Design of reduced-order state/unknown input observers: a descriptor system approach

This paper addresses the problem of estimating simultaneously a linear function of both the state and unknown input of linear system with unknown inputs. By adopting the descriptor system approach, the problem can be conveniently solved. Observers proposed in this paper are of low-order and do not include the derivatives of the outputs. New conditions for the existence of reduced-order observers are derived. A design procedure for the determination of the observer parameters can also be easily derived based on the derived existence conditions

An algebraic approach for delay-independent and delay-dependent stability of linear time-delay systems

This paper addresses the problem of asymptotic stability of a linear system with many delay units. A novel algebraic test is proposed for the delay-independent stability of the system, based on the root distribution of the system's characteristic equation. If the system is only stable dependent of delay, the whole stable regions of the system can be perfectly obtained. Two algorithms are derived to examine the delay-independent stability, and to compute the whole stable regions if the system is of delay-dependent stability. These algorithms are computationally efficient and applicable to both certain and uncertain systems. Some illustrative examples demonstrate the validity of the approach.

Pole placement method using the system matrix transfer function and sparsity

This paper presents a pole placement method using both the augmented Jacobian and the corresponding system transfer function matrices. From the manipulation of these matrices a straightforward approach results to get the coefficients of a non-linear system, whose solution gives the parameters of the stabilizers that can provide a pre-specified minimum damping to the system. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

System identification and active vibration control of a flexible structure

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

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

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)

Sufficients conditions for analysis of extrema in the step-response of the linear control systems

This note deals whith the problem of extrema which may occur in the step-response of a stable linear system with real zeros and poles. Some simple sufficients conditions and necessary conditions are presented for analyses when zeros located between the dominant and fastest pole does not cause extrema in the step-response. These conditions require knowledge of the pole-zero configuration of the corresponding transfer-function.

Effect of a heat-treatment on the linear dimensional change of a hard chairside reline resin

Statement of problem. Little data are available regarding the effect of heat-treatments on the dimensional stability of hard chairside reline resins. Purpose. The objective of this in vitro study was to evaluate whether a heat-treatment improves the dimensional stability of the reline resin Duraliner II and to compare the linear dimensional changes of this material with the heat-polymerized acrylic resin Lucitone 550. Material and methods. The materials were mixed according to the manufacturer's instructions and packed into a stainless steel split mold (50.0 mm diameter and 0.5 mm thickness) with reference points (A, B, C, and D). Duraliner II specimens were polymerized for 12 minutes in water at 37°C and bench cooled to room temperature before being removed from the mold. Twelve specimens were made and divided into 2 groups: group 1 specimens (n=6) were left untreated, and group 2 specimens (n=6) were submitted to a heat-treatment in a water bath at 55°C for 10 minutes and then bench cooled to room temperature. The 6 Lucitone specimens (control group) were polymerized in a water bath for 9 hours at 71°C. The specimens were removed after the mold reached the room temperature. A Nikon optical comparator was used to measure the distances between the reference points (AB and CD) on the stainless steel mold (baseline readings) and on the specimens to the nearest 0.001 mm. Measurements were made after processing and after the specimens had been stored in distilled water at 37°C for 8 different periods of time. Data were subjected to analysis of variance with repeated measures, followed by Tukey's multiple comparison test (P<.05). Results. All specimens exhibited shrinkage after processing (control, -0.41%; group 1, -0.26%; and group 2, -0.51%). Group 1 specimens showed greater shrinkage (-1.23%) than the control (-0.23%) and group 2 (-0.81%) specimens after 60 days of storage in water (P<.05). Conclusion. Within the limitations of this study, a significant improvement of the long-term dimensional stability of the Duraliner II reline resin was observed when the specimens were heat-treated. However, the shrinkage remained considerably higher than the denture base resin Lucitone 550. Copyright © 2002 by The Editorial Council of The Journal of Prosthetic Dentistry.

Substitution-newton-Raphson method for the solution of electric network equations

The power flow problem, in transmission networks, has been well solved, for most cases, using Newton-Raphson method (NR) and its decoupled versions. Generally speaking, the solution of a non-linear system of equations refers to two methods: NR and Successive Substitution. The proposal of this paper is to evaluate the potential of the Substitution-Newton-Raphson Method (SNR), which combines both methods, on the solution of the power flow problem. Simulations were performed using a two-bus test network in order to observe the characteristics of these methods. It was verified that the NR is faster than SNR, in terms of convergence, considering non-stressed scenarios. For those cases where the power flow in the network is closed to the limits (stressed system), the SNR converges faster. This paper presents the power flow formulation of the SNR and describes its potential for its application in special cases such as stressed scenarios. © 2006 IEEE.

Comparison between the performances of a linear isolator and an isolator with a geometrically nonlinear damper

Pós-graduação em Engenharia Mecânica - FEIS

Vibration Control Applied in a Semi-Active Suspension using Magneto Rheological Damper and Optimal Linear Control Design

In this paper we study the behavior of a semi-active suspension witch external vibrations. The mathematical model is proposed coupled to a magneto rheological (MR) damper. The goal of this work is stabilize of the external vibration that affect the comfort and durability an vehicle, to control these vibrations we propose the combination of two control strategies, the optimal linear control and the magneto rheological (MR) damper. The optimal linear control is a linear feedback control problem for nonlinear systems, under the optimal control theory viewpoint We also developed the optimal linear control design with the scope in to reducing the external vibrating of the nonlinear systems in a stable point. Here, we discuss the conditions that allow us to the linear optimal control for this kind of non-linear system.

Bifurcations Leading to Nonlinear Oscillations in a 3D Piecewise Linear Memristor Oscillator

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

A hybrid method for the solution of a sparse power system matrices on vector computers

This paper describes a methodology for solving a linear system of equations on vector computer. The methodology combines direct and inverse factors. The decomposition and implementation of the direct solution in a CRAY Y-MPZE/232, and the performance results are discussed.

Switching-off in a minimal time a fitzhugh-nagumo system

This paper deals with a system that describes an electrical circuitcomposed by a linear system coupled to a nonlinear one involving a tunneldiode in a flush-and-fill circuit. One of the most comprehensive models for thiskind of circuits was introduced by R. Fitzhugh in 1961, when taking on carebiological tasks. The equation has in its phase plane only two periodic solutions,namely, the unstable singular point S0 and the stable cycle Γ. If the system isat rest on S0, the natural flow of orbits seeks to switch-on the process by going- as time goes by - toward its steady-state, Γ. By using suitable controls it ispossible to reverse such natural tendency going in a minimal time from Γ toS0, switching-off in this way the system. To achieve this goal it is mandatorya minimal enough strength on controls. These facts will be shown by means ofconsiderations on the null control sets in the process.

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.