A note on the attenuation of the sommerfeld effect of a non-ideal system taking into account a MR damper and the complete model of a DC motor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Robust tori-like Lagrangian coherent structures

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

Boundary oscillations and nonlinear boundary conditions

We study how oscillations in the boundary of a domain affect the behavior of solutions of elliptic equations with nonlinear boundary conditions of the type partial derivative u/partial derivative n + g(x, u) = 0. We show that there exists a function gamma defined on the boundary, that depends on an the oscillations at the boundary, such that, if gamma is a bounded function, then, for all nonlinearities g, the limiting boundary condition is given by partial derivative u/partial derivative n + gamma(x)g(x, u) = 0 (Theorem 2.1, Case 1). Moreover, if g is dissipative and gamma infinity then we obtain a Dirichlet an boundary condition (Theorem 2.1, Case 2).

On non-ideal and non-linear portal frame dynamics analysis using Bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management

The investigation of the dynamics of a discrete soliton in an array of Bose-Einstein condensates under the action of a periodically time-modulated atomic scattering length [Feshbach-resonance management (FRM)] was discussed. The slow and rapid modulations, in comparison with the tunneling frequency were considered. An averaged equation, which was a generalized discrete nonlinear Schrödinger equation, including higher-order effective nonlinearities and intersite nonlinear interactions was derived in the case of the rapid modulation. It was demonstrated that the modulations of sufficient strength results in splitting of the soliton by direct simulations.

Local dimension and finite time prediction in coupled map lattices

Forecasting, for obvious reasons, often become the most important goal to be achieved. For spatially extended systems (e.g. atmospheric system) where the local nonlinearities lead to the most unpredictable chaotic evolution, it is highly desirable to have a simple diagnostic tool to identify regions of predictable behaviour. In this paper, we discuss the use of the bred vector (BV) dimension, a recently introduced statistics, to identify the regimes where a finite time forecast is feasible. Using the tools from dynamical systems theory and Bayesian modelling, we show the finite time predictability in two-dimensional coupled map lattices in the regions of low BV dimension. © Indian Academy of Sciences.

Design of SPR systems with dynamic compensators and output variable structure control

This paper presents necessary and sufficient conditions for the following problem: given a linear time invariant plant G(s) = N(s)D(s)-1 = C(sI - A]-1B, with m inputs, p outputs, p > m, rank(C) = p, rank(B) = rank(CB) = m, £nd a tandem dynamic controller Gc(s) = D c(s)-1Nc(s) = Cc(sI - A c)-1Bc + Dc, with p inputs and m outputs and a constant output feedback matrix Ko ε ℝm×p such that the feedback system is Strictly Positive Real (SPR). It is shown that this problem has solution if and only if all transmission zeros of the plant have negative real parts. When there exists solution, the proposed method firstly obtains Gc(s) in order to all transmission zeros of Gc(s)G(s) present negative real parts and then Ko is found as the solution of some Linear Matrix Inequalities (LMIs). Then, taking into account this result, a new LMI based design for output Variable Structure Control (VSC) of uncertain dynamic plants is presented. The method can consider the following design specifications: matched disturbances or nonlinearities of the plant, output constraints, decay rate and matched and nonmatched plant uncertainties. © 2006 IEEE.

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.

Degenerate hope bifurcations in Chua's system

In this paper we study the local codimension one, two and three Hopf bifurcations which occur in the classical Chua's differential equations with cubic nonlinearity. A detailed analytical description of the regions in the parameter space for which multiple small periodic solutions bifurcate from the equilibria of the system is obtained. As a consequence, a complete answer for the challenge proposed in [Moiola & Chua, 1999] is provided. © 2009 World Scientific Publishing Company.

Realimentação derivativa e modelo fuzzy Takagi-Sugeno paracontrole da articulação do joelho de pacientes paraplégicos com o uso de acelerômetros

Feedback control systems have been used to move the muscles and joints of the limbs of paraplegic patients. The feedback signal, related to the knee joint angle, can be obtained by using an electrogoniometer. However, the use of accelerometers can help the measurements due the facility of adhering these devices to the skin. Accelerometers are also very suitable for these applications due their small dimensions and weight. In this paper a new method for designing a control system that can vary the knee joint angle using Functional Electrical Stimulation (FES) is presented, as well as a simulation with parameters values available in the literature. The nonlinear control system was represented by a Takagi-Sugeno fuzzy model and the feedback signals were obtained by using accelerometers. The design method considered all plant nonlinearities and was efficient and reliable to control the leg position of a paraplegic patient with the angle of the knee ranging from 0° to 30°, considering electric stimulation at the quadriceps muscle. The proposed method is viable and offers a new alternative for designing control systems of the knee joint angle using more comfortable sensors for the patients.

Networked control system for the guidance of a four-wheel steering agricultural robotic platform

A current trend in the agricultural area is the development of mobile robots and autonomous vehicles for precision agriculture (PA). One of the major challenges in the design of these robots is the development of the electronic architecture for the control of the devices. In a joint project among research institutions and a private company in Brazil a multifunctional robotic platform for information acquisition in PA is being designed. This platform has as main characteristics four-wheel propulsion and independent steering, adjustable width, span of 1,80m in height, diesel engine, hydraulic system, and a CAN-based networked control system (NCS). This paper presents a NCS solution for the platform guidance by the four-wheel hydraulic steering distributed control. The control strategy, centered on the robot manipulators control theory, is based on the difference between the desired and actual position and considering the angular speed of the wheels. The results demonstrate that the NCS was simple and efficient, providing suitable steering performance for the platform guidance. Even though the simplicity of the NCS solution developed, it also overcame some verified control challenges in the robot guidance system design such as the hydraulic system delay, nonlinearities in the steering actuators, and inertia in the steering system due the friction of different terrains. Copyright © 2012 Eduardo Pacincia Godoy et al.

Nonlinear dynamic model and simulation of morphing wing profile actuated by shape memory alloys

Morphing aircraft have the ability to actively adapt and change their shape to achieve different missions efficiently. The development of morphing structures is deeply related with the ability to model precisely different designs in order to evaluate its characteristics. This paper addresses the dynamic modeling of a sectioned wing profile (morphing airfoil) connected by rotational joints (hinges). In this proposal, a pair of shape memory alloy (SMA) wires are connected to subsequent sections providing torque by reducing its length (changing airfoil camber). The dynamic model of the structure is presented for one pair of sections considering the system with one degree of freedom. The motion equations are solved using numerical techniques due the nonlinearities of the model. The numerical results are compared with experimental data and a discussion of how good this approach captures the physical phenomena associated with this problem. © The Society for Experimental Mechanics, Inc. 2012.

On Non-ideal and Chaotic Energy Harvester Behavior

In this paper, we deal with the research of a proposed mathematical model of energy harvesting, including nonlinearities in the piezoelectric coupling and a non-ideal force of excitation. We showed using numerical simulations to analysis of the dynamic responses that, the power harvested was influenced by the nonlinear vibrations of the structure, as well as by the influence of the non-linearities in the piezoelectric coupling. We concluded through of the numerical results that the limited energy source was interacting with the system. Thus, the increasing of the voltage in DC motor led the system produce a good power response, especially in high-energy orbits in the resonance region, but the Sommerfeld effect occurs in the system and a chaotic behavior was found in the post-resonance region. So the power harvested along the time decreases because occurs loses of energy due the interaction between energy source and structure. Keeping the energy harvested constant over time is essential to make possible the use of energy harvesting systems in real applications. To achieve this objective, we applied a control technique in order to stabilize the chaotic system in a periodic stable orbit. We announced that the results were satisfactory and the control maintained the system in a stable condition. © 2012 Foundation for Scientific Research and Technological Innovation.

The non-ideal problem behavior using a dynamic vibration absorber with nonlinear essential stiffness and timedependent damping properties

The purpose of this study is to develop a dynamic vibration absorber using viscoelastic material with nonlinear essential stiffness and time-dependent damping properties for a non-ideal vibrating system with Sommerfeld effect, resonance capture, and jump phenomenon. The absorber is a mass-bar subsystem that consists of a viscoelastic bar with memory attached to mass, in which the internal dissipative forces depend on current, deformations, and its operational frequency varies with limited temperature. The non-ideal vibrating system consists of a linear (nonlinear) oscillator (plane frame structure) under excitation, via spring connector, of a DC-motor with limited power supply. A viscoelastic dynamic absorber modeled with elastic stiffness essentially nonlinearities was developed to further reduce the Sommerfeld effect and the response of the structure. The numerical results show the performance of the absorber on the non-ideal system response through the resonance curves, time histories, and Poincarésections. Furthermore, the structure responses using the viscoelastic damper with and without memory were studied. © IMechE 2012.

Decoupled reference generator for shunt active filters using the conservative power theory

Based on the framework of the Conservative Power Theory (CPT), this paper proposes some compensation strategies for shunt current compensators. CPT current decompositions result in several current-related terms associated with specific load characteristics, such as power consumption, energy storage, unbalances and load nonlinearities. These current components are decoupled (orthogonal) from each other and are used here to define different compensation strategies, which can be selective in minimizing particular effects of disturbing loads. Compensation strategies for single- and three-phase four-wire circuits are also considered. Simulated and experimental results are described to validate the possibilities and performance of the proposed strategies. © 2013 Brazilian Society for Automatics - SBA.