Analysis of System Signals Based on Cross Recurrence Method for System Dynamics Characterization

Natural systems are inherently non linear. Recurrent behaviours are typical of natural systems. Recurrence is a fundamental property of non linear dynamical systems which can be exploited to characterize the system behaviour effectively. Cross recurrence based analysis of sensor signals from non linear dynamical system is presented in this thesis. The mutual dependency among relatively independent components of a system is referred as coupling. The analysis is done for a mechanically coupled system specifically designed for conducting experiment. Further, cross recurrence method is extended to the actual machining process in a lathe to characterize the chatter during turning. The result is verified by permutation entropy method. Conventional linear methods or models are incapable of capturing the critical and strange behaviours associated with the dynamical process. Hence any effective feature extraction methodologies should invariably gather information thorough nonlinear time series analysis. The sensor signals from the dynamical system normally contain noise and non stationarity. In an effort to get over these two issues to the maximum possible extent, this work adopts the cross recurrence quantification analysis (CRQA) methodology since it is found to be robust against noise and stationarity in the signals. The study reveals that the CRQA is capable of characterizing even weak coupling among system signals. It also divulges the dependence of certain CRQA variables like percent determinism, percent recurrence and entropy to chatter unambiguously. The surrogate data test shows that the results obtained by CRQA are the true properties of the temporal evolution of the dynamics and contain a degree of deterministic structure. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP based methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material. The results establish this methodology to be feasible for detection of chatter in metal cutting operation in a lathe.

Linear-wavelet models for system identification

A model structure comprising a wavelet network and a linear term is proposed for nonlinear system identification. It is shown that under certain conditions wavelets are orthogonal to linear functions and, as a result, the two parts of the model can be identified separately. The linear-wavelet model is compared to a standard wavelet network using data from a simulated fermentation process. The results show that the linear-wavelet model yields a smaller modelling error when compared to a wavelet network using the same number of regressors.

On the stability radius of a generalized state-space system

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.

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.

Identificação e comparação entre controle preditivo com modelo não linear e PI sintonizados com PSO em sistema de separação gravitacional de águia-óleo

The separation methods are reduced applications as a result of the operational costs, the low output and the long time to separate the uids. But, these treatment methods are important because of the need for extraction of unwanted contaminants in the oil production. The water and the concentration of oil in water should be minimal (around 40 to 20 ppm) in order to take it to the sea. Because of the need of primary treatment, the objective of this project is to study and implement algorithms for identification of polynomial NARX (Nonlinear Auto-Regressive with Exogenous Input) models in closed loop, implement a structural identification, and compare strategies using PI control and updated on-line NARX predictive models on a combination of three-phase separator in series with three hydro cyclones batteries. The main goal of this project is to: obtain an optimized process of phase separation that will regulate the system, even in the presence of oil gushes; Show that it is possible to get optimized tunings for controllers analyzing the mesh as a whole, and evaluate and compare the strategies of PI and predictive control applied to the process. To accomplish these goals a simulator was used to represent the three phase separator and hydro cyclones. Algorithms were developed for system identification (NARX) using RLS(Recursive Least Square), along with methods for structure models detection. Predictive Control Algorithms were also implemented with NARX model updated on-line, and optimization algorithms using PSO (Particle Swarm Optimization). This project ends with a comparison of results obtained from the use of PI and predictive controllers (both with optimal state through the algorithm of cloud particles) in the simulated system. Thus, concluding that the performed optimizations make the system less sensitive to external perturbations and when optimized, the two controllers show similar results with the assessment of predictive control somewhat less sensitive to disturbances

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)

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.

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.