Diego Colón

Cartan’s Connection, Fiber Bundles and Quaternions in Kinematics and Dynamics Calculations

It is used the concept of Cartan’s connection and principal fiber bundles to obtain formulas for kinematics and dynamics calculations for robotic manipulators. A principal fiber bundle is a differentiable manifold formed by a base space B (in this case ℝ3)) plus all possible reference frames attached to a point p ∈ B (that is the fiber Sp). Cartan’s connections are the most general way to represent velocity of frames. In previous works, those ideas were applied to fiber bundles with fibers homomorphic to the Lie group SO(3) (or SE(3)). In this paper, it is applied to the case of fibers homomorphic either to the group SU(2) (for rotational motion) or to the group of unit dual quaternions (for translational plus rotational motion). It is also presented some results of calculations, and indicate future directions for research.Copyright

Robustness analysis of an air heating plant and control law by using polynomial chaos

This paper presents a robustness analysis of an air heating plant with a multivariable closed-loop control law by using the polynomial chaos methodology (MPC). The plant consists of a PVC tube with a fan in the air input (that forces the air through the tube) and a mass flux sensor in the output. A heating resistance warms the air as it flows inside the tube, and a thermo-couple sensor measures the air temperature. The plant has thus two inputs (the fans rotation intensity and heat generated by the resistance, both measured in percent of the maximum value) and two outputs (air temperature and air mass flux, also in percent of the maximal value). The mathematical model is obtained by System Identification techniques. The mass flux sensor, which is nonlinear, is linearized and the delays in the transfer functions are properly approximated by non-minimum phase transfer functions. The resulting model is transformed to a state-space model, which is used for control design purposes. The multivariable robust co...

Geometric Modeling and Robust Control of a Gyroscopic System

Gyroscopic systems are multi-body systems which present coupled three dimensional motion. The configuration space and the state space are differentiable manifolds, and differential geometric concepts are frequently useful in the process of modeling. This paper deals with a Control Moment Gyroscope (CMG), which is not asymptotically stable, so it needs a stabilizing control law. We apply a new methodology of modeling kinematics and dynamics of rigid multi-body systems, based in the concept of Cartan’s connection and covariant derivative. The systems has two inputs (torques) and two outputs (angles) that will be controlled by a robust linear closed-loop control technique (LQG/LTR). Experimental results are presented in order to validate the proposal.Copyright

Integrated subsea production system: An overview on energy distribution and remote control

In 2012, Brasil had a proved reserve of 15.3 billions of BOE (barrel of oil equivalent). The offshore reserve corresponds to more 94% of this amount. Petrobras, the Brasilian E&P company, leads the offshore production in ultra-deep water (deeper than 1500 m of water depth) worldwide. The current offshore production in ultra-deep waters deploys a Floating Production Unit (FPU), and some subsea equipments, such as, wet Christmas trees, manifolds, separation & booster systems, risers and pipelines. However, on board of the FPU, there are several other systems, namely, power generators, separators, gas treatment system, water treatment system, artificial lift system, injection system, etc. A future paradigm shift in the offshore petroleum production shall be the installation of all necessary systems on the sea floor. This article addresses to two challenges that raise with this new integrated operations with subsea oilfield production: the “remote operation and monitoring”, and the “power generation and distribution”. Remote operation and monitoring come from the need to transfer the process operators to shore and optimize the number of operators, to improve the processes availability by reducing the operator response time to a specific task, to provide continuous and predictive monitoring of vital processes, among other factors. Within the context of integrated operations, a remote operating center provides a broad and integrated overview of several processes in the asset, by using modern supervisory software (3D and 4D), database, remote sensoring, among others technologies. Part of this article also provides a comparative discussion between some technologies used in the implementation of remote operation and monitoring. Due to the substantial amount of electrical power required by subsea process units and their relatively long life cycle, typical aspects related to power generation and distribution have been changing. Alternatives, which were not cost effective before, are considered as new trends in the development of new process units due to political aspects and advances in the technology involved. Subsea high-voltage power distribution systems have become an alternative to supply the total load of subsea process units. According to this approach, electrical power distribution is located near the load center, as on shore installations. Normally, such installations are supplied from shore through long power umbilicals, as the supply of individual loads is not economically interesting. The advances in the use of renewable sources have also promoted new alternatives in power generation. These approaches become more interesting due to the possibility of installing large power generation plants using renewable sources on shallow water and transmitting the power to a set of subsea process units. Thus, new alternatives arise, such as the possibility of power transmission in high voltage direct current systems (HVDC), avoiding common problems faced in power transfer capacity using high voltage alternate current systems (HVAC), as large amount of reactive power needed to compensate cables capacitance. This paper discusses these issues aroused due to power supply of subsea process units.

Algoritmo de Busca em Vizinhança Variável para Determinação de Controle Otimizado para a População de Aedes aegypti

O controle populacional do mosquito Aedes aegypti na fase aquatica e uma pratica comum no Brasil. Agentes sanitarios removem criadouros dos mosquitos e/ou aplicam larvicidas em varios locais das cidades. Mas estas praticas, alem de muito caras para os orgaos de vigilância sanitaria, sao muitas vezes realizadas de forma insuficiente. Portanto, neste trabalho propomos um modelo de otimizacao multiobjetivo visando determinar estrategias otimizadas para o controle do mosquito, visando utilizar o minimo possivel de controle aquatico e que manter a populacao de mosquitos em um nivel minimo. Para resolucao deste modelo foi proposto um algoritmo heuristico baseado em busca em vizinhanca variavel (VNS-Variable neighborhood search). Ao final sao apresentadas simulacoes computacionais.

H-infinity current control of the LC coupled voltage source inverter

The hybrid active harmonic filters use a series capacitor in order to reduce the voltage rating of the inverter compared to regular inductive-coupled active filters. Different control strategies are applied on this topology in the literature. The main contribution of this paper is to apply a H-infinity controller in order to achieve current tracking in voltage source inverters connected to the grid through a series LC coupling impedance. The primary goal of this control system is to track a harmonic reference current, in order to address power quality issues on the grid. An overview on the controller synthesis process is given. The discretization process is shown together with the controller robustness investigation using mu-analysis. Finally, the simulations are validated through experimental measurements using the synthesized controller.

An Application of the Lurie Problem in Hopfield Neural Networks

The goal of this work is to present applications of recent results in the Lurie problem, also known as the absolute stability problem, to Hopfield neural networks, aiming its stability analysis. We show how to obtain the mathematical model of a neural network, in terms of differential equations, and present simulations for some examples. We give special attention to networks with multiple inputs and outputs, and point future directions of research to be followed.

The Application of a Polynomial Chaos Approach to the Vibration Analysis of an Elevator System

The paper presents the uncertainty quantification of an elevator system by the Method of Polynomial Chaos. Initially, the mathematical model (the equations of motion) of an elevator system is derived and the sources of randomness are identified, which are in the elevator’s trail. The method of polynomial chaos is then presented in its two versions (intrusive and non-intrusive) and the non-intrusive version is applied (numerically) in order to evaluate the uncertainties in the amplitude of the rope and car vibration by means of an auto-covariance function.

Nonlinear Ball and Beam Control System Identification

The Ball and Beam system is a common didactical experiment in control laboratories that can be used to illustrate many different closed-loop control techniques. The plant itself is subjected to many nonlinear effects, which the most common comes from the relative motion between the ball and the beam. The modeling process normally uses the lagrangean formulation. However, many other nonlinear effects, such as non-viscous friction, beam flexibility, ball slip, actuator elasticity, collisions at the end of the beam, to name a few, are present. Besides that, the system is naturally unstable. In this work, we analyze a subset of these characteristics, in which the ball rolls with slipping and the friction force between the ball and the beam is non-viscous (Coulomb friction). Also, we consider collisions at the ends of the beam, the actuator consists of a (rubber made) belt attached at the free ends of the beam and connected to a DC motor. The model becomes, with those nonlinearities, a differential inclusion system. The elastic coefficients of the belt are experimentally identified, as well as the collision coefficients. The nonlinear behavior of the system is studied and a control strategy is proposed.

Modeling and Analysis of a Ball and Beam System Including Impacts and Dry Friction

The Ball and Beam system is a common didactical plant that presents a complex nonlinear dynamics. This comes from the fact that the ball rolls over the beam, which rotates around its barycenter. In order to deduce the system’s equations, composition of movement must be applied, using a non-inertial reference frame attached to the beam. In the Literature, a common hypothesis is to suppose that the ball rolls without slipping. If a viscous friction is supposed to be present, a simpler situation is obtained, where Lagrangean mechanics can be applied, and no contact force is known. Even then, the dynamics is very nonlinear.However, this model does not include all the relevant phenomena, such as ball’s slipping at higher beam’s inclination angles, dry friction between the ball and the beam, and impacts between: 1) the ball and the ends of the beam, and 2) the beam and the base (ground). These additions to the model impose the necessity to calculate, in a simulation setting, the contact forces, and the Newton’s approach to determine the system’s equations becomes more convenient. Also, discontinuities in the model are introduced, and the simpler mathematical object for model such systems are the differential inclusion systems.In this work, we deduce the Ball and Beam differential inclusion system, including dry friction and the impact between the ball and beam. We also present simulation results for the corresponding differential inclusion system in a typical situation.Copyright