Discrete inequalities based on multiple auxiliary functions and their applications to stability analysis of time-delay systems

Abstract
This paper presents new discrete inequalities for single summation and double summation. These inequalities are based on multiple auxiliary functions and include the Jensen discrete inequality and the discrete Wirtinger-based inequality as special cases. An application of these discrete inequalities to analyse stability of linear discrete systems with an interval time-varying delay is studied and a less conservative stability condition is obtained. Three numerical examples are given to show the effectiveness of the obtained stability condition.

Proportional controllers: Direct method for stability analysis and MATLAB implementation

In most cases, the cost of a control system increases based on its complexity. Proportional (P) controller is the simplest and most intuitive structure for the implementation of linear control systems. The difficulty to find the stability range of feedback systems with P controllers, using the Routh-Hurwitz criterion, increases with the order of the plant. For high order plants, the stability range cannot be easily obtained from the investigation of the coefficient signs in the first column of the Routh's array. A direct method for the determination of the stability range is presented. The method is easy to understand, to compute, and to offer the students a better comprehension on this subject. A program in MATLAB language, based on the proposed method, design examples, and class assessments, is provided in order to help the pedagogical issues. The method and the program enable the user to specify a decay rate and also extend to proportional-integral (PI), proportional-derivative (PD), and proportional-integral-derivative (PID) controllers.

Stability analysis of the attitude of artificial satellites subject to gravity gradient torque

Using a canonical formulation, the stability of the rotational motion of artificial satellites is analyzed considering perturbations due to the gravity gradient torque. Here Andoyer's variables are used to describe the rotational motion. One of the approaches that allow the analysis of the stability of Hamiltonian systems needs the reduction of the Hamiltonian to a normal form. Firstly equilibrium points are found. Using generalized coordinates, the Hamiltonian is expanded in the neighborhood of the linearly stable equilibrium points. In a next step a canonical linear transformation is used to diagonalize the matrix associated to the linear part of the system. The quadratic part of the Hamiltonian is normalized. Based in a Lie-Hori algorithm a semi-analytic process for normalization is applied and the Hamiltonian is normalized up to the fourth order. Once the Hamiltonian is normalized up to order four, the analysis of stability of the equilibrium point is performed using the theorem of Kovalev and Savichenko. This semi-analytical approach was applied considering some data sets of hypothetical satellites. For the considered satellites it was observed few cases of stable motion. This work contributes for space missions where the maintenance of spacecraft attitude stability is required.

Aeroelastic stability analysis considering a continuous flight envelope

This paper presents a new methodology to analyze aeroelastic stability in a continuous range of flight envelope with varying parameter of velocity and altitude. The focus of the paper is to demonstrate that linear matrix inequalities can be used to evaluate the aeroelastic stability in a region of flight envelope instead of a single point, like classical methods. The proposed methodology can also be used to study if a system remains stable during an arbitrary motion from one point to another in the flight envelope, i.e., when the problem becomes time-variant. The main idea is to represent the system as a polytopic differential inclusion system using rational function approximation to write the model in time domain. The theory is outlined and simulations are carried out on the benchmark AGARD 445.6 wing to demonstrate the method. The classical pk-method is used for comparing results and validating the approach. It is shown that this method is efficient to identify stability regions in the flight envelope. (C) 2014 Elsevier Ltd. All rights reserved.

Contribution to assessing the stiffness reduction of structural elements in the global stability analysis of precast concrete multi-storey buildings

This study deals with the reduction of the stiffness in precast concrete structural elements of multi-storey buildings to analyze global stability. Having reviewed the technical literature, this paper present indications of stiffness reduction in different codes, standards, and recommendations and compare these to the values found in the present study. The structural model analyzed in this study was constructed with finite elements using ANSYS® software. Physical Non-Linearity (PNL) was considered in relation to the diagrams M x N x 1/r, and Geometric Non-Linearity (GNL) was calculated following the Newton-Raphson method. Using a typical precast concrete structure with multiple floors and a semi-rigid beam-to-column connection, expressions for a stiffness reduction coefficient are presented. The main conclusions of the study are as follows: the reduction coefficients obtained from the diagram M x N x 1/r differ from standards that use a simplified consideration of PNL; the stiffness reduction coefficient for columns in the arrangements analyzed were approximately 0.5 to 0.6; and the variation of values found for stiffness reduction coefficient in concrete beams, which were subjected to the effects of creep with linear coefficients from 0 to 3, ranged from 0.45 to 0.2 for positive bending moments and 0.3 to 0.2 for negative bending moments.

A New Prediction Model for Slope Stability Analysis

The instability of river bank can result in considerable human and land losses. The Po river is the most important in Italy, characterized by main banks of significant and constantly increasing height. This study presents multilayer perceptron of artificial neural network (ANN) to construct prediction models for the stability analysis of river banks along the Po River, under various river and groundwater boundary conditions. For this aim, a number of networks of threshold logic unit are tested using different combinations of the input parameters. Factor of safety (FS), as an index of slope stability, is formulated in terms of several influencing geometrical and geotechnical parameters. In order to obtain a comprehensive geotechnical database, several cone penetration tests from the study site have been interpreted. The proposed models are developed upon stability analyses using finite element code over different representative sections of river embankments. For the validity verification, the ANN models are employed to predict the FS values of a part of the database beyond the calibration data domain. The results indicate that the proposed ANN models are effective tools for evaluating the slope stability. The ANN models notably outperform the derived multiple linear regression models.

Stability analysis of a mono inverter dual sensorless motors system

When a single brush-less dc motor is fed by an inverter with a sensor-less algorithm embedded in the switching controller, the system exhibits a linear and stable output in terms of the speed and torque. However, with two motors modulated by the same inverter, the system is unstable and rendered useless for a steady application, unless provided with some resistive damping on the supply lines. The project discusses and analysis the stability of such a system through simulations and hardware demonstrations and also will discuss a method to derive the values of these damping.

Efficient numerical methods for global linear instability. Analysis and modeling of non-orthogonal swept attachment-line boundary layer flow

The aim of this thesis is to study the mechanisms of instability that occur in swept wings when the angle of attack increases. For this, a simplified model for the a simplified model for the non-orthogonal swept leading edge boundary layer has been used as well as different numerical techniques in order to solve the linear stability problem that describes the behavior of perturbations superposed upon this base flow. Two different approaches, matrix-free and matrix forming methods, have been validated using direct numerical simulations with spectral resolution. In this way, flow instability in the non-orthogonal swept attachment-line boundary layer is addressed in a linear analysis framework via the solution of the pertinent global (Bi-Global) PDE-based eigenvalue problem. Subsequently, a simple extension of the extended G¨ortler-H¨ammerlin ODEbased polynomial model proposed by Theofilis, Fedorov, Obrist & Dallmann (2003) for orthogonal flow, which includes previous models as particular cases and recovers global instability analysis results, is presented for non-orthogonal flow. Direct numerical simulations have been used to verify the stability results and unravel the limits of validity of the basic flow model analyzed. The effect of the angle of attack, AoA, on the critical conditions of the non-orthogonal problem has been documented; an increase of the angle of attack, from AoA = 0 (orthogonal flow) up to values close to _/2 which make the assumptions under which the basic flow is derived questionable, is found to systematically destabilize the flow. The critical conditions of non-orthogonal flows at 0 _ AoA _ _/2 are shown to be recoverable from those of orthogonal flow, via a simple analytical transformation involving AoA. These results can help to understand the mechanisms of destabilization that occurs in the attachment line of wings at finite angles of attack. Studies taking into account variations of the pressure field in the basic flow or the extension to compressible flows are issues that remain open. El objetivo de esta tesis es estudiar los mecanismos de la inestabilidad que se producen en ciertos dispositivos aerodinámicos cuando se aumenta el ángulo de ataque. Para ello se ha utilizado un modelo simplificado del flujo de base, así como diferentes técnicas numéricas, con el fin de resolver el problema de estabilidad lineal asociado que describe el comportamiento de las perturbaciones. Estos métodos; sin y con formación de matriz, se han validado utilizando simulaciones numéricas directas con resolución espectral. De esta manera, la inestabilidad del flujo de capa límite laminar oblicuo entorno a la línea de estancamiento se aborda en un marco de análisis lineal por medio del método Bi-Global de resolución del problema de valores propios en derivadas parciales. Posteriormente se propone una extensión simple para el flujo no-ortogonal del modelo polinomial de ecuaciones diferenciales ordinarias, G¨ortler-H¨ammerlin extendido, propuesto por Theofilis et al. (2003) para el flujo ortogonal, que incluye los modelos previos como casos particulares y recupera los resultados del analisis global de estabilidad lineal. Se han realizado simulaciones directas con el fin de verificar los resultados del análisis de estabilidad así como para investigar los límites de validez del modelo de flujo base utilizado. En este trabajo se ha documentado el efecto del ángulo de ataque AoA en las condiciones críticas del problema no ortogonal obteniendo que el incremento del ángulo de ataque, de AoA = 0 (flujo ortogonal) hasta valores próximos a _/2, en el cual las hipótesis sobre las que se basa el flujo base dejan de ser válidas, tiende sistemáticamente a desestabilizar el flujo. Las condiciones críticas del caso no ortogonal 0 _ AoA _ _/2 pueden recuperarse a partir del caso ortogonal mediante el uso de una transformación analítica simple que implica el ángulo de ataque AoA. Estos resultados pueden ayudar a comprender los mecanismos de desestabilización que se producen en el borde de ataque de las alas de los aviones a ángulos de ataque finitos. Como tareas pendientes quedaría realizar estudios que tengan en cuenta variaciones del campo de presión en el flujo base así como la extensión de éste al caso de flujos compresibles.

Refined Jensen-based inequality approach to stability analysis of time-delay systems

© 2015 The Institution of Engineering and Technology. In this study, the authors derive some new refined Jensen-based inequalities, which encompass both the Jensen inequality and its most recent improvement based on the Wirtinger integral inequality. The potential capability of this approach is demonstrated through applications to stability analysis of time-delay systems. More precisely, by using the newly derived inequalities, they establish new stability criteria for two classes of time-delay systems, namely discrete and distributed constant delays systems and interval time-varying delay systems. The resulting stability conditions are derived in terms of linear matrix inequalities, which can be efficiently solved by various convex optimisation algorithms. Numerical examples are given to show the effectiveness and least conservativeness of the results obtained in this study.

Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities

This paper is concerned with the problem of stochastic stability analysis of discrete-time two-dimensional (2-D) Markovian jump systems (MJSs) described by the Roesser model with interval time-varying delays. The transition probabilities of the jumping process/Markov chain are assumed to be uncertain, that is, they are not exactly known but can be estimated. A Lyapunov-like scheme is first extended to 2-D MJSs with delays. Based on some novel 2-D summation inequalities proposed in this paper, delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities (LMIs) which can be computationally solved by various convex optimization algorithms. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

Stability analysis and control of multiple converter based autonomous microgrid

In this paper, the stability of an autonomous microgrid with multiple distributed generators (DG) is studied through eigenvalue analysis. It is assumed that all the DGs are connected through Voltage Source Converter (VSC) and all connected loads are passive. The VSCs are controlled by state feedback controller to achieve desired voltage and current outputs that are decided by a droop controller. The state space models of each of the converters with its associated feedback are derived. These are then connected with the state space models of the droop, network and loads to form a homogeneous model, through which the eigenvalues are evaluated. The system stability is then investigated as a function of the droop controller real and reac-tive power coefficients. These observations are then verified through simulation studies using PSCAD/EMTDC. It will be shown that the simulation results closely agree with stability be-havior predicted by the eigenvalue analysis.

Power system stability analysis based on descriptive study of electrical indices

In a power network, when a propagation energy wave caused by a disturbance hits a weak link, a reflection is appeared and some of energy is transferred across the link. In this work, an analytical descriptive methodology is proposed to study the dynamical stability of a large scale power system. For this purpose, the measured electrical indices (angle, or voltage/frequency) following a fault in different points among the network are used, and the behaviors of the propagated waves through the lines, nodes and buses are studied. This work addresses a new tool for power system stability analysis based on a descriptive study of electrical measurements. The proposed methodology is also useful to detect the contingency condition and synthesis of an effective emergency control scheme.

Stability analysis based on birfurcation theory of the DSTATCOM operating in current control mode

This paper presents the stability analysis for a distribution static compensator (DSTATCOM) that operates in current control mode based on bifurcation theory. Bifurcations delimit the operating zones of nonlinear circuits and, hence, the capability to compute these bifurcations is of important interest for practical design. A control design for the DSTATCOM is proposed. Along with this control, a suitable mathematical representation of the DSTATCOM is proposed to carry out the bifurcation analysis efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the point of common coupling. In addition, the stability regions in the control gain space, as well as the contour lines for different Floquet multipliers are computed. It is demonstrated through bifurcation analysis that the loss of stability in the DSTATCOM is due to the emergence of a Neimark bifurcation. The observations are verified through simulation studies.

On the application of the probabilistic linear discriminant analysis to face recognition across expression

Facial expression is one of the main issues of face recognition in uncontrolled environments. In this paper, we apply the probabilistic linear discriminant analysis (PLDA) method to recognize faces across expressions. Several PLDA approaches are tested and cross-evaluated on the Cohn-Kanade and JAFFE databases. With less samples per gallery subject, high recognition rates comparable to previous works have been achieved indicating the robustness of the approaches. Among the approaches, the mixture of PLDAs has demonstrated better performances. The experimental results also indicate that facial regions around the cheeks, eyes, and eyebrows are more discriminative than regions around the mouth, jaw, chin, and nose.