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Second-order Systems (second-order + system)

Distribution by Scientific Domains

Engineering	50%
Mathematics and Statistics	20%

Selected Abstracts

DIRECT ADAPTIVE CONTROL FOR NONLINEAR MATRIX SECOND-ORDER SYSTEMS WITH TIME-VARYING AND SIGN-INDEFINITE DAMPING AND STIFFNESS OPERATORS

ASIAN JOURNAL OF CONTROL, Issue 1 2007
Wassim M. Haddad
ABSTRACT A direct adaptive control framework for a class of nonlinear matrix second-order systems with time-varying and sign-indefinite damping and stiffness operators is developed. The proposed framework guarantees global asymptotic stability of the closed-loop system states associated with the plant dynamics without requiring any knowledge of the system nonlinearities other than the assumption that they are continuous and bounded. The proposed adaptive control approach is used to design adaptive controllers for suppressing thermoacoustic oscillations in combustion chambers. [source]

Stochastic models for simulation of strong ground motion in Iceland

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2001
Símon Ólafsson
Abstract Two types of modelling approaches for simulating ground motion in Iceland are studied and compared. The first type of models, named discrete-time series models (ARMA), are based solely on measured acceleration in earthquakes occurring in Iceland. The second type of models are based on a theoretical seismic source model called the extended Brune model. Based on measured acceleration in Iceland during the period 1986,1996, the parameters for the extended Brune models have been estimated. The seismic source models are presented here as ARMA models, which simplifies the simulation process. A single-layer soil amplification model is used in conjunction with the extended Brune model to estimate local site amplification. Emphasis is put on the ground motion models representing the variability in the measured earthquakes, with respect to energy, duration and frequency content. Demonstration is made using these models for constructing linear and non-linear probabilistic response spectra using a discretised version of the Bouc,Wen model for the hysteresis of the second-order system. Copyright © 2001 John Wiley & Sons, Ltd. [source]

A simple mechanism for stabilizing network queues in TCP/IP networks

INTERNATIONAL JOURNAL OF NETWORK MANAGEMENT, Issue 4 2007
James Aweya
In this paper we determine the stability bounds for the DRED active queue management (AQM) algorithm using a previously developed nonlinear dynamic model of TCP. We develop a second-order linear model with time delay by linearizing the nonlinear model. Using the Pade approximation of time-delayed system e,R0s, where R0 is the delay in the system, we then determine the range of stabilizing gains of DRED when controlling the second-order system with time delay R0. We also present examples showing the stability bounds of the DRED controller gain for networks with different parameters such as link capacity, load level, and round-trip time. In addition, we describe an efficient implementation of the DRED AQM algorithm. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Signal fluctuations induced by non-T1 -related confounds in variable TR fMRI experiments

JOURNAL OF MAGNETIC RESONANCE IMAGING, Issue 5 2009
Shuowen Hu BS
Abstract Purpose To assess and model signal fluctuations induced by non-T1 -related confounds in variable repetition time (TR) functional magnetic resonance imaging (fMRI) and to develop a compensation procedure to correct for the non-T1 -related artifacts. Materials and Methods Radiofrequency disabled volume gradient sequences were effected at variable offsets between actual image acquisitions, enabling perturbation of the measurement system without perturbing longitudinal magnetization, allowing the study of non-T1 -related confounds that may arise in variable TR experiments. Three imaging sessions utilizing a daily quality assurance (DQA) phantom were conducted to assess the signal fluctuations, which were then modeled as a second-order system. A modified projection procedure was implemented to correct for signal fluctuations arising from non-T1 -related confounds, and statistical analysis was performed to assess the significance of the artifacts with and without compensation. Results Assessment using phantom data reveals that the signal fluctuations induced by non-T1 -related confounds was consistent in shape across the phantom and well-modeled by a second-order system. The phantom exhibited significant spurious detections (at P < 0.01) almost uniformly across the central slices of the phantom. Conclusion Second-order system modeling and compensation of non-T1 -related confounds achieves significant reduction of spurious detection of fMRI activity in a phantom. J. Magn. Reson. Imaging 2009;29:1234,1239. © 2009 Wiley-Liss, Inc. [source]

Stability of linear time-periodic delay-differential equations via Chebyshev polynomials

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2004
Eric A. Butcher
Abstract This paper presents a new technique for studying the stability properties of dynamic systems modeled by delay-differential equations (DDEs) with time-periodic parameters. By employing a shifted Chebyshev polynomial approximation in each time interval with length equal to the delay and parametric excitation period, the dynamic system can be reduced to a set of linear difference equations for the Chebyshev expansion coefficients of the state vector in the previous and current intervals. This defines a linear map which is the ,infinite-dimensional Floquet transition matrix U'. Two different formulas for the computation of the approximate U, whose size is determined by the number of polynomials employed, are given. The first one uses the direct integral form of the original system in state space form while the second uses a convolution integral (variation of parameters) formulation. Additionally, a variation on the former method for direct application to second-order systems is also shown. An error analysis is presented which allows the number of polynomials employed in the approximation to be selected in advance for a desired tolerance. An extension of the method to the case where the delay and parametric periods are commensurate is also shown. Stability charts are produced for several examples of time-periodic DDEs, including the delayed Mathieu equation and a model for regenerative chatter in impedance-modulated turning. The results indicate that this method is an effective way to study the stability of time-periodic DDEs. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Practical stabilization of exponentially unstable linear systems subject to actuator saturation nonlinearity and disturbance

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2001
Tingshu Hu
Abstract This paper investigates the problem of practical stabilization for linear systems subject to actuator saturation and input additive disturbance. Attention is restricted to systems with two anti-stable modes. For such a system, a family of linear feedback laws is constructed that achieves semi-global practical stabilization on the asymptotically null controllable region. This is in the sense that, for any set ,0 in the interior of the asymptotically null controllable region, any (arbitrarily small) set ,, containing the origin in its interior, and any (arbitrarily large) bound on the disturbance, there is a feedback law from the family such that any trajectory of the closed-loop system enters and remains in the set ,, in a finite time as long as it starts from the set ,0. In proving the main results, the continuity and monotonicity of the domain of attraction for a class of second-order systems are revealed. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Model-based synthesis of nonlinear PI and PID controllers

AICHE JOURNAL, Issue 8 2001
Raymond A. Wright
PI and PID controllers continue to be popular methods in industrial applications. It is well known that linear PI and PID controllers result from the application of model-based controller design methods to linear first- and second-order systems. It is shown that nonlinear PI and PID controllers result from the application of nonlinear controller design methods to nonlinear first- and second-order systems. As a result, the controllers resulting from nonlinear model-based control theory are put in a convenient form, more amenable to industrial implementation. Additionally, the quantities used in the controller are useful for monitoring the process and quantifying modeling error. Chemical engineering examples are used to illustrate the resulting control laws. A simulation example further demonstrates the performance of the nonlinear controllers, as well as their useful process monitoring quantities. [source]

Non-standard finite difference schemes for multi-dimensional second-order systems in non-smooth mechanics

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2007
Yves Dumont
Abstract This work is an extension of the paper (Proc. R. Soc. London 2005; 461A:1927,1950) to impact oscillators with more than one degree of freedom. Given the complex and even chaotic behaviour of these non-smooth mechanical systems, it is essential to incorporate their qualitative physical properties, such as the impact law and the frequencies of the systems, into the envisaged numerical methods if the latter is to be reliable. Based on this strategy, we design several non-standard finite difference schemes. Apart from their excellent error bounds and unconditional stability, the schemes are analysed for their efficiency to preserve some important physical properties of the systems including, among others, the conservation of energy between consecutive impact times, the periodicity of the motion and the boundedness of the solutions. Numerical simulations that support the theory are provided. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Partial pole assignment for the vibrating system with aerodynamic effect

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2004
Wen-Wei Lin
Abstract The partial pole assignment (PPA) problem is the one of reassigning a few unwanted eigenvalues of a control system by feedback to suitably chosen ones, while keeping the remaining large number of eigenvalues unchanged. The problem naturally arises in modifying dynamical behaviour of the system. The PPA has been considered by several authors in the past for standard state,space systems and for quadratic matrix polynomials associated with second-order systems. In this paper, we consider the PPA for a cubic matrix polynomial arising from modelling of a vibrating system with aerodynamics effects and derive explicit formulas for feedback matrices in terms of the coefficient matrices of the polynomial. Our results generalize those of a quadratic matrix polynomial by Datta et al. (Linear Algebra Appl. 1997;257: 29) and is based on some new orthogonality relations for eigenvectors of the cubic matrix polynomial, which also generalize the similar ones reported in Datta et al. (Linear Algebra Appl. 1997;257: 29) for the symmetric definite quadratic pencil. Besides playing an important role in our solution for the PPA, these orthogonality relations are of independent interests, and believed to be an important contribution to linear algebra in its own right. Copyright © 2003 John Wiley & Sons, Ltd. [source]