Editorial dynamics and control of aerospace and vertical transportation systems

This Special Issue presents a selection of papers initially presented at the 11th International Conference on Vibration Problems (ICOVP-2013), held from 9 to 12 September 2013 in Lisbon, Portugal. The main topics of this Special Issue are linear and, mainly, nonlinear dynamics, chaos and control of systems and structures and their applications in different field of science and engineering. According to the goal of the Special Issue, the selected contributions are divided into three major parts: “Vibration Problems in Vertical Transportation Systems”, “Nonlinear Dynamics, Chaos and Control of Elastic Structures” and “New Strategies and Challenges for Aerospace and Ocean Structures Dynamics and Control”.

Stability and convergence analysis of a neural model applied in nonlinear systems optimization

A neural model for solving nonlinear optimization problems is presented in this paper. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The network is shown to be completely stable and globally convergent to the solutions of nonlinear optimization problems. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are presented to validate the developed methodology.

Implementation of two-stage Hopfield model and its application in nonlinear systems

This paper presents an efficient neural network for solving constrained nonlinear optimization problems. More specifically, a two-stage neural network architecture is developed and its internal parameters are computed using the valid-subspace technique. The main advantage of the developed network is that it treats optimization and constraint terms in different stages with no interference with each other. Moreover, the proposed approach does not require specification of penalty or weighting parameters for its initialization.

Parameter-dependent Lyapunov functions for state-derivative feedback control in polytopic linear systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Control aspects in nonlinear Hill's equation

The Hill's equations-even in the linear original version are a describer of phenomenon having chaotic flavor, giving sometimes very unusual situations. The theory of the so called intervals of instability in the equation provides the precise description for most of these phenomena. Considerations on nonlinearities into the Hill's equation is a quite recent task. The linearized version for almost of these systems it reduces to the Hill's classical linear one. In this paper, some indicative facts are pointed out on the possibility of having the linear system stabilizable and/or exactly controllable. As consequence of such an approach we get results having strong classical aspects, like the one talking about location of parameters in intervals of stability. A result for nonlinear proper periodic controls, is considered too. (C) 2010 Elsevier B.V. All rights reserved.

On saturation control of a non-ideal vibrating portal frame foundation type shear-building

In this paper, we examine the nonlinear control method based on the saturation phenomenon and of systems coupled with quadratic nonlinear ties applied to a shear-building portal plane frame foundation that supports an unbalanced direct cut-rent with limited power supply (non-ideal system). We analyze the equations of motion by using the method of averaging and numerical simulation. The interaction of the non-ideal structure with the saturation controller may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the systems. Special attention is focused on passage through resonance when the non-ideal excitation frequency is near the portal frame natural frequency and when the non-ideal system frequency is approximately twice the controller frequency (two-to-one internal resonance).

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 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.

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled 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 nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

Uniform estimates of attracting sets of extended Lurie systems using LMIs

This research presents a systematic procedure to obtain estimates, via extended Lyapunov functions, of attracting sets of a class of nonlinear systems, as well as an estimate of their stability regions. The considered class of nonlinear systems, called in this note the extended Lurie system, consists of nonlinear systems like those of the Lurie problem where one of the nonlinear functions can violate the sector conditions of the Lurie problem around the origin. In case of nonautonomous systems the concept of absolute stability is extended and uniform estimates of the attracting set are obtained. Two classical nonlinear systems, the forced duffing equation and the Van der Pol system, are analyzed with the proposed procedure.

Control of nonlinear absorption and amplification of light in Er3+-doped fluoroindate glass

Nonlinear absorption and amplification of a probe laser beam can be controlled by adjustment of the intensity-modulation frequency and the wavelength of a pump laser beam. A demonstration of this effect in Er3+-doped fluoroindate glass is presented. The results show maximum amplification of the probe beam (∼12%) when a pump laser emitting 16 mW of power is modulated at ∼30 Hz. In the limit of low modulation frequencies, or cw pumping, induced absorption of the probe beam is the dominant nonlinear process. © 1999 Optical Society of America.

Evaluation of systems for timing of fungicide sprays for control of postbloom fruit drop of citrus in Brazil

Postbloom fruit drop (PFD) of citrus, caused by Colletotrichum acutatum, infects petals of citrus flowers and produces orange-brown lesions that induce the abscission of young fruitlets and the retention of calyces. Proper timing of fungicide applications is essential for good disease control. Different systems for timing of fungicide applications for control of PFD in a major citrus-growing region in southern São Paulo state in Brazil were evaluated from 1999 to 2002. The following programs were compared to an unsprayed control using counts of diseased flowers, persistent calyces, or fruit: (i) a phenology-based program currently recommended in Brazil with one application at early and another at peak bloom; (ii) the Florida PFD model; (iii) the postbloom fruit drop-fungicide application decision system (PFD-FAD), a new computer-assisted decision method; and (iv) grower's choice. In 1999, no disease developed, sprays applied with the phenology-based program had no effect, and the Florida PFD model saved two sprays compared with the phenology-based program. In 2000, PFD was moderate and the phenology-based and growers' choice treatments had a significantly lower number of persistent calyces and higher fruit numbers than the control, but no differences were found between those treatments and the PFD model. In 2001, PFD was severe with considerable yield loss. The PFD model, the phenology-based program, and the grower's choice reduced flower blight and the number of persistent calyces, and improved fruit yields with two to three applications, but the PFD-FAD achieved comparable yields with only one spray. In 2002, the disease was mild, with no yield loss, and the Florida PFD model and the PFD-FAD saved one spray compared with the other systems. The PFD model and the PFD-FAD were equally effective for timing fungicide applications to control PFD in Brazil. Scouting of trees is simpler with PFD-FAD; therefore, this system is recommended and should eliminate unnecessary sprays and reduce costs for growers.

Linear quadratic Gaussian control of discrete-time Markov jump linear systems with horizon defined by stopping times

The linear quadratic Gaussian control of discrete-time Markov jump linear systems is addressed in this paper, first for state feedback, and also for dynamic output feedback using state estimation. in the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (T N), or the occurrence of a crucial failure event (τ δ), after which the system paralyzed. From the constructive method used here a separation principle holds, and the solutions are given in terms of a Kalman filter and a state feedback sequence of controls. The control gains are obtained by recursions from a set of algebraic Riccati equations for the former case or by a coupled set of algebraic Riccati equation for the latter case. Copyright © 2005 IFAC.

Variable structure control of switched systems based on Lyapunov-Metzler-SPR systems

This paper presents two Variable Structure Controllers (VSC) for continuous-time switched plants. It is assumed that the state vector is available for feedback. The proposed control system provides a switching rule and also the variable structure control input. The design is based on Lyapunov-Metzler (LM) inequalities and also on Strictly Positive Real (SPR) systems stability results. The definition of Lyapunov-Metzler-SPR (LMS) systems and its direct application in the design of VSC for switched systems are introduced in this paper. Two examples illustrate the design of the proposed VSC, considering a plant given by a switched system with a switched-state control law and two linear time-invariant systems, that are not controllable and also can not be stabilized with state feedback. ©2008 IEEE.