Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

Simultaneous analysis of v1, v4, 2v2, v2+v5, and 2v5 bands of 12CH3F

The Fourier-transform spectrum of CH3F from 2800 to 3100 cm−1, obtained by Guelachvili in Orsay at a resolution of about 0.003 cm−1, was analyzed. The effective Hamiltonian used contained all symmetry allowed interactions up to second order in the Amat-Nielsen classification, together with selected third-order terms, amongst the set of nine vibrational basis functions represented by the states ν1(A1), ν4(E), 2ν2(A1), ν2 + ν5(E), 2ν50(A1), and 2ν5±2(E). A number of strong Fermi and Coriolis resonances are involved. The vibrational Hamiltonian matrix was not factorized beyond the requirements of symmetry. A total of 59 molecular parameters were refined in a simultaneous least-squares analysis to over 1500 upper-state energy levels for J ≤ 20 with a standard deviation of 0.013 cm−1. Although the standard deviation remains an order of magnitude greater than the precision of the measurements, this work breaks new ground in the simultaneous analysis of interacting symmetric top vibrational levels, in terms of the number of interacting vibrational states and the number of parameters in the Hamiltonian.

Pseudolikelihood equations for Potts MRF model parameter estimation on higher order neighborhood systems

This letter presents pseudolikelihood equations for the estimation of the Potts Markov random field model parameter on higher order neighborhood systems. The derived equation for second-order systems is a significantly reduced version of a recent result found in the literature (from 67 to 22 terms). Also, with the proposed method, a completely original equation for Potts model parameter estimation in third-order systems was obtained. These equations allow the modeling of less restrictive contextual systems for a large number of applications in a computationally feasible way. Experiments with both simulated and real remote sensing images provided good results.

ENO adaptive method for solving one-dimensional conservation laws

In this work an efficient third order non-linear finite difference scheme for solving adaptively hyperbolic systems of one-dimensional conservation laws is developed. The method is based oil applying to the solution of the differential equation an interpolating wavelet transform at each time step, generating a multilevel representation for the solution, which is thresholded and a sparse point representation is generated. The numerical fluxes obtained by a Lax-Friedrichs flux splitting are evaluated oil the sparse grid by an essentially non-oscillatory (ENO) approximation, which chooses the locally smoothest stencil among all the possibilities for each point of the sparse grid. The time evolution of the differential operator is done on this sparse representation by a total variation diminishing (TVD) Runge-Kutta method. Four classical examples of initial value problems for the Euler equations of gas dynamics are accurately solved and their sparse solutions are analyzed with respect to the threshold parameters, confirming the efficiency of the wavelet transform as an adaptive grid generation technique. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Morfometria de microbacias do Córrego Rico, afluente do Rio Mogi-Guaçu, Estado de São Paulo, Brasil

Este trabalho teve como objetivo avaliar as características morfométricas das microbacias (2ª, 3ª, 4ª e 5ª ordens de magnitude) da bacia hidrográfica do córrego Rico, sub-bacia do Rio Mogi-Guaçu, localizada na região administrativa de Ribeirão Preto, Estado de São Paulo, Brasil. Para tanto, foram determinados os parâmetros físicos e a configuração topográfica natural do sistema de drenagem. Os procedimentos para a obtenção dos dados foram fundamentados em técnicas de sensoriamento remoto e geoprocessamento. A partir da vetorização das cartas topográficas correspondentes à área de estudo, realizou-se a análise morfométrica quanto às características dimensionais, do padrão de drenagem e do relevo no sistema de informação geográfica ArcView. A microbacia é considerada de sexta ordem de magnitude, com área estimada de 542 km², com 85 microbacias de segunda ordem, 22 de terceira, sete de quarta ordem e duas de quinta. Utilizando o critério geométrico, na disposição fluvial das sub-bacias de cabeceiras observou-se a predominância dos modelos dendríticos e subdendríticos, enquanto a jusante predominava o modelo subparalelo, respectivamente, nas áreas de ocorrências dos arenitos Bauru e rochas efusivas básicas.

Random regressions models to describe the genetic variation of milk yield over multiple parities in Buffaloes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Aerofotos convencionais e imagens orbitais TM/LANDSAT no mapeamento morfopedológico em Santa Bárbara D'Oeste (SP)

Foram estudados, com o auxílio de fotografias aéreas, aspectos qualitativos e quantitativos do relevo e da rede de drenagem de solos de uma área de Santa Bárbara D'Oeste, SP. Esta região compreende 14.625 ha, onde foram selecionadas bacias hidrográficas de 3ª ordem de ramificação e amostras circulares de 5km². As unidades de mapeamento simples ou associações de solos são: Latossolo Vermelho Escuro, Podzólico, Litossolo + Podzólico, Terra Roxa Estruturada + Latossolo Roxo distrófico. Após a caracterização das feições fisiográficas, da área de ocorrência desses solos, foram realizados dois mapas morfopedológicos. No primeiro utilizou-se fotografias aéreas verticais pancromáticas na escala 1: 35.000 (data de 25/6/78) e no segundo imagens orbitais do sensor Thematic Mapper do LANDSAT-5, nas bandas 3, 4 e 5 e composição colorida 3/4/5 na escala 1: 100.000 (data de 12/9/91). As análises qualitativas e quantitativas do relevo (índice de declividade média) e rede de drenagem (densidade de drenagem, freqüência de rios, razão de textura) mostraram-se eficientes na diferenciação das unidades de solo estudadas, tanto em bacias hidrográficas como em amostras circulares. A utilização de fotografias aéreas, permitiu maior riqueza de detalhes na precisão dos limites das unidades de mapeamento e no maior número de unidades de mapeamento discriminadas em relação as imagens orbitais. A composição colorida 3/4/5 permitiu diferenciar os Latossolos argilosos dos Latossolos de textura média, assim como o Latossolo Húmico.

Higher order ionospheric effects in GNSS positioning in the European region

After removal of the Selective Availability in 2000, the ionosphere became the dominant error source for Global Navigation Satellite Systems (GNSS), especially for the high-accuracy (cm-mm) demanding applications like the Precise Point Positioning (PPP) and Real Time Kinematic (RTK) positioning.The common practice of eliminating the ionospheric error, e. g. by the ionosphere free (IF) observable, which is a linear combination of observables on two frequencies such as GPS L1 and L2, accounts for about 99% of the total ionospheric effect, known as the first order ionospheric effect (Ion1). The remaining 1% residual range errors (RREs) in the IF observable are due to the higher - second and third, order ionospheric effects, Ion2 and Ion3, respectively. Both terms are related with the electron content along the signal path; moreover Ion2 term is associated with the influence of the geomagnetic field on the ionospheric refractive index and Ion3 with the ray bending effect of the ionosphere, which can cause significant deviation in the ray trajectory (due to strong electron density gradients in the ionosphere) such that the error contribution of Ion3 can exceed that of Ion2 (Kim and Tinin, 2007).The higher order error terms do not cancel out in the (first order) ionospherically corrected observable and as such, when not accounted for, they can degrade the accuracy of GNSS positioning, depending on the level of the solar activity and geomagnetic and ionospheric conditions (Hoque and Jakowski, 2007). Simulation results from early 1990s show that Ion2 and Ion3 would contribute to the ionospheric error budget by less than 1% of the Ion1 term at GPS frequencies (Datta-Barua et al., 2008). Although the IF observable may provide sufficient accuracy for most GNSS applications, Ion2 and Ion3 need to be considered for higher accuracy demanding applications especially at times of higher solar activity.This paper investigates the higher order ionospheric effects (Ion2 and Ion3, however excluding the ray bending effects associated with Ion3) in the European region in the GNSS positioning considering the precise point positioning (PPP) method. For this purpose observations from four European stations were considered. These observations were taken in four time intervals corresponding to various geophysical conditions: the active and quiet periods of the solar cycle, 2001 and 2006, respectively, excluding the effects of disturbances in the geomagnetic field (i.e. geomagnetic storms), as well as the years of 2001 and 2003, this time including the impact of geomagnetic disturbances. The program RINEX_HO (Marques et al., 2011) was used to calculate the magnitudes of Ion2 and Ion3 on the range measurements as well as the total electron content (TEC) observed on each receiver-satellite link. The program also corrects the GPS observation files for Ion2 and Ion3; thereafter it is possible to perform PPP with both the original and corrected GPS observation files to analyze the impact of the higher order ionospheric error terms excluding the ray bending effect which may become significant especially at low elevation angles (Ioannides and Strangeways, 2002) on the estimated station coordinates.

A linearly tunable low-voltage CMOS transconductor with improved common-mode stability and its application to (gm)-C filters

A linearly tunable low-voltage CMOS transconductor featuring a new adaptative-bias mechanism that considerably improves the stability of the processed-signal common,mode voltage over the tuning range, critical for very-low voltage applications, is introduced. It embeds a feedback loop that holds input devices on triode region while boosting the output resistance. Analysis of the integrator frequency response gives an insight into the location of secondary poles and zeros as function of design parameters. A third-order low-pass Cauer filter employing the proposed transconductor was designed and integrated on a 0.8-mum n-well CMOS standard process. For a 1.8-V supply, filter characterization revealed f(p) = 0.93 MHz, f(s) = 1.82 MHz, A(min) = 44.08, dB, and A(max) = 0.64 dB at nominal tuning. Mined by a de voltage V-TUNE, the filter bandwidth was linearly adjusted at a rate of 11.48 kHz/mV over nearly one frequency decade. A maximum 13-mV deviation on the common-mode voltage at the filter output was measured over the interval 25 mV less than or equal to V-TUNE less than or equal to 200 mV. For V-out = 300 mV(pp) and V-TUNE = 100 mV, THD was -55.4 dB. Noise spectral density was 0.84 muV/Hz(1/2) @1 kHz and S/N = 41 dB @ V-out = 300 mV(pp) and 1-MHz bandwidth. Idle power consumption was 1.73 mW @V-TUNE = 100 mV. A tradeoff between dynamic range, bandwidth, power consumption, and chip area has then been achieved.

Absorption and emission spectroscopic parameters of Nd3+ and Eu3+ ions in their hexamethylphosphoramide complexes

Syntheses of the following complexes are reported: LnX3·6L, LnX′3·4L, LnX″3·3L and Eu(NCS)3·3L, where Ln = Nd3+, Eu3+; L = hexamethylphosphoramide (hmpa); X = ClO4 -, PF6 -; X′ = NCS-, NO3 -, Br-, ClO4 -; X″=Cl-. Spectra of the complexes of Nd3+ (absorption) and Eu3+ (emission) in dichloromethane solutions were measured. The oscillator strengths of the Nd3+ f-f absorption bands within the 11 000-30 000 cm-1 region were determined and the τλ intensity parameters were obtained according to the Judd-Ofelt formalism. Covalency parameters were also determined for the Nd3+ complexes. The intensities relationship η21 of the 5D0→7F2 and 5D0→7F1 transitions of the Eu3+ was calculated. A good correlation between τ2 and the oscillator strength of the hypersensitive band of Nd3+ was found, as well as a correlation between τ2 and η21. There are only qualitative relations between τ2 and the covalency parameter. © 1991.

Crystallization of ZrF4-LaF3-AlF3 glasses

0.7125ZrF4-0.2375(1 - xLaF3 • xLnF3)-0.05AIF3 with x = 0.01, 0.02 and 0.03 for Ln = Er and x = 0.03 for Ln = Pr, Nd glasses were studied by differential thermal analysis (DTA), X-ray diffraction and optical spectroscopy. Avrami parameters (Ec and n) were obtained from DTA curves. With La3+ substitution a decrease in the stability against crystallization was observed. This decrease follows the order Er3+ > Nd3+ ≈ Pr3+ for 3% molar substitution. n values suggest an interface controlled growth mechanism with grain edge nucleation abler saturation. Two crystalline polymorphs of the LaZr3F15 phase were identified. With the substitution of 3 mol% of Pr3+, Nd3+ or Er3+ for La3+ only the crystallization of the rhombohedral α-LnZr3F15 phase was observed. An increase in Ω6 Judd's intensity parameter occurs with crystallization and also an increase in the 1.04 μm peak emission cross-section for Nd3+ 4I3/2 state suggesting the potential application of these glass ceramics in optical amplification devices. © 1997 Elsevier Science B.V.

Preparation, characterization and spectroscopy of the europium diphenylphosphinate complex

The purpose of this work is to study the preparation and spectroscopic behavior of the europium diphenylphosphinate complex -Eu(DPP)3. Elemental and thermogravimetric analysis, powder X-ray diffractometry, and infrared spectroscopy were applied to characterize the formula of the final product and the sixfold coordination of the Eu3+ ion. Excitation and emission spectra have been recorded at liquid nitrogen and room temperatures. The 5D0→7F2 transition intensity decreases when T decreases in comparison to the 5D0→7F1 transition intensity. Molecular mechanic calculations were developed in order to obtain the spatial coordinates of the Eu3+ and ligand ions. The simple overlap model was used to calculate the total splitting of the 5D0→7F1 transition, 5D0→7F0/5D 0→7F2 ntensity ratio and the intensity parameters, Ωλ (λ=2 and 4). Good agreements between theoretical predictions and experimental results have been obtained with g=2/3 as the effective charge and α=0.8×10-24 cm3 as the isotropic polarizability of the oxygen. © 1998 Elsevier Science S.A.

L-Histidine-europium(III) complex: A spectroscopical study

Chemical characterization as well as spectroscopical study of the L-histidine-europium(III) complex were developed both experimental and theoretically. Molecular mechanics (MM) simulation was performed in order to have indication of the compound structure and the Eu 3+ chemical environment. The Simple Overlap Model (SOM) was applied to predict spectroscopic quantities as 5D 0→ 7F 0/ 5D 0→ 7F 2 intensity ratio, 5D 0→ 7F 1 transition splitting and the intensity Ω λ parameters (λ = 2 and 4). Satisfactory results are obtained with 0.1 and 2/3 as the effective charges of the nitrogen (gN) and oxygen (gO) respectively, and their polarizabilities (α) depend on the distance. © 1999 Elsevier Science B.V. All rights reserved.

Análise multivariada de microbacias em relação ao tipo de solo

The objective of this work was to study the dimensional parameters of the drainage net using 12 third-order ramification hydrological watersheds: 4 watersheds per soil unit (LVA, RL and RQ). The soil distinction was realized using ''t'' test to verify the orthogonal contrast among three soil averages and the grouping analysis and mean components. The results showed that the multivariance analysis was not able to discriminate three soils using the dimensional analysis. The t test of this isolated variable allowed discriminating RQ soil from LVA and RL soil units; but it was not sensitive to discriminate the LVA soil and RL unit.