-Acquisition board. The temperature data were collected by the three thermocouples in the three Beckers, simultaneously, in function of freezing time. We will present the behavior of temperature versus freezing time for the three substances. The results show the characterization of the transitions of the liquid

Efeitos de acoplamentos biquadráticos e campos aleatórios em vidros de spins

In this work we have studied the effects of random biquadratic and random fields in spin-glass models using the replica method. The effect of a random biquadratic coupling was studied in two spin-1 spin-glass models: in one case the interactions occur between pairs of spins, whereas in the second one the interactions occur between p spins and the limit p > oo is considered. Both couplings (spin glass and biquadratic) have zero-mean Gaussian probability distributions. In the first model, the replica-symmetric assumption reveals that the system presents two pha¬ses, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic cou¬plings between the spins. For the case p oo, the replica-symmetric assumption yields again only two phases, namely, paramagnetic and quadrupolar. In both these phases the spin-glass parameter is zero. Besides, it is shown that they are stable under the Almeida-Thouless stability analysis. One of them presents negative entropy at low temperatures. We developed one step of replica simmetry breaking and noticed that a new phase, the biquadratic glass phase, emerge. In this way we have obtained the correct phase diagram, with.three first-order transition lines. These lines merges in a common triple point. The effects of random fields were studied in the Sherrington-Kirkpatrick model consi¬dered in the presence of an external random magnetic field following a trimodal distribu¬tion {P{hi) = p+S(hi - h0) +Po${hi) +pS(hi + h0))- It is shown that the border of the ferromagnetic phase may present, for conveniently chosen values of p0 and hQ, first-order phase transitions, as well as tricritical points at finite temperatures. It is verified that the first-order phase transitions are directly related to the dilution in the fields: the extensions of these transitions are reduced for increasing values of po- In fact, the threshold value pg, above which all phase transitions are continuous, is calculated analytically. The stability analysis of the replica-symmetric solution is performed and the regions of validity of such a solution are identified

Efeito de campo aleatório no modelo Sherrington-Kirkpatrick

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Efeitos da interação dipolar na nucleação de vórtices em nano-cilindros magnéticos

The effect of confinement on the magnetic structure of vortices of dipolar coupled ferromagnetic nanoelements is an issue of current interest, not only for academic reasons, but also for the potential impact in a number of promising applications. Most applications, such as nano-oscillators for wireless data transmission, benefit from the possibility of tailoring the vortex core magnetic pattern. We report a theoretical study of vortex nucleation in pairs of coaxial iron and Permalloy cylinders, with diameters ranging from 21nm to 150nm, and 12nm and 21nm thicknesses, separated by a non-magnetic layer. 12nm thick iron and Permalloy isolated (single) cylinders do not hold a vortex, and 21nm isolated cylinders hold a vortex. Our results indicate that one may tailor the magnetic structure of the vortices, and the relative chirality, by selecting the thickness of the non-magnetic spacer and the values of the cylinders diameters and thicknesses. Also, the dipolar interaction may induce vortex formation in pairs of 12nm thick nanocylinders and inhibit the formation of vortices in pairs of 21nm thick nanocylinders. These new phases are formed according to the value of the distance between the cylinderes. Furthermore, we show that the preparation route may control relative chirality and polarity of the vortex pair. For instance: by saturating a pair of Fe 81nm diameter, 21nm thickness cylinders, along the crystalline anisotropy direction, a pair of 36nm core diameter vortices, with same chirality and polarity is prepared. By saturating along the perpendicular direction, one prepares a 30nm diameter core vortex pair, with opposite chirality and opposite polarity. We also present a theoretical discussion of the impact of vortices on the thermal hysteresis of a pair of interface biased elliptical iron nanoelements, separated by an ultrathin nonmagnetic insulating layer. We have found that iron nanoelements exchange coupled to a noncompensated NiO substrate, display thermal hysteresis at room temperature, well below the iron Curie temperature. The thermal hysteresis consists in different sequences of magnetic states in the heating and cooling branches of a thermal loop, and originates in the thermal reduction of the interface field, and on the rearrangements of the magnetic structure at high temperatures, 5 produce by the strong dipolar coupling. The width of the thermal hysteresis varies from 500 K to 100 K for lateral dimensions of 125 nm x 65 nm and 145 nm x 65 nm. We focus on the thermal effects on two particular states: the antiparallel state, which has, at low temperatures, the interface biased nanoelement with the magnetization aligned with the interface field and the second nanoelement aligned opposite to the interface field; and in the parallel state, which has both nanoelements with the magnetization aligned with the interface field at low temperatures. We show that the dipolar interaction leads to enhanced thermal stability of the antiparallel state, and reduces the thermal stability of the parallel state. These states are the key phases in the application of pairs of ferromagnetic nanoelements, separated by a thin insulating layer, for tunneling magnetic memory cells. We have found that for a pair of 125nm x 65nm nanoelements, separated by 1.1nm, and low temperature interface field strength of 5.88kOe, the low temperature state (T = 100K) consists of a pair of nearly parallel buckle-states. This low temperature phase is kept with minor changes up to T= 249 K when the magnetization is reduced to 50% of the low temperature value due to nucleation of a vortex centered around the middle of the free surface nanoelement. By further increasing the temperature, there is another small change in the magnetization due to vortex motion. Apart from minor changes in the vortex position, the high temperature vortex state remains stable, in the cooling branch, down to low temperatures. We note that wide loop thermal hysteresis may pose limits on the design of tunneling magnetic memory cells