This thesis aims to address the real-time planning and nonlinear control of quadrupedal locomotion such that the resulting gaits are robust to various kinds of disturbances. Specifically, this work addresses two scenarios. Namely, a quasi-static formulation in which an inertial appendage (i.e., a tail) is used to assist the quadruped in negating external push disturbances, and an agile formulation which is derived in a manner such that an appendage could easily be added in future work to examine the affect of tails on agile and high-speed motions. Initially, this work presents a unified method in which bio-inspired articulated serpentine robotic tails may be integrated with walking robots, specifically quadrupeds, in order to produce stable and highly robust locomotion. The design and analysis of a holonomically constrained 2 degree of freedom (DOF) tail is shown and its accompanying nonlinear dynamic model is presented. The model created is used to develop a hierarchical control scheme which consists of a high-level path planner and a full-order nonlinear low-level controller. The high-level controller is based on model predictive control (MPC) and acts on a linear inverted pendulum (LIP) model which has been extended to include the forces produced by the tail by augmenting the LIP model with linearized tail dynamics. The MPC is used to generate center of mass (COM) and tail trajectories and is subject to the net ground reaction forces of the system, tail shape, and torque saturation of the tail in order to ensure overall feasibility of locomotion. At the lower level, a full-order nonlinear controller is implemented to track the generated trajectories using quadratic program (QP) based input-output (I-O) feedback linearization which acts on virtual constraints. The analytical results of the proposed approach are verified numerically through simulations using a full-order nonlinear model for the quadrupedal robot, Vision60, augmented with a tail, totaling at 20 DOF. The simulations include a variety of disturbances to show the robustness of the presented hierarchical control scheme. The aforementioned control scheme is then extended in the latter portion of this thesis to achieve more dynamic, agile, and robust locomotion. In particular, we examine the use of a single rigid body model as the template model for the real-time high-level MPC, which is linearized using variational based linearization (VBL) and is solved at 200 Hz as opposed to an event-based manner. The previously defined virtual constraints controller is also extended so as to include a control Lyapunov function (CLF) which contributes to both numerical stability of the QP and aids in stability of the output dynamics. This new hierarchical scheme is validated on the A1 robot, with a total of 18 DOF, through extensive simulations to display agility and robustness to ground height variations and external disturbances. The low-level controller is then further validated through a series of experiments displaying the ability for this algorithm to be readily transferred to hardware platforms. / Master of Science / This thesis aims to address the real-time planning and nonlinear control of four legged walking robots such that the resulting gaits are robust to various kinds of disturbances. Initially, this work presents a method in which a robotic tail can be integrated with legged robots to produce very stable walking patterns. A model is subsequently created to develop a multi-layer control scheme which consists of a high-level path planner, based on a reduced-order model and model predictive control techniques, that determines the trajectory for the quadruped and tail, followed by a low-level controller that considers the full-order dynamics of the robot and tail for robust tracking of the planned trajectory. The reduced-order model considered here enforces quasi-static motions which are slow but generally stable. This formulation is validated numerically through extensive full-order simulations of the Vision60 robot. This work then proceeds to develop an agile formulation using a similar multi-layer structure, but uses a reduced-order model which is more amenable to dynamic walking patterns. The low-level controller is also augmented slightly to provide additional robustness and theoretical guarantees. The latter control algorithm is extensively numerically validated in simulation using the A1 robot to show the large increase in robustness compared to the quasi-static formulation. Finally, this work presents experimental validation of the low-level controller formulated in the latter half of this work.

Control Designs for Low-Loss Active Magnetic Bearings: Theory and Implementation Brian C. D. Wilson 327 Pages Directed by Dr. Panagiotis Tsiotras and Dr. Bonnie Heck-Ferri Active Magnetic Bearings (AMB) have been proposed for use in Electromechanical Flywheel Batteries. In these devices, kinetic energy is stored in a magnetically levitated flywheel which spins in a vacuum. The AMB eliminates all mechanical losses, however, electrical loss, hich is proportional to the square of the magnetic flux, is still significant. For fficient operation, the flux bias, which is typically introduced into the electromagnets to improve the AMB stiffness, must be reduced, preferably to zero. This zero-bias (ZB) mode of operation cripples the classical control techniques which are customarily used and nonlinear control is required. As a compromise between AMB stiffness and efficiency, a new flux bias scheme is proposed called the generalized complementary flux condition(gcfc). A flux-bias dependent trade-off exists between AMB stiffness, power consumption, and power loss. This work theoretically develops and experimentally verifies new low-loss AMB control designs which employ the gcfc condition. Particular attention is paid to the removal of the singularity present in the standard nonlinear control techniques when operating in ZB. Experimental verification is conduced on a 6-DOF AMB reaction wheel. Practical aspects of the gcfc implementation such as flux measurement and flux-bias implementation with voltage mode amplifiers using IR compensation are investigated. Comparisons are made between the gcfc bias technique and the standard constant-flux-sum (cfs) bias method. Under typical operating circumstances, theoretical analysis and experimental data show that the new gcfc bias scheme is more efficient in producing the control flux required for rotor stabilization than the ordinary cfs bias strategy.

Thesis (MEng)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: The growth in intelligent control has primarily been a reaction to the realisation that nonlinear control theory has been unable to provide practical solutions to present day control challenges. Consequently the chemical industry may be cited for numerous instances of overdesign, which result as an attempt to avoiding operation near or within complex (often more economically viable) operating regimes. Within these complex operating regimes robust control system performance may prove difficult to achieve using conventional (algorithmic) control methodologies. Biological neuronal control mechanisms demonstrate a remarkable ability to make accurate generalisations from sparse environmental information. Neural networks, with their ability to learn and their inherent massive parallel processing ability, introduce numerous opportunities for developing superior control structures for complex nonlinear systems. To facilitate neural network learning, reinforcement learning techniques provide a framework which allows for learning from direct interactions with a dynamic environment. lts promise as a means of automating the knowledge acquisition process is beguiling, as it provides a means of developing control strategies from cause and effect (reward and punishment) interaction information, without needing to specify how the goal is to be achieved. This study aims to establish evolutionary reinforcement learning as a powerful tool for developing robust neurocontrollers for application in highly nonlinear process systems. A novel evolutionary algorithm; Symbiotic, Adaptive Neuro-Evolution (SANE), is utilised to facilitate neurocontroller development. This study also aims to introduce SANE as a means of integrating the process design and process control development functions, to obtain a single comprehensive calculation step for maximum economic benefit. This approach thus provides a tool with which to limit the occurrence of overdesign in the process industry. To investigate the feasibility of evolutionary reinforcement learning in achieving these aims, the SANE algorithm is implemented in an event-driven software environment (developed in Delphi 4.0), which may be applied for both simulation and real world control problems. Four highly nonlinear reactor arrangements are considered in simulation studies. As a real world application, a novel batch distillation pilot plant, a Multi-Effect Batch Distillation (MEBAD) column, was constructed and commissioned. The neurocontrollers developed using SANE in the complex simulation studies, were found to exhibit excellent robustness and generalisation capabilities. In comparison with model predictive control implementations, the neurocontrollers proved far less sensitive to model parameter uncertainties, removing the need for model mismatch compensation to eliminate steady state off-set. The SANE algorithm also proved highly effective in discovering the operating region of greatest economic return, while simultaneously developing a neurocontroller for this optimal operating point. SANE, however, demonstrated limited success in learning an effective control policy for the MEBAD pilot plant (poor generalisation), possibly due to limiting the algorithm's search to a too small region of the state space and the disruptive effects of sensor noise on the evaluation process. For industrial applications, starting the evolutionary process from a random initial genetic algorithm population may prove too costly in terms of time and financial considerations. Pretraining the genetic algorithm population on approximate simulation models of the real process, may result in an acceptable search duration for the optimal control policy. The application of this neurocontrol development approach from a plantwide perspective should also have significant benefits, as individual controller interactions are so doing implicitly eliminated. / AFRIKAANSE OPSOMMING: The huidige groei in intelligente beheerstelsels is primêr 'n reaksie op die besef dat nie-liniêre beheerstelsel teorie nie instaat is daartoe om praktiese oplossings te bied vir huidige beheer kwelkwessies nie. Gevolglik kan talle insidente van oorontwerp in die chemiese nywerhede aangevoer word, wat voortvloei uit 'n poging om bedryf in of naby komplekse bedryfsgebiede (dikwels meer ekonomies vatbaar) te vermy. Die ontwikkeling van robuuste beheerstelsels, met konvensionele (algoritmiese ) beheertegnieke, in die komplekse bedryfsgebiede mag problematies wees. Biologiese neurobeheer megamsmes vertoon 'n merkwaardige vermoë om te veralgemeen vanaf yl omgewingsdata. Neurale netwerke, met hulle vermoë om te leer en hulle inherente paralleie verwerkingsvermoë, bied talle geleenthede vir die ontwikkeling van meer doeltreffende beheerstelsels vir gebruik in komplekse nieliniêre sisteme. Versterkingsleer bied a raamwerk waarbinne 'n neurale netwerk leer deur direkte interaksie met 'n dinamiese omgewing. Versterkingsleer hou belofte in vir die inwin van kennis, deur die ontwikkeling van beheerstrategieë vanaf aksie en reaksie (loon en straf) interaksies - sonder om te spesifiseer hoe die taak voltooi moet word. Hierdie studie beaam om evolutionêre versterkingsleer as 'n kragtige strategie vir die ontwikkeling van robuuste neurobeheerders in nie-liniêre prosesomgewings, te vestig. 'n Nuwe evolutionêre algoritme; Simbiotiese, Aanpasbare, Neuro-Evolusie (SANE), word aangewend vir die onwikkeling van die neurobeheerders. Hierdie studie beoog ook die daarstelling van SANE as 'n weg om prosesontwerp en prosesbeheer ontwikkeling vir maksimale ekonomiese uitkering, te integreer. Hierdie benadering bied dus 'n strategie waardeur die insidente van oorontwerp beperk kan word. Om die haalbaarheid van hierdie doelwitte, deur die gebruik van evolusionêre versterkingsleer te ondersoek, is die SANE algoritme aangewend in 'n Windows omgewing (ontwikkel in Delphi 4.0). Die Delphi programmatuur geniet toepassing in beide die simulasie en werklike beheer probleme. Vier nie-liniêre reaktore ontwerpe is oorweeg in die simulasie studies. As 'n werklike beheer toepassing, is 'n nuwe enkelladingsdistillasie kolom, 'n Multi-Effek Enkelladingskolom (MEBAD) gebou en in bedryf gestel. Die neurobeheerders vir die komplekse simulasie studies, wat deur SANE ontwikkel is, het uitstekende robuustheid en veralgemeningsvermoë ten toon gestel. In vergelyking met model voorspellingsbeheer implementasies, is gevind dat die neurobeheerders heelwat minder sensitief is vir model parameter onsekerheid. Die noodsaak na modelonsekerheid kompensasie om gestadigde toestand afset te elimineer, word gevolglik verwyder. The SANE algoritme is ook hoogs effektief vir die soek na die mees ekonomies bedryfstoestand, terwyl 'n effektiewe neurobeheerder gelyktydig vir hierdie ekonomies optimumgebied ontwikkel word. SANE het egter beperkte sukses in die leer van 'n effektiewe beheerstrategie vanaf die MEBAD toetsaanleg getoon (swak veralgemening). Die swak veralgemening kan toegeskryf word aan 'n te klein bedryfsgebied waarin die algoritme moes soek en die negatiewe effek van sensor geraas op die evaluasie proses. Vir industriële applikasies blyk dit dat die uitvoer van die evolutionêre proses vanaf 'n wisselkeurige begintoestand nie koste effektief is in terme van tyd en finansies nie. Deur die genetiese algoritme populasie vooraf op 'n benaderde modelop te lei, kan die soek tydperk na 'n optimale beheerstrategie aansienlik verkort word. Die aanwending van die neurobeheer ontwikkelingstrategie vanuit 'n aanlegwye oogpunt mag aanleiding gee tot aansienlike voordele, aaangesien individuele beheerder interaksies sodoende implisiet uitgeskakel word.

GMAW (Gas Metal Arc Welding) is one of the most important arc welding processes being adopted in modern manufacturing industry due to its advantages in productivity, energy efficiency and automation. By monitoring and improving some of the important properties of GMAW such as production rate, metal transfer and base metal heat input, researchers could bring the process efficiency and stability to a new level. In recent years, some innovative modifications of GMAW such as Twins, Tandem and laser-MIG hybrid welding have been adopted into many industrial applications for better productivity. In this dissertation, a novel GMAW called DB-GMAW (Dual Bypass Gas Metal Arc Welding) using two GTAW torches and one GMAW torch to construct a welding system, is proposed and developed. In DB-GMAW, two GTAW torches perform the bypass system which decouples the total welding current into base metal current and bypass current after the melt down of filler wire. Compared to conventional GMAW, DB-GMAW has many advantages in droplet formation, base metal heat input and penetration achievement due to its unique characteristics in welding arc and current flow. In the first place of the research, experimental system of DB-GMAW is constructed. Then, sufficient experiments under different parameters are performed to provide us a good understanding of the behaviors and characteristics of this novel GMAW process. Observation about metal transfer formation and base metal heat input is studied to verify its theoretical analysis. Full penetration of work piece via DB-GMAW is achieved based on a series of parameter testing experiments. Moreover, image processing techniques are applied to DB-GMAW to monitor the welding process and construct a feedback system for control. Considering the importance of maintaining stable full penetration during many welding applications, a nonlinear model of DB-GMAW full penetration is developed in this dissertation. To do that, we use machine vision techniques to monitor the welding profile of the work piece. A control algorithm based on the nonlinear model using adaptive control technique is also designed. The achievement of this dissertation provides a fundamental knowledge of a novel welding process: DB-GMAW, and a good guidance for further studies about DBGMAW.

The subject of this thesis is the motion planning algorithm known as the continuation method. To solve motion planning problems, the continuation method proceeds by lifting curves in state space to curves in control space; the lifted curves are the solutions of special initial value problems called path-lifting equations. To validate this procedure, three distinct obstructions must be overcome. The first obstruction is that the endpoint maps of the control system under study must be twice continuously differentiable. By extending a result of A. Margheri, we show that this differentiability property is satisfied by an inclusive class of time-varying fully nonlinear control systems. The second obstruction is the existence of singular controls, which are simply the singular points of a fixed endpoint map. Rather than attempting to completely characterize such controls, we demonstrate how to isolate control systems for which no controls are singular. To this end, we build on the work of S. A. Vakhrameev to obtain a necessary and sufficient condition. In particular, this result accommodates time-varying fully nonlinear control systems. The final obstruction is that the solutions of path-lifting equations may not exist globally. To study this problem, we work under the standing assumption that the control system under study is control-affine. By extending a result of Y. Chitour, we show that the question of global existence can be resolved by examining Lie bracket configurations and momentum functions. Finally, we show that if the control system under study is completely unobstructed with respect to a fixed motion planning problem, then its corresponding endpoint map is a fiber bundle. In this sense, we obtain a necessary condition for unobstructed motion planning by the continuation method. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2012-12-18 20:53:43.272

Modern power systems are characterized by an increasing penetration of renewable energy generating units. These aim to reduce the carbon emissions in the environment by replacing conventional energy generating units which rely on fossil fuels. In this new power systems composition, wind generators (WGs) dominate, being one of the largest and fastest-growing sources of renewable energy production. Nevertheless, their unpredictable and highly volatile power output hinders their efficient and secure large-scale deployment, and poses challenges for the transient stability of power systems. Given that, we identify two challenges in the operation of modern power systems: rendering WGs capable of reguating their power output while securing transient stabilization of conventional synchronous generators (SGs). This dissertation makes several contributions for effectively dealing with these major challenges by introducing new distributed control techniques for SGs, storage devices and state-of-the-art (SoA) WGs. Initially, this dissertation introduces a novel nonlinear control design which is able to coordinate a storage device and a SG to attain transient stabilization and concurrent voltage regulation on their terminal bus. Thereafter, it proposes control designs that SoA WGs can adopt to effectively regulate their power out- put to meet local or group objectives. In this context, the rst control design is a decentralized nonlinear energy-based control design, that can be employed by a wind double-fed induction generator (DFIG) with an incorporated energy storage device (namely a SoA WG) to regulate its power output by harnessing stored energy, with guaranteed performance for a wide-range of operating conditions. Recognizing that, today, albeit wind farms (WFs) are comprised of numerous WGs which are sparsely located in large geographical areas, they are required to respond rapidly and provide services to the grid in an efficient, reliable and timely fashion. To this end, this dissertation proposes distributed control methods for power output regulation of WFs comprised of SoA WGs. In particular, a novel distributed control design is proposed, which can be adopted by SoA WGs to continuously, dynamically and distributively self-organize and control their power outputs by leveraging limited peer-to-peer communication. By employing the proposed control design, WGs can exploit their storage devices in a fair load-sharing manner so that their total power output tracks a total power reference under highly dynamical conditions. Finally, this dissertation proposes a distributed control design for wind DFIGs without a storage device, the most common type of WGs deployed today. With this control design, wind DFIGs can dynamically, distributively and fairly self-dispatch and adjust the power they extract from the wind for the purpose of their total power tracking a dynamic reference. The effectiveness of the control designs proposed in this dissertation is illustrated through several case studies on a 3-bus power system and the IEEE 24-bus Reliability Test System.

Within the field of multi-agent systems theory, we study the problems of consensus and pursuit-evasion. In our study of the consensus problem, we first provide some theoretical results and then consider the problem of consensus on SO(3) or attitude synchronization. In Chapter 2, for agents with states in R^m, we present two theorems along the lines of Lyapunov’s second method that, under different conditions, guarantee asymptotic state consensus in multi-agent systems where the interconnection topologies are switching. The first theorem is formulated by using the states of the agents in the multi-agent system, whereas the second theorem is formulated by using the pairwise states for pairs of agents in the multi-agent system. In Chapter 3, the problem of consensus on SO(3) for a multi-agent system with directed and switching interconnection topologies is addressed. We provide two different types of kinematic control laws for a broad class of local representations of SO(3). The first control law consists of a weighted sum of pairwise differences between positions of neighboring agents, expressed as coordinates in a local representation. The structure of the control law is well known in the consensus community for being used in systems of agents in the Euclidean space, and here we show that the same type of control law can be used in the context of consensus on SO(3). In a later part of this chapter, based on the kinematic control laws, we introduce torque control laws for a system of rigid bodies in space and show that the system reaches consensus when these control laws are used. Chapter 4 addresses the problem of consensus on SO(3) for networks of uncalibrated cameras. Under the assumption that each agent uses a camera in order to measure its rotation, we prove convergence to the consensus set for two types of kinematic control laws, where only conjugate rotation matrices are available for the agents. In these conjugate rotations, the rotation matrix can be seen as distorted by the (unknown) intrinsic parameters of the camera. For the conjugate rotations we introduce distorted versions of well known local parameterizations of SO(3) and show consensus by using control laws that are similar to the ones in Chapter 3, with the difference that the distorted local representations are used instead. In Chapter 5, we study the output consensus problem for homogeneous systems of agents with linear continuous time-invariant dynamics. We derive control laws that solve the problem, while minimizing a cost functional of the control signal. Instead of considering a fixed communication topology for the system, we derive the optimal control law without any restrictions on the topology. We show that for all linear output controllable homogeneous systems, the optimal control law uses only relative information but requires the connectivity graph to be complete and in general requires measurements of the state errors. We identify cases where the optimal control law is only based on output errors. In Chapter 6, we address the multi-pursuer version of the visibility pursuit-evasion problem in polygonal environments. By discretizing the problem and applying a Mixed Integer Linear Programming (MILP) framework, we are able to address problems requiring so called recontamination and also impose additional constraints, such as connectivity between the pursuers. The proposed MILP formulation is less conservative than solutions based on graph discretizations of the environment, but still somewhat more conservative than the original underlying problem. It is well known that MILPs, as well as multi-pursuer pursuit-evasion problems, are NP-hard. Therefore we apply an iterative Receding Horizon Control (RHC) scheme, where a number of smaller MILPs are solved over shorter planning horizons. The proposed approach is illustrated by a number of solved examples. / <p>QC 20140327</p>

Dans ce travail, la modélisation, la simulation, l'optimisation dynamique et la commande nonlinéaire d'un procédé industriel de polymérisation en émulsion produisant du polyacétate de vinyle (PVAc) sont étudiées. La réaction est modélisée comme un système à deux phases constitué d'une phase aqueuse et une phase particulaire. Un modèle détaillé est développé pour calculer la masse molaire moyenne en poids, la masse molaire moyenne en nombre et la dispersité. Les moments de chaînes en croissance et terminés sont utilisés pour représenter l'état du polymère et pour calculer la distribution de masse molaire (MWD). L'étude de cas correspond à un réacteur industriel fonctionnant dans une entreprise de produits chimiques à Bogotá. Un réacteur à l'échelle industrielle (11 m3 de capacité) est simulé dans lequel une réaction semi-batch de polymérisation en émulsion de l'acétate de vinyle est effectuée. Le problème d'optimisation dynamique est résolu directement en utilisant un solveur de programmation non linéaire. L'intégration des équations différentielles est faite en utilisant la méthode de Runge-Kutta. Trois problèmes d'optimisation différents sont résolus, depuis le plus simpliste (une seule variable d'optimisation : la température du réacteur) au plus complexe (trois variables d'optimisation : la température du réacteur, le débit de l'amorceur et le débit du monomère) en vue de minimiser le temps final de réaction. Une réduction de 25% du temps de traitement par batchs est réalisée par rapport aux conditions normales de fonctionnement appliquées dans l'entreprise. Les résultats montrent qu'il est possible de minimiser la durée de réaction alors que certaines qualités de polymères souhaitées (conversion, masse molaire et contenu en solides) satisfont les contraintes définies. Une technique de commande non linéaire géométrique à l'aide de la linéarisation entrée/sortie est adaptée à la régulation de la température du réacteur. Un filtre Kalman étendu (EKF) est mis en oeuvre pour estimer les états non mesurés et il est testé dans différents cas, dont une étude de robustesse où des erreurs du modèle sont introduites pour vérifier son bon fonctionnement. Après vérification des performances du régulateur, certains changements d'opération du procédé ont été proposés afin d'améliorer la productivité du procédé et la qualité du polymère. Enfin, le profil de température optimale et les politiques d'alimentation optimales de débits du monomère et de l'amorceur, obtenues dans l'étape d'optimisation dynamique, ont fourni les consignes optimales pour la commande non linéaire. Les résultats montrent que le régulateur non linéaire conçu ici convient pour suivre les trajectoires optimales de température calculées précédemment / In this work, modeling, simulation, dynamic optimization and nonlinear control of an industrial emulsion polymerization process to produce poly-vinyl acetate (PVAc) are proposed. The reaction is modeled as a two-phase system composed of an aqueous phase and a particle phase. A detailed model is used to calculate the weight average molecular weight, the number average molecular weight and the dispersity. The moments of the growing and dead chains are used to represent the state of the polymer and to calculate the molecular weight distribution (MWD). The case study corresponds to an industrial reactor operated at a chemical company in Bogotá. An industrial scale reactor (11 m3 of capacity) is simulated where a semi-batch emulsion polymerization reaction of vinyl acetate is performed. Dynamic optimization problem is solved directly using a Nonlinear Programming solver. Integration of differential equations is made using Runge-Kutta method. Three different optimization problems are solved from the more simplistic (only one control variable: reactor temperature) to the more complex (three control variables : reactor temperature, initiator flow rate and monomer flow rate) in order to minimize the reaction time. A reduction of 25% of the batch time is achieved with respect to the normal operating conditions applied at the company. The results show that is possible to minimize the reaction time while some polymer desired qualities (conversion, molecular weight and solids content) satisfy the defined constraints. A nonlinear geometric control technique by using input/output linearization is adapted to the reactor temperature control. An extended Kalman filter (EKF) is implemented to estimate unmeasured states and it is tested in different cases including a robustness study where model errors are introduced to verify its good performance. After verification of controller performance, some process changes were proposed in order to improve process productivity and polymer quality. Finally, the optimal temperature profile and optimal feed policies of the monomer and initiator, obtained in a dynamic optimization step, are used to provide the optimal set points for the nonlinear control. The results show that the nonlinear controller designed here is appropriate to follow the optimal temperature trajectories calculated previously

Orientador: Marcelo Minhoto Carvalho Teixeira / Banca: Edvaldo Assunção / Banca: Vilma Alves de Oliveira / Banca: Leonardo Amaral Mozelli / Banca: Edson Italo Mainardi Junior / Resumo: Neste trabalho são apresentadas duas novas propostas de condições de estabilidade para sistemas não lineares descritos através de modelos fuzzy Takagi-Sugeno (TS) baseadas em funções de Lyapunov fuzzy (FLF). A primeira proposta e baseada na determinação algébrica do hiper-retângulo composto pelo conjunto fechado das derivadas temporais das funções de pertinência de sistemas fuzzy TS e é formulada em termos de desigualdades matriciais lineares, em inglês Linear Matrix Inequalities (LMIs). A segunda proposta é baseada na obtenção também algébrica, de um politopo formado pela interseção do hiper-plano das derivadas temporais das funções de pertinência com o hiper-retângulo. são propostos dois teoremas que fornecem condições necessárias e suficientes para esse problema de estabilidade. Exemplos, utilizando o software MATLAB, ilustram os resultados numéricos, mostrando que o hiper-retângulo fornece resultados mais relaxados, no sentido de reduzir o conservadorismo, em relação aos da literatura e a estrutura proposta através de politopos apresenta os mesmos resultados com tempos de execução computacionais consideravelmente menores. Portanto, as propostas apresentadas generalizam as já existentes na literatura, para o estudo da estabilidade assintótica de sistemas não lineares baseados em FLF, para sistemas fuzzy TS / Abstract: This thesis proposes two new stability conditions regarding nonlinear systems des- cribed by Takagi-Sugeno (TS) fuzzy models, based on Fuzzy Lyapunov Functions (FLF). The first result is based on the hyper-rectangle defined by the closed set of the time deriva- tives of the membership functions of TS fuzzy systems, and is described by a set of Linear Matrix Inequalities (LMIs). The second result is based on the obtention of a polytope composed by the intersection of the hyperplane of the time derivatives of the membership functions with the hyper-rectangle. Two proposed theorems offer necessary and sufficient conditions for this stability problem. Examples, using the MATLAB software, illustrate the numerical results and show that the hyper-rectangle allows the reduction of the con- servatism of the stability analysis considering similar results available in the literature and with the polytope it is possible to obtain the same results with a smaller computati- onal time. Therefore, the proposed methods generalize previous results about asymptotic stability available in the literature, for nonlinear systems described by TS fuzzy models, based on FLF / Doutor

Navios aliviadores com sistemas de posicionamento dinâmico (SPD) são dispendiosos. Dessa forma, é desejável que se otimize sua utilização, por exemplo, através da redução da quantidade de viagens entre as plataformas em alto-mar e os terminais na costa. Quando o petróleo produzido é destinado à exportação, uma solução é transferi-lo diretamente do aliviador ao navio exportador (geralmente um VLCC) através das operações conhecidas como ship-to-ship, ainda em alto-mar e próximo aos campos de produção. No entanto, uma vez que VLCCs raramente são providos de SPD, é necessário que se desenvolvam formas de se assegurar a controlabilidade de ambos os navios durante a operação de transferência. Nesse sentido, duas diferentes configurações de operações ship-to-ship são propostas. Uma delas consiste em realizar a transferência com os navios avançando lado a lado. As embarcações são amarradas e então o VLCC desenvolve potência avante, rebocando o aliviador que mantém suas máquinas ociosas. A outra solução consiste em transferir o petróleo enquanto os navios mantêm uma formação em comboio, com o VLCC seguindo uma trajetória arbitrária e sendo seguido pelo aliviador, que mantém uma distância relativa através de uma estratégia específica de piloto automático. Os modelos dinâmicos para ambas as operações são desenvolvidos e implementados em simuladores numéricos. Os resultados das simulações são discutidos e utilizados para que se avalie a viabilidade operacional das operações sob diferentes condições ambientais e de carregamento dos navios. / Shuttle tankers with dynamic positioning (DP) systems are expensive ships. Therefore, it is desirable to optimize their usage by, e.g., eliminating the travels between offshore platforms and the terminals in the coast. When the oil is intended to exportation, an attractive idea is to transfer it between the shuttle tanker and the exporter ship (usually a VLCC) in open sea, close to the oil fields. However, since a VLCC is rarely provided with a DP system, it is necessary to develop alternative ways of attaining controllability of both vessels while the transfer operation is performed. In this sense, two configurations for the so-called ship-to-ship operations are proposed. One of them consists in performing the transfer with underway ships, arranged side-by-side. The vessels are moored together and the VLCC develops power ahead, towing the idle shuttle tanker. Another alternative is to transfer the oil while the ships maintain a convoy formation, with the VLCC trailing a given trajectory and being followed by the shuttle tanker, which keeps a constant relative position by means of an appropriate autopilot strategy. Dynamic models are developed for both operations and implemented in numerical simulators. The simulations results are discussed and used to outline the operational viability under different combinations of environment and loading conditions.