Dissertations / Theses on the topic 'E-optimal Design'

Statistics
Ph.D.
Choice-based conjoint experiments are used when choice alternatives can be described in terms of attributes. The objective is to infer the value that respondents attach to attribute levels. This method involves the design of profiles on the basis of attributes specified at certain levels. Respondents are presented sets of profiles called choice sets, and asked to select the one they consider best. Sets with no dominating or dominated profiles are called Pareto Optimal sets. Information Per Profile (IPP) is used as an optimality criteria to compare designs with different numbers of profiles. For a 2^n experiment, the optimality of connected main effects plans based on two consecutive choice sets, Sl and Sl+1, has been examined in the literature. In this thesis we examine the IPP of both consecutive and non-consecutive choice sets and show that IPP can be maximized under certain conditions. We show that non-consecutive choice sets have higher IPP than consecutive choice sets for n ≥ 4. We also examine the optimality of connected first-order-interaction designs based on three choice sets and show that non-consecutive choice sets have higher IPP than consecutive choice sets under certain conditions. Further, we examine the D-, A- and E-optimality of consecutive and non-consecutive PO choice sets with maximum IPP. Finally, we consider 3^n choice experiments. We look for the optimal PO choice sets and examine their IPP, D-, A- and E-optimality, as well as comparing consecutive and non-consecutive choice sets.
Temple University--Theses

The problem of designing control systems for entire plants is studied. A review of previous works, available techniques and current research challenges is presented, followed by the description of some theoretical tools to improve plantwide control, including the proposal of an augmented lexicographic multi-objective optimization procedure. With these, an augmented hierarchical plantwide control design technique and an optimal multi-objective technique for integrated control structure selection and controller tuning are proposed. The main contributions of these proposed techniques are the inclusion of system identification and optimal control tuning as part of the plantwide design procedure for improved results, support to multi-objective control specifications and support to any type of plant and controllers. Finally, the proposed techniques are applied to industrial benchmarks to demonstrate and validate its applicability.
O problema de projetar sistemas de controle para plantas inteiras é estudado. Uma revisão de trabalhos anteriores, técnicas disponíveis e atuais desafios de pesquisa é apresentada, seguida da descrição de algumas ferramentas teóricas para melhorar o controle plantwide, incluindo a proposta de um procedimento de otimização multi-objetivo lexicográfico aumentado. Com tais elementos, são propostas uma nova técnica hierárquica aumentada de projeto de sistemas de controle plantwide e uma técnica multi-objetivo para seleção de estrutura de controlador integrada à sintonia ótima do controlador. As principais contribuições das técnicas propostas são a inclusão de identificação de sistemas e sintonia ótima de controladores como parte do procedimento de projeto de controle plantwide para melhores resultados, suporte a especificações multi-objetivo e suporte a quaisquer tipos de plantas e controladores. Finalmente, as técnicas propostas são aplicadas a benchmarks industriais para demonstrar e validar sua aplicabilidade.

The study of microirrigation hydraulic design has been widely addressed over many decades to enhance on-farm water use efficiency and water distribution uniformity with minimal impact on energy consumption through introducing innovative engineering solutions for better control of the system. The thesis first reviewed the literature, providing an overview of the microirrigation system, its performance, and its hydraulic design procedures are provided along with a review of some approaches that were developed for the hydraulic design, and examine their assumptions and theories. Among this literature are IRRIPRO and IRRILAB software, which were developed among the research activities carried out at the University of Palermo (Italy). IRRILAB software is based on analytical solutions and allows saving energy, but requires a rectangular shape of the sector defined by two uniform slopes one for the laterals and one for the manifold, whereas IRRIPRO finds numerical solutions that required a lot of attempts but can be applied on any shape of the sectors. These two software may offer a unique solution in designing microirrigation units through capturing the positive aspects of both and in the meanwhile overcoming the negative ones. This thesis investigates the performance of IRRILAB and IRRIPRO software applications, using pressure-compensating-emitters and not-pressure-compensating ones, to design microirrigation systems in an apple farm in Sicily, which is characterized by a high irregular topography, thus it is suitable for the purpose of this study. Several investigations were carried out through both theoretical verification and experimental validation in the field. To begin with, the theoretical study to verify the performance of IRRILAB software application in designing a large number of microirrigation sectors characterized by different irregularities degree in sector's slope and planform geometry was carried out by using the design parameters of IRRILAB as input in the IRRIPRO software that is able to show the pressure head distribution maps for each sector. The results of this study have shown that the IRRILAB software could be recommended because it is easy to use, making it possible to save energy, especially when sectors are almost rectangular and uniform in slopes. In addition, a further investigation was carried out for IRRILAB software by performing an experimental study for only one sector extended to 7,369 m2. Without considering the minor losses caused due to the presence of emitters along the laterals, the microirrigation sector for this experiment was designed as recommended by IRRILAB software using a not-pressure-compensating emitter, aimed at validating that the measured emitter’s flow rates fall within the corresponding limits of IRRILAB acceptability. Results showed that for some emitters, flow rates fall below the minimum admitted value. This was ascribed to the irregularity of the sector planform geometry, not exactly rectangular as IRRILAB requires, as well as the effect of minor losses that were neglected in the design. Subsequently, the latter issue was then investigated by using a new methodology introduced recently that makes it possible to quantify the amount of minor losses in terms of the equivalent length. Based on the calculation, a new experiment different from the previous one that neglects minor losses to a new one in which minor losses are considered was performed. Results have shown that a certain improvement of the emitters' flow rates was obtained, referring to the important role of the minor losses that are playing in microirrigation systems design. This study concluded that the recently introduced procedure to account for minor losses could be successfully implemented in IRRILAB to improve microirrigation systems design. In conclusion, an experimental investigation study is carried out to assess the performance of the IRRIPRO software in simulating the field situation of microirrigation systems under different operating pressures. This study is based on field measurements of emitter flow rates aimed at validating that the measured emitter’s flow rates in the field match the results obtained through IRRIPRO simulations. Different statistical analyses were performed in order to show the accuracy of IRRIPRO software prediction for the emitters' flow rates. The experiment results showed how the use of IRRIPRO software allows representing the field situation, thereby, can be used to improve the performance of any microirrigation system, provided that a similar design layout is applied.

This text focuses on advanced torque control of permanent magnet synchronous motor drives. A novel modular structure is introduced to simplify the design and implementation of Model Predictive Control (MPC). The layout consists of the control and the control framework. The dynamic control is the novel virtual flux controller, which is used to reach desired reference values, and the state observer, which is used to reduce effects of non-modeled system properties. The control framework consists of static mappings to simplify the control problem. Besides the alpha-beta and d-q transformations, a reference generation procedure is used to generate state references based on optimality criteria. Also, the actuation scheme is part of the control framework and defines the available input set and the resulting control properties. The first method actuates directly switch states, i.e. voltage vectors, which yield an integer set named Finite Control Set (FCS). The other method actuates duty cycles via modulation, which yield the Convex Control Set (CCS). A stability analysis is carried out for both, CCS-MPC and FCS-MPC. MPC is called stable, if it is feasible and convergent, which can be ensured using the main MPC stability theorem. However, stringent computation requirements make it difficult to apply the theorem in practice. Thus, the Lyapunov based MPC approach is applied to the motor drive, which provides stability guarantees independent of the prediction horizon. A stability constraint based on control Lyapunov functions (CLF) ensures convergence to the origin and the resulting optimal control problem is shown to be feasible for all time. In other words, a control input can be found at each sampling instant, which satisfies all constraints and yields a stable closed-loop system. The properties of CCS-MPC are derived using a nonlinear controller and the constrained closed-loop system is shown to be stable in the sense of Lyapunov. The stability properties of FCS-MPC are more complex due to the integer input set. Using set-theoretical methods, it is shown that a sufficiently large control error can be steered towards the origin. In other words, the proposed FCS-MPC is shown to be set stable, i.e. the control error is guaranteed to converge to a well-defined neighborhood of the origin. MPC requires that a Constrained Finite Time Optimal Control (CFTOC) problem is solved at each sampling time. Small sampling periods and limited computation capabilities of embedded hardware require the CFTOC to be sufficiently simple, which is achieved using the virtual flux model in the static reference frame. The problem size is contained using a sufficiently small prediction horizon and efficient algorithms are necessary to provide a result within a sampling period. The CFTOC of the proposed CCS-MPC is a (convex) linear or quadratic programming problem, which can be solved using existing efficient algorithms. To provide a minimal approach, an efficient algorithm is introduced to solve the one-step-ahead prediction CFTOC analytically. FCS-MPC results in a mixed integer programming problem and is therefore more difficult to solve with standard numerical methods. In practice, the CFTOC is solved by enumeration, which is combined with branch-and-bound, i.e. branch-and-cut, techniques to improve the computational efficiency. The control algorithms have been developed on a Software-in-the-Loop (SiL) platform based on Matlab/Simulink and the code is implemented without modification on an experimental test-bench. The evaluation confirms the design and implementation of CCS-MPC and FCS-MPC and shows good results in dynamic and steady-state operation. The two MPC approaches have complimentary properties, which can be used to target different applications. CCS-MPC achieves a constant switching frequency and is a promising alternative to proportional-integral (PI) vector control. The concept can be combined with different modulation schemes, e.g. the Symmetric Space Vector Modulation (SSVM) and the Discontinuous Space Vector Modulation (DSVM) are used in this text. FCS-MPC takes the inverter switching into account and achieves an approximately constant switching ripple but a variable switching frequency. The concept is most profitably applied to systems where a high sampling frequency compared to the switching frequency is desired, e.g. high power or servo drives. Moreover, FCS-MPC lacks Pulse Width Modulation (PWM) harmonics in its current spectrum. Consequently, it is advantageous in terms of acoustic noise since emphasized tones are missing. However, the distinguished PWM harmonics of CCS-MPC are simpler to filter. In summary, it can be said that the work on advanced torque control of permanent magnet synchronous motor drives has produced an innovative strategy. The introduction of a new structure has significantly simplified the model predictive control problem, the concept of stability in particular. Moreover, this structure results in the implementation of simple algorithms, which can be computed efficiently.
Il soggetto affrontato dal presente lavoro sono i controlli avanzati di coppia per azionamenti con un motore sincrono a magneti permanenti. A questo scopo, è stata introdotta una struttura modulare che semplifica la progettazione e l’implementazione del controllo predittivo basato su un modello (model predictive control, MPC): lo schema è costituito dal controllo dinamico e dal quadro di controllo. Il controllo dinamico è un regolatore di flusso virtuale, utilizzato per raggiungere un valore di riferimento voluto e un osservatore di stato che serve a ridurre gli effetti delle proprietà non modellizzate del sistema. Il problema del controllo è stato semplificato tramite l’utilizzo di trasformate statiche chiamate quadro di controllo. Accanto alle trasformate alpha-beta e d-q viene usata una procedura per la generazione di riferimenti di stato, basati su un criterio ottimale. Il quadro di controllo contiene anche lo schema di attuazione, che serve per definire l’insieme di ingressi disponibili. Da un lato, il controllore comanda in modo diretto l’accensione e lo spegnimento dei semiconduttori, ovvero i vettori di tensione, ottenendo un insieme finito d’ingressi (Finite Control Set, FCS). Dall’altro lato vengono attuati cicli di accensione (duty-cycles) attraverso una modulazione (pulse width modulation, PWM): ciò risulta in un insieme convesso d’ingressi (convex control set, CCS). È stata eseguita un’analisi di stabilità sia per CCS-MPC sia per FCS-MPC. MPC è stabile, se il problema di controllo ottimale ad esso associato è risolvibile e l’errore di stato converge all’origine. Tale stabilità può essere garantita attraverso il principale teorema di stabilità di MPC. Tuttavia, i requisiti di calcolo restrittivi rendono il teorema difficilmente applicabile nella pratica. Di conseguenza, viene introdotto l’approccio MPC basato su Lyapunov (Lyapunov-based MPC) per gli azionamenti, il quale fornisce garanzie sulla stabilità indipendentemente dall’orizzonte di predizione. Un vincolo di stabilità basato sulle funzioni di controllo di Lyapunov (control Lyapunov function, CLF) assicura la convergenza all’origine ed è stato provato che il problema ottimale di controllo risultante è sempre risolvibile. In altre parole, ad ogni istante di campionamento si può trovare un ingresso che soddisfi tutti i vincoli del sistema e renda stabile il sistema a circuito chiuso. Le proprietà di CCS-MPC vengono ottenute utilizzando un controllo non lineare ed è dimostrato che il sistema vincolato ad anello chiuso è stabile secondo Lyapunov. Le proprietà di stabilità di FCS-MPC sono più complesse a causa dell’insieme non continuo d’ingressi. Utilizzando metodi della teoria degli insiemi si dimostra che un errore di controllo sufficientemente ampio può essere diretto verso l’origine e tenuto in un dintorno dell’origine ben definito. MPC richiede che in ogni istante di campionamento si risolva un problema di ottimizzazione (constrained finite time optimal control, CFTOC). La limitata potenza di calcolo dei microcontrollori e la brevità dei periodi di campionamento richiedono un CFTOC relativamente semplice, che si può ottenere utilizzando un modello di flusso virtuale nel sistema statico di riferimento. Scegliendo piccoli orizzonti di predizione si limita la dimensione del CFTOC, la cui risoluzione necessità di algoritmi efficienti, che permettano di ottenere un risultato all’interno di un periodo di campionamento. Il CFTOC di CCS-MPC è un programma (convesso) lineare o quadratico (linear program, lp; quadratic program, qp) che può essere risolto tramite algoritmi efficienti e noti. Al fine di elaborare una strategia di tipo minimalista, viene introdotto un algoritmo efficiente che risolve analiticamente il problema con un orizzonte di predizione di un passo. Il CFTOC di FCS-MPC è un problema di programmazione lineare o quadratico a numeri misti interi (mixed-integer) ed è quindi più difficile da risolvere con metodi numerici standard. In pratica si calcolano tutte le soluzioni possibili, tra le quali viene scelta la soluzione ottimale. Per migliorare l’efficienza di calcolo si combina quest’approccio con tecniche branch-and-bound e branch-and-cut. Gli algoritmi di controllo sono stati sviluppati su una piattaforma software-in-the-loop (SiL) basata su Matlab/Simulink e il codice di programmazione è stato implementato su un banco di prova sperimentale, senza modifiche. La valutazione approva la progettazione e la realizzazione di CCS-MPC e FCS-MPC e indica buoni risultati sia nell’operazione dinamica che in quella stazionaria. I due approcci MPC hanno proprietà diverse che risultano vantaggiose per applicazioni differenti. CCS-MPC ha una frequenza di commutazione costante ed è un’alternativa promettente al controllo vettoriale proporzionale-integrale (PI). Il concetto può essere combinato con diversi schemi di modulazione, nella fattispecie si usa la modulazione simmetrica di vettori spaziali (symmetric space vector modulation, SSVM) e la modulazione discontinua di vettori spaziali (discontinuous space vector modulation, DSVM). FCS-MPC tiene conto della commutazione dell’inverter e raggiunge all’incirca un ripple di commutazione costante, ma ottiene una frequenza di commutazione variabile. Il concetto è vantaggioso per sistemi dove è richiesta un frequenza di campionamento alta rispetto alla frequenza di commutazione, per esempio azionamenti ad alta potenza o servoazionamenti. Inoltre, lo spettro della corrente di FCS-MPC non contiene armoniche PWM e di conseguenza è vantaggioso in termini di rumore acustico, data la mancanza di toni distinti. Tuttavia, le armoniche PWM distinte di CCS-MPC sono più semplici da filtrare. Si può concludere affermando che lo studio del problema dei controlli avanzati di coppia per azionamenti con un motore sincrono a magneti permanenti, ha portato all’individuazione di una strategia innovativa. L’introduzione di una nuova struttura di controllo ha semplificato notevolmente il problema di controllo predittivo, con particolare attenzione al concetto di stabilità. Inoltre, le implementazioni di tale struttura si sono rivelate particolarmente efficaci su piano computazionale.

This dissertation presents a methodology for the near optimal design of fixture layouts in multi-station assembly processes. An optimal fixture layout improves the robustness of a fixture system, reduces product variability and leads to manufacturing cost reduction. Three key aspects of the multi-station fixture layout design are addressed: a multi-station variation propagation model, a quantitative measure of fixture design, and an effective and efficient optimization algorithm. Multi-station design may have high dimensions of design space, which can contain a lot of local optima. In this dissertation, I investigated two algorithms for optimal fixture layout designs. The first algorithm is an exchange algorithm, which was originally developed in the research of optimal experimental designs. I revised the exchange routine so that it can remarkably reduce the computing time without sacrificing the optimal values. The second algorithm uses data-mining methods such as clustering and classification. It appears that the data-mining method can find valuable design selection rules that can in turn help to locate the optimal design efficiently. Compared with other non-linear optimization algorithms such as the simplex search method, simulated annealing, genetic algorithm, the data-mining method performs the best and the revised exchange algorithm performs comparably to simulated annealing, but better than the others. A four-station assembly process for a sport utility vehicle (SUV) side frame is used throughout the dissertation to illustrate the relevant concepts and the resulting methodology.

Design optimality plays a central role in the area of statistical experimental design. In gen- eral, problems in design optimality are composed of two vital, but separable, components. One of these is determining conditions under which a design is optimal (such as criterion bounds, values of design parameters, or special structure in the information matrix). The other is construction of designs satisfying those conditions. Most papers deal with either optimality conditions, or design construction in accordance with desired combinatorial prop- erties, but not both. This dissertation determines optimal designs for three treatments in the one-way and multi-way heterogeneity settings, first proving optimality through a series of bounding arguments, then applying combinatorial techniques for their construction. Among the results established are optimality with respect to the well known E and A criteria. A- and E-optimal block designs and row-column designs with three treatments are found, for any parameter set. E-optimal hyperrectangles with three treatments are also found, for any parameter set. Systems of distinct representatives theory is used for the construction of optimal designs. Efficiencies relative to optimal criterion values are used to determine robustness of block designs against loss of a small number of blocks. Nonisomorphic bal- anced incomplete block designs are ranked based on their robustness. A complete list of most robust BIBDs for vâ ¤10, râ ¤15 is compiled.
Ph. D.

Beam-based Compliant Mechanisms (CMs) are increasingly studied and implemented in precision engineering due to their advantages over the classic rigid-body mechanisms, such as scalability and reduced need for maintenance. Straight beams with uniform cross section are the basic modules in several concepts, and can be analyzed with a large variety of techniques, such as Euler-Bernoulli beam theory, Pseudo-Rigid Body (PRB) method, chain algorithms (e.g.~the Chained Beam-Constraint Model, CBCM) and Finite Element Analysis (FEA). This variety is unquestionably reduced for problems involving special geometries, such as curved or spline beams, variable section beams, nontrivial shapes and, eventually, contacts between bodies. 3D FEA (solid elements) can provide excellent results but the solutions require high computational times. This work compares the characteristics of modern and computationally efficient modeling techniques (1D FEA, PRB method and CBCM), focusing on their applicability in nonstandard problems. In parallel, as an attempt to provide an easy-to-use environment for CM analysis and design, a multi-purpose tool comprising Matlab and modern Computer-Aided Design/Engineering (CAD/CAE) packages is presented. The framework can implement different solvers depending on the adopted behavioral models. Summary tables are reported to guide the designers in the selection of the most appropriate technique and software architecture. The second part of this work reports demonstrative case studies involving either complex shapes of the flexible members or contacts between the members. To improve the clarity, each example has been accurately defined so as to present a specific set of features, which leads in the choice of a technique rather than others. When available, theoretical models are provided for supporting the design studies, which are solved using optimization approaches. Software implementations are discussed throughout the thesis. Starting from previous works found in the literature, this research introduces novel concepts in the fields of constant force CMs and statically balanced CMs. Finally, it provides a first formulation for modeling mutual contacts with the CBCM. For validation purposes, the majority of the computed behaviors are compared with experimental data, obtained from purposely designed test rigs.

Il mercato dei materiali compositi è in rapida crescita, soprattutto a causa dell'interesse del settore automobilistico nell'utilizzo di materiali leggeri, come le fibre di carbonio, per aumentare il consumo di carburante delle auto ed aumentarne l’autonomia. Uno dei processi di produzione più promettenti è il CRTM in quanto consente di ottenere componenti ad alte prestazioni limitando i costi di investimento. Infatti, il processo richiede una bassa pressione per l'iniezione della resina liquida attraverso le fibre grazie a un gap presente sopra la preforma in fibra di carbonio che consente alla resina di raggiungere facilmente ogni parte dello stampo. Un altro aspetto degno di attenzione è la possibilità di utilizzare nanocariche disperse nella matrice per migliorare le proprietà dei laminati finiti. Queste proprietà comprendono il comportamento meccanico, termico, elettrico e di smorzamento. Metodi per la progettazione di stampi e attrezzature per il CRTM non sono presenti in letteratura. Anche la dispersione di nanocariche nella matrice utilizzata per il CRTM non è stata completamente affrontata nello stato dell'arte e sono ancora presenti alcune incertezze sulla processabilità e sulle proprietà di queste matrici nano-additivate. Gli obiettivi di ricerca potrebbero essere sintetizzati come lo sviluppo di metodi e strumenti per la progettazione di stampi e attrezzature ausiliarie per il CRTM se si utilizzano matrici nanocaricate. Inoltre, è stata analizzata la correlazione tra i parametri di processo e le prestazioni dei prodotti. Questo lavoro di ricerca rappresenterebbe un passo verso l'adozione del processo CRTM su scala industriale per la produzione di componenti CFRP ad alte prestazioni in modo economicamente vantaggioso. I metodi e gli strumenti proposti possono rappresentare il modo per aumentare l'adozione del processo CRTM basato su matrici nano-additivate nel mercato automobilistico. Al fine di verificare la fattibilità e l'affidabilità di tali strumenti sono stati condotti diversi casi di studio per convalidare i metodi di progettazione scelti. I sistemi sviluppati sono stati progettati tenendo conto dei tre vincoli fondamentali dell'ingegneria di processo: tempi di produzione, costi di produzione e prestazioni dei prodotti.
The market of composite materials is rapidly growing, especially due to the interest of the automotive sector in using lightweight materials, such as carbon fibres, to increase the fuel efficiency of the cars. One of the most promising manufacturing processes is the CRTM as it allows to obtain highperformance components containing investment costs. Indeed, the process requires low pressure for the injection of the liquid resin through the fiber thanks to a gap present over the carbon fiber preform that allows the resin to easily reach every part of the mold. Another aspect worth of attention is the possibility of using nanofillers in addition to the matrix in order to improve the properties of the finished laminates. These properties encompass the mechanical, the thermal, the electrical and the damping behaviour. The use of these nanofillers dispersed in the matrix is possible thanks to the low pressure involved in this process. Methods for the design of molds and ancillary equipment for this process are not present in the literature. Also the presence of nanofillers in the matrix used for the CRTM has not been fully addressed in the state of the art and some uncertainties about the processability and the properties of these nano-additivated matrices are still present. The research goals could be synthesized as the development of methods and tools for the design of molds and ancillary equipment for the CRTM if nanoadditivated matrices are used. Moreover, the correlation between process parameters and performances of the products has been analysed. This research work would represent a step towards the adoption of the CRTM process on an industrial scale for producing high performance CFRP components in a cost/time-effective way. The proposed methods and tools can represent the way to increase the adoption of CRTM process based on nano-additivated matrices in the automotive market. In order to verify the feasibility and the reliability of such tools, different case studies have been conducted with the aim of validate the chosen design methods. The developed systems have been designed taking into account the three fundamental constraints of the process engineering: manufacturing time, manufacturing costs and performances of the products.

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O presente trabalho propõe uma nova metodologia de Geração de Sinal Sub-Ótimo de Excitação e Estimação Ótima de Parâmetros de sistemas não lineares. É proposto que a avaliação de cada sinal deva considerar, entre outros fatores, a diferença entre os parâmetros reais da planta e os obtidos pela estimação. Entretanto esta métrica não é trivial de ser obtida uma vez que os valores reais são desconhecidos. Para tanto é adotada a hipótese de que, se um sistema real puder ser razoavelmente aproximado por uma caixa branca, é possível utilizar este modelo como referência para indicar o impacto de um sinal sobre a estimação paramétrica. Desta forma, é utilizada uma metodologia de otimização dividida em dois níveis: (i) Nível Interno; para um dado sinal de excitação um método de otimização não linear busca o conjunto ótimo de parâmetros que minimiza o erro entre os sinais de saída do modelos original e do de referência. (ii) No nível externo um método de otimização baseado em meta-heurística é responsável por encontrar o melhor sinal de excitação com base na função custo composta de uma soma ponderada de métricas que consideram o erro entre os sinais de saída do modelo otimizado e do de referência, a diferença quadrática entre seus parâmetros, e o custo em relação ao tempo e espaço necessários para executar o experimento. Portanto, a aplicação da metodologia proposta vem suprir a necessidade de estimar sistemas não lineares apropriadamente, encontrando um conjunto de parâmetros capaz de generalizar o comportamento do sistema real, através de um sinal de excitação que cumpra requisitos práticos do processo. A eficácia da metodologia proposta é analisada em detalhes através de resultados obtidos utilizando sistemas de fluídos, sistemas caóticos e de robótica móvel, tanto sobre rodas quanto subaquática.
The present work proposes a novel methodology for Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation of nonlinear systems. It is proposed that the evaluation of each signal must to take into account, among other factors, the difference between real system parameters and the obtained by estimation. However, this metric is not trivially obtained once the real parameters values are unknown. To do so it is adopted the hypothesis that, if the system can be fairly approximate by a white box model, it is possible to use this model as a benchmark to indicate the impact of a signal on a parametric estimation. In this way, the method uses an optimization methodology divided into two levels: (i) Inner Level; For a given excitation signal a nonlinear optimization method searches for the optimal set of parameters that minimizes the error between the output signals of the original and the benchmark models. (ii) At the outer level, an optimization method based on metaheuristics is responsible for finding the best excitation signal, based on the cost function composed of a weighted sum of metrics, that considers the error between the output signals of the optimized model and the benchmark, the quadratic difference between its parameters, and the cost in relation to the time and space required to execute the experiment. Thus, the application of the proposed methodology comes to supply the need to estimate nonlinear systems appropriately, finding a set of parameters capable of generalizing the behavior of the real system, through an excitation signal that fulfills practical requirements of the process. The proposed methodology is analyzed in detail through results obtained using fluid systems, chaotic systems and mobile robotics, both wheeled and underwater.

Time-resolved fluorescence measurements enable the study of structure of molecular systems and dynamical processes inside them. This is possible because of a very high sensitivity of fluorescence lifetime to the physical and chemical properties of micro-environment in which fluorophores are situated. However, proper detection of the fluorescence lifetime is a challenging task, due to the fact that the fluorescence decay time of commonly used fluorophores lies in a nanosecond range. This puts strict requirements on the parameters of the fluorescence detectors. The features of single-photon avalanche diodes (SPAD) make these optical detectors a good alternative to conventional photomultiplier tubes and micro-channel plates. CMOS technology allows cointegration of a SPAD and electronic circuits on the same substrate and provides advantages in time resolution and noise characteristics. Monolithic integration of signal processing circuits and detectors on the same chip allows using such detectors without additional external hardware. New SPAD sensors with improved characteristics are produced every year. However, the designers consider various performance metrics while the importance of each particular detector characteristic depends on its application. Therefore, the validation and optimization of SPAD characteristics should be performed in a close connection with the analysis of a specific system, wherein this detector will be used. This work was aimed at developing of a model able to describe a typical fluorescence experiment with SPAD-based detector. The model simulates all essential parts of the fluorescence experiment starting from the light emission, through photo-physical processes occurring inside a bio-sample, to a detector itself and read-out electronics. The ability of the developed model to simulate various light sources (laser and micro-LED), fluorescence measurement techniques (time-correlated single photon counting and time-gating) was verified. The simulated results were in good agreement with the experimental data and the model proved its flexibility. Furthermore, the model provided the explanation of the distortions in experimental fluorescent curves measured under a very high ambient light when pile-up effects appear. Finally, a set of virtual experiments were established to investigate the influence of noisy pixels in SPAD array on a lifetime estimation and to study the feasibility of time-filtering instead of conventional optical filtering. Simulation results are in good agreement with data available in literature.

Power Generation Systems (PGSs) based on Hybrid Renewable Energy (HRE) are one of the promising solutions for future distributed generation systems. Among different configurations, Hybrid Photovoltaic - Wind turbine (PV-WT) grid connected PGSs are the most adopted for their good performance. However, due to the complexity of the system caused by wind power variability and solar radiation intermittency, the optimal balance between these two energy sources requires particular attention to achieve a good engineering solution. This thesis deals with the optimal sharing and sizing of PV-WT by adopting different Multi Criteria Decision Making (MCDM) optimization approaches. Different approaches have been developed using Multi attribute decision Making (MADM) and Multi Objective Decision Making (MODM). Moreover, sensitivity and uncertainty of MCDM algorithms have been analyzed, by considering different weighting criteria techniques with different fluctuation scenarios of wind speed and solar radiation profiles, and by considering stochastic analysis to solar radiation, wind speed, and load demand input data , thus highlighting advantages and drawbacks of the proposed optimal sizing approaches. The developed approaches could be assumed as a powerful roadmap for decision makers, analysts, and policy makers.

The latest labour market reforms in Italy have brought the issue of strengthening public employment services (PES) and active labour market policies (ALMPs). With the decree 150/2015, a new policy tool has been introduced for activation purposes: the “reintegration voucher” (assegno di ricollocazione - AdR). It is interesting to consider the nature of this tool, as implementation of a quasi-market model in Italian PES. Labour market policies in Italy have already undergone deep reform process between the second half of the Nineties and the early Two-Thousands. During this phase, there was a combination between marketization and decentralization reforms. Italian regions received policy competence for ALMPs and the responsibility for outsourcing employment services to private providers. These started to follow different logics of contracting-out, thus creating the conditions for a high level of territorial differentiation. Contracting-out of services, however, requires governance mechanisms that can mitigate the risks of opportunistic behaviour of private operators, who can tend to place only less disadvantaged people on the labour market (creaming) or avoid higher efforts to go faster toward remuneration (parking). These effects lead to sub-optimal results in terms of the equitability of the performance. In these terms, an “optimal design” could be approximated as the one able to take into account both economic (efficiency and effectiveness of the performance) and social goals (equity of the performance, avoiding opportunistic behaviour of private providers involved). This analysis is realized by means of a comparison between two regions considered as the two most dissimilar cases in the context of PES Italian regional differentiation: Lombardy and Emilia-Romagna. These two cases can be placed at the extremes of a hypothetical continuum defined on the basis of the degree of market exposure of PES regional models. Lombardy in particular has caught the attention showing a quasi-market model very similar to that of the AdR, giving the possibility to test the mechanisms of the new national scheme, not yet fully implemented, using a local experience already well established. In this way it will be possible to know what the consequences of a greater market exposure of Italian regional PES could be, considering both the impact in terms of effectiveness and equitability of the outcomes. The two cases are comparable not only in terms of capacity building and level of economic development, but especially regarding their political and institutional contexts, being characterized by a symmetrical and divergent trajectory of formation of their models. This has been the result of a layering process favoured in both the cases by a similar strength of different actors’ coalitions. The research then will go for an in-depth analysis of market-based governance in regional contexts, relying on the methodology of policy evaluation, much used for studies in this field.

Optimization problems (to which is dedicated this dissertation) of structural mechanics are introductory stage of structure optimum design based on principles of solid deformable body mechanics, mathematical programming theory, its methods and their mechanical interpretation. In order to base calculation on real operating conditions of structure, it is necessary evaluate as exact as possible structure material properties, external effects and other factors in mathematical models of optimization problems. Partially it is achieved by including plastic properties of material. Calculation and design of the structures, taking in to account plastic strains, allows to use their bearing capacity more efficiently and make more economic project (in this dissertation research is developed on the basis of perfect plasticity theory). From the other side, real effect for structure are often cyclic (variable repeated load character is also evaluated in this work). In the dissertation it is assumed that load is quasi–static and is characterised by load variation bounds (deterministic formulation of problems is considered). Under repeated loading a structure can lose its serviceability because of its progressive plastic failure or because of alternating strain. But, if residual forces together with variable part that do not violate the admissible bounds appear in the initial stage of loading, the structure adapts to existing load and further behaves elastically. This phenomenon is... [to full text]

Etanol é um dos combustíveis renováveis mais importantes e contribui com a redução dos impactos negativos causados pela utilização de combustíveis fósseis por todo o mundo. É obtido principalmente pela fermentação dos açúcares provenientes da cana-de-açúcar e do milho. O produto da fermentação possui aproximadamente 96,5% molar de água, e um dos desafios é a obtenção econômica de um produto com pureza acima dos 99% molar em etanol para a utilização no setor de transporte. O presente trabalho tem por objetivo a otimização do processo de destilação extrativa do etanol utilizando glicerol como agente extrator. Esse solvente é um subproduto no processo de produção do diesel renovável, e estudou-se sua viabilidade como substituto do solvente derivado de fontes naturais não-renováveis, etileno glicol. Vinte e duas diferentes configurações de colunas de destilação simples e complexas foram avaliadas nesta investigação. O recente modelo de coeficientes de atividade F-SAC foi ajustado para a melhor representação de dados de equilíbrio líquido-vapor e de coeficiente de atividade em diluição infinita coletados na literatura. A predição do modelo F-SAC foi superior comparando-se a outros modelos de atividade. A média na diferença absoluta, quando comparado ao modelo NRTL chegou a valores aproximadamente 47% menores. O modelo do processo foi construído em um simulador baseado em equações, onde balanços de massa e de energia são resolvidas simultaneamente, buscando possíveis alterações para a redução do consumo energético e aumento na produtividade. A influência dos principais parâmetros do processo foi avaliada via simulações e descobriu-se que uma configuração e operação ótimas do sistema por destilação extrativa podem gerar significativa redução no consumo energético do processo. A economia em termos energéticos pode atingir valores de até 10% quando comparados com a melhor configuração disponível na literatura.
Ethanol is one of the most important renewable fuels and contributes to reducing the negative impacts caused by the use of fossil fuels worldwide. It is mainly obtained by the fermentation of sugars from sugar cane and corn. The fermentation broth has approximately 96.5% of water molar, and an economic challenge is to obtain a product with purity above 99% of ethanol molar to use in the transportation sector. The present work aims at optimizing the process of extractive distillation of ethanol using glycerol as extracting agent. This solvent is a byproduct in the renewable diesel production and was then studied as an alternative for ethylene glycol, the curently used non-renewable solvent. Twenty-two different configurations of simple and complex column sequences were evaluated in this investigation. The recent F-SAC activity coefficient model was adjusted to the best representation of vapor-liquid equilibrium and infinite dilution activity coefficient data from the literature. The prediction of the F-SAC model was superior when compared with other activity coefficient models. The average absolute difference was up to 47% smaller when compared with the NRTL model. The process model was built on an equation-based simulator, where mass and energy balances are solved simultaneously, looking for possible changes to reduce the energy demands and raise the production. The influence of the main process parameters was evaluated via simulations and we have found that an optimal operation of the system by extractive distillation with glycerol can lead to significant reduction in the energy consumption of the process. The energy savings could reach values up to 10% when compared with the best configuration available in the literature using ethylene glycol as entrainer.

Darbo tikslas – tampriųjų-plastinių strypų konstrukcijų (santvaros, rėmų), veikiamų kartotinės kintamosios apkrovos, prisitaikomumo proceso ir būvio įtempių ir deformacijų analizė optimalaus konstrukcijų projektavimo kontekste. Darbo aktualumas grindžiamas prisitaikančių konstrukcijų optimizavimo uždaviniuose figūruojančių standumo sąlygų-apribojimų kokybės gerinimo būtinumu. Prisitaikančių konstrukcijų deformacijų būvis priklauso nuo apkrovimo istorijos, o poslinkių ribojimui taikoma nepakankamai tiksli Koiterio sąlyga arba liekamųjų poslinkių influentinė matrica, nepagrįstai laikant, kad plastinio deformavimo procesas yra išimtinai holonominis. Anotuojamame darbe apkrovimo istoriją siūloma įvertinti, atliekant papildomą inkrementinę deformacijų būvio analizę. Tyrimai atlikti taikant idealiai tamprių plastinių santvarų ir rėmų techniškosios skaičiavimo teorijos prielaidas (maži poslinkiai ir deformacijos). Taikomi ekstreminiai energiniai mechanikos principai, matematinio programavimo teorija ir metodai. Inkrementinės analizės matematiniai modeliai sudaryti, besikeičiančias plastines deformacijas tapatinant su distorsijomis. Taip nustatomos konkrečios apkrovimo istorijos liekamųjų poslinkių kitimo maksimalios ir minimalios reikšmės. Gautieji rezultatai panaudoti optimizavimo uždavinių sprendiniams tikslinti ir, esant būtinumui, leidžiantys keisti pradines pagrindinio optimizavimo uždavinio sąlygas. Pateikti išsamūs skaitinių eksperimentų rezultatai.
The purpose of this work is analysis of stress-deformation state of perfectly elastic-plastic shakedown structures (truss, frames) subjected to repeated variable load in the context of optimal design. Relevance of this work is based on a need of improvement of accurateness of stiffness constrains in optimization problems of structures. Stress-deformation state of shakedown structures depends on its loading history, while for the restriction of displacements inaccurate Koiter’s condition or an influence matrix of residual displacements, on the wrong supposition that the process of plastic deformation is exclusively holonomic, is used. In this work is proposed to evaluate loading history by performing an additional incremental analysis of stress-deformation state. This research was performed invoking the assumptions of technical computing theory of perfectly elastic-plastic trusses and frames (small deformations and displacements). Mechanics extremum energy principles, mathematical programming theory and methods are applied. Mathematical models of incremental analysis are composed by indentifying volatile plastic deformations with distortions. Thus particular maximum and minimum values of residual displacements are found. Obtained results are used to verify optimal design problems solutions and change the restrictions of main optimimization problem if necessary. Comprehensive results of numerical experiments presented.

碩士
國立臺灣海洋大學
輪機工程系
92
Modern control systems are becoming more and more complex, so that fault diagnosis systems are getting more and more important. In all approaches of fault diagnosis systems, the model-based fault diagnosis systems are accepted and used popularly for its cost efficiency and reliability. Because of the appearances of disturbances and modeling error in the system, they will affect the normal operation of fault diagnosis system so that the robust residual generation should be used to eliminate the influences of the unknown inputs and let the faults be detected exactly. However, the robust FDI design required that the disturbance distribution matrix E should be known. Patton&Chen provide one design procedure for the estimation of the matrix E, but this approach can only be used in the system with the output matrix C is full-rank. This restriction obstructs the use and development of the estimation technique. In this thesis, we provide a new design procedure to overcome this problem. The simulation results demonstrate that the developed approach is practicable and effective. Keywords： fault diagnosis system、model-based fault diagnosis、robust residual generation、disturbance distribution matrix E、unknown input

碩士
國立中正大學
化學工程研究所
104
Currently, there are more than two hundred thousand kinds of known plant natural products, some of which have pharmacological activity or important biological properties. This study focused on two plant natural products: 2S-naringenin and p-coumaryl alcohol. 2S-naringenin belongs to flavonoids and it has anti-inflammatory, anti-bacterial and anti-cancer effect; p-coumaryl alcohol is one of precursors of lignin and it is also used in the industrial synthesis applications. The methods of microbial production are becoming more important. Microbial metabolic engineering means by modifying metabolic pathways to make microorganisms demonstrate desired characteristics. Two cases were built, the case 1 used iAF1260 model of E. coli, then added the flavonoid metabolic pathway about 2S-naringenin and related genes (TAL, 4CL, CHS, CHI) ; the case 2 also used iAF1260 model of E. coli, then added phenylpropanoid metabolic pathway about p-coumaryl alcohol and related genes (TAL, 4CL, CCR, CAD). Genes and other information from the previous literature were reconstructed in iAF1260 model. And then calculated flux balance by the analysis method (Flux balance analysis, FBA) and used Nested Hybrid Differential Evolution(NHDE) and Flux envelope. The result of the first case, 2S-naringenin produced need oxygen flux of 20 mmol gDW-1h-1 and when the regulation of gene TAL was 0.6, to obtain the maximum yield; the second case, p-coumaryl alcohol produced need oxygen flux of 15 mmol gDW-1h-1 and when the regulation of gene TAL was 0.6, to obtain the maximum yield.

Game theory and mechanism design have emerged as an important tool to model, analyze,and solve decentralized design problems involving multiple agents that interact strategically in a rational and intelligent way. Some examples of these design problems include: auctions and markets in electronic commerce; network economics; dynamic pricing; routing protocols in wireless networks; resource allocation in computational grids; algorithms for selfish agents;etc. The motivation for this doctoral work springs from the high level of current interest indesigning innovative mechanisms for solving emerging game theoretic problems in the area of electronic commerce. In this thesis, we focus on three such problems and advance the current art in mechanism design while developing new, innovative mechanisms to solve the problems. The first problem we explore is the highly strategic problem of forming a high value E-business supply chain by choosing the best mix of supply chain partners. In our research, we formulate the supply chain formation problem as a mechanism design problem in a generic wayand show that the well known VCG (Vickrey-Clarke-Groves) mechanisms provide an apt frame-work for solving this problem. We provide a compelling example of a three stage automotive distribution network to illustrate the power and e±cacy of the proposed methodology. The second problem we model and solve is that of designing a revenue maximizing sponsored search auction. This is a problem that is faced by every Internet search engine, such as Google,MSN, and Yahoo!, whenever it receives a search query. In our research, we take a comprehensivelook at existing auction mechanisms for this problem. Our work leads to an innovative new auction mechanism, which we call OPT (optimal mechanism), that exhibits a superior level ofperformance. The proposed mechanism extends, in a non-trivial way, the well known Myersonoptimal auction to the specific setting of sponsored search auctions. The proposed mechanism maximizes the revenue to the search engine and also satisfies two crucial properties, Bayesian incentive compatibility and interim individual rationality. The third contribution is in respect of Stackelberg problems, which are game theoretic problems that involve hierarchical and sequential decision making. By focusing attention on an important subclass of these problems, namely the Single-Leader-Rest-Followers (SLRF) problems, we extend all relevant aspects of classical mechanism design theory to the case of SLRF problems. We derive many important results in respect of procurement auctions with reserve prices using the developed theory. The research carried out as part of this doctoral work, we believe, advances the current art in mechanism design while developing innovative mechanisms to solve those problems.

Game theory and mechanism design have emerged as an important tool to model, analyze,and solve decentralized design problems involving multiple agents that interact strategically in a rational and intelligent way. Some examples of these design problems include: auctions and markets in electronic commerce; network economics; dynamic pricing; routing protocols in wireless networks; resource allocation in computational grids; algorithms for selfish agents;etc. The motivation for this doctoral work springs from the high level of current interest indesigning innovative mechanisms for solving emerging game theoretic problems in the area of electronic commerce. In this thesis, we focus on three such problems and advance the current art in mechanism design while developing new, innovative mechanisms to solve the problems. The first problem we explore is the highly strategic problem of forming a high value E-business supply chain by choosing the best mix of supply chain partners. In our research, we formulate the supply chain formation problem as a mechanism design problem in a generic wayand show that the well known VCG (Vickrey-Clarke-Groves) mechanisms provide an apt frame-work for solving this problem. We provide a compelling example of a three stage automotive distribution network to illustrate the power and e±cacy of the proposed methodology. The second problem we model and solve is that of designing a revenue maximizing sponsored search auction. This is a problem that is faced by every Internet search engine, such as Google,MSN, and Yahoo!, whenever it receives a search query. In our research, we take a comprehensivelook at existing auction mechanisms for this problem. Our work leads to an innovative new auction mechanism, which we call OPT (optimal mechanism), that exhibits a superior level ofperformance. The proposed mechanism extends, in a non-trivial way, the well known Myersonoptimal auction to the specific setting of sponsored search auctions. The proposed mechanism maximizes the revenue to the search engine and also satisfies two crucial properties, Bayesian incentive compatibility and interim individual rationality. The third contribution is in respect of Stackelberg problems, which are game theoretic problems that involve hierarchical and sequential decision making. By focusing attention on an important subclass of these problems, namely the Single-Leader-Rest-Followers (SLRF) problems, we extend all relevant aspects of classical mechanism design theory to the case of SLRF problems. We derive many important results in respect of procurement auctions with reserve prices using the developed theory. The research carried out as part of this doctoral work, we believe, advances the current art in mechanism design while developing innovative mechanisms to solve those problems.

碩士
國立中山大學
應用數學研究所
82
In a recent paper Pukelsheim and Studden (1993) determined the E-optimal designs for polynomial regression with constant term model on the interval [-1,1]. In this thesis we will use their result, the inclusion principle and induction to determine the E-optimal designs for the model f_{\cal P}(x) (see (1.1)) on the interval [-1,1]. Moreover, for the polynomial regression without intercept when degree is odd, we have more precisely result. These derivations are based on the interplay between E- optimality and scalar optimality. The scalar parameter systems are obtained as transformations of the part of coefficient vector t of the Chebyshev polynomial. Moreover, we use the method of numerical analysis to solve the E-optimal designs for even degree polynomial regression without intercept model on the interval [-1,1]. We also consider the threshold of b values for polynomial regression with constant term model and the polynomial regression without intercept model.

Optimal design of LCL filter for grid connected inverter system is studied. For that, initially normal design is considered. Higher order LCL filters are essential in meeting the interconnection standard requirement for grid-connected voltage source converters. The IEEE 1547-2008 specifications for high-frequency current ripple are used as a major constraint early in the design to ensure that all subsequent optimizations are still compliant with the standards. The LCL filter is designed accordingly and optimal inductance and capacitance values are obtained. Novel small signal model of a three phase grid connected VSI has been derived and its relevant transfer functions have been deduced from it so as to analyze the system for designing a controller and also bode plots have been plotted. Stability Analysis of Grid-Connected Inverters with an LCL Filter Considering Grid Impedance and comparative study between unipolar and bi-polar switching scheme for grid-connected inverter system is also done. Simulation is done in MATLAB SIMULINK environment for feasibility of the study.

Simulated moving bed (SMB) chromatography is attracting more and more attention since it is a powerful technique for complex separation tasks. Nowadays, more than 60% of preparative SMB units are installed in the pharmaceutical and in the food in- dustry [SDI, Preparative and Process Liquid Chromatography: The Future of Process Separations, International Strategic Directions, Los Angeles, USA, 2002. http://www. strategicdirections.com]. Chromatography is the method of choice in these ¯elds, be- cause often pharmaceuticals and ¯ne-chemicals have physico-chemical properties which di®er little from those of the by-products, and they may be thermally instable. In these cases, standard separation techniques as distillation and extraction are not applicable. The noteworthiness of preparative chromatography, particulary SMB process, as a sep- aration and puri¯cation process in the above mentioned industries has been increasing, due to its °exibility, energy e±ciency and higher product purity performance. Consequently, a new SMB paradigm is requested by the large number of potential small- scale applications of the SMB technology, which exploits the °exibility and versatility of the technology. In this new SMB paradigm, a number of possibilities for improving SMB performance through variation of parameters during a switching interval, are pushing the trend toward the use of units with smaller number of columns because less stationary phase is used and the setup is more economical. This is especially important for the phar- maceutical industry, where SMBs are seen as multipurpose units that can be applied to di®erent separations in all stages of the drug-development cycle. In order to reduce the experimental e®ort and accordingly the coast associated with the development of separation processes, simulation models are intensively used. One impor- tant aspect in this context refers to the determination of the adsorption isotherms in SMB chromatography, where separations are usually carried out under strongly nonlinear conditions in order to achieve higher productivities. The accurate determination of the competitive adsorption equilibrium of the enantiomeric species is thus of fundamental importance to allow computer-assisted optimization or process scale-up. Two major SMB operating problems are apparent at production scale: the assessment of product quality and the maintenance of long-term stable and controlled operation. Constraints regarding product purity, dictated by pharmaceutical and food regulatory organizations, have drastically increased the demand for product quality control. The strict imposed regulations are increasing the need for developing optically pure drugs.(...)

The present dissertation seeks to optimize the unit cell of a two-dimensional cellular material, pursuing the minimization of the peak equivalent stress in the microstructure. This class of materials is particularly relevant to the design of lightweight structures. By minimizing the peak stress in the microstructure, it is possible to use material in a more rational way. Given the periodic nature of the problem, asymptotic homogenization is employed to compute the stress distribution in the microstructure when a macroscopic load is applied, since periodicity boundary conditions are imposed. With this being a purely conceptual study, only three macroscopic loads are considered: the hydrostatic, biaxial, and pure shear ones. Initially, the single-material problem is solved through shape optimization. Then, the potential to reduce the peak equivalent stress through the introduction of additional material phases is explored. Also with shape optimization, the in uence of one additional material phase is studied. Additionally, topology optimization is used to discover the functionally graded material that minimizes the peak stress in the microstructure. The obtained results show that an increased design exibility always leads to milder stress states. The known theoretical results were successfully replicated, with minimal error measures associated. By increasing the number of material phases in the microstructure, peak stress reduction are attainable. A uniformly stressed microstructure is possible to obtain, by means of a functionally graded material.

Optimal design problems aim at selecting design points optimally with respect to certain statistical criteria. The research of this thesis focuses on optimal design problems with respect to A-, D- and E-optimal criteria, which minimize the trace, determinant and largest eigenvalue of the information matrix, respectively. Semide nite programming (SDP) is concerned with optimizing a linear objective function subject to a linear matrix being positive semide nite. Two powerful MATLAB add-ons, SeDuMi and CVX, have been developed to solve SDP problems e ciently. In this paper, we show in detail how to formulate A- and E-optimal design problems as SDP problems and solve them by SeDuMi and CVX. This technique can be used to construct approximate A-optimal and E-optimal designs for all linear and non-linear models with discrete design spaces. The results can also provide guidance to nd optimal designs on continuous design spaces. For one variable polynomial regression models, we solve the A- and E- optimal designs on the continuous design space by using a two-stage procedure. In the rst stage we nd the optimal moments by casting it as an SDP problem and in the second stage we extract the optimal designs from the optimal moments obtained from the rst stage. Unlike E- and A-optimal design problems, the objective function of D-optimal design problem is nonlinear. So D-optimal design problems cannot be reformulated as an SDP. However, it can be cast as a convex problem and solved by an interior point method. In this thesis we give details on how to use the interior point method to solve D-optimal design problems. Finally several numerical examples for A-, D-, and E-optimal designs along with the MATLAB codes are presented.
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