財務危機模型的研究一般納入財務正常公司與財務危機公司兩者當樣本，探討區分危機與正常公司的因素，本研究則進一步以財務危機公司為樣本，探討在財務危機公司中區分舞弊公司與正常經營公司的基本因素。 本研究從財務危機公司中，分出財務舞弊公司與正常經營公司，因此研究樣本包含發生舞弊的財務危機公司與正常經營而發生財務危機的公司。研究變數則從文獻篩選23個財務解釋變數，以及13個公司治理解釋變數，運用羅吉斯迴歸法進行實證，結果顯示3個財務變數和1個公司治理變數在區分財務危機公司中的財務舞弊公司與正常經營公司有顯著的區別能力，公司治理變數的董監事持股比率尤其顯著。 / Financial distress prediction is usually based on both financial distressed firms and non-distressed firms. Based on financial distressed firms, this study further investigates the factors distinguishing financial fraud firms from non-fraud firms. The sample includes fraud and no-fraud firms while both are financial distressed. Twenty-three financial and thirteen corporate governance variables are surveyed from literature. The empirical result of logit regression shows that three financial variables and one corporate governance variable are significant factors in distinguishing fraud from no-fraud firms in distressed companies. Especially, the percentage of holding stocks of board of directors is the most significant variable.

1999年新巴塞爾協定規定鼓勵銀行採用內部信用評等法(internal ratings based approach)，以衡量貸款者無法償還之風險以計提最低資本。為因應此一授信風險控管之需要，銀行亟需建立一套有效之財務危機預警系統，以判定銀行授信客戶發生財務危機之機率。 本研究運用羅吉斯迴歸分析(logistic regression analysis)與離散時間涉險分析(discrete-time survival analysis)分法於三種相互具有巢狀式關連性之財務危機預測模型，逐步加入財務、非財務及公司治理變數，以便在同一種分析方法下比較三種模型，以及在同一種模型下比較兩種分析方法。實證結果顯示，就樣本期間內而言，同一種分析方法下模型之財務危機預測能力，隨著不同種類解釋變數之加入而逐步提高。然而，就樣本期間外而言，同一種分析方法下模型之財務危機預測能力，並未隨著不同種類解釋變數之加入而逐步提高，但分類能力皆十分優良；而在同一種模型下離散時間涉險分析方法之整體分類能力皆高於羅吉斯迴歸分析方法。 / The 1999 Basel II Accord suggests banks measure the impossibility of reimbursement of debtors to calculate capital minimums by internal ratings-based approach. To reduce the credit risk, it is important that banks construct accurate financial distress prediction systems to determine the probability of financial distress of debtors. This study employs logistic regression and discrete-time hazard analysis to construct nested models to which the financial, non-financial, and corporate governance corporate variables are added step by step. I therefore make comparison of the performance of three models under logistic regression and discrete-time hazard analysis, respectively. Meanwhile, the comparison of the performance of logistic regression and discrete-time hazard analyses under each of three models is also made. The empirical results show that the in-sample predictive ability of financial distress is enhanced by gradually incorporating different kinds of variables in both analyses. Although the out-of-the-sample predictive ability of financial distress is not improved by gradually incorporating different kinds of variables in one analysis, the model performance is quite well overall. The entire discriminability of discrete-time hazard analysis is better than logistic regression under each model.

Este trabalho aborda o problema de controle ótimo por modos deslizantes via função penalidade para sistemas de tempo discreto. Para resolver este problema será desenvolvido uma estrutura matricial alternativa baseada no problema de mínimos quadrados ponderados e funções penalidade. A partir desta nova formulação é possível obter a lei de controle ótimo por modos deslizantes, as equações de Riccati e a matriz do ganho de realimentação através desta estrutura matricial alternativa. A motivação para propormos essa nova abordagem é mostrar que é possível obter uma solução alternativa para o problema clássico de controle ótimo por modos deslizantes. / This work introduces a penalty function approach to deal with the optimal sliding mode control problem for discrete-time systems. To solve this problem an alternative array structure based on the problem of weighted least squares penalty function will be developed. Using this alternative matrix structure, the optimal sliding mode control law of, the matrix Riccati equations and feedback gain were obtained. The motivation of this new approach is to show that it is possible to obtain an alternative solution to the classic problem of optimal sliding mode control.

Made available in DSpace on 2014-06-11T19:30:49Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-11-12Bitstream added on 2014-06-13T20:40:35Z : No. of bitstreams: 1 mendes_rat_dr_ilha.pdf: 2326436 bytes, checksum: 60aa15eb5fb66a63b31662bee7904bfa (MD5) / Neste trabalho sao propostas metodologias de modificacao de zeros para solucionar o problema do rastreamento do sinal de referencia em sistemas discretos determinısticos, sistemas discretos incertos e sistemas discretos nao-lineares considerando-se uma entrada de perturbacao na planta. Em um primeiro momento e projetado um controlador discreto para minimizar a norma H∞ entre a entrada ex´ogena e o sinal de saıda com o objetivo de reduzir o efeito da perturbacao sobre a saıda do sistema determinıstico. Posteriormente, minimiza-se a norma H∞ entre o sinal de referencia e o erro de rastreamento atraves da modificacao otima de zeros do sistema discreto, constituindo desta maneira o rastreador de sinal de referencia. Essa nova estrutura de projeto do controlador e estendida para o projeto do controlador robusto H∞, supondo incertezas politopicas na planta e tambem para sistemas nao-lineares. No caso de sistemas com incertezas politopicas na planta, um controlador discreto e projetado para minimizar o custo garantido H∞ entre a entrada exogena e o sinal de saıda com o objetivo de reduzir o efeito da perturbacao sobre a saıda do sistema discreto incerto. Posteriormente e projetado um rastreador para sinais de referˆencia em sistemas com incertezas politopicas, utilizando-se modificacao de zeros. Por fim, estende-se a metodologia de rastreamento do sinal de referencia com rejeicao do disturbio para sistemas nao-lineares. A formulacao do projeto e descrita na forma de inequacoes matriciais lineares, pois estas permitem a descricao de problemas de otimizacao convexa / The tracking problems in uncertain, deterministic and nonlinear discrete time systems, with the presence of a disturbance signal in the plant, are solved in this work proposing a zero variation methodology. A discrete state feedback controller is designed in order to minimize the H∞-norm between the exogen input and the output signal, such that the effect of the disturbance is attenuated in deterministic systems. After, the tracking problem is solved using the variation of the zeros minimizing the H∞-norm from the reference input signal to the error tracking signal. This new structure is extended to design of H∞ robust controller, supposing politopic uncertainties and other one supposing nonlinearities in the plant. In uncertain systems case, a discrete controller is designed in order to minimize the H∞ guaranteed cost between the exogen input and the output signal such that the effect of the disturbance is attenuated in uncertain systems. Then, the tracking problem in uncertain systems is solved using the variation of the zeros minimizing the H∞ guaranteed cost from the reference input signal to the error tracking signal. Finally, the zero variation methodology is extended to nonlinear systems. The design is formulated in the Linear Matrix Inequalities (LMI) framework, such that the optimal solution of the stated control problem is obtained when feasible solution exists

Made available in DSpace on 2014-06-11T19:30:51Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-08-30Bitstream added on 2014-06-13T20:47:24Z : No. of bitstreams: 1 ribeiro_jms_me_ilha.pdf: 1485185 bytes, checksum: 5ab0628a95f1aed7502862f70ee550ce (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho apresenta três novas estratégias de controle discreto. O enfoque principal do trabalho foi dado ao Controle Discreto com Modos Deslizantes (CDMD) aplicados em sistemas que possuem atraso no processamento do sinal de controle. As novas estratégias de controle objetivam a elaboração de leis de fácil implementação prática e que ao mesmo tempo sejam robustas a incertezas da planta. Uma característica destas novas abordagens para controle discreto com atraso no tempo é a utilização de um Controle com Modos Deslizantes sem a necessidade de predição do sinal de controle. Os métodos de projeto propostos podem ser aplicados no controle de plantas estáveis ou instáveis com atraso no sinal de controle. Uma das estratégias foi elaborada para realizar controle apenas em sistemas discretos que não possuem atraso no sinal de controle, enquanto que as demais são utilizadas para controle em sistemas com atraso. São apresentadas simulações e resultados de implementações práticas, sobre uma planta estável de Controle Automático da Geração (CAG) e sobre um Sistema Pêndulo Invertido, que caracteriza bem uma planta instável. Os resultados comprovam a eficácia dos novos controladores. / This work presents three new strategies of discrete-time control. The main focus of the work was given to the Sliding Mode Control (SMC) applied in systems that present delay in the processing of the control sign. The new control strategies provide laws of control of easy practical implementation and that at the same time are robust to uncertainties of the plant. A characteristic of these new approaches, for discrete-time control with delay-time, is the use of a Sliding Mode Control without the need of prediction of the control signal. The proposed design methods can be applied in the control of stable or unstable plants, with delay in the control signal. One of the strategies was elaborated to accomplish control just in discrete-time system without delay-time in the control sign, while the others are used for control in systems with delay-time. Simulations and experimental results are shown on a stable plant of Automatic Generation Control (AGC) and on Inverted Pendulum System, that is an unstable plant. The results prove the controllers' effectiveness.

Orientador: Edvaldo Assunção / Banca: Marcelo Carvalho Minhoto Teixeira / Banca: José Paulo Fernandes Garcia / Banca: Cristiano Quevedo Andrea / Banca: Márcio Roberto Covacic / Resumo: Neste trabalho sao propostas metodologias de modificacao de zeros para solucionar o problema do rastreamento do sinal de referencia em sistemas discretos determinısticos, sistemas discretos incertos e sistemas discretos nao-lineares considerando-se uma entrada de perturbacao na planta. Em um primeiro momento e projetado um controlador discreto para minimizar a norma H∞ entre a entrada ex'ogena e o sinal de saıda com o objetivo de reduzir o efeito da perturbacao sobre a saıda do sistema determinıstico. Posteriormente, minimiza-se a norma H∞ entre o sinal de referencia e o erro de rastreamento atraves da modificacao otima de zeros do sistema discreto, constituindo desta maneira o rastreador de sinal de referencia. Essa nova estrutura de projeto do controlador e estendida para o projeto do controlador robusto H∞, supondo incertezas politopicas na planta e tambem para sistemas nao-lineares. No caso de sistemas com incertezas politopicas na planta, um controlador discreto e projetado para minimizar o custo garantido H∞ entre a entrada exogena e o sinal de saıda com o objetivo de reduzir o efeito da perturbacao sobre a saıda do sistema discreto incerto. Posteriormente e projetado um rastreador para sinais de referˆencia em sistemas com incertezas politopicas, utilizando-se modificacao de zeros. Por fim, estende-se a metodologia de rastreamento do sinal de referencia com rejeicao do disturbio para sistemas nao-lineares. A formulacao do projeto e descrita na forma de inequacoes matriciais lineares, pois estas permitem a descricao de problemas de otimizacao convexa / Abstract: The tracking problems in uncertain, deterministic and nonlinear discrete time systems, with the presence of a disturbance signal in the plant, are solved in this work proposing a zero variation methodology. A discrete state feedback controller is designed in order to minimize the H∞-norm between the exogen input and the output signal, such that the effect of the disturbance is attenuated in deterministic systems. After, the tracking problem is solved using the variation of the zeros minimizing the H∞-norm from the reference input signal to the error tracking signal. This new structure is extended to design of H∞ robust controller, supposing politopic uncertainties and other one supposing nonlinearities in the plant. In uncertain systems case, a discrete controller is designed in order to minimize the H∞ guaranteed cost between the exogen input and the output signal such that the effect of the disturbance is attenuated in uncertain systems. Then, the tracking problem in uncertain systems is solved using the variation of the zeros minimizing the H∞ guaranteed cost from the reference input signal to the error tracking signal. Finally, the zero variation methodology is extended to nonlinear systems. The design is formulated in the Linear Matrix Inequalities (LMI) framework, such that the optimal solution of the stated control problem is obtained when feasible solution exists / Doutor

Le contrôle par mode glissant est une technique d'automatique qui possède une longue histoire, la littérature remontant jusqu'au année 50. Son essence est la suivante : le contrôle est définit comme étant l'image d'une fonction discontinue de la variable de glissement, contraignant le système à évolué sur une variété, le système glisse alors dessus, d'où le nom. Cette variable de glissement est elle définie à partir de l'état du système. Les développements ont mené à la constitution d'une théorie bien établie à propos de cette technique, avec de nombreuses propriétés théoriques fort intéressante. Toutefois ceci ne porte que sur la version continue, c'est à dire quand le contrôle peut changer de valeur à chaque instant. En comparaison la version discrète du ce contrôleur est définie par le fait que la valeur du contrôle ne peut changer qu'à des instants isolés discrets. On a alors une fonction en escalier, constante sur la période d'échantillonnage. Cette situation est rencontrée par exemple lorsque le contrôleur est implémenté à l'aide d'un micro-contrôleur, ce qui est le cas dans nombre d'applications industrielles. Le principal problème avec le mode glissant est l'apparition d'un phénomène largement indésirable, le chattering (ou broutement) avec la version discrète du contrôleur, où même déjà en simulation. Dans ce dernier cas, nous appelons ceci du chattering numérique que nous attribuons à une mauvaise discrétisation du contrôle. L'approche développée ici se focalise sur ce point et est largement inspirée par les travaux effectués en mécanique non régulière, où ce type de comportement a aussi été observé lors de la simulation de système avec frottements et/où impacts. L'idée principale est de discretisé le contrôle de manière implicite et non explicite. Ceci permet d'éliminer le chattering numérique dans les cas simples (systèmes linéaires par exemple) où bien de le réduire grandement. Pour mener à bien l'analyse, des outils provenant de l'analyse convexe ainsi que des inégalités variationnelles en dimension finie sont utilisés. Le contrôleur proposé possède des propriétés intéressantes et proches de celles du temps continu. Ainsi on peut montrer que la variable de glissement est régie par une dynamique stable en temps finie, avec une fonction de Lyapunov. Le contrôle discret convergence vers celui du cas continu quand la période d'échantillonnage tends vers 0. Une atténuation d'éventuelles perturbations de type "matching" peut être établie. Ces travaux ont essentiellement portés sur le contrôle par mode glissant classique. L'algorithme dit twisting a pu être discrétisé avec la même technique et sa stabilité en temps finie grâce à une fonction de Lyapunov a pu être montrée. Ces propriétés ont été vérifiée en simulation, mais aussi de manière expérimentale. Ainsi des essais ont pu être menés sur deux banc d'essai: le premier est basé sur un système electropneumatique où à la fois le contrôle par mode glissant classique ainsi que le twisting ont pu être implémentés. L'objectif étant de suivre une trajectoire de référence. Le second système est un pendule inverse où le système doit être stabilisé à la position d'équilibre instable. Ici seul le contrôleur classique a été testé. L'analyse des données expérimentales a permis de mettre en lumière les performances supérieures des contrôleurs proposés par rapport à ceux classiquement usités. Les objectifs de contrôle sont mieux atteint et le chattering est grandement diminué. / Sliding Mode Control is a control technique with a long history, with research efforts dating back to the 50's. The basic idea is to define the control input as a discontinuous function of the sliding variable, which solely depends on the state, and to constraint the system to evolve on a manifold, hence the term sliding. Over the years a strong theory was build around this technique, but only in continuous time. In our context, this means that control input value can change value at any time. The discrete-time case is when the control input can only change at isolated time instants and the dynamical system on which the control is still a continuous-time process. The control input is therefore a step function. This case appears when the controller is digitally implemented, for instance with the help of a microcontroller. This kind of setup is nowadays ubiquitous in benchmarks and industrial applications. One of the main limitation of the applicability of sliding mode control is the chattering phenomenon that is witnessed when this control technique is applied in practice, but already in simulations. In contrast to previous approaches, we single out the chattering that is already witnessed in simulation, even with no disturbance and with perfect knowledge of the dynamics. This is called the numerical chattering and one of its distinct feature is the constant chattering, or high-frequency bang-bang behavior, of the control input. This naturally induces a chattering of the sliding variable. The claim that this type of chattering is usually predominant and that it is due to a bad discretization of the signum multifunction. The approach developed in this work was inspired by the research effort in the nonsmooth mechanical to properly simulate some systems like those with dry friction and/or unilateral constraints. The main point is to discretize the signum in an implicit fashion, that is its argument is the value of the sliding variable at the end of the next sampling period. With this change, the numerical chattering can be removed in the simplest cases, largely attenuated. The research effort was focused on classical sliding mode controller, rather than the higher order ones. The frameworks used to perform the analysis are convex analysis and variational inequalities. This discrete-time controller enjoys several interesting theoretical properties. First it is finite-time Lyapunov stable: the sliding variable goes to 0 in finite-time. The discrete-time control input converges to the continuous-time one as the sampling period goes to 0. The control action also attenuates the effect of matched perturbations. Also the increase of the gain of the controller does not affect the performances when the system is sliding. The twisting controller can be discretized in the same way and is also finite-time Lyapunov stable. This good theoretical properties have been verified in simulations, but also on experimental setups. Two tests were conducted: the first one on an electropneumatic system, where both the classical first-order sliding mode controller and the twisting algorithm were tested. The objective was to track a reference trajectory. The second one was an inverted pendulum on a cart with only the classical SMC. The goal was to stabilize the system at the unstable equilibrium. The analysis from the data collected during those experiments shows that the proposed controllers perform better than the their explicitly discretized versions. The performances are better and the chattering is effectively reduced.

Orientador: José Paulo Fernandes Garcia / Banca: Marcelo Carvalho M. Teixeira / Banca: Edvaldo Assunção / Banca: Fuad Kassab Junior / Banca: Marco Henrique Terra / Resumo: Este trabalho apresenta três novas estratégias de controle discreto. O enfoque principal do trabalho foi dado ao Controle Discreto com Modos Deslizantes (CDMD) aplicados em sistemas que possuem atraso no processamento do sinal de controle. As novas estratégias de controle objetivam a elaboração de leis de fácil implementação prática e que ao mesmo tempo sejam robustas a incertezas da planta. Uma característica destas novas abordagens para controle discreto com atraso no tempo é a utilização de um Controle com Modos Deslizantes sem a necessidade de predição do sinal de controle. Os métodos de projeto propostos podem ser aplicados no controle de plantas estáveis ou instáveis com atraso no sinal de controle. Uma das estratégias foi elaborada para realizar controle apenas em sistemas discretos que não possuem atraso no sinal de controle, enquanto que as demais são utilizadas para controle em sistemas com atraso. São apresentadas simulações e resultados de implementações práticas, sobre uma planta estável de Controle Automático da Geração (CAG) e sobre um Sistema Pêndulo Invertido, que caracteriza bem uma planta instável. Os resultados comprovam a eficácia dos novos controladores. / Abstract: This work presents three new strategies of discrete-time control. The main focus of the work was given to the Sliding Mode Control (SMC) applied in systems that present delay in the processing of the control sign. The new control strategies provide laws of control of easy practical implementation and that at the same time are robust to uncertainties of the plant. A characteristic of these new approaches, for discrete-time control with delay-time, is the use of a Sliding Mode Control without the need of prediction of the control signal. The proposed design methods can be applied in the control of stable or unstable plants, with delay in the control signal. One of the strategies was elaborated to accomplish control just in discrete-time system without delay-time in the control sign, while the others are used for control in systems with delay-time. Simulations and experimental results are shown on a stable plant of Automatic Generation Control (AGC) and on Inverted Pendulum System, that is an unstable plant. The results prove the controllers' effectiveness. / Doutor

CAPES / As crescentes preocupações com as questões ambientais têm levado à consideração de alternativas na mobilidade e transporte urbanos. Dentre as opções disponíveis, os ônibus elétricos movidos a bateria têm sido bastante considerados em termos de flexibilidade, sustentabilidade e emissão de poluentes. Estes ônibus possuem um sistema plug-in de recarga (PEV) que permite sua circulação sem a necessidade de alimentação constante por vias exclusivas. Entretanto, devido à necessidade de recarga das baterias, o número e posicionamento das estações de recarga tem papel fundamental na viabilização da operação deste sistema de transporte. Este trabalho apresenta um modelo de simulação de eventos discretos que captura o padrão de movimentação dos ônibus e respectivo consumo de energia. Uma estratégia de otimização que utiliza um algoritmo genético biobjetivo é então associada à simulação (otimização com simulação) para minimizar tanto o número de estações de recarga quanto o tempo extra necessário para recarga dos ônibus. Foram utilizados dados reais de demanda de passageiros, velocidade dos ônibus, distâncias, relevos, entre outros, do sistema de transporte da cidade de Curitiba. Os parâmetros de mobilidade dos ônibus estão baseados em dados reais adquiridos, filtrados e analisados através de um sistema informatizado da empresa que controla o sistema público e urbanização da cidade para um total de seis linhas expressas. O modelo utilizado para o consumo de energia dos ônibus é baseado no cálculo da energia necessária para movimentar um ônibus, levando em conta diferentes carregamentos e forças de resistência ao movimento. Nas paradas que possuem estações de recarga, considera-se recarga rápida da bateria ajustada para os parâmetros típicos de um ônibus elétrico. Os resultados mostram diferentes arranjos para o número de estações de recarga e atrasos nos itinerários programados, assim como os níveis de operação das baterias. / Growing concerns with environmental issues have resulted in considering alternatives for urban mobility and public transportation. Among the available options, battery- powered electric buses have been fairly considered in terms of flexibility, sustainability and emission of pollutants. These buses have a plug-in recharge system (PEV) that allows their driving in exclusive lanes without providing external power. However, recharge of batteries is necessary, and the number and placement of charging stations have a fundamental role in the operation of this transport system. This work presents a discrete event simulation model that captures the pattern of bus dynamics and its corresponding energy consumption. An optimization strategy that utilizes a biobjective genetic algorithm is then associated with the simulation (simulation with optimization) to minimize both the number of charging stations and average extra time needed to recharge batteries. Information for passenger demand, bus speed, distances, road elevations, among others, have been obtained from the Curitiba public transportation system. The parameters of buses’ mobility are based on real data acquired, filtered and analyzed for six express lines from raw data provided by a computational system of a company that controls the public transportation system and urban area of the city. The mathematical model used to compute the power consumption of a bus is based on the energy required to run it, taking into account different loadings and friction forces. Fast battery recharge with typical parameters of an electric bus is considered at bus stops with charging stations. The results show different arrangements for the number of recharge stations and delays in the bus schedule, as well as the corresponding energy levels of batteries.

CAPES / As crescentes preocupações com as questões ambientais têm levado à consideração de alternativas na mobilidade e transporte urbanos. Dentre as opções disponíveis, os ônibus elétricos movidos a bateria têm sido bastante considerados em termos de flexibilidade, sustentabilidade e emissão de poluentes. Estes ônibus possuem um sistema plug-in de recarga (PEV) que permite sua circulação sem a necessidade de alimentação constante por vias exclusivas. Entretanto, devido à necessidade de recarga das baterias, o número e posicionamento das estações de recarga tem papel fundamental na viabilização da operação deste sistema de transporte. Este trabalho apresenta um modelo de simulação de eventos discretos que captura o padrão de movimentação dos ônibus e respectivo consumo de energia. Uma estratégia de otimização que utiliza um algoritmo genético biobjetivo é então associada à simulação (otimização com simulação) para minimizar tanto o número de estações de recarga quanto o tempo extra necessário para recarga dos ônibus. Foram utilizados dados reais de demanda de passageiros, velocidade dos ônibus, distâncias, relevos, entre outros, do sistema de transporte da cidade de Curitiba. Os parâmetros de mobilidade dos ônibus estão baseados em dados reais adquiridos, filtrados e analisados através de um sistema informatizado da empresa que controla o sistema público e urbanização da cidade para um total de seis linhas expressas. O modelo utilizado para o consumo de energia dos ônibus é baseado no cálculo da energia necessária para movimentar um ônibus, levando em conta diferentes carregamentos e forças de resistência ao movimento. Nas paradas que possuem estações de recarga, considera-se recarga rápida da bateria ajustada para os parâmetros típicos de um ônibus elétrico. Os resultados mostram diferentes arranjos para o número de estações de recarga e atrasos nos itinerários programados, assim como os níveis de operação das baterias. / Growing concerns with environmental issues have resulted in considering alternatives for urban mobility and public transportation. Among the available options, battery- powered electric buses have been fairly considered in terms of flexibility, sustainability and emission of pollutants. These buses have a plug-in recharge system (PEV) that allows their driving in exclusive lanes without providing external power. However, recharge of batteries is necessary, and the number and placement of charging stations have a fundamental role in the operation of this transport system. This work presents a discrete event simulation model that captures the pattern of bus dynamics and its corresponding energy consumption. An optimization strategy that utilizes a biobjective genetic algorithm is then associated with the simulation (simulation with optimization) to minimize both the number of charging stations and average extra time needed to recharge batteries. Information for passenger demand, bus speed, distances, road elevations, among others, have been obtained from the Curitiba public transportation system. The parameters of buses’ mobility are based on real data acquired, filtered and analyzed for six express lines from raw data provided by a computational system of a company that controls the public transportation system and urban area of the city. The mathematical model used to compute the power consumption of a bus is based on the energy required to run it, taking into account different loadings and friction forces. Fast battery recharge with typical parameters of an electric bus is considered at bus stops with charging stations. The results show different arrangements for the number of recharge stations and delays in the bus schedule, as well as the corresponding energy levels of batteries.