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Averaging and dithering


The research activity is dedicated to:

  • averaging for switched systems

  • dithering


  • Stephan Trenn, University of Kaiserslautern, Germany


Averaging of fast switching systems is an effective technique used in many engineering applications. Practical stability and control design for a nonsmooth switched system can be inferred by analyzing the smooth averaged system. On the other hand only few formal approaches have been proposed in the literature to deal with the averaging of nonsmooth systems. The dithering, the phasor dynamics and the hybrid framework techniques can be recast and compared by considering pulse-modulated switched linear systems as the common modeling platform.

In particular, dither signals provide an effective way to compensate for nonlinearities in control systems. Previous studies presents tools for systematic design of  dithered systems, but the results rely only on a Lipschitz assumption on the nonlinearity, thus they don’t cover important applications with discontinuities. We obtained initial results on how to analyze and design dither in nonsmooth systems. In particular, we showed how a dither relay feedback system can be approximated by a smoothed system, and we gave guidelines for tuning the amplitude and the period time of the dither signal, in order to  stabilize one class of 
particularly interesting nonsmooth systems, namely relay feedback systems with triangular dither. Then the study of dither signals is enlarged by considering square and trapezoidal dither; we have shown how the dither shape affects the behavior of nonsmooth feedback system, differently from the case of dither in Lipschitz continuous systems. A process used to show the results obtained is the DC/DC power converter.

PhD Theses
  • ongoing
    • Elisa Mostacciuolo, PhD student in Automatic Control, University of Sannio, "Averaging for switched systems".

  • 2013
    • Carmen Pedicini, PhD student in Automatic Control, University of Sannio, "Averaging for switched systems", co-tutor prof. Luigi Iannelli.
  • 2007
    • Roberto Frasca, PhD in Automatic Control, University of Sannio, "Modeling and simulation of switched electrical networks: A complementarity systems approach", co-tutor prof. Luigi Iannelli.

Laurea Magistralis Theses
  • 2013
    1. Elisa Mostacciuolo, LM Ingegneria Elettronica per l'Automazione e le Telecomunicazioni, febbraio 2013, "Analisi di tecniche di inseguimento del punto di massima potenza di moduli fotovoltaici", 110 e lode, co-relatori ing. Silvio Baccari, ing. Giovanna Adinolfi.
  • 2012
    1. Mariateresa Cilenti, LS Ingegneria dell'Automazione, maggio 2012, "Controllo dei LED: regolazione ottima di flusso luminoso e temperatura", 110 e lode, co-relatore ing. Silvio Baccari.
  • 2011
    1. Guido Memmolo, LS Ingegneria dell'Automazione, dicembre 2011, "Controllo di convertitori DC-DC Boost per MPPT nei sistemi fotovoltaici".
    2. Viviana Verdino, L Vecchio Ordinamento Ingegneria Informatica, giugno 2011, "Modello termo-elettrico per il controllo dei LED", 110 e lode, co-relatore ing. Massimo Tipaldi.


  • 2013
    • L. Iannelli, C. Pedicini, S. Trenn, F. Vasca, "An averaging result for switched DAEs with multiple modes'', 52nd IEEE Conference on Decision and Control, Florence, Italy, December 2013, p.
    • L. Iannelli, C. Pedicini, S. Trenn, F. Vasca, "On Averaging for Switched Linear Differential Algebraic Equations'', European Control Conference, Zurich, July 2013, p. 1023-1028.

  • 2012
    • C. Pedicini, F. Vasca, L. Iannelli, "The averaging method for control design and stability analysis of practical switched systems", 2012 IEEE Multi-Conference on Systems and Control, Dubrovnik, Croatia, October 2012, p. 1285-1290.
    • F. Vasca, L. Iannelli, (eds.), "Dynamics and Control of Switched Electronic Systems", Advances in Industrial Control Series, Springer Verlag, Berlin, Germany, 2012, ISBN: 978-1-4471-2884-7,