Generalized Higher-Order Voronoi Diagrams on Polyhedral Surfaces

We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex polyhedral surface in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) on a polyhedral surface with obstacles. To obtain the discrete Voronoi diagrams our algorithms, exploiting hardware graphics capabilities, compute shortest path distances defined by the sites

Computationally reliable approaches of contractive MPC for discrete-time systems

La tesis pretende explorar acercamientos computacionalmente confiables y eficientes de contractivo MPC para sistemas de tiempo discreto. Dos tipos de contractivo MPC han sido estudiados: MPC con coacción contractiva obligatoria y MPC con una secuencia contractiva de conjuntos controlables. Las técnicas basadas en optimización convexa y análisis de intervalos son aplicadas para tratar MPC contractivo lineal y no lineal, respectivamente. El análisis de intervalos clásicos es ampliado a zonotopes en la geometría para diseñar un conjunto invariante de control terminal para el modo dual de MPC. También es ampliado a intervalos modales para tener en cuenta la modalidad al calcula de conjuntos controlables robustos con una interpretación semántica clara. Los instrumentos de optimización convexa y análisis de intervalos han sido combinados para mejorar la eficacia de contractive MPC para varias clases de sistemas de tiempo discreto inciertos no lineales limitados. Finalmente, los dos tipos dirigidos de contractivo MPC han sido aplicados para controlar un Torneo de Fútbol de Copa Mundial de Micro Robot (MiroSot) y un Tanque-Reactor de Mezcla Continua (CSTR), respectivamente.

Extending the friction cone algorithm for arbitrary polygon based haptic objects

Most haptic environments are based on single point interactions whereas in practice, object manipulation requires multiple contact points between the object, fingers, thumb and palm. The Friction Cone Algorithm was developed specifically to work well in a multi-finger haptic environment where object manipulation would occur. However, the Friction Cone Algorithm has two shortcomings when applied to polygon meshes: there is no means of transitioning polygon boundaries or feeling non-convex edges. In order to overcome these deficiencies, Face Directed Connection Graphs have been developed as well as a robust method for applying friction to non-convex edges. Both these extensions are described herein, as well as the implementation issues associated with them.

Synthesis method for visible and infrared broadband spaceflight antireflection coatings

Evolutionary synthesis methods, as originally described by Dobrowolski, have been shown in previous literature to be an effective method of obtaining anti-reflection coating designs. To make this method even more effective, the combination of a good starting design, the best suited thin-film materials, a realistic optimization target function and a non-gradient optimization method are used in an algorithm written for a PC. Several broadband anti-reflection designs obtained by this new design method are given as examples of its usefulness.

Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.

Controle preditivo robusto baseado em desigualdades matriciais lineares aplicado a um sistema de tanques acoplados

This work deals with an on-line control strategy based on Robust Model Predictive Control (RMPC) technique applied in a real coupled tanks system. This process consists of two coupled tanks and a pump to feed the liquid to the system. The control objective (regulator problem) is to keep the tanks levels in the considered operation point even in the presence of disturbance. The RMPC is a technique that allows explicit incorporation of the plant uncertainty in the problem formulation. The goal is to design, at each time step, a state-feedback control law that minimizes a 'worst-case' infinite horizon objective function, subject to constraint in the control. The existence of a feedback control law satisfying the input constraints is reduced to a convex optimization over linear matrix inequalities (LMIs) problem. It is shown in this work that for the plant uncertainty described by the polytope, the feasible receding horizon state feedback control design is robustly stabilizing. The software implementation of the RMPC is made using Scilab, and its communication with Coupled Tanks Systems is done through the OLE for Process Control (OPC) industrial protocol

Mathematical tool to size rural digesters

Os biodigestores têm sido objetos de grande destaque devido a atual crise de energia e conseqüente busca de fontes alternativas. Outro fator que coloca os biodigestores em evidência é o intenso processo de modernização da agropecuária, que além da grande demanda de energia, produz um volume de resíduos animais e de culturas, que ocasiona muitas vezes problemas de ordem sanitária. O objetivo deste trabalho é fornecer uma ferramenta matemática para determinação de parâmetros para projetos de construção de biodigestores rurais, levando-se em consideração o atendimento de necessidades energéticas, obedecendo os dimensionamentos dos sistemas, fatores de rendimento e garantindo a funcionalidade. Para isto, foram formulados modelos de otimização não lineares, de fácil resolução, para os três principais tipos de biodigestores rurais. Com a resolução destes modelos são determinados a altura e o diâmetro que levem a um volume mínimo para cada tipo, com isto reduz-se a quantidade necessária de materiais de alvenaria e consequentemente o custo do biodigestor é diminuído.

H-2 and H-infinity - norm control of intelligent structures using LMI techniques

Linear Matrix Inequalities (LMIs) is a powerful too] that has been used in many areas ranging from control engineering to system identification and structural design. There are many factors that make LMI appealing. One is the fact that a lot of design specifications and constrains can be formulated as LMIs [1]. Once formulated in terms of LMIs a problem can be solved efficiently by convex optimization algorithms. The basic idea of the LMI method is to formulate a given problem as an optimization problem with linear objective function and linear matrix inequalities constrains. An intelligent structure involves distributed sensors and actuators and a control law to apply localized actions, in order to minimize or reduce the response at selected conditions. The objective of this work is to implement techniques of control based on LMIs applied to smart structures.

Robust control applications for smart truss structure

A finite element modeling of an intelligent truss structure with piezoelectric stack actuators for the purpose of active damping and structural vibration attenuation is presented. This paper concerns with the following issues aspects: the design of intelligent truss structure considering electro-mechanical coupling between the host structure and piezoelectric stack actuators; the H 2 norm approach to search for optimal placement of actuators and sensors; and finally some aspects in robust control techniques. The electro-mechanical behavior of piezoelectric elements is directly related to the successful application of the actuators in truss structures. In order to achieve the desired damping in the interested bandwidth frequency it is used the H ∞ output feedback solved by convex optimization. The constraints to be reached are written by linear matrix inequalities (LMI). The paper concludes with a numerical example, using Matlab and Simulink, in a cantilevered, 2-bay space truss structure. The results demonstrated the approach applicability.

Active control in flexible plates with piezoelectric actuators using linear matrix inequalities

The study of algorithms for active vibrations control in flexible structures became an area of enormous interest, mainly due to the countless demands of an optimal performance of mechanical systems as aircraft, aerospace and automotive structures. Smart structures, formed by a structure base, coupled with piezoelectric actuators and sensor are capable to guarantee the conditions demanded through the application of several types of controllers. The actuator/sensor materials are composed by piezoelectric ceramic (PZT - Lead Zirconate Titanate), commonly used as distributed actuators, and piezoelectric plastic films (PVDF-PolyVinyliDeno Floride), highly indicated for distributed sensors. The design process of such system encompasses three main phases: structural design; optimal placement of sensor/actuator (PVDF and PZT); and controller design. Consequently, for optimal design purposes, the structure, the sensor/actuator placement and the controller have to be considered simultaneously. This article addresses the optimal placement of actuators and sensors for design of controller for vibration attenuation in a flexible plate. Techniques involving linear matrix inequalities (LMI) to solve the Riccati's equation are used. The controller's gain is calculated using the linear quadratic regulator (LQR). The major advantage of LMI design is to enable specifications such as stability degree requirements, decay rate, input force limitation in the actuators and output peak bounder. It is also possible to assume that the model parameters involve uncertainties. LMI is a very useful tool for problems with constraints, where the parameters vary in a range of values. Once formulated in terms of LMI a problem can be solved efficiently by convex optimization algorithms.

Novas aplicações de metaheurísticas na solução do problema de planejamento da expansão do sistema de transmissão de energia elétrica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Implementação de um gerador tridimensional de malhas de elementos finitos, com aplicações à simulação computacional em odontologia

Pós-graduação em Matemática - IBILCE

Identificação experimental e controle ativo de vibrações aplicadas em estruturas inteligentes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Projeto de controladores robustos para aplicações em estruturas inteligentes utilizando desigualdades matriciais lineares

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Controle ativo de vibrações em estruturas flexíveis utilizando desigualdades matriciais lineares (LMIs)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)