Neste trabalho, aborda-se o problema de estabilização de sistemas lineares com atrasos nos estados e sujeitos a ação de atuadores saturantes. Em particular, são propostos métodos para a síntese de leis de controle estabilizantes do tipo realimentação de estados, realimentação dinâmica de saída, bem como para a síntese de compensadores de "anti-windup" estáticos e dinâmicos. Como objetivo de síntese consideram-se duas possibilidades, que o sistema esteja livre ou não de perturbações. No primeiro caso, determina-se uma lei de controle estabilizante de tal forma a maximizar um conjunto de condições iniciais admissíveis D. No caso do conjunto D ser dado, a lei de controle estabilizante que se determina, deve garantir estabilidade assintótica do sistema em malha-fechada para toda condição inicial pertencente a D. No segundo caso, considerando-se os problemas de atenuação e tolerância à perturbação, as leis de controle são obtidas com o intuito de minimizar o ganho-L2 entre a perturbação e a saída regulada do sistema ou de maximizar o limite superior da norma L2 das perturbações admissíveis, para as quais garante-se que as trajetórias do sistema em malha-fechada permaneçam limitadas. Condições locais e globais de estabilização são obtidas a partir da teoria de Lyapunov e da modelagem por zona-morta da saturação, com a conseqüente aplicação de uma condição de setor generalizada. Em se tratando de sistemas contínuos, para que as condições obtidas sejam dependentes do atraso, combinam-se estas ferramentas com a representação do sistema através de sistema descritor. Já no caso de sistemas discretos, combinam-se estas duas ferramentas com a utilização do Lema de Finsler. A utilização destas ferramentas possibilita que as condições obtidas sejam na forma de desigualdades matriciais lineares (LMI's) ou quase lineares, permitindo assim, a formulação de problemas de otimização convexos. / In this work, we deal with the problem of stabilization of linear systems with delayed state and saturating inputs. Specifically, methods are proposed for the synthesis of stabilizing control laws of state feedback and dynamic output feedback types, as well as for the synthesis of static and dynamic anti-windup compensators. Regarding synthesis objectives two possibilities were considered, that the system is free or not of disturbances. In the first case, the stabilizing control law is computed considering the maximization of the set of admissible initial conditions D. In the case the set D is given, this stabilizing control law should guarantee asymptotic stability of the closed-loop system. In the second case, considering the problems of tolerance and disturbance attenuation, the control laws are proposed in order to minimize the L2 gain between to disturbance and the regulated output of system, or in order to maximize the bound on the admissible disturbances for which the trajectories are bounded. Local and global conditions for stabilization are obtained from the theory of Lyapunov and the modeling of the saturation by means of deadzone nonlinearities and the consequent application of a modified sector condition. For continuous systems, in order to obtain delay dependent conditions, these tools are combined with descriptor approach. In the case of discrete-time systems, these two tools are combined with the utilization of Finsler's Lemma. The use of these leads to the conditions in the form of Linear Matrix Inequalities (LMI's) or almost linear, allowing the formulation of convex optimization problems.

Thesis (PhD)-- Stellenbosch University, 2013. / ENGLISH ABSTRACT: Control of beta-type free-piston Stirling engines has been the topic of research and development for many years. In this dissertation, an alternative approach to free-piston Stirling engine control, namely direct piston displacement control, is proposed. Direct piston displacement control entails the instantaneous and direct control of the piston displacement to control the engine according to preferred criteria, e.g. maximum power conversion or efficiency. To control free-piston engines in this manner, it is necessary to independently control both the displacement of the displacer and the power piston in real time. The primary arrangement by which to achieve this is through external control of the instantaneous forces exerted by the linear electrical machines fixed to the pistons. The challenge of displacement control is whether suitable linear machine technology exists or whether technology could be established that would adhere to the requirements of real time direct control. To answer the question whether direct piston displacement control is at all possible, a process was followed to set specifications that linear machines should adhere to and to set design guidelines for linear machines and free-piston Stirling engines. The first step was to establish the ability to simulate free-piston Stirling engine dynamics accurately. This was done by adapting a second order formulation and to verify and improve the accuracy thereof by comparing simulated results with experimental results of one of the best documented Stirling engines, namely the GPU-3 engine. It was found that this second order formulation could simulate the GPU-3 engine to a fair degree of accuracy. Key indicators were defined and later refined with the view of setting specifications. A case study of the influence of a range of variations, including operational, dimensional and other variations, on the dynamics of the GPU-3 was then undertaken. From the findings of this case study, specifications of the key indicators and design guidelines were established. A design optimisation approach was proposed to evaluate linear machine topologies. This approach makes specific provision for the specifications that linear machines need to adhere to, as well as for representative dynamic responses of the forces exerted on the linear machine by the displacer or the power piston. These representative responses and the associated piston displacement were determined for the displacer, the power piston and the combination of the two from the study conducted to set specifications. An air-core, longitudinal flux linear machine with surface mounted permanent magnets (LFPM) was then evaluated to determine its suitability for direct piston displacement control. This linear machine topology was optimised for the traditional approach to establish a benchmark with which to compare subsequent optimisations. The LFPM linear machine not only compared well with other topologies for the traditional application in resonant free-piston Stirling engines, but it was found also to be able to perform displacement control for both the displacer and the power piston. For both pistons, displacement should however be limited to sinusoidal displacement, and in the case of the displacer, an important qualification is that the linear machine should be assisted by spring forces to reach practical design optimisations. Direct piston displacement control is shown to be possible. Future work should concentrate on the practical implementation thereof in free-piston Stirling engines. / AFRIKAANSE OPSOMMING: Die beheer van beta-tipe vrysuier Stirling enjins is al vir baie jare die onderwerp van navorsing en ontwikkeling. In hierdie proefskrif word ’n alternatiewe benadering tot vrysuier Stirlingenjins voorgestel, naamlik direkte suierverplasingsbeheer. Direkte suierverplasingsbeheer behels die oombliklike en direkte beheer van die suierverplasing om die enjin volgens voorkeur kriteria, soos maksimum drywingsomsetting of benuttingsgraad, te beheer. Om vrysuier enjins op hierdie wyse te beheer, is dit noodsaaklik om intyds die verplasing van beide die verplaser en die werksuier onafhanklik te beheer. Die primêre wyse om dit te bereik is deur eksterne beheer van die oomblikskragte wat uitgevoer word deur die lineêre masjiene wat vas is aan die suiers. Die uitdaging van verplasingsbeheer is of toepaslike lineêre masjien tegnologie bestaan en of tegnologie gevestig kan word wat sal voldoen aan die vereistes van intydse direkte beheer. Om die vraag te beantwoord of direkte suierverplasingsbeheer hoegenaamd moontlik is, is ’n proses gevolg om spesifikasies daar te stel waaraan lineêre masjiene moet voldoen en om ontwerpsriglyne vir lineêre masjiene en vrysuier Stirling enjins te stel. Die eerste stap was om die vermoë daar te stel om vrysuier Stirling enjin dinamika akkuraat te simuleer. Dit is gedoen deur ’n tweede orde formulering aan te pas en om die akkuraatheid daarvan te kontroleer en te verbeter deur gesimuleerde resultate met eksperimentele resultate van een van die bes gedokumenteerde Stirling enjins, naamlik die GPU-3 enjin, te vergelyk. Daar is bevind dat die tweede orde formulering die GPU-3 tot ’n redelike mate akkuraat kon simuleer. Sleutel aanwysers is gedefinieer en later verfyn met die oog op die daarstelling van spesifikasies. ’n Gevallestudie van die invloed van ’n reeks variasies, insluitende operasionele, dimensionele en ander variasies, op die dinamika van die GPU-3 is onderneem. Gegrond op die bevindinge van hierdie gevallestudie kon spesifikasies en ontwerpsriglyne vasgestel word. ’n Ontwerpsoptimeringsbenadering is voorgestel om lineêre masjiene te evalueer. Hierdie benadering maak spesifiek voorsiening vir die spesifikasies waaraan lineêre masjiene moet voldoen, sowel as verteenwoordigende dinamiese response van die kragte wat op die lineêre masjien van die verplaser en die werksuier uitgeoefen word. Vanaf die bevindinge van die studie wat uitgevoer is om spesifikasies daar te stel, is verteenwoordigende response en gepaardgaande suierverplasing bepaal vir die verplaser, die werksuier en die kombinasie van die twee. ’n Lugkern, longitudinale vloed lineêre masjien met oppervlak-gemonteerde permanente magnete (LVPM) is toe geëvalueer om die geskiktheid daarvan te bepaal vir direkte suierverplasingsbeheer. Hierdie lineêre masjien topologie is geoptimeer vir die tradisionele benadering om ’n maatstaf te vestig waarteen daaropvolgende optimerings vergelyk kan word. Die LVPM lineêre masjien vergelyk nie net goed met ander topologieë vir die tradisionele toepassing in resonante vrysuier Stirling enjins nie, maar daar is ook bevind dat dit in staat is om verplasingsbeheer te doen vir beide die verplaser en die werksuier. Vir beide suiers moet die verplasing egter tot sinusvormige verplasing beperk word en in die geval van die verplaser, is ’n belangrike kwalifikasie dat die lineêre masjien ondersteun moet word deur veerkragte om praktiese ontwerpsoptimerings te bereik. Daar is aangetoon dat direkte suierverplasingsbeheer moontlik is. Toekomstige werk moet konsentreer op die praktiese implementering daarvan in vrysuier Stirling enjins.

Este trabalho aborda diversas técnicas de controle, com o intuito de comparação do desempenho e robustez ao aplicá-los a um conversor Buck. Iniciando pelo controlador PID (Proporcional, Integral e Derivativo), amplamente explorado e dominado no meio industrial, ele é adotado neste trabalho como referência de comparação para as demais técnicas desenvolvidas. Outra estratégia aqui apresentada é o GANLPID (Gaussian Adaptative Non Linear PID ou PID Adaptativo Não Linear Gaussiano), trata-se de uma técnica não linear, possui ganhos variantes em função do erro baseados em uma função gaussiana. O controle por alocação de polos é uma técnica de controle que em sua forma básica não possui parcela integral, sendo necessária a inclusão deste termo para minimizar o erro em regime permanente. As principais características de análise de desempenho são o tempo de acomodação e overshoot. Todas as técnicas são exploradas a fim de serem implementadas em dispositivos FPGA (Field Programmable Gate Array), possuindo algumas vantagens sobre microcontroladores e DSP’s (Digital Signal Processor), pois conseguem executar tarefas em paralelo deixando a execução do algoritmo mais rápida. As técnicas de controle escolhidas foram simuladas utilizando a ferramenta DSP Builder e compiladas diretamente em código HDL (linguagem de descrição de hardware). Os resultados de simulação e experimentais são apresentados e comentados para validar os projetos propostos. / This work discuss several techniques of control, with an intention of comparison of performance and robustness to apply them to Buck coverter. Starting with PID (Proportional, Integral, Derivative) controller, widely explored and dominated in an industrial environment, it’s used in this work as comparison reference for the others techniques developed. Another strategy presented here is the GANLPID (Gaussian Adaptative Non LinearPID), it’s a case of non linear technique, has won variants in function of the based on a Gaussian error function. variants have gains on function of error based on a Gaussian function. The pole placement control technique not having full part in their basic forms, being necessary to include this term to eliminate the steady-state error. The main performance analysis features are the settling time and overshoot. All the techniques are explored in order to be implemented in FPGA (Field Programmable Gate Array) devices, having some advantages over microcontrollers and DSP’s (Digital Signal Processor), because can execute tasks in parallel allowing the implementation of the algorithm more faster. The chosen control techniques were simulated using the DSP Builder tool and and compiled directly in HDL (hardware description language) code. The results of simulation and experimental are presented and discussed in order to validate the proposed projects.

Neural network-based adaptive output feedback approaches that augment a linear control design are described in this thesis, and emphasis is placed on their real-time implementation with flexible systems. Two different control architectures that are robust to parametric uncertainties and unmodelled dynamics are presented. The unmodelled effects can consist of minimum phase internal dynamics of the system together with external disturbance process. Within this context, adaptive compensation for external disturbances is addressed. In the first approach, internal model-following control, adaptive elements are designed using feedback inversion. The effect of an actuator limit is treated using control hedging, and the effect of other actuation nonlinearities, such as dead zone and backlash, is mitigated by a disturbance observer-based control design. The effectiveness of the approach is illustrated through simulation and experimental testing with a three-disk torsional system, which is subjected to control voltage limit and stiction. While the internal model-following control is limited to minimum phase systems, the second approach, external model-following control, does not involve feedback linearization and can be applied to non-minimum phase systems. The unstable zero dynamics are assumed to have been modelled in the design of the existing linear controller. The laboratory tests for this method include a three-disk torsional pendulum, an inverted pendulum, and a flexible-base robot manipulator. The external model-following control architecture is further extended in three ways. The first extension is an approach for control of multivariable nonlinear systems. The second extension is a decentralized adaptive control approach for large-scale interconnected systems. The third extension is to make use of an adaptive observer to augment a linear observer-based controller. In this extension, augmenting terms for the adaptive observer can be used to achieve adaptation in both the observer and the controller. Simulations to illustrate these approaches include an inverted pendulum with its cart serially attached to two carts (one unmodelled), three spring-coupled inverted pendulums, and an inverted pendulum with its initial condition in a range in which a linear controller is destabilizing.

This work presents an investigation into the parameter estimation of suspension components and the vertical motions of wheeled vehicles from experimental data. The estimation problems considered were for suspension dampers, a single wheel station and a full vehicle. Using conventional methods (gradient-based (GB), Downhill Simplex (DS)) and stochastic methods (Genetic Algorithm (GA) and Differential Evolution (DE)), three major problems were encountered. These were concerned with the ability and consistency of finding the global optimum solution, time consumption in the estimation process, and the difficulties in setting the algorithm's control parameters. To overcome these problems, a new technique named the discrete variable Hybrid Differential Evolution (dvHDE) method is presented. The new dvHDE method employs an integer-encoding technique and treats all parameters involved in the same unified way as discrete variables, and embeds two mechanisms that can be used to deal with convergence difficulties and reduce the time consumed in the optimisation process. The dvHDE algorithm has been validated against the conventional GB, DS and DE techniques and was shown to be more efficient and effective in all but the simplest cases. Its robustness was demonstrated by its application to a number of vehicle related problems of increasing complexity. These include case studies involving parameter estimation using experimental data from tests on automotive dampers, a single wheel station and a full vehicle. The investigation has shown that the proposed dvHDE method, when compared to the other methods, was the best for finding the global optimum solutions in a short time. It is recommended for nonlinear vehicle suspension models and other similar systems.

Este trabalho aborda diversas técnicas de controle, com o intuito de comparação do desempenho e robustez ao aplicá-los a um conversor Buck. Iniciando pelo controlador PID (Proporcional, Integral e Derivativo), amplamente explorado e dominado no meio industrial, ele é adotado neste trabalho como referência de comparação para as demais técnicas desenvolvidas. Outra estratégia aqui apresentada é o GANLPID (Gaussian Adaptative Non Linear PID ou PID Adaptativo Não Linear Gaussiano), trata-se de uma técnica não linear, possui ganhos variantes em função do erro baseados em uma função gaussiana. O controle por alocação de polos é uma técnica de controle que em sua forma básica não possui parcela integral, sendo necessária a inclusão deste termo para minimizar o erro em regime permanente. As principais características de análise de desempenho são o tempo de acomodação e overshoot. Todas as técnicas são exploradas a fim de serem implementadas em dispositivos FPGA (Field Programmable Gate Array), possuindo algumas vantagens sobre microcontroladores e DSP’s (Digital Signal Processor), pois conseguem executar tarefas em paralelo deixando a execução do algoritmo mais rápida. As técnicas de controle escolhidas foram simuladas utilizando a ferramenta DSP Builder e compiladas diretamente em código HDL (linguagem de descrição de hardware). Os resultados de simulação e experimentais são apresentados e comentados para validar os projetos propostos. / This work discuss several techniques of control, with an intention of comparison of performance and robustness to apply them to Buck coverter. Starting with PID (Proportional, Integral, Derivative) controller, widely explored and dominated in an industrial environment, it’s used in this work as comparison reference for the others techniques developed. Another strategy presented here is the GANLPID (Gaussian Adaptative Non LinearPID), it’s a case of non linear technique, has won variants in function of the based on a Gaussian error function. variants have gains on function of error based on a Gaussian function. The pole placement control technique not having full part in their basic forms, being necessary to include this term to eliminate the steady-state error. The main performance analysis features are the settling time and overshoot. All the techniques are explored in order to be implemented in FPGA (Field Programmable Gate Array) devices, having some advantages over microcontrollers and DSP’s (Digital Signal Processor), because can execute tasks in parallel allowing the implementation of the algorithm more faster. The chosen control techniques were simulated using the DSP Builder tool and and compiled directly in HDL (hardware description language) code. The results of simulation and experimental are presented and discussed in order to validate the proposed projects.

This work presents an investigation into the parameter estimation of suspension components and the vertical motions of wheeled vehicles from experimental data. The estimation problems considered were for suspension dampers, a single wheel station and a full vehicle. Using conventional methods (gradient-based (GB), Downhill Simplex (DS)) and stochastic methods (Genetic Algorithm (GA) and Differential Evolution (DE)), three major problems were encountered. These were concerned with the ability and consistency of finding the global optimum solution, time consumption in the estimation process, and the difficulties in setting the algorithm's control parameters. To overcome these problems, a new technique named the discrete variable Hybrid Differential Evolution (dvHDE) method is presented. The new dvHDE method employs an integer-encoding technique and treats all parameters involved in the same unified way as discrete variables, and embeds two mechanisms that can be used to deal with convergence difficulties and reduce the time consumed in the optimisation process. The dvHDE algorithm has been validated against the conventional GB, DS and DE techniques and was shown to be more efficient and effective in all but the simplest cases. Its robustness was demonstrated by its application to a number of vehicle related problems of increasing complexity. These include case studies involving parameter estimation using experimental data from tests on automotive dampers, a single wheel station and a full vehicle. The investigation has shown that the proposed dvHDE method, when compared to the other methods, was the best for finding the global optimum solutions in a short time. It is recommended for nonlinear vehicle suspension models and other similar systems.

Abstract not available

PAE / O transporte rodoviário é um dos modais mais utilizados para o transporte de passageiros principalmente devido à sua acessibilidade, tanto no contexto nacional como mundial. As organizações buscam métodos e sistemas cada vez mais eficientes para atender de forma satisfatória seus clientes, oferencendo serviços de qualidade e confiáveis. O presente trabalho teve como objetivo propor um modelo matemático de veículos para a minimização de ônibus, evitando ao máximo o desbalanceamento da rede de transporte. O modelo buscou abranger as restrições inerentes aos fluxos em rodoviárias de modo a cobrir todas as viagens de uma tabela de horários já definida, alocando apenas um veículo para cada viagem e aproveitando o mesmo para outras viagens quando possível, atendendo à função objetivo. O modelo foi aplicado à uma empresa de transportes de passageiros com quatro cidades envolvidas e 105 viagens em um tempo de 24 horas. As variáveis e restrições foram identificadas a partir de entrevistas semi -estruturadas e visitas à organização, observando roteiros de viagens a serem cumpridos por dois modelos de ônibus: metropolitanos e articulados. Neste contexto, dois modelos distintos foram montados de forma a atender as viagens, sendo analisadas separadamente. Os resultados definiram um total necessário de 12 ônibus metropolitanos e 4 ônibus articulados para atender às exigências da empresa e da tabela viagens, sendo que todas as restrições foram satisfeitas, detectando -se a necessidade da realização de seis viagens mortas (sem passageiros) para suprir a necessidade de d emanda de ônibus para cada tabela de viagens diárias. Com os resultados, fez-se uma comparação com a programação que a empresa necessitava para cumprir a tabela de viagens, identificando a diminuição de um ônibus metropolitano, sem deixar de cumprir a restrição de autonomia de cada ônibus poder rodar 400 quilômetros sem necessidade de reabastecimento. Algumas melhorias foram identificadasanalisando-se a rede resultante, sendo discutidas ao final da pesquisa e norteando novas intenções de trabalhos futuros. / Road transport is one of the most used modes for passenger transport mainly due to its affordability, in the national and global context. Organizations seek for a better methods and systems to meet the satisfaction of its customers, offering quality and reliable services. This research aimed to propose a vehicle scheduling model to minimize buses, avoiding the transmission system imbalance. The model tried to cover the restrictions inherent about the vehicle flow on bus stations to cover all travel in a given timetable, allocating only one vehicle for each trip and using it for other trips when it is possible, given the objective function. The model was applied to a passenger transportation company with four cities involved and 105 trips in a time of 24 hours. The variables and constraints were identified from semi-structured interviews and visits at organization, identifying the tours to be met by two bus models: articulated and metropolitan. In this context, two different models were fitted to meet the travel , and analyzed separately. The results defined a required total of twelve metropolitan buses and four articulated buses to meet the company and timetable requirements and all constraints were satisfied, detecting the need of perform six deadheading trips (without passengers) to meet the need for demand bus for each table in the daily trips. With the results, a comparison was made between the old programming system adopted by the organization to fulfill the timetable, identifying the reduction of a metropolitan bus, while fulfilling the constraint of autonomy that each bus can travel 400 kilometers. Some improvements were identified by observing the resulting route network, being discussed at the end of the research and guiding for a new works in the future.

This paper deals with the consensus problem under communication network inducing delays. It is well-known that introducing a delay leads in general to a reduction of the performance or to instability due to the fact that timedelay systems are infinite dimensional. For instance, the set of initial conditions of a time-delay system is not a vector but a function taken in an interval. Therefore, investigating the effect of time-delays in the consensus problem is an important issue. In the present paper, we assume that each agent receives instantaneously its own state information but receives the state information from its neighbors after a constant delay. Two stability criteria are provided based on the frequency approach and on Lyapunov-Krasovskii techniques given in terms of LMI. An analytic expression of the consensus equilibrium which depends on the delay and on the initial conditions taken in an interval is derived. The efficiency of the method is tested for different network communication schemes. / <p>QC 20110120</p>