Multi-parameter sensitivity analysis of power-system stability by Popov's method†

Popov's method of frequency-domain stability criteria is used to conduct the multiparameter sensitivity analysis of power system stability. The two-parameter parametric sensitivity mode] of a one-machine infinite-bus system is developed, This model involves stability measure ξ, defined in terms of Lur'o-type Liapunov functions constructed systematically. Based on the application of the model to a specific numerical example, results and conclusions are given. This type of sensitivity analysis is useful for optimum design and operation of the power system. The criterion of optimality is zero sensitivity. In general, this form of analysis is applicable to any dynamic engineering system.     

Robustness of absolute stability†

The stability of a class of single-input, single-output singularly perturbed systems formed by a linear time-invariant feedforward block with a sector bounded time varying feedback is considered. It is shown that if the reduced order ‘ slow ’ subsystem is absolutely stable and the parasitics are asymptotically stable and sufficiently fast then the full system is absolutely stable. Bounds on the singular perturbation parameter for uniform asymptotic stability and absolute stability are obtained.     

On the stability of interconnected systems†

This paper investigates the stability of systems which can be regarded as composed of interconnected subsystems. A sufficient condition for inputs-output L ^p stability, in terms of the L ^p gains of the subsystems and their interconnections is derived. For the case of L ² stability, it is compared with other criteria for asymptotic stability, obtained by Lyapunov techniques, and shown to give better results for a certain class of systems.     

Circle criterion and transient stability of power systems†

An increasing familiarity of power system engineers with frequency domain techniques has motivated the search for stability criteria for power systems that could be applied in the frequency domain. Following the advent of phase plane methods for second -order systems and the second method of Lyapunov, the Popov method gained popularity. This investigation attempts to apply an extension of Popov's method to determine the transient stability of a single machine infinite bus system under a large transient disturbance. Circle criterion provides simple rules for examining both the linear and non-linear portions of the power system in the frequency domain and for arriving at conditions to be imposed on these portions in order to ensure absolute stability. An upper and lower bound is established for the non-linear gain by treating the system's mathematical model as a set of non-linear algebraic equations and limiting values of gains are estimated by solving these equations. A numerical example is solved to illustrate the method of approach.     

Principal component analysis of aerial video imagery†

Abstract

Aerial video images of an agricultural test site were analysed using principal component analysis and image processing techniques. The site (six treatments and four replications of cotton, sorghum, cantaloupe, johnsongrass, pigweed and soil) was imaged using blue, yellow-green, red and infrared filters over the lenses of four black-and-white video cameras on 31 May and 24 July 1983. Separate principal component analysis procedures were applied to the May and July data as part of a methodology to assess data dimensionality and structure. Supervisedminimum Euclidean distance classification procedures were conducted on sets of data that consisted of all four principal components, the first three principal components, the first two principal components and the first principal component. Results indicated that the number of components required to represent the four band data sets accurately was three for the May data and two for the July data. Scatter diagrams of plant means for principal components 1 and 2 showed good potential for determining the relative level of plant development.     

Construction of regions of stability for non-linear systems containing time delays†

A method has been developed for constructing regions of stability for non-linear systems containing time delays. This method, based on modified Liapunov stability theorems, is applicable to higher-dimensional systems containing several time delays or time-varying delays. A reactor example is presented to illustrate the method.     

Application of homotopy perturbation and variational iteration methods for nonlinear imprecise prey–predator model with stability analysis

The Journal of Supercomputing - A coupled nonlinear prey–predator system is presented. The system formulation is based on nonlinear ordinary differential equations with imprecise parameter...     

Computer aided stability analysis of gravity dams—CADAM

This paper presents the main features and organisation of CADAM, a computer program, freely available, that has been developed for the static and seismic stability evaluations of concrete gravity dams. CADAM is based on the gravity method using rigid body equilibrium and beam theory to perform stress analyses, compute crack lengths, and safety factors. Seismic analyses could be done using either the pseudo-static or a simplified response spectrum method. CADAM is primarily designed to provide support for learning the principles of structural stability evaluation of gravity dams. It could also be used for research and development on stability of gravity dams. In adopting several different world-wide published dam safety guidelines, a large number of modelling options have been implemented. These include (i) crack initiation and propagation, (ii) effects of drainage and cracking under static, seismic, and post-seismic uplift pressure conditions, and (iii) safety evaluation procedures using deterministic, allowable stresses and limit states probabilistic analyses (Monte-Carlo simulations). Structural stability evaluation of a 30 m dam is presented to illustrate the use of CADAM.     

The numerical solution of parabolic partial differential equations by the method of integral operators†

The numerical solution of parabolic partial differential equations is accomplished by the use of , integral operators and a complete family of solutions. This method is one where the kernel of the integral operator and the special solutions of the differential equation are expanded in long (20-term) Taylor series. Once the series for the functions have been obtained, numerical integration can be performed by a term-by-term integration (a simple shifting of terms). Thus, the integraloperator solutions of parabolic differential equations are evaluated numerically with ease. The solutions of example problems are given.     

Limit cycle analysis for control systems of high order†

A generalized method for the limit cycle analysis of a class of nth-order systems is proposed. The method utilizes describing function technique and is applicable to dynamical systems with both memoryless and with memory non-linearities. The critical gain for self-sustained oscillations is found without explicitly solving the system characteristic equation. Relatively simple expressions are derived for the evaluation of limit cycle frequency. The results reduce to the conventional Routh equation for memoryless non-linearities. Application of the proposed method is demonstrated by several examples.     

Weighted residual methods and the suboptimal control of distributed parameter systems†

A suboptimal control algorithm for distributed parameter systems is developed in a framework which synthesizes weighted residual methods and mathematical programming. The heat exchanger example of Koppel et al. (1968) is employed for introducing the algorithm. First, the Galerkin procedure with polynomial modes is applied to obtain a lumped ODE model for the distributed parameter system. Then the state and control variables of the lumped control problem are approximated by cubic splines on a uniform mesh. Through collocation at the knots, the ODE model is reduced to a sot of linear algebraic equations and the suboptimal control is determined from the solution of a quadratic programming problem with sparse matrices.

Numerical results for the heat exchanger example are presented and compared with those obtained by the authors (Neuman and Sen 1972) using the Ritz-Trefftz algorithm (Bosarge and Johnson 1970) for the lumped control problem. For this example, the two algorithms yield essentially identical results with comparable computational requirements. Application of the Ritz-Trefftz algorithm, however, is limited to lumped, linear-quadratic control problems without constraints on the state or control. The approach advocated in this paper, therefore, offers a viable approach to control problems in distributed parameter systems.     

The use of model following methods to generate suboptimal feedback control†

Implementation of linear optimal control laws oftentimes requires that all system state variables be physically available for measurement and feedback. The well known impracticality of this requirement motivates the work described in this paper which is addressed to the use of model following methods in the synthesis of sub-optimal feedback controllers which do not require sensing all of the system state variables. The approach presented here consists of first computing a complete set of optimal feedback gains and thus generating optimum system response which is then used as a model toward which a suboptimal design can strive. A suboptimal control is postulated with zero feedback gains as desired, the remaining gains being as yet arbitrary. The average integrated difference between the model closed loop response and the suboptimal closed loop response is then minimized by selection of these remaining feedback gains. For a given feedback configuration, the method thus determines the suboptimal closed loop control yielding a response which is as close as possible in a given well-defined sense to the model response. Defining equations are derived and parameter optimisation methods are utilized to compute the free feedback gains. The method is particularly well suited to digital computation requiring only the use of standard parameter optimization algorithms as well as an algorithm to solve a set of bilinear matrix equations. An example involving regulation of the longitudinal modes of a VTOL flight vehicle is presented to illustrate the model following capabilities of the synthesis procedure.     

Visual analysis of machine learning methods in the field of ergonomics — Based on Cite Space V

To analyze the research hotspots on the application of machine learning methods in the field of ergonomics, we collected 1141 articles related to machine learning methods in the field of ergonomics from 2014 to 2021 on the Web of Science (WoS) database. Then we used Cite Space V 6.1. R2 to generate network maps and analyze the authors, institutions, countries, co-cited literature, and keywords. Results show that the correlation between authors in the formed author co-occurrence network is not strong, which indicates low cooperation among authors. In the analysis of research institutions, the University of Southampton is the most frequently cited literature in the United Kingdom. However, the US is leading in the country's co-occurrence network. “System” and “Model” are the top two cited keywords, while “Methodology” and “Decision-making” were active from 2015 to 2018, with a longer development time. Other keywords, including “Musculoskeletal disorders”, “Performance”, “Low back pain”, “Health”, and “Risk Factors”, are the most frequently cited keywords and have a high betweenness centrality. “Validation” and “Prediction” have recently become popular keywords in this field. Therefore, we conclude that the application of machine learning methods in the field of ergonomics will continue to increase year by year and that the development of machine learning methods in the field of ergonomics is gaining importance due to its cross-disciplinary nature. In ergonomics, machine learning methods will be further developed and widely used.     

A generalized Nyquist plot and its use in sensitivity analysis†

The Nyquist plot of a single variate transfer function provides the motivation for a graphical technique relevant to linear and non-linear operators on a Hilbert space. The graphical method is developed so as to retain the geometrical interpretation and physical insight which characterizes the conventional Nyquist plot. The extended Nyquist plot is then utilized to analyze selected system sensitivity problems in the Hilbert space setting.     

On the asymptotic stability of a particular class of distributed parameter feedback control systems†

In this paper the stability problem for a particular class of non-linear feedback control systems governed by a parabolic partial differential equation is considered. A sufficient condition for global asymptotic stability of the null equilibrium state is derived by the method of comparison functions.     

Dissipative exponentially-fitted methods for the numerical solution of the Schrödinger equation

The first dissipative exponentially fitted method for the numerical integration of the Schr?dinger equation is developed in this paper. The technique presented is a nonsymmetric multistep (dissipative) method. An application to the bound-states problem and the resonance problem of the radial Schr?dinger equation indicates that the new method is more efficient than the classical dissipative method and other well-known methods. Based on the new method and the method of Raptis and Allison (Comput. Phys. Commun. 14 (1978) 1-5) a new variable-step method is obtained. The application of the new variable-step method to the coupled differential equations arising from the Schr?dinger equation indicates the power of the new approach.     

More on the phase-plane analysis of a relay control system†

The transcendental equation relating the parameters of a closed trajectory of a relay system containing a symmetrical two-position element, a dead element and a rational part of the second order has two solutions. It will be shown that only one of these solutions supplies the self-oscillation of the system.

The phase-plane method is developed for systems containing a relay element with hysteresis. The effect of varying any parameter of the system on the period and amplitude of the self-oscillation can be predicted from the transcendental equation.     

New insights in the development of Numerov-type methods with minimal phase-lag for the numerical solution of the Schrödinger equation

Explicit Numerov-type methods with minimal phase-lag are developed in this paper. These methods are of algebraic order five and have phase-lag order eight and ten. The methods have new features; namely that they are dissipative, i.e. they are not symmetric and they have no interval of periodicity. Numerical illustrations using (i) the radial Schr?dinger equation and (ii) coupled differential equations arising from the Schr?dinger equation, indicate that these new methods are more efficient than older ones. It is seen that the property of the phase-lag is more important than the non-empty interval of periodicity in constructing numerical methods for the solution of the Schr?dinger equations and related problems.     

Graphical analysis of a class of non-linear feedback control systems with step input†

The class of systems considered in this investigation is a cascade combination of a linear memory system and a non-linear no-memory system in the forward path of a unity feedback control system. The output of the non-linear no-memory system is assumed to be a polynomial function of the input. Regardless of the exact nature of the non-linearity, the objective of this method of analysis is to predict the behaviour of higher-order non-linear systems with different initial conditions for step inputs.

Two different cascade combinations of linear and non-linear blocks in the forward path are considered. For both configurations a similar non-linear differential equation is obtained for some variable in the system. The non-linear differential equation is further reduced to a first-order equation, explicitly independent of the independent variable, time t. Treating all other coefficients as parameters and eliminating each in turn, finally the required phase-plane trajectory is obtained.     

L2-bounded stability for a stochastic system†

Both types of linear and non-linear systems with random coefficients are treated in this paper. Four theorems are proved by using the stochastic Liapunov functional, which give the sufficient condition in matrix form for exponential asymptotic stability in the largo with probability one and L₂-bounded stability with probability one.