Control Design Applied to a Micro Electro Mechanical System: MEMS Comb drive

This paper presents the linear optimal control technique for reducing the chaotic movement of the micro-electro-mechanical Comb Drive system to a small periodic orbit. We analyze the non-linear dynamics in a micro-electro-mechanical Comb Drive and demonstrated that this model has a chaotic behavior. Chaos control problems consist of attempts to stabilize a chaotic system to an equilibrium point, a periodic orbit, or more general, about a given reference trajectory. This technique is applied in analyzes the nonlinear dynamics in an MEMS Comb drive. The simulation results show the identification by linear optimal control is very effective.

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)

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.

Swarm control designs applied to a micro-electro-mechanical gyroscope system (MEMS)

This paper analyzes the non-linear dynamics of a MEMS Gyroscope system, modeled with a proof mass constrained to move in a plane with two resonant modes, which are nominally orthogonal. The two modes are ideally coupled only by the rotation of the gyro about the plane's normal vector. We demonstrated that this model has an unstable behavior. Control problems consist of attempts to stabilize a system to an equilibrium point, a periodic orbit, or more general, about a given reference trajectory. We also developed a particle swarm optimization technique for reducing the oscillatory movement of the nonlinear system to a periodic orbit. © 2010 Springer-Verlag.

Chaotic vibrations of a nonideal electro-mechanical system

Nonideal systems are those in which one takes account of the influence of the oscillatory system on the energy supply with a limited power (Kononenko, 1969). In this paper, a particular nonideal system is investigated, consisting of a pendulum whose support point is vibrated along a horizontal guide by a two bar linkage driven by a DC motor, considered to be a limited power supply. Under these conditions, the oscillations of the pendulum are analyzed through the variation of a control parameter. The voltage supply of the motor is considered to be a reliable control parameter. Each simulation starts from zero speed and reaches a steady-state condition when the motor oscillates around a medium speed. Near the fundamental resonance region, the system presents some interesting nonlinear phenomena, including multi-periodic, quasiperiodic, and chaotic motion. The loss of stability of the system occurs through a saddle-node bifurcation, where there is a collision of a stable orbit with an unstable one, which is approximately located close to the value of the pendulum's angular displacement given by alpha (C)= pi /2. The aims of this study are to better understand nonideal systems using numerical simulation, to identify the bifurcations that occur in the system, and to report the existence of a chaotic attractor near the fundamental resonance. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Escape in a nonideal electro-mechanical system

In this work a particular system is investigated consisting of a pendalum whose point of support is vibrated along a horizontal guide by a two bar linkage driven from a DC motor, considered as a limited power source. This system is nonideal since the oscillatory motion of the pendulum influences the speed of the motor and vice-versa, reflecting in a more complicated dynamical process. This work comprises the investigation of the phenomena that appear when the frequency of the pendulum draws near a secondary resonance region, due to the existing nonlinear interactions in the system. Also in this domain due to the power limitation of the motor, the frequency of the pendulum can be captured at resonance modifying completely the final response of the system. This behavior is known as Sommerfield effect and it will be studied here for a nonlinear system.

On stick-slip homoclinic chaos and bifurcations in a mechanical system with dry friction

In this paper we consider a self-excited mechanical system by dry friction in order to study the bifurcational behavior of the arisen vibrations. The oscillating system consists of a mass block-belt-system which is self-excited by static and Coulomb friction. We analyze the system behavior numerically through bifurcation diagrams, phase portraits, frequency spectra and Poincare maps, which show the existence of nonhomoclinic and homoclinic chaos and a route to homoclinic chaos. The homoclinic chaos is also analyzed analytically via the Melnikov prediction method. The system dynamic is characterized by the existence of two potential wells in the phase plane which exhibit rich bifurcational and chaotic behavior.

On an Active Control for a Structurally Nonlinear Mechanical System, Taking Into Account an Energy Pumping

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

On a Nonideal (MRD) Damper-Electro-mechanical Absorber Dynamics

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

Harmonical oscillator and electro-mechanical analogy: an interdiscinary experiment to high precision mass variation measurements

De forma geral, os cursos de física clássica oferecidos nas universidades carecem de exemplos de aplicações nas áreas de química e biologia, o que por vezes desmotivam os alunos de graduação destas áreas a estudarem os conceitos físicos desenvolvidos em sala de aula. Neste texto, a analogia entre os osciladores elétrico e mecânico é explorada visando possívies aplicações em química e biologia, mostrando-se de grande valia devido ao seu uso em técnicas de medição de variação de massa com alta precisão, tanto de forma direta como indireta. Estas técnicas são conhecidas como técnicas eletrogravimétricas e são de especial importância em aplicações que envolvem biossensores. Desta forma, o texto explora o estudo da analogia eletromecânica de forma interdisciplinar envolvendo as áreas de física, química e biologia. Baseado nessa analogia é proposto um experimento que permite a sua aplicação em diferentes níveis conceituais dessas disciplinas, tanto em abordagem básica como mais profunda.

Behavioural Analysis of a Nonlinear Mechanical System Using Transient Trajectories

This work aims at a better comprehension of the features of the solution surface of a dynamical system presenting a numerical procedure based on transient trajectories. For a given set of initial conditions an analysis is made, similar to that of a return map, looking for the new configuration of this set in the first Poincaré sections. The mentioned set of I.C. will result in a curve that can be fitted by a polynomial, i.e. an analytical expression that will be called initial function in the undamped case and transient function in the damped situation. Thus, it is possible to identify using analytical methods the main stable regions of the phase portrait without a long computational time, making easier a global comprehension of the nonlinear dynamics and the corresponding stability analysis of its solutions. This strategy allows foreseeing the dynamic behavior of the system close to the region of fundamental resonance, providing a better visualization of the structure of its phase portrait. The application chosen to present this methodology is a mechanical pendulum driven through a crankshaft that moves horizontally its suspension point.

Quenching in a non-ideal mechanical system and the Averaging Method

In this paper, for the first time, a quenching result in a non-ideal system is rigorously obtained. In order to do this a new mechanical hypothesis is assumed, it means that the moment of inertia of the rotating parts of the energy source is big. From this is possible to use the Averaging Method. © 2012 American Institute of Physics.

Application of Volterra series in nonlinear mechanical system identification and in structural health monitoring problems

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

A mechanical analogous model for the power system with Automatic Voltage Regulator

This paper deals with the subject-matter of teaching immaterial issues like power system dynamics where the phenomena and events are not sense-perceptible. The dynamics of the power system are recognized as analogous to the dynamics of a simple mechanical pendulum taken into account the well-known classical model for the synchronous machine. It is shown that even for more sophisticated models including flux decay and Automatic Voltage Regulator the mechanical device can be taken as an analogous, since provided some considerations about variation and control of the pendulum length using certain control laws. The resulting mathematical model represents a mechanical system that can be built for use in laboratory teaching of power system dynamics. © 2010 Praise Worthy Prize S.r.l. - All rights reserved.

Using transient and steady state considerations to investigate the mechanism of loss of stability of a dynamical system

This work presents the complete set of features for solutions of a particular non-ideal mechanical system near the fundamental and near to a secondary resonance region. The system comprises a pendulum with a horizontally moving suspension point. Its motion is the result of a non-ideal rotating power source (limited power supply), acting oil the Suspension point through a crank mechanism. Main emphasis is given to the loss of stability, which occurs by a sequence of events, including intermittence and crisis, when the system reaches a chaotic attractor. The system also undergoes a boundary-crisis, which presents a different aspect in the bifurcation diagram due to the non-ideal supposition. (c) 2004 Published by Elsevier B.V.