A method for analysis of dynamics in generator swing based on nonlinear system theory

Presenting an important potential in the representation of nonlinear systems, the multimodel approach remains an attractive axis for research. One of the important problems in the multimodel structure concerns the validity calculation which is a fundamental point especially when the process is corrupted with noise and/or its parameters are of high variations. A new approach based on the use of both two type of validity is proposed. A developed specification of the need of each one is explained by an optimization procedure. The conduct of this approach requires, first, the classification of the numerical data into a set of clusters. The frequency-sensitive competitive learning (FSCL) algorithm is used to select the number of models and the fuzzy k-means algorithm identify the operating clusters. From the satisfactory results in terms of precision and robustness obtained on theoretical examples, we are incited to confirm our contribution to real process reactor. The results obtained are compared to the classical approaches showing its ability to represent adequately the nonlinear process with a superior precision and accuracy and from this the classic strategy of multimodel representation is oriented towards a multifaceted approach.

: The Commanding General, Marine Corps Combat Development Command (MCCDC) asked the Center for Naval Analyses to assess the general applicability of the new science to land warfare. New Sciences is a catch-all phrase that refers to the tools and methodologies used in nonlinear dynamics and complex systems theory to study physical dynamical systems exhibiting a complicated dynamics. This report concludes that the concepts, ideas, theories, tools and general methodologies of nonlinear dynamics and complex systems theory show enormous, almost unlimited, potential for not just providing better solutions for certain existing problems of land combat, but for fundamentally altering our general understanding of the basic processes of war, at all levels. Indeed, the new sciences' greatest legacy may, in the end, prove to be not just a set of creative answers to old questions but and entirely new set of questions to be asked of what really happens on the battlefield The central thesis of this paper is that land combat is a complex adaptive system. That is to say, that land combat is essentially a nonlinear dynamical system composed of many interacting semi-autonomous and hierarchically organized agents continuously adapting to a changing environment.

In today’s competitive business environment, organizations are being challenged to improve performance by improving processes, minimizing costs, and increasing output. Such changes can only be made by looking beyond traditional management systems. Continuous improvement (CI) and total quality management (TQM) have been the focus of recent quality improvement initiatives. However, in many ways, the results have not been as dramatic as desired. Business process reengineering (BPR) focuses on innovation and creativity in redesigning processes in an effort to meet customers’ needs and expectations. Experience using nonlinear systems theory in applied health care settings has revealed that nonlinear science does offer a practical new frame of reference for BPR initiatives. This article describes why radically different approaches are necessary to sustain continued quality improvement, provides the key practical insights offered by nonlinear systems theory, and provides a clinical example of multidimensional thinking as applied in an acute care setting.

Theory of nonlinear systems

The aim of this review was to present research work on the development of the Malmquist index (MI) in various aspects based on the Data Envelopment Analysis (DEA) method. The MI is one of the three methods of dynamic analysis and also the main one, as it is the most commonly used to measure productivity changes. However, over the years, from being a simple productivity index like the models within the DEA method, it has become a more complex and useful index as it has seen many developments and extensions. Modifications and developments of the MI have taken place in many directions. A review of MI studies from 1990 to 2025 shows that the authors considered various aspects of the MI: Alternative ways of decomposing, different ways of measuring, different types of efficiency, different nature of data and variables and network structure or combined dynamic analysis methods into a single framework. The direction of changes and modifications of the MI can be divided into three groups: Adapting DEA solutions within the MI, presenting new MI solutions without being inspired by the DEA method and combining two methods of dynamic analysis into one framework.

This paper mainly focuses on the attitude control problem of rigid spacecraft, and conducts the design and research of control methods based on the theory of nonlinear negative imaginary systems. A feedback control law is designed for the attitude control model of the rigid spacecraft, ensuring that the closed-loop system satisfies the nonlinear negative imaginary property. Subsequently, according to the stability theory of nonlinear negative imaginary interconnected systems, a strictly negative imaginary controller is designed to achieve the asymptotic stability of the attitude of the rigid spacecraft during its operation. The numerical simulation results verify the effectiveness of the proposed control synthesis method for the rigid spacecraft system.

Systems theory and some canonical representations are introduced for a class of nonlinear systems. Techniques are devised to identify, synthesize, and model such systems and their signals. Nonlinear systems theory is introduced at a fundamental level. To identify a system from input and output (or just output) data, parameters are estimated for a canonical state-space or difference-equation representation, depending on which representation is most convenient for further analysis. >

Special issue on: nonlinear systems theory and design

The accurate prediction of dynamic characteristics of high speed rotors, such as gas turbines, is important to avoid the possibility of operating the machinery near the critical speeds or unstable speed regions. However, the dynamic analysis methods and softwares for gas turbines have been developed in the process of producing many gas turbines by manufacturers and most of them have seldom been disclosed to the public. Recently, commercial FEM softwares, such as SAMCEF, ANSYS and NASTRAN, started supporting some rotordynamics analysis modules based on 3-D finite elements. In this paper, the dynamic analysis method using commercial S/W, especially ANSYS, is attempted for the small-size gas turbine engine rotor, and the analysis capability and limitations of its rotordyamics module are evaluated for further improvement of the module. As the preliminary procedure, the rotordyamic analysis capability of ANSYS was tested and evaluated with the reference models of the well-known dynamics. The limitations in application of the rotordynamics module were then identified. Under the current capability and limitations of ANSYS, it is shown that Lee diagram, a new frequency-speed diagram enhanced with the concept of <TEX>$H{\infty}$</TEX> in rotating machinery, can be indirectly obtained from FRFs computed from harmonic response analysis of ANSYS. Finally, it is demonstrated based on the modeling and analysis method developed in the process of the S/W verification that the conventional Campbell diagram, Lee diagram, mode shapes and critical speeds of the small-size gas turbine engine rotor can be computed using the ANSYS rotordynamics module.

In this review we examined the emerging science of deterministic chaos (nonlinear systems theory) and its application to selected physiological systems. Although many of the popular images of fractals represent fascination and beauty that by analogy corresponds to nature as we see it, the question remains as to its ultimate meaning for physiological processes. It was our intent to help clarify this somewhat popular, somewhat obscure area of nonlinear dynamics in the context of an ever-changing procedural base. We examined not only the basic concepts of chaos, but also its applications ranging from observations in single cells to the complexity of the EEG. We have not suggested that nonlinear dynamics will answer all of our questions; however, we did attempt to illustrate ways in which this approach may help us to answer new questions and to rearticulate old ones. Chaos is revolutionary in that the overall approach requires us to adopt a different frame of reference which, at times, may move us away from previous concerns and methods of data analysis. In sections I-IV, we summarized the nonlinear dynamics approach and described its application to physiology and neural systems. First, we presented a general overview of the application of nonlinear dynamical techniques to neural systems. We discussed the manner in which even apparently simple deterministic systems can behave in an unpredictable manner. Second, we described the principles of nonlinear dynamical systems including the derived analytical techniques. We now see a variety of procedures for delineating whether frenetic chaotic behavior results from a nonlinear dynamical system with a few degrees of freedom, or whether it is caused by an infinite number of variables, i.e., noise. Third, we approached the applications of nonlinear procedures to the cardiovascular systems and to the neurosciences. In terms of time series, we described initial studies which applied the now "traditional" measures of dimensionality (e.g., based on the algorithm by Grassberger and Procaccia) and information change (e.g., Lyapunov exponents). Examples include our own work and that of Pritchard et al., demonstrating that the dynamics of neural mass activity reflect psychopathological states. Today, however, the trend has expanded to include the use of surrogate data and statistical null hypotheses testing to examine whether a given time series can be considered different from that of white or colored noise (cf. Ref. 262). One of the most important potential applications is that of quantifying changes in nonlinear dynamics to predict future states of the system.(ABSTRACT TRUNCATED AT 400 WORDS)

The concept of generalized polynomial operators is introduced and applied to the theory of non-linear systems. Several properties similar to those previously derived for systems described e.g. by Volterra functional series are studied. The main attention is given to inverting of the operators in question. A local inverse is constructed and the region where it is valid is determined. The construction is applied to solving of certain types of non-linear differential equations and to seeking sufficient conditions for BIBO stability of the corresponding systems.

: This report deals with research results obtained in the field of mathematical system theory. Special emphasis was given to the following areas: (1) Linear system theory over a field: parametrization of multi-input, multi-output systems and the geometric structure of classes of systems of constant dimension. (2) Linear systems over a ring: development of the theory for very general classes of rings. (3) Nonlinear system theory: basic properties of polynomial (discrete-time) systems and their realization theory. The present report is only a brief summary of findings, which are far too technical to be explained in a few pages. The results are being gradually published in the open literature. For details, refer to previous proposals and/or to the publications listed in the references.

Analysis of heart rate (HR) variability has become an important widely used method for assessing cardiac autonomic regulation. Conventionally, HR variability has been analyzed with time and frequency domain methods. Analysis of HR dynamics by methods based on nonlinear systems theory has opened a novel approach for studying the abnormalities in HR behavior. Recent studies have shown that these measures, particularly scaling analysis methods of HR dynamics, are altered among various patients populations with cardiovascular diseases, and they provide prognostic information. Altered long-term scaling properties of HR dynamics and more random short-term HR fluctuation has been observed, e.g., among patients with previous myocardial infarction, and these alterations have been shown to be associated with increased mortality rate. A relatively large body of data indicate that altered scaling properties of R-R intervals are physiologically deleterious. These findings support the notion that some nonlinear methods, such as scaling and complexity measures, give clinically valuable information for risk stratification among various patient populations. This article provides a review of our current knowledge of the usefulness of dynamical measures of HR fluctuation.

The dynamic characteristic as one key feature determines the earthquake response and seismic performance of structures.Curved box beams occur coupling of flexural and torsional modes,which companied with warping.Based on the precise transfer matrix method,precise transfer matrixs for solving the natural frequencies and modes of curved box beam out plane have been derivated.The analysis of vibration characteristics of single-span curved box beam with pinned-pinned ends has been done. Example shows that the precise transfer matrix method is a simple and effective method for dynamic characteristic analysis of curved box beams.

Exact linearization is a traditional method for nonlinear system in the nonlinear system theory, the basic idea of which is to linearize the whole or parts of a nonlinear system using nonlinear coordinate transformation and nonlinear state feedback method. The input-output relationship of the nonlinear system can be represented by a linearized model which can be built using linear system design method. In order to enhance the robustness of an established system which has been linearized via feedback method, the robust control strategy should be adopted. As a result, the control law is composed of feedback linearization control and robust control. Sliding mode variable structure control is a robust control method which is proposed in this paper as a robust control strategy for the exact linearization system.