On an Optimal Linear Control of a Chaotic Non-Ideal Duffing System

In this work, we use a nonlinear control based on Optimal Linear Control. We used as mathematical model a Duffing equation to model a supporting structure for an unbalanced rotating machine with limited power (non-ideal motor). Numerical simulations are performed for a set control parameter (depending on the voltage of the motor, that is, in the static and dynamic characteristic of the motor) The interaction of the non-ideal excitation with the structure may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the system. Chaotic behavior is obtained for values of the parameters. Then, the proposed control strategy is applied in order to regulate the chaotic behavior, in order to obtain a periodic orbit and to decrease its amplitude. Both methodologies were used in complete agreement between them. The purpose of the paper is to give suggestions and recommendations to designers and engineers on how to drive this kind of system through resonance.

Determination of the optimal quantity of crop residues for energy in sugarcane crop management using linear programming in variety selection and planting strategy

The aim of this work was to present organizational models for optimizing the reduction of crop residue generated by the sugarcane culture. The first model consisted of the selection of varieties of sugarcane to be planted meeting the mill requirements and, at the same time, to minimize the quantity of residue produced. The second model discussed the use of residue to produce energy. This is related to the selection of variety and quantity to be planted, in order to meet the requirements of the mill, to reduce the quantity of residue, and to maximize as much as possible the energy production. The use of linear programming was proposed. The two models presented similar results in this study, and both may be used to define the varieties and areas to be cultivated. (C) 2001 Published by Elsevier B.V. Ltd.

A study of a numerical solution of the steady two dimensions Navier-Stokes equations in a constricted channel problem by a compact fourth order method

We present a numerical solution for the steady 2D Navier-Stokes equations using a fourth order compact-type method. The geometry of the problem is a constricted symmetric channel, where the boundary can be varied, via a parameter, from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular. The set of non-linear equations is solved by the Newton method. Results have been obtained for Reynolds number up to 500. Estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method. (C) 2002 Elsevier B.V. All rights reserved.

Gauge formulation for higher order gravity

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained that includes derivatives of the curvature. We analyze the form of the second field strength, G=partial derivative F+fAF, in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of F and quadratic contractions of G are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his generalized electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behavior at short distances as well as a meso-large distance modification.

Applicability of the linear delta expansion for the lambda phi(4) field theory at finite temperature in the symmetric and broken phases

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Statements on chaos control designs, including a fractional order dynamical system, applied to a MEMS comb-drive actuator

In this work, we deal with a micro electromechanical system (MEMS), represented by a micro-accelerometer. Through numerical simulations, it was found that for certain parameters, the system has a chaotic behavior. The chaotic behaviors in a fractional order are also studied numerically, by historical time and phase portraits, and the results are validated by the existence of positive maximal Lyapunov exponent. Three control strategies are used for controlling the trajectory of the system: State Dependent Riccati Equation (SDRE) Control, Optimal Linear Feedback Control, and Fuzzy Sliding Mode Control. The controls proved effective in controlling the trajectory of the system studied and robust in the presence of parametric errors.

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

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

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.

Correlação linear e espacial entre a produtividade de forragem, a porosidade total e a densidade do solo de Pereira Barreto (SP)

Em relação aos sistemas de manejo adotados pelo homem, a porosidade total e a densidade do solo são atributos ativamente alterados, refletindo decisivamente sobre a produtividade vegetal agrícola. No ano agrícola de 2005, na Fazenda Bonança, no município de Pereira Barreto, Estado de São Paulo, Brasil, foram analisadas a produtividade de forragem do milho outonal (MSF) no sistema plantio direto irrigado, a porosidade total (PT) e a densidade do solo (DS) em profundidade, em um Latossolo Vermelho distrófico. O objetivo foi estudar a variabilidade e as correlações lineares e espaciais entre os atributos da planta e do solo, visando selecionar um indicador da qualidade física do solo de boa representatividade para produtividade da forragem. Foi instalada a malha geoestatística, para coleta de dados do solo e planta, contendo 125 pontos amostrais, numa área de 2.500 m². Os atributos estudados, além de não terem variado aleatoriamente, apresentaram variabilidade dos dados entre média e baixa e seguiram padrões espaciais bem definidos, com alcance entre 6,8 e 23,7 m. Por sua vez, a correlação linear entre o atributo da planta e os do solo, em razão do elevado número de observações, foi baixa. As observações de melhor correlação com a MSF foram a DS1 e a PT1. Entretanto, do ponto de vista espacial, houve excelente correlação inversa entre a MSF e a DS1, assim como entre a DS1 e a PT1. Nos sítios onde a DS1 aumentou (1,45-1,64 kg dm-3) a MSF variou entre 11.653 e 14.552 kg ha-1; já naqueles onde diminuiu (1,35-1,45 kg dm-3) a MSF, ficou entre 14.552 e 17.450 kg ha-1. Portanto, a densidade global, avaliada na camada de 0-0,10 m (DS1), apresentou-se como satisfatório indicador da qualidade física do solo de Pereira Barreto (SP), quando destinado à produtividade de forragem do milho outonal.

Spatial and linear correlations between soil and corn

O conjunto de tecnologias aplicadas ao sistema de produção agrícola tem como características principais a verticalização da produtividade, diminuição de custos, melhoria nas características físicas, químicas e biológicas do solo para proporcionarem o crescimento sustentável do meio de produção. Desta forma, o trabalho teve como objetivo determinar a variabilidade e as correlações lineares e especiais entre os atributos da planta e do solo, visando selecionar um indicador da qualidade física do solo de boa representatividade para produção de forragem. No ano agrícola de 2006, na Fazenda Bonança, município de Pereira Barreto (SP), foram analisados a produtividade de forragem do milho outonal (FDM) em sistema plantio direto irrigado e os atributos físicos do solo, num Latossolo Vermelho distrófico. O objetivo foi estudar a variabilidade e as correlações lineares e espaciais entre os atributos da planta e os do solo, visando selecionar um indicador da qualidade física do solo de boa representatividade para a produtividade da forragem. Foi instalada a malha geoestatística, para coleta de dados do solo e planta, contendo 125 pontos amostrais, numa área de 2.500 m². Os atributos estudados, além de não terem variado aleatoriamente, apresentaram variabilidade dos dados entre baixa e muito alta e seguiram padrões espaciais bem definidos, com alcances entre 7,8 e 38,0 m. Por outro lado, a correlação linear entre os atributos da planta com o do solo foi baixa e extremamente significativa. Os pares Massa Seca de forragem versus Microporosidade e Diâmetro do colmo versus Densidade do Solo foram melhor correlacionados na camada de 0-0.10m, enquanto os outros pares - Massa Seca de Forragem versus Macroporosidade - e Porosidade Total - apresentaram correlação inversa para a mesma camada. Entretanto, do ponto de vista espacial, houve uma alta correlação inversa entre Massa Seca de Forragem com Microporosidade, de modo que a microporosidade na camada de 0-0.10m pode ser considerada um bom indicador de qualidade física do solo, tendo em vista a produção de forragem de milho.

Combinação linear ponderada na definição de áreas prioritárias à conectividade entre fragmentos florestais em ambiente SIG

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The symmetry group of Z(q)(n) in the Lee space and the Z(qn)-linear codes

The Z(4)-linearity is a construction technique of good binary codes. Motivated by this property, we address the problem of extending the Z(4)-linearity to Z(q)n-linearity. In this direction, we consider the n-dimensional Lee space of order q, that is, (Z(q)(n), d(L)), as one of the most interesting spaces for coding applications. We establish the symmetry group of Z(q)(n) for any n and q by determining its isometries. We also show that there is no cyclic subgroup of order q(n) in Gamma(Z(q)(n)) acting transitively in Z(q)(n). Therefore, there exists no Z(q)n-linear code with respect to the cyclic subgroup.

Ghost poles in the nucleon propagator in the linear sigma model approach and its role in pi N low-energy theorems

Complex mass poles, or ghost poles, are present in the Hartree-Fock solution of the Schwinger-Dyson equation for the nucleon propagator in renormalizable models with Yukawa-type meson-nucleon couplings, as shown many years ago by Brown, Puff and Wilets (BPW), These ghosts violate basic theorems of quantum field theory and their origin is related to the ultraviolet behavior of the model interactions, Recently, Krein et.al, proved that the ghosts disappear when vertex corrections are included in a self-consistent way, softening the interaction sufficiently in the ultraviolet region. In previous studies of pi N scattering using ''dressed'' nucleon propagator and bare vertices, did by Nutt and Wilets in the 70's (NW), it was found that if these poles are explicitly included, the value of the isospin-even amplitude A((+)) is satisfied within 20% at threshold. The absence of a theoretical explanation for the ghosts and the lack of chiral symmetry in these previous studies led us to re-investigate the subject using the approach of the linear sigma-model and study the interplay of low-energy theorems for pi N scattering and ghost poles. For bare interaction vertices we find that ghosts are present in this model as well and that the A((+)) value is badly described, As a first approach to remove these complex poles, we dress the vertices with phenomenological form factors and a reasonable agreement with experiment is achieved, In order to fix the two cutoff parameters, we use the A((+)) value for the chiral limit (m(pi) --> 0) and the experimental value of the isoscalar scattering length, Finally, we test our model by calculating the phase shifts for the S waves and we find a good agreement at threshold. (C) 1997 Elsevier B.V. B.V.

Linear relationship between potential and concentration in flow potentiometry

In potentiometric-flow systems, linear-potential responses for logarithmic concentrations can be attained for first-(or pseudo-first-) order reactions in which the monitored chemical species react with the analyte during a fixed time interval. To demonstrate this property, the determination of glycerol based on its oxidation by periodate and potentiometric monitoring of the remaining periodate was selected. Influence of reagent concentration and timing on the linearity of the analytical curve were investigated. A mathematical treatment was derived, and potentialities/limitations of the approach were outlined. The system was applied to analysis of soap and lixivia samples. The analytical curve within 200 and 2000 mg L-1 (r = 0.99975; n = 5) was described as E = 8.166 + 0.0478 (glycerol). The sample throughput was 100 h(-1), and a measurement repeatability within 0.5 mV was always observed. By applying a t-test, there was no statistical difference between the results obtained by the proposed procedure and by iodimetric titration at the 95% confidence level. (C) 2000 John Wiley & Sons, Inc. Lab Robotics and Automation 12:41-45, 2000.