Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

Desenvolvimento do sistema de tracção de um veículo eléctrico ecológico com travagem regenerativa

Nesta dissertação descreve-se uma metodologia de dimensionamento do sistema de tracção para equipar um veículo eléctrico ecológico (VEECO) com inclusão de um sistema de travagem regenerativa. Apresenta-se uma perspectiva geral de diversas topologias de sistemas de tracção utilizadas nos veículos eléctricos e realiza-se a sua comparação através do estudo e análise dos acionamentos electromecânicos que podem ser utilizados nesses sistemas de tracção eléctrica. Utilizando ferramentas de simulação numérica, estuda-se o modelo matemático de um veículo eléctrico com travagem regenerativa. A partir deste modelo matemático é adoptado uma possível configuração para o seu sistema de tracção eléctrica e são obtidas características teóricas de desempenho do veículo eléctrico, através da análise de testes padrão ao veículo. Em banco de ensaios, constrói-se um sistema de tracção eléctrica que permite a validação experimental do modelo matemático do veículo eléctrico. Para a construção deste banco de ensaios foram concebidos os sistemas de tracção eléctrica, de carga mecânica e de controlo e monitorização do banco de ensaios. A validação experimental realiza-se através dos mesmos testes padrão ao veículo eléctrico, como o teste NEDC (New European Driving Cycle), o teste de aceleração entre 0 e 100km/h e o teste de gradeabilidade. Desenvolve-se o dimensionamento do sistema de tracção eléctrica a equipar o VEECO, através da componente de modelação paramétrica do modelo matemático do veículo eléctrico. Com esta metodologia é adoptado um conjunto de variáveis paramétricas relacionadas com os elementos que constituem o sistema de tracção eléctrica do VEECO. Estuda-se a influência destas variáveis paramétricas nas características de desempenho pretendidas para o VEECO. Como resultado da análise de modelação paramétrica é apresentada uma solução para o sistema de tracção eléctrica do VEECO que cumpre a execução do NEDC, apresenta um tempo de aceleração entre 0 e 100km/h inferior a 10 segundos, supera uma gradeabilidade de 10% e uma autonomia de 200 km. O sistema de tracção do VEECO também permite realizar a travagem regenerativa com rendimento até 33%. Possui controlo de tracção e anti bloqueio da roda motora, através de uma unidade de controlo que permite reduzir a potência transmitida ao veio, quando a velocidade da roda de tracção difere do valor de referência da velocidade do veículo. Os conhecimentos adquiridos através do processo de investigação e desenvolvimento, para a realização da presente dissertação permitem apresentar perspectivas de desenvolvimento futuro com aplicação nos sistemas de tracção de veículos eléctricos rodoviários.

Dynamical behaviour on the parameter space: new populational growth models proportional to beta densities

We present new populational growth models, generalized logistic models which are proportional to beta densities with shape parameters p and 2, where p > 1, with Malthusian parameter r. The complex dynamical behaviour of these models is investigated in the parameter space (r, p), in terms of topological entropy, using explicit methods, when the Malthusian parameter r increases. This parameter space is split into different regions, according to the chaotic behaviour of the models.

Comparative study of power converter topologies and control strategies for the harmonic performance of variable-speed wind turbine generator systems

Power converters play a vital role in the integration of wind power into the electrical grid. Variable-speed wind turbine generator systems have a considerable interest of application for grid connection at constant frequency. In this paper, comprehensive simulation studies are carried out with three power converter topologies: matrix, two-level and multilevel. A fractional-order control strategy is studied for the variable-speed operation of wind turbine generator systems. The studies are in order to compare power converter topologies and control strategies. The studies reveal that the multilevel converter and the proposed fractional-order control strategy enable an improvement in the power quality, in comparison with the other power converters using a classical integer-order control strategy. (C) 2010 Elsevier Ltd. All rights reserved.

Transient analysis of variable-speed wind turbines at wind speed disturbances and a pitch control malfunction

As wind power generation undergoes rapid growth, new technical challenges emerge: dynamic stability and power quality. The influence of wind speed disturbances and a pitch control malfunction on the quality of the energy injected into the electric grid is studied for variable-speed wind turbines with different power-electronic converter topologies. Additionally, a new control strategy is proposed for the variable-speed operation of wind turbines with permanent magnet synchronous generators. The performance of disturbance attenuation and system robustness is ascertained. Simulation results are presented and conclusions are duly drawn. (C) 2010 Elsevier Ltd. All rights reserved.

Modeling Allee Effect from Beta(p, 2) Densities

In this work we develop and investigate generalized populational growth models, adjusted from Beta(p, 2) densities, with Allee effect. The use of a positive parameter leads the presented generalization, which yields some more flexible models with variable extinction rates. An Allee limit is incorporated so that the models under study have strong Allee effect.

Neural-network approach to modeling liquid crystals in complex confinement

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy minimization. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the multilayer perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible, and refinable. Furthermore, it can be readily generalized to the richer experimental patterned-substrate geometries that are now experimentally realizable but very problematic to conventional theoretical treatments.

Fuzzy, integer and fractional-order control: Application on a wind turbine benchmark model

This paper presents a comparison between proportional integral control approaches for variable speed wind turbines. Integer and fractional-order controllers are designed using linearized wind turbine model whilst fuzzy controller also takes into account system nonlinearities. These controllers operate in the full load region and the main objective is to extract maximum power from the wind turbine while ensuring the performance and reliability required to be integrated into an electric grid. The main contribution focuses on the use of fractional-order proportional integral (FOPI) controller which benefits from the introduction of one more tuning parameter, the integral fractional-order, taking advantage over integer order proportional integral (PI) controller. A comparison between proposed control approaches for the variable speed wind turbines is presented using a wind turbine benchmark model in the Matlab/Simulink environment. Results show that FOPI has improved system performance when compared with classical PI and fuzzy PI controller outperforms the integer and fractional-order control due to its capability to deal with system nonlinearities and uncertainties. © 2014 IEEE.

Fuzzy, integer and fractional-order control: application on a wind turbine benchmark model

This paper presents a comparison between proportional integral control approaches for variable speed wind turbines. Integer and fractional-order controllers are designed using linearized wind turbine model whilst fuzzy controller also takes into account system nonlinearities. These controllers operate in the full load region and the main objective is to extract maximum power from the wind turbine while ensuring the performance and reliability required to be integrated into an electric grid. The main contribution focuses on the use of fractional-order proportional integral (FOPI) controller which benefits from the introduction of one more tuning parameter, the integral fractional-order, taking advantage over integer order proportional integral (PI) controller. A comparison between proposed control approaches for the variable speed wind turbines is presented using a wind turbine benchmark model in the Matlab/Simulink environment. Results show that FOPI has improved system performance when compared with classical PI and fuzzy PI controller outperforms the integer and fractional-order control due to its capability to deal with system nonlinearities and uncertainties. © 2014 IEEE.

Neural-network approach to modeling liquid crystals in complex confinement

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy minimization. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the multilayer perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible, and refinable. Furthermore, it can be readily generalized to the richer experimental patterned-substrate geometries that are now experimentally realizable but very problematic to conventional theoretical treatments.

Complex variable positive definite functions

In this paper we develop an appropriate theory of positive definite functions on the complex plane from first principles and show some consequences of positive definiteness for meromorphic functions.

Evaluation of the influence of testing parameters on the melt flow index of thermoplastics

The main goals of the present work are the evaluation of the influence of several variables and test parameters on the melt flow index (MFI) of thermoplastics, and the determination of the uncertainty associated with the measurements. To evaluate the influence of test parameters on the measurement of MFI the design of experiments (DOE) approach has been used. The uncertainty has been calculated using a "bottom-up" approach given in the "Guide to the Expression of the Uncertainty of Measurement" (GUM). Since an analytical expression relating the output response (MFI) with input parameters does not exist, it has been necessary to build mathematical models by adjusting the experimental observations of the response variable in accordance with each input parameter. Subsequently, the determination of the uncertainty associated with the measurement of MFI has been performed by applying the law of propagation of uncertainty to the values of uncertainty of the input parameters. Finally, the activation energy (Ea) of the melt flow at around 200 degrees C and the respective uncertainty have also been determined.

Supervisory control of a variable speed wind turbine with doubly fed induction generator

This paper is on an onshore variable speed wind turbine with doubly fed induction generator and under supervisory control. The control architecture is equipped with an event-based supervisor for the supervision level and fuzzy proportional integral or discrete adaptive linear quadratic as proposed controllers for the execution level. The supervisory control assesses the operational state of the variable speed wind turbine and sends the state to the execution level. Controllers operation are in the full load region to extract energy at full power from the wind while ensuring safety conditions required to inject the energy into the electric grid. A comparison between the simulations of the proposed controllers with the inclusion of the supervisory control on the variable speed wind turbine benchmark model is presented to assess advantages of these controls. (C) 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Optimal brake specific fuel consumption trajectory for stand-alone variable speed Diesel Gen-Set

Energy efficiency plays an important role to the CO2 emissions reduction, combating climate change and improving the competitiveness of the economy. The problem presented here is related to the use of stand-alone diesel gen-sets and its high specific fuel consumptions when operates at low loads. The variable speed gen-set concept is explained as an energy-saving solution to improve this system efficiency. This paper details how an optimum fuel consumption trajectory based on experimentally Diesel engine power map is obtained.

PV systems linked to the grid: parameter identification with a heuristic procedure

This paper focuses on a PV system linked to the electric grid by power electronic converters, identification of the five parameters modeling for photovoltaic systems and the assessment of the shading effect. Normally, the technical information for photovoltaic panels is too restricted to identify the five parameters. An undemanding heuristic method is used to find the five parameters for photovoltaic systems, requiring only the open circuit, maximum power, and short circuit data. The I- V and the P- V curves for a monocrystalline, polycrystalline and amorphous photovoltaic systems are computed from the parameters identification and validated by comparison with experimental ones. Also, the I- V and the P- V curves under the effect of partial shading are obtained from those parameters. The modeling for the converters emulates the association of a DC-DC boost with a two-level power inverter in order to follow the performance of a testing commercial inverter employed on an experimental system. © 2015 Elsevier Ltd.