An adaptive-order rational Arnoldi method for model-order reductions of linear time-invariant systems

AbstractThis work proposes a model reduction method, the adaptive-order rational Arnoldi (AORA) method, to be applied to large-scale linear systems. It is based on an extension of the classical multi-point Padé approximation (or the so-called multi-point moment matching), using the rational Arnoldi iteration approach. Given a set of predetermined expansion points, an exact expression for the error between the output moment of the original system and that of the reduced-order system, related to each expansion point, is derived first. In each iteration of the proposed adaptive-order rational Arnoldi algorithm, the expansion frequency corresponding to the maximum output moment error will be chosen. Hence, the corresponding reduced-order model yields the greatest improvement in output moments among all reduced-order models of the same order. A detailed theoretical study is described. The proposed method is very appropriate for large-scale electronic systems, including VLSI interconnect models and digital filter designs. Several examples are considered to demonstrate the effectiveness and efficiency of the proposed method

Krylov Subspace Model Order Reduction for Nonlinear and Bilinear Control Systems

The use of Krylov subspace model order reduction for nonlinear/bilinear systems, over the past few years, has become an increasingly researched area of study. The need for model order reduction has never been higher, as faster computations for control, diagnosis and prognosis have never been higher to achieve better system performance. Krylov subspace model order reduction techniques enable this to be done more quickly and efficiently than what can be achieved at present. The most recent advances in the use of Krylov subspaces for reducing bilinear models match moments and multimoments at some expansion points which have to be obtained through an optimisation scheme. This therefore removes the computational advantage of the Krylov subspace techniques implemented at an expansion point zero. This thesis demonstrates two improved approaches for the use of one-sided Krylov subspace projection for reducing bilinear models at the expansion point zero. This work proposes that an alternate linear approximation can be used for model order reduction. The advantages of using this approach are improved input-output preservation at a simulation cost similar to some earlier works and reduction of bilinear systems models which have singular state transition matrices. The comparison of the proposed methods and other original works done in this area of research is illustrated using various examples of single input single output (SISO) and multi input multi output (MIMO) models

Reduced-order modeling of power electronics components and systems

This dissertation addresses the seemingly inevitable compromise between modeling fidelity and simulation speed in power electronics. Higher-order effects are considered at the component and system levels. Order-reduction techniques are applied to provide insight into accurate, computationally efficient component-level (via reduced-order physics-based model) and system-level simulations (via multiresolution simulation). Proposed high-order models, verified with hardware measurements, are, in turn, used to verify the accuracy of final reduced-order models for both small- and large-signal excitations. At the component level, dynamic high-fidelity magnetic equivalent circuits are introduced for laminated and solid magnetic cores. Automated linear and nonlinear order-reduction techniques are introduced for linear magnetic systems, saturated systems, systems with relative motion, and multiple-winding systems, to extract the desired essential system dynamics. Finite-element models of magnetic components incorporating relative motion are set forth and then reduced. At the system level, a framework for multiresolution simulation of switching converters is developed. Multiresolution simulation provides an alternative method to analyze power converters by providing an appropriate amount of detail based on the time scale and phenomenon being considered. A detailed full-order converter model is built based upon high-order component models and accurate switching transitions. Efficient order-reduction techniques are used to extract several lower-order models for the desired resolution of the simulation. This simulation framework is extended to higher-order converters, converters with nonlinear elements, and closed-loop systems. The resulting rapid-to-integrate component models and flexible simulation frameworks could form the computational core of future virtual prototyping design and analysis environments for energy processing units

Automatic adaptive multi-point moment matching for descriptor system model order reduction

We propose a novel automatic adaptive multi-point moment matching algorithm for model order reduction (MOR) of descriptor systems. The algorithm implements both adaptive frequency expansion point selection and automatic moment order control via a transfer function based error metric. Without a priori information of the system response, the proposed algorithm guarantees a much higher global accuracy compared with standard multi-point moment matching without adaptation. The moments are computed via a generalized Sylvester equation which is subsequently solved by a newly proposed generalized alternating direction implicit (GADI) method. Numerical examples then confirm the efficacy of the proposed schemes. © 2013 IEEE.published_or_final_versio

Implicitly restarted Krylov subspace methods for stable partial realizations

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