Model reduction by matching the steady-state response of explicit signal generators

© 2015 IEEE.Model reduction by moment matching for interpolation signals which do not have an implicit model, i.e., they do not satisfy a differential equation, is considered. Particular attention is devoted to discontinuous, possibly periodic, signals. The notion of moment is reformulated using an integral matrix equation. It is shown that, under specific conditions, the new definition and the one based on the Sylvester equation are equivalent. New parameterized families of models achieving moment matching are given. The results are illustrated by means of a numerical example

A note on the electrical equivalent of the moment theory

In this short note the relation between the moments of a linear system and the phasors of an electric circuit is discussed. We show that the phasors are a special case of moments and we prove that the components of the solution of a Sylvester equation are the phasors of the currents of the system. We point out several directions in which the phasor theory can be extended using recent generalizations of the moment theory, which can benefit the analysis of circuits and power electronics

A geometric characterization of feedforward forms

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Model reduction for nonlinear systems and nonlinear time-delay systems from input/output data

© 2015 IEEE.An algorithm for the estimation of the moments of nonlinear systems and nonlinear time-delay systems from input/output data is proposed. The estimate is exploited to construct a family of reduced order models. The use of the technique is illustrated by a few examples based on the averaged model of the DC-to-DC Cuk converter

Moment-based discontinuous phasor transform and its application to the steady-state analysis of inverters and wireless power transfer systems

Power electronic devices are inherently discontinuous systems. Square waves, produced by interconnected transistors, are commonly used to control inverters. This paper proposes a novel phasor transform, based on the theory of moments, which allows to analyze the steady-state behavior of discontinuous power electronic devices in closed-form, i.e. without approximations. In the first part of the paper it is shown that the phasors of an electric circuit are the moments on the imaginary axis of the linear system describing the circuit. Exploiting this observation, in the second part of the paper, we focus on the analysis of circuits powered by discontinuous sources. The new “discontinuous phasor transform” is defined and the v-i characteristics for inductors, capacitors and resistors are described in terms of this new phasor transform. Since the new quantities maintain their physical meaning, the instantaneous power and average power can be computed in the phasor domain. The analytic potential of the new tool is illustrated studying the steady-state response of power inverters and of wireless power transfer systems with non-ideal switches

Model reduction for hybrid systems with state-dependent jumps

In this paper we present a model reduction technique based on moment matching for a class of hybrid systems with state-dependent jumps. The problem of characterizing the steady-state for this class of systems is studied and a result which allows to described the steadystate response of hybrid systems through the use of a hybrid mapping is given. Then a family of hybrid reduced order models which achieve moment matching and are easily parameterizable is provided. The special case of periodic input signals is analyzed and conditions for applying the technique are given for this class. A numerical simulation illustrates the results

Music for Piano and Electronics: Jeri-Mae G. Astolfi

Kemp Recital HallJanuary 24, 2013Thursday Evening8:00 p.m

Norm estimators and global output feedback stabilization of nonlinear systems with ISS inverse dynamics

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