George C. Verghese

A generalized state-space for singular systems

Systems of the form E\dot{x}=Ax + Bu, y=Cx , with E singular, are studied. Of particular interest are the impulsive modes that may appear in the free-response of such systems when arbitrary initial conditions are permitted, modes that are associated with natural system frequencies at infinity. A generalized definition of system order that incorporates these impulsive degrees of freedom is proposed, and concepts of controllability and observability are defined for the impulsive modes. Allowable equivalence transformations of such singular systems are specified. The present framework is shown to overcome several difficulties inherent in other treatments of singular systems, and to extend, in a natural and satisfying way, many results previously known only for regular state-space systems.

Generalized averaging method for power conversion circuits

The method of state-space averaging has been successfully applied to pulse-width modulated power converters, but has its limitations with switched circuits that do not satisfy a small-ripple condition. A more general averaging procedure that encompasses state-space averaging and is potentially applicable to a much broader class of circuits and systems is considered. In particular, the technique is shown to be effective on a number of examples, including resonant-type converters. The method may find applications in simulation as well as design, since it is considerably easier to simulate an averaged model than a switched model.<<ETX>>

Failure detection and identification

Using the geometric concept of an unobservability subspace, a solution is given to the problem of detecting and identifying control system component failures in linear, time-invariant systems. Conditions are developed for the existence of a causal, linear, time-invariant processor that can detect and uniquely identify a component failure, first for the case where components can fail simultaneously, and then for the case where they fail only one at a time. Explicit design algorithms are provided when these conditions are satisfied. In addition to time-domain solvability conditions, frequency-domain interpretations of the results are given, and connections are drawn with results already available in the literature. >

Observers for flux estimation in induction machines

Flux estimation in induction machines is examined from the viewpoint of observer theory. It is pointed out that estimators presently used in connection with schemes such as field-oriented control are typically real-time simulations of machine equations, without feedback of any corrective prediction error. It is shown that corrective feedback can be used to speed up convergence of the flux estimates. It can also reduce the sensitivity of the estimates to parameter variations. >

Modeling and simulation of power electronic converters

This paper reviews some of the major approaches to modeling and simulation in power electronics, and provides references that can serve as a starting point for the extensive literature on the subject. The major focus of the paper is on averaged models of various kinds, but sampled-data models are also introduced. The importance of hierarchical modeling and simulation is emphasized.

Optimally robust redundancy relations for failure detection in uncertain systems

All failure detection methods are based, either explicitly or implicitly, on the use of redundancy, i.e. on (possibly dynamic) relations among the measured variables. The robustness of the failure detection process consequently depends to a great degree on the reliability of the redundancy relations, which in turn is affected by the inevitable presence of model uncertainties. In this paper the problem of determining redundancy relations that are optimally robust is addressed in a sense that includes several major issues of importance in practical failure detection and that provides a significant amount of intuition concerning the geometry of robust failure detection. A procedure is given involving the construction of a single matrix and its singular value decomposition for the determination of a complete sequence of redundancy relations, ordered in terms of their level of robustness. This procedure also provides the basis for comparing levels of robustness in redundancy provided by different sets of sensors.

Combining and updating of local estimates and regional maps along sets of one-dimensional tracks

In this paper we consider the problem of combining and updating estimates that may have been generated in a distributed fashion or may represent estimates, generated at different times, of the same process sample path. The first of these cases has applications in decentralized estimation, while the second has applications in updating maps of spatially-distributed random quantities given measurements along several tracks. The method of solution for the second problem uses the result of the first, and the similarity in the formulation and solution of these problems emphasizes the conceptual similarity between many problems in decentralized control and in the analysis of random fields.

Lyapunov-based control for switched power converters

The fundamental properties, such as passivity or incremental passivity, of the network elements making up a switched power converter are examined. The nominal open-loop operation of a broad class of such converters is shown to be stable in the large via a Lyapunov argument. The obtained Lyapunov function is then shown to be useful for designing globally stabilizing controls that include adaptive schemes for handling uncertain nominal parameters. Numerical simulations illustrate the application of this control approach in DC-DC converters.<<ETX>>

Analysis and synthesis of randomized modulation schemes for power converters

After establishing that the proper objects of study for randomized modulation of converters are the power spectra of signals, we classify such modulation schemes and present associated spectral formulas, several of which are new. We also discuss numerical (Monte Carlo) verification issues for power spectral formulas. A general spectral formula for stationary randomized modulation schemes is presented, and specialized to several modulation schemes of practical interest for DC/DC converters. Analytical results are then given for block-stationary randomized modulation schemes that are suitable for inverter operation. In the process, we present results for several modulation schemes that have been reported in the literature without analytical explanations. Experimental verifications of some of our analytical results are presented. We formulate narrow-band and wide-band synthesis problems in randomized modulation, and solve them numerically. Our results suggest that randomized modulation is very effective in satisfying narrow-band power constraints, but has limited effectiveness in meeting wide-band constraints. >

On sensitivities, residues and participations

This paper presents techniques for the evaluation and interpretation of eigenvalue sensitivities, in the context of the analysis and control of oscillatory stability in multimachine power systems. These techniques combine the numeric power of modal analysis of state-space models with the insight that can be obtained from transfer function descriptions. Relationships with tools from Selective Modal Analysis (namely, participations) are stressed. Examples of applications to a detailed multimachine power system model are given.