On local analysis of oscillations of a non-ideal and non-linear mechanical model

It is of major importance to consider non-ideal energy sources in engineering problems. They act on an oscillating system and at the same time experience a reciprocal action from the system. Here, a non-ideal system is studied. In this system, the interaction between source energy and motion is accomplished through a special kind of friction. Results about the stability and instability of the equilibrium point of this system are obtained. Moreover, its bifurcation curves are determined. Hopf bifurcations are found in the set of parameters of the oscillating system.

Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part I: Ideal energy source

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

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

Non-linear dynamics of a tower orchard sprayer based on an inverted pendulum model

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

Remarks on an Optimal Linear Control Design Applied to a Nonideal and an Ideal Structure Coupled to an Essentially Nonlinear Oscillator

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

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)

Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part II: Nonideal energy source

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On energy transfer between vibrating systems under linear and nonlinear interactions

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

On energy transfer between linear and nonlinear oscillators

In this paper energy transfer in a dissipative mechanical system is analysed. Such system is composed of a linear and a nonlinear oscillator with a nonlinearizable cubic stiffness. Depending on initial conditions, we find energy transfer either from linear to nonlinear oscillator (energy pumping) or from nonlinear to linear. Such results are valid for two different potentials. However, under resonance and absence of external excitation, if the mass of the nonlinear oscillator is adequately small then the linear oscillator always loses energy. Our approach uses rigorous Regular Perturbation Theory. Besides, we have included the case of two linear oscillators under linear or cubic interactions. Comparisons with the earlier case are made. (c) 2008 Elsevier Ltd. All rights reserved.

Short Comments on an Energy Pumping Levels in a MEMS Gyroscope Vibrating Problem, by Using of an Global and Local Optimal Linear Control Design

This paper deals with an energy pumping that occurs in a (MEMS) Gyroscope nonlinear dynamical 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 also developed a linear optimal control design for reducing the oscillatory movement of the nonlinear systems to a stable point.

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.

An Optimal Linear Control Design for Nonlinear Systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)