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Efficient calculations of the transient behaviour after disturbances of large-scale power systems are complex because of, among other things, the non-linearity and the stiffness of the overall state equation system (SES). Because of the rising amount of flexible transmission system elements, there is an increasing need for reduced order models with a negligible loss of accuracy. With the Extended Nodal Approach and the application of the singular perturbation method, it is possible to reduce the order of the SES adapted to the respective setting of the desired tasks and accuracy requirements.

Based on a differential-algebraic equation for the electric power system which is formulated with the Extended Nodal Approach, the automatic decomposition into reduced order models is shown in this paper. The paper investigates the effects of different coordinate systems for an automatic order reduction with the singular perturbation method, as well as a comparison of results calculated with the full and reduced order models.

The eigenvalues of the full system are approximated sufficiently by the three subsystems. A simulation example demonstrates the good agreement between the reduced order models and the full model independent of the choice of the coordinate system. The decomposed subsystems in rotating coordinates have benefits as compared to those in static coordinates.

The paper presents a systematic decomposition based only on a differential-algebraic equation system of the electric power system into three subsystems.

The aim of this paper is to propose a new coning correction algorithm, based on the singular perturbation technique, for the attitude update computation with non‐ideal angular rate information.

Unlike conventional coning correction algorithms, the new method uses angular rate two‐time scale model to construct the coning correction term of attitude update. In order to achieve balanced real/pseudo coning correction performance, the selection guidelines of the new algorithm parameters are established.

Performance of the new algorithm is evaluated by comparison with the conventional algorithm in no ideal sensors undergoing stochastic coning environments. The accuracy of attitude update can be improved effectively with reduced computational workload by using this new coning algorithm as compared with conventional ones.

The proposed coning correction algorithm can be implemented with angular rate sensors in UAV (unmanned aerial vehicle) and other aircrafts attitude estimation for navigation and control applications.

Singular perturbation is an effective method for structuring coning correction algorithm with filtered angular rate outputs in stochastic coning environments. The improved coning correction algorithm based on singular perturbations reduces the real and pseudo coning effects effectively as compared with conventional ones. It is proved to be valid for improvement of accuracy with reduced computations of the attitude update.

We present a qualitative analysis of the fundamental static semiconductor device equations which is based on singular perturbation theory. By appropriate scaling the semiconductor device equations are reformulated as singularly perturbed elliptic system (the Laplacian in Poisson's equation is multiplied by a small parameter ?2, the so‐called singular perturbation parameter). Physically the singular perturbation parameter is identified with the square of the normed minimal Debye length of the device under consideration. Using matched asymptotic expansions for small A we characterize the behaviour of the solutions locally at pn junctions, Schottky contacts and oxide‐semiconductor interfaces and demonstrate the occurrence of exponential internal/boundary layers at these surfaces. The derivatives of the solutions blow up within these layer regions (as ?2 decreases) and they remain bounded away from the layers. We demonstrate that the solutions of the ‘zero‐space charge approximation’ are close to the solutions of the ‘full’ semiconductor problem (when ? is small) away from layer regions and derive a second‐order ordinary differential equation which (when subjected to appropriate boundary/interface conditions) ‘describes’ the solutions within layer regions.

When considering the one dimensional semiconductor device equations, the condition number turns out to be so large that a numeric solution of the equation is meaningless. Applying singular perturbation methods to the linearized model the solution can be separated into two parts: One, which is very sensitive to perturbations, and one, which is robust against perturbations of the equations.

The singular perturbation character of the semiconductor device problem is well known by now. Various results on the structure of solutions (i.e. existence of spatial and temporal layers) have been obtained by means of singular perturbation theory. We use a rescaled form of the equations, which describes the evolution on the fast time scale, and discuss the asymptotic behavior of this system, i.e. its relationship to the initial layer problem, to the corresponding stationary problem and to the reduced problem. We show that the transient semiconductor problem fits in the framework of ‘fast reaction‐slow diffusion’ type equations, which are known from the analysis of chemical reacting systems. We use a multiple time scale expansion to give a new ‘dynamical’ derivation of the reduced problem.

To generalize the traditional 2nd order stochastic perturbation technique for input random variables and fields and to demonstrate for flow problems.

The methodology is based on an n‐th order expansion (perturbation) for input random parameters and state functions around their expected value to recover probabilistic moments of the response. A finite element formulation permits stochastic simulations on irregular meshes for practical applications.

The methodology permits approximation of expected values and covariances of quantities such as the fluid pressure and flow velocity using both symbolic and discrete FEM computations. It is applied to inviscid irrotational flow, Poiseulle flow and viscous Couette flow with randomly perturbed boundary conditions, channel height and fluid viscosity to illustrate the scheme.

The focus of the present work is on the basic concepts as a foundation for extension to engineering applications. The formulation for the viscous incompressible problem can be implemented by extending a 3D viscous primitive variable finite element code as outlined in the paper. For the case where the physical parameters are temperature dependent this will necessitate solution of highly non‐linear stochastic differential equations.

Techniques presented here provide an efficient approach for numerical analyses of heat transfer and fluid flow problems, where input design parameters and/or physical quantities may have small random fluctuations. Such an analysis provides a basis for stochastic computational reliability analysis.

The mathematical formulation and computational implementation of the generalized perturbation‐based stochastic finite element method (SFEM) is the main contribution of the paper.

The dynamics of coupling between spectrum and resolvent under ε‐perturbations of operator and matrix spectra are studied both theoretically and numerically. The phenomenon of non‐trivial pseudospectra encountered in these dynamics is treated by relating information in the complex plane to the behaviour of operators and matrices. On a number of numerical results we show how an intrinsic blend of theory with symbolic and numerical computations can be used effectively for the analysis of spectral problems arising from engineering applications.

In this paper, the authors revisit the computation of closed-form expressions of the topological indicator function for a one step imaging algorithm of two- and three-dimensional sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions) in the free space.

From the addition theorem for translated harmonics, explicit expressions of the scattered waves by infinitesimal circular (and spherical) holes subject to an incident plane wave or a compactly supported distribution of point sources are available. Then the authors derive the first-order term in the asymptotic expansion of the Dirichlet and Neumann traces and their surface derivatives on the boundary of the singular medium perturbation.

As the shape gradient of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.

The authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function that generates initial guesses in the iterated numerical solution of any shape optimization problem or imaging problems relying on time-harmonic acoustic wave propagation.

To design a reduced‐order controller with loosing little accuracy.

Singular perturbation approach by quasi‐steady state approximation and by Matrix block diagonalization technique is used.

It is shown that few errors occur between the uncorrected and corrected solutions for the fast subsystems while a few errors occur between the two kinds of solutions for the slow subsystems. The uncorrected solution is admissible for most dynamics. If not, it is recommended that the corrected solution be used.

Proportional feedback control gain is obtained by Pole placement method, which may produce an unwanted overshoot in the response.

This paper shows that the corrected controller is successfully applied in the aircraft dynamics and control.

This paper deals with the production and preventive maintenance planning control problem for a multi‐machine flexible manufacturing system (FMS). A two‐level hierarchical control model is developed according to the discrepancy between the time scale of the discounting cost event and one of the machine state processes. The proposed model extends the classical singular perturbation approach by considering age‐dependent machine failure rates and controlling both production and preventive maintenance rates. We replace the stochastic optimal control problem by a deterministic one termed limiting control problem. With this approach, we compute an age‐dependent near‐optimal control policy of the stochastic initial control problem from the optimal solution of the equivalent limiting control problem. A numerical example is used to illustrate the procedure and to show the reduction of the control problem size.