Thesis--Auburn University, 2006. / Abstract. Vita. Includes bibliographic references (p.53-58).

Electromagnetic levitation has been commonly researched for the use in ground transit systems. It is ideal for high-speed applications that require low friction. The principle is simple, use electromagnetic force to balance the force imposed by gravity. However, for attractive levitation the system is unstable and nonlinear. Two dominant approaches to this problem have been to use a state feedback control system or a simple linear PID compensated control architecture. State feedback is a well-known control technique, but is complicated to implement and can rely on linearization of the system dynamics. The simple PID control structure is very easy to implement, but can have severe performance degradation in the presence of noise. This system can usually be identified by its large acoustic noise. This is primarily due to the differential term in the controller. This thesis proposes a solution that uses two concepts: Current Command Generation (CCG) and a closed velocity loop. CCG linearizes the control structure by utilizing the known magnetic properties of the system to convert a desired force to a current for any given air gap. This removes squared command terms from the control structure. This allows for a reliable and predictable implementation of linear feedback control systems. The PID implementation of an attractive levitation system uses two control loops. The inner loop is a current controller, which receives current commands from the outer position loop. The proposed control architecture uses three loops. The innermost loop is the current controller, which receives current commands for the CCG. The middle loop is a velocity controller, which receives commands from the position (outer most) loop and produces force command output used as inputs to the CCG. The three loops consist of two Proportional Integral (PI) controllers for the current and velocity controllers and a Proportional (P) controller. There is no derivative term, making the proposed solution's performance far less dependent on noise. This architecture removes the necessity of nonlinear elements in the control architectures and improves noise rejection through the use of the velocity loop. The acoustic noise performance of this system is enhanced by both of these methodologies and is shown in the experimental setup. / Master of Science

O controle e otimização da operação da suspensão eletromagnética de um protótipo de veículo MAGLEV são apresentados neste trabalho. Este tipo de sistema é inerentemente instável e altamente não linear, sendo um excelente exemplo para o estudo e comparação de diferentes metodologias de controle. Nos últimos anos, experiências significativas com veículos levitados têm ganhado força. A arquitetura do veículo consiste de quatro atuadores eletromagnéticos, quatro sensores de entreferros e quatro acelerômetros, todos instalados nos cantos do veículo. A dinâmica do sistema é descrita através de três modelos matemáticos diferentes: modelo de corpo rígido com três graus de liberdade (movimentos vertical, de rolagem e de arfagem), modelo de corpo não rígido, onde está presente mais um grau de liberdade (movimento de torção), e modelo SISO com quatro movimentos verticais independentes. Blocos de compatibilização de variáveis são utilizados devido à diferença no número de variáveis do modelo matemático com o número de variáveis medidas e de atuação disponíveis no veículo. Os acelerômetros, usados para estimar as velocidades do veículo, foram instalados com o objetivo de estudar-se o controle ótimo da suspensão por realimentação de estados com o emprego da técnica do Regulador Linear Quadrático (RLQ) e utilização do método do lugar das raízes para definição dos pólos de malha fechada. Para efeito de comparação foi implementado um controle H'IND.2'/H'INFINITO' por realimentação da saída. Controladores independentes para cada grau de liberdade foram simulados no software MATLAB e depois implementados e testados no veículo utilizando uma placa de aquisição de dados instalada no microcomputador. A preocupação principal do projeto dos controladores foi a estabilidade do sistema na ocorrência de perturbações que desviem o entreferro de seu valor nominal.Exceto para o sistema com controle RLQ e modelo de corpo rígido, os resultados experimentais obtidos com o protótipo mostram que o sistema em malha fechada é estável e apresenta uma resposta transiente satisfatória. O sistema com controle RLQ e modelo de corpo não rígido apresentou a melhor performance entre todas as alternativas testadas. / The control and optimization of the electromagnetic suspension operation of a MAGLEV vehicle prototype are presented in this work. This kind of system is inherently unstable and highly nonlinear, being an excellent example for the study and comparison of different control methodologies. In the last years significant experience has been gained with levitated vehicles. The vehicle architecture consists of four electromagnetic actuators, four air gap sensors and four accelerometers, all located at the corners of the vehicle. The vehicle dynamics is described through three different mathematical models: rigid body model, with three degrees of freedom (heave, roll and pitch motions), not-rigid body model, with an additional degree of freedom (torsion motion) and SISO model, with four independent heave motions. Blocks to make variables compatible are used in based on the difference between the number of variables of the mathematical model and the number of measured and actuation variables available in the vehicle. The accelerometers, used to estimate the speeds of the vehicle, were installed in order to study the optimal control of the suspension for states feedback. The Linear Quadratic Regulator (LQR) technique combined with the root locus method for definition of the closed-loop poles were used. The H'IND.2'/H'INFINITE' controller with output feedback was implemented for sake of comparison. Independent controllers for each degree of freedom were simulated with MATLAB then implemented and tested in the vehicle using AD/DA converter installed in the microcomputer. The first goal of the controllers' design was the system stability when subject to disturbances that drive the air away from its nominal value. Except for the system with RLQ controller and rigid body model, the experimental results obtained with the prototype show that the closed-loop system is stable and exhibits a satisfactory transient response.The system with the RLQ controller and not-rigid body model exhibits the best performance among all the alternatives tested.

<p>The aim of this work has been to develop new knowledge about macromodelling of microsystems. Doing that, we have followed two different approaches for generating macromodels, namely model order reduction and lumped modelling. The latter is a rather mature method that has been widely recognized and used for a relatively long period of time. Model order reduction, on the other hand, is a relatively new area still in rapid development. Due to this, the parts considering reduced order modelling is strongly biased towards methodology and concepts, whereas parts on lumped modelling are biased towards systems and devices.</p><p>In the first part of this thesis, we focus on model order reduction. We introduce some approaches for reducing model order for linear systems, and we give an example related to squeeze-film damping. We then move on to investigate model order reduction of nonlinear systems, where we present and use the concept of invariant manifolds. While the concept of invariant manifolds is general, we utilize it for reducing models. An obvious advantage of using invariant manifold theory is that it offers a conceptually clear understanding of effects and behaviour of nonlinear system.</p><p>We exemplify and investigate the accuracy of one method for identifying invariant manifolds. The example is based on an industrialized dual-axis accelerometer.</p><p>A new geometrical interpretation of external forcing, relating to invariant manifolds, is presented. We show how this can be utilized to deal with external forcing in a manner consistent with the invariance property of the manifold. The interpretation also aids in reducing errors for reduce models.</p><p>We extend the asymptotic approach in a manner that makes it possible to create design-parameter sensitive models. We investigate an industrialized dual-axis accelerometer by means of the method and demonstrate capabilities of the method. We also discuss how manifolds for nonlinear dissipative systems can be found.</p><p>Focusing on lumped modelling, we analyse a microresonator. We also discuss the two analogies that can be used to build electrical equivalents of mechanical systems. It is shown how the f → V analogy, linking velocity to voltage, is the natural choice. General properties of lumped modelling are investigated using models with varying degrees of freedom.</p><p>Finally, we analyse an electromagnetic system, intended for levitating objects, and we demonstrate the scaling effects of the system. Furthermore, we prove the intrinsic stability of the system, although the floating disc will be slightly tilted. This is the first analysis done assessing the stability criterions of such a systems. The knowledge arising from the analysis gives strong indications on how such a system can be utilized, designed, and improved.</p>

The aim of this work has been to develop new knowledge about macromodelling of microsystems. Doing that, we have followed two different approaches for generating macromodels, namely model order reduction and lumped modelling. The latter is a rather mature method that has been widely recognized and used for a relatively long period of time. Model order reduction, on the other hand, is a relatively new area still in rapid development. Due to this, the parts considering reduced order modelling is strongly biased towards methodology and concepts, whereas parts on lumped modelling are biased towards systems and devices. In the first part of this thesis, we focus on model order reduction. We introduce some approaches for reducing model order for linear systems, and we give an example related to squeeze-film damping. We then move on to investigate model order reduction of nonlinear systems, where we present and use the concept of invariant manifolds. While the concept of invariant manifolds is general, we utilize it for reducing models. An obvious advantage of using invariant manifold theory is that it offers a conceptually clear understanding of effects and behaviour of nonlinear system. We exemplify and investigate the accuracy of one method for identifying invariant manifolds. The example is based on an industrialized dual-axis accelerometer. A new geometrical interpretation of external forcing, relating to invariant manifolds, is presented. We show how this can be utilized to deal with external forcing in a manner consistent with the invariance property of the manifold. The interpretation also aids in reducing errors for reduce models. We extend the asymptotic approach in a manner that makes it possible to create design-parameter sensitive models. We investigate an industrialized dual-axis accelerometer by means of the method and demonstrate capabilities of the method. We also discuss how manifolds for nonlinear dissipative systems can be found. Focusing on lumped modelling, we analyse a microresonator. We also discuss the two analogies that can be used to build electrical equivalents of mechanical systems. It is shown how the f → V analogy, linking velocity to voltage, is the natural choice. General properties of lumped modelling are investigated using models with varying degrees of freedom. Finally, we analyse an electromagnetic system, intended for levitating objects, and we demonstrate the scaling effects of the system. Furthermore, we prove the intrinsic stability of the system, although the floating disc will be slightly tilted. This is the first analysis done assessing the stability criterions of such a systems. The knowledge arising from the analysis gives strong indications on how such a system can be utilized, designed, and improved.

O controle e otimização da operação da suspensão eletromagnética de um protótipo de veículo MAGLEV são apresentados neste trabalho. Este tipo de sistema é inerentemente instável e altamente não linear, sendo um excelente exemplo para o estudo e comparação de diferentes metodologias de controle. Nos últimos anos, experiências significativas com veículos levitados têm ganhado força. A arquitetura do veículo consiste de quatro atuadores eletromagnéticos, quatro sensores de entreferros e quatro acelerômetros, todos instalados nos cantos do veículo. A dinâmica do sistema é descrita através de três modelos matemáticos diferentes: modelo de corpo rígido com três graus de liberdade (movimentos vertical, de rolagem e de arfagem), modelo de corpo não rígido, onde está presente mais um grau de liberdade (movimento de torção), e modelo SISO com quatro movimentos verticais independentes. Blocos de compatibilização de variáveis são utilizados devido à diferença no número de variáveis do modelo matemático com o número de variáveis medidas e de atuação disponíveis no veículo. Os acelerômetros, usados para estimar as velocidades do veículo, foram instalados com o objetivo de estudar-se o controle ótimo da suspensão por realimentação de estados com o emprego da técnica do Regulador Linear Quadrático (RLQ) e utilização do método do lugar das raízes para definição dos pólos de malha fechada. Para efeito de comparação foi implementado um controle H'IND.2'/H'INFINITO' por realimentação da saída. Controladores independentes para cada grau de liberdade foram simulados no software MATLAB e depois implementados e testados no veículo utilizando uma placa de aquisição de dados instalada no microcomputador. A preocupação principal do projeto dos controladores foi a estabilidade do sistema na ocorrência de perturbações que desviem o entreferro de seu valor nominal.Exceto para o sistema com controle RLQ e modelo de corpo rígido, os resultados experimentais obtidos com o protótipo mostram que o sistema em malha fechada é estável e apresenta uma resposta transiente satisfatória. O sistema com controle RLQ e modelo de corpo não rígido apresentou a melhor performance entre todas as alternativas testadas. / The control and optimization of the electromagnetic suspension operation of a MAGLEV vehicle prototype are presented in this work. This kind of system is inherently unstable and highly nonlinear, being an excellent example for the study and comparison of different control methodologies. In the last years significant experience has been gained with levitated vehicles. The vehicle architecture consists of four electromagnetic actuators, four air gap sensors and four accelerometers, all located at the corners of the vehicle. The vehicle dynamics is described through three different mathematical models: rigid body model, with three degrees of freedom (heave, roll and pitch motions), not-rigid body model, with an additional degree of freedom (torsion motion) and SISO model, with four independent heave motions. Blocks to make variables compatible are used in based on the difference between the number of variables of the mathematical model and the number of measured and actuation variables available in the vehicle. The accelerometers, used to estimate the speeds of the vehicle, were installed in order to study the optimal control of the suspension for states feedback. The Linear Quadratic Regulator (LQR) technique combined with the root locus method for definition of the closed-loop poles were used. The H'IND.2'/H'INFINITE' controller with output feedback was implemented for sake of comparison. Independent controllers for each degree of freedom were simulated with MATLAB then implemented and tested in the vehicle using AD/DA converter installed in the microcomputer. The first goal of the controllers' design was the system stability when subject to disturbances that drive the air away from its nominal value. Except for the system with RLQ controller and rigid body model, the experimental results obtained with the prototype show that the closed-loop system is stable and exhibits a satisfactory transient response.The system with the RLQ controller and not-rigid body model exhibits the best performance among all the alternatives tested.

Electromagnetic levitation experiments provide a powerful tool that allows for the study of nucleation, solidification and growth in a containerless processing environment. Containerless processing allows for the study of reactive melts at elevated temperatures without chemical interactions or contamination from a container. Further, by removing the interface between the liquid and its container, this processing technique allows for greater access to the undercooled region for solidification studies. However, in these experiments it is important to understand the magnetohydrodynamic flow within the sample and the effects that this fluid flow has on the experiment. A recent solidification study found that aluminum-nickel alloy sample have an unusual response of the growth rate of the solid to changes in undercooling. This alloy experienced a decrease in the growth velocity as the initial undercooling deepened, instead of the expected increase in solidification velocity with deepening undercoolings. Current work is exploring several different theories to explain this phenomenon. Distinguishing among these theories requires a comprehensive understanding of the behavior of the internal fluid flow. Our project, USTIP, has done flow modeling to support this and multiple other collaborators on ISS-EML. The fluid flow models presented for the aluminum-nickel sample provide critical insights into the nature of the flow within the aluminum-nickel alloy experiments conducted in the ISS-EML facility. These models have found that for this sample the RNG k-ε model should be used with this sample at temperatures greater than 1800 K and the laminar flow model should be used at temperatures lower than 1600 K. Other work in the ISS-EML, has studied the thermophysical properties of liquid germanium and has found the most recent measurements using oscillating drop techniques to have a discrepancy from the expected property measurements taken terrestrially. Investigating this discrepancy required the quantification of the velocity and characterization of the internal fluid flow in the drop. The models have found that the flow within the sample maintains turbulent behavior throughout cooling. This thesis presents the analysis of the internal flow of four additional samples processed in the International Space Station Electromagnetic Levitation facility. These samples consist of the following alloys: Ti39.5Zr39.5Ni21, Cu50Zr50, Vitreloy 106, and Zr64Ni36. Our collaborators work required the internal flow to be characterized and quantified for their work on solidification. In addition to quantifying the velocity of the flow, the Reynolds number was calculated to characterize the flow during processing. Additionally, the shear-strain rate was calculated for the flow during processing up to the recalescence of the melt.

Experimental investigations of high temperature industrial processes, for example the melting and smelting processes taking place inside furnaces, are complicated by the high temperatures and the chemically reactive environment in which they take place. Fortunately, mathematical models can be used in conjunction with the limited experimental results that are available to gain insight into these high temperature processes. However, mathematical models of high temperature processes require high temperature material properties, which are difficult to measure experimentally since container materials are often unable to withstand high enough temperatures, and sample contamination often occurs. These difficulties can be overcome by employing containerless processing techniques such as electromagnetic levitation melting to allow for characterisation of high temperature material properties. Efficient design of electromagnetic levitation cells is challenging since the effects of changes in coil design, sample size and sample material on levitation force and sample temperature are not yet well understood. In this work a numerical model of the electromagnetic levitation cell is implemented and used to investigate the sensitivity of levitation cell operation to variations in coil design, sample material and sample size. Various levitation cell modelling methods in literature are reviewed and a suitable model is chosen, adapted for the current application, and implemented in Python. The finite volume electromagnetic component of the model is derived from Maxwell’s equations, while heat transfer is modelled using a lumped parameter energy balance based on the first law of thermodynamics. The implemented model is verified for a simple case with a known analytical solution, and validated against published experimental results. It is found that a calibrated model can successfully predict the lifting force inside the levitation cell, as well as the sample temperature at low coil currents. The validated model is used to characterise the operation of a levitation cell for a number of different sample materials and sample sizes, and for variations in coil geometry and coil current. The model can be used in this way to investigate a variety of cases and hence to support experimental levitation cell design. Based on model results, a number of operating procedure recommendations are also made. / Dissertation (MEng)--University of Pretoria, 2016. / Mechanical and Aeronautical Engineering / MEng / Unrestricted

Sistemas de levitação eletromagnética são de interesse quando se necessita de tecnologia envolvendo redução de atrito, atuação sem contato físico, máquinas rotativas e trens de alta velocidade. Devido à presença de não linearidades em sua dinâmica, pesquisadores têm dado atenção ao desenvolvimento de controladores mais sofisticados, com o objetivo de melhorar o desempenho desses sistemas. Controladores lineares apresentam limitações na faixa de operação da variável controlada e, geralmente apresentam baixa robustez quando aplicados em sistemas não lineares. O objetivo deste trabalho é desenvolver controladores não lineares com diferentes estruturas e analisá-los quando aplicados em um protótipo do sistema físico. Inicialmente, o sistema é modelado matematicamente através da abordagem fenomenológica. Em seguida, os parâmetros do modelo são identificados através de dados obtidos experimentalmente. Conhecendo bem a dinâmica do sistema através do modelo, são projetados três controladores de diferentes estruturas utilizando simulações computacionais. O primeiro é o PID clássico, controle linear amplamente utilizado em processos industriais. O segundo controlador é um PID com topologia não linear, denominado NPID. Este visa reduzir as limitações encontradas no PID linear, através de funções não lineares em seus termos. O último e mais complexo se trata do controle por modos deslizantes (SMC). Também com estrutura não linear, o SMC possui como característica intrínseca a robustez a variações da planta. Ao final, são realizadas simulações e os controladores avaliados são implementados de maneira digital em um hardware de controle e aplicados em uma planta piloto de levitação eletromagnética. Os resultados de desempenho obtidos permitem avaliar qual topologia de controlador melhor se enquadra diante dessa aplicação. / Electromagnetic levitation systems are of interest when it is necessary the use of technology involving reduction of friction, acting without physical contact, rotating machinery and high speed trains. Due to the nonlinear dynamics, researchers have paid attention to the development of more sophisticated controllers, in order to improve the performance of these systems. Linear controllers have limitations in the operating range of the controlled variable and generally have low robustness when applied to linear systems. The objective of this work is to develop nonlinear controllers with different structures and analyze them, when applied to a prototype of the physical system. Initially the system is modeled mathematically through the phenomenological approach. Then the model parameters are identified by experimentally obtained data. Knowing the dynamic of the system through the model, three different controllers are designed using computer simulations. The first is the classic PID, a linear control widely used in industrial processes. The second controller is a PID with nonlinear topology, called NPID. This controller is intended to reduce the limitations found in the linear PID through non linear functions on its terms. The last and most complex is the sliding mode control (SMC). Also a nonlinear structure, the SMC has the intrinsic characteristic of robustness to variations of the plant. In the end, the simulations are performed and the evaluated controllers are implemented in digital form in a hardware control and applied in a pilot plant of an electromagnetic levitation system. With the performance results it is possible to verify which controller topology best fits this application.

Sistemas de levitação eletromagnética são de interesse quando se necessita de tecnologia envolvendo redução de atrito, atuação sem contato físico, máquinas rotativas e trens de alta velocidade. Devido à presença de não linearidades em sua dinâmica, pesquisadores têm dado atenção ao desenvolvimento de controladores mais sofisticados, com o objetivo de melhorar o desempenho desses sistemas. Controladores lineares apresentam limitações na faixa de operação da variável controlada e, geralmente apresentam baixa robustez quando aplicados em sistemas não lineares. O objetivo deste trabalho é desenvolver controladores não lineares com diferentes estruturas e analisá-los quando aplicados em um protótipo do sistema físico. Inicialmente, o sistema é modelado matematicamente através da abordagem fenomenológica. Em seguida, os parâmetros do modelo são identificados através de dados obtidos experimentalmente. Conhecendo bem a dinâmica do sistema através do modelo, são projetados três controladores de diferentes estruturas utilizando simulações computacionais. O primeiro é o PID clássico, controle linear amplamente utilizado em processos industriais. O segundo controlador é um PID com topologia não linear, denominado NPID. Este visa reduzir as limitações encontradas no PID linear, através de funções não lineares em seus termos. O último e mais complexo se trata do controle por modos deslizantes (SMC). Também com estrutura não linear, o SMC possui como característica intrínseca a robustez a variações da planta. Ao final, são realizadas simulações e os controladores avaliados são implementados de maneira digital em um hardware de controle e aplicados em uma planta piloto de levitação eletromagnética. Os resultados de desempenho obtidos permitem avaliar qual topologia de controlador melhor se enquadra diante dessa aplicação. / Electromagnetic levitation systems are of interest when it is necessary the use of technology involving reduction of friction, acting without physical contact, rotating machinery and high speed trains. Due to the nonlinear dynamics, researchers have paid attention to the development of more sophisticated controllers, in order to improve the performance of these systems. Linear controllers have limitations in the operating range of the controlled variable and generally have low robustness when applied to linear systems. The objective of this work is to develop nonlinear controllers with different structures and analyze them, when applied to a prototype of the physical system. Initially the system is modeled mathematically through the phenomenological approach. Then the model parameters are identified by experimentally obtained data. Knowing the dynamic of the system through the model, three different controllers are designed using computer simulations. The first is the classic PID, a linear control widely used in industrial processes. The second controller is a PID with nonlinear topology, called NPID. This controller is intended to reduce the limitations found in the linear PID through non linear functions on its terms. The last and most complex is the sliding mode control (SMC). Also a nonlinear structure, the SMC has the intrinsic characteristic of robustness to variations of the plant. In the end, the simulations are performed and the evaluated controllers are implemented in digital form in a hardware control and applied in a pilot plant of an electromagnetic levitation system. With the performance results it is possible to verify which controller topology best fits this application.