Design of a control system using linear matrix inequalities for the active vibration control of a plate

The study of algorithms for active vibration control in smart structures is an area of interest, mainly due to the demand for better performance of mechanical systems, such as aircraft and aerospace structures. Smart structures, formed using actuators and sensors, can improve the dynamic performance with the application of several kinds of controllers. This article describes the application of a technique based on linear matrix inequalities (LMI) to design an active control system. The positioning of the actuators, the design of a robust state feedback controller and the design of an observer are all achieved using LMI. The following are considered in the controller design: limited actuator input, bounded output (energy) and robustness to parametric uncertainties. Active vibration control of a flat plate is chosen as an application example. The model is identified using experimental data by an eigensystem realization algorithm (ERA) and the placement of the two piezoelectric actuators and single sensor is determined using a finite element model (FEM) and an optimization procedure. A robust controller for active damping is designed using an LMI framework, and a reduced model with observation and control spillover effects is implemented using a computer. The simulation results demonstrate the efficacy of the approach, and show that the control system increases the damping in some of the modes.

On an Optimal Linear Control of a Chaotic Non-Ideal Duffing System

In this work, we use a nonlinear control based on Optimal Linear Control. We used as mathematical model a Duffing equation to model a supporting structure for an unbalanced rotating machine with limited power (non-ideal motor). Numerical simulations are performed for a set control parameter (depending on the voltage of the motor, that is, in the static and dynamic characteristic of the motor) The interaction of the non-ideal excitation with the structure may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the system. Chaotic behavior is obtained for values of the parameters. Then, the proposed control strategy is applied in order to regulate the chaotic behavior, in order to obtain a periodic orbit and to decrease its amplitude. Both methodologies were used in complete agreement between them. The purpose of the paper is to give suggestions and recommendations to designers and engineers on how to drive this kind of system through resonance.

On an Optimal Linear Control Applied to a Non-Ideal Load Transportation System, Modeled with Periodic Coefficients

In this paper, a load transportation system in platforms or suspended by cables is considered. It is a monorail device and is modelled as an inverted pendulum built on a car driven by a DC motor. The governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the DC motor and the dynamical system, that is, we have a so-called non-ideal periodic problem. The problem is analysed and we also developed an optimal linear control design to stabilize the problem.

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

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

Designing a modified Hopfield network to solve an Economic Dispatch problem with nonlinear cost function

Economic Dispatch (ED) problems have recently been solved by artificial neural networks approaches. In most of these dispatch models, the cost function must be linear or quadratic. Therefore, functions that have several minimum points represent a problem to the simulation since these approaches have not accepted nonlinear cost function. Another drawback pointed out in the literature is that some of these neural approaches fail to converge efficiently towards feasible equilibrium points. This paper discusses the application of a modified Hopfield architecture for solving ED problems defined by nonlinear cost function. The internal parameters of the neural network adopted here are computed using the valid-subspace technique, which guarantees convergence to equilibrium points that represent a solution for the ED problem. Simulation results and a comparative analysis involving a 3-bus test system are presented to illustrate efficiency of the proposed approach.

Linear low density polyethylene (LLDPE) from ethylene using Tp(Ms)NiCl (Tp(Ms) = hydridotris(3-mesitylpyrazol-1-yl)) and CP2ZrCl2 as a tandem catalyst system

Linear low density polyethylene (LLDPE) with different branching contents were prepared from ethylene, without the addition of alpha-olefin comonomer, using a combination of catalyst precursors {Tp(Ms)}NiCl (1) (Tp(Ms) = hydridotris(3-mesitylpyrazol-1-yl)) and Cp2ZrCl2 (2) activated with MAO/TMA (1:1) in toluene at 0degreesC and by varying the nickel loading mole fraction (x(Ni)). The polymerization results showed that the turnover frequencies are strongly dependent on the x(Ni) varying from 6.6 x 10(3) to 32.1 x 10(3) mol[C2H4]/mol[Zr] h. The C-13 NMR spectra of the copolymers showed that the branch contents of the polymers increase as the x(Ni) increase in the medium promoting the production of polymers with a wide range of melting point (T-m) (C) 2004 Elsevier B.V. All rights reserved.

On the effects of system parameters on the response of a harmonically excited system consisting of weakly coupled nonlinear and linear oscillators

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment having linear and cubic restoring forces. The effects of the system parameters on the shape of the frequency-response curve are investigated, in particular those yielding the appearance and disappearance of outer and inner detached resonance curves. In contrast to the case when the linear stiffness of the attachment is zero, it is found that multivaluedness occurs at low frequencies as the resonant peak bends to the right. It is also found that as the coefficient of the linear term increases, the range of parameters yielding detached curves reduces. Compared to the case when the attached system has no linear stiffness term, this range of parameters corresponds to smaller values of the damping and nonlinear coefficients. Approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are also derived. (C) 2011 Elsevier Ltd. All rights reserved.

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.

On the analytical solution for the slewing flexible beam-like system: analysis of the linear part of the perturbed problem

The dynamical system investigated in this work is a nonlinear flexible beam-like structure in slewing motion. Non-dimensional and perturbed governing equations of motion are presented. The analytical solution for the linear part of these perturbed equations for ideal and for non-ideal cases are obtained. This solution is necessary for the investigation of the complete weak nonlinear problem where all nonlinearities are small perturbations around a linear known solution. This investigation shall help the analyst in the modelling of dynamical systems with structure- actuator interactions.

A set of linear equations to calculate the steady-state operation of an electrical distribution system

In this paper, the calculation of the steady-state operation of a radial/meshed electrical distribution system (EDS) through solving a system of linear equations (non-iterative load flow) is presented. The constant power type demand of the EDS is modeled through linear approximations in terms of real and imaginary parts of the voltage taking into account the typical operating conditions of the EDS's. To illustrate the use of the proposed set of linear equations, a linear model for the optimal power flow with distributed generator is presented. Results using some test and real systems show the excellent performance of the proposed methodology when is compared with conventional methods. © 2011 IEEE.

Optimal linear control to parametric uncertainties in a micro electro mechanical system

This paper, a micro-electro-mechanical systems (MEMS) with parametric uncertainties is considered. The non-linear dynamics in MEMS system is demonstrated with a chaotic behavior. We present the linear optimal control technique for reducing the chaotic movement of the micro-electromechanical system with parametric uncertainties to a small periodic orbit. The simulation results show the identification by linear optimal control is very effective. © 2013 Academic Publications, Ltd.

Alocação ótima de reguladores de tensão em sistemas de distribuição de energia elétrica radiais usando uma formulação linear inteira mista. -

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Times assíncronos inicializadores para o planejamento da expansão da transmissão de energia elétrica baseados no modelo híbrido linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Desenvolvimento de técnicas eficientes de programação linear na utilização de metaheurísticas para o problema de planejamento da expansão de sistemas de transmissão

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Planejamento de reativos em sistemas de energia elétrica através de um algoritmo de Branch-and-Bound não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)