Complementarity: limit cycles and power converters
The research activity is dedicated to the analysis of the complemenatity framework for:
modeling of switched electronic systems (power converters, in particular)
computation of steady state solutions in switched systems and limit cycles in Lur'e systems
Kanat Camlibel, University of Groningen, The Netherlands
The classic approaches for modeling and simulating power converters (averaged, switched and hybrid models) and the commercial tools available (e.g. PSpice, Power System Blockset in the Matlab environment, PLECS) often do not allow the analysis of non-standard innovative converter topologies or operating conditions. The problem is tackled by using the complementarity systems theory. The complementarity approach, coming from the nonsmooth mechanics, allows to model the electronic devices by using piecewise affine characteristics, and then integrating them with detailed models of the converter and the network. The complementarity framework allows the formal and simulation analysis of innovative power converters topologies and electrical networks in terms of dynamic performance, failure and fault conditions, high frequency phenomena, switching behavior of the converters, frequency domain response. Further, the complementarity approach with respect to simulation tools based on standard hybrid models, it also allows to gain in terms of simulation time and numerical convergence.
A similar approach to that used for the computation of steady state solutions for switched electronic systems can be used for the computation of limit cycles in Lur'e systems. It can be shown that the complementarity representation of the feedback characteristic allows to represent the discretized closed loop system as a linear complementarity system. A static linear complementarity problem, whose solutions correspond to periodic solutions of the discrete–time system, can then be formulated. The proposed technique is able to compute steady state oscillations with known period for continuous–time systems, so as demonstrated by simulation results on Lur’e systems which exhibit asymmetric unstable and sliding limit cycles.
Valentina Sessa, PhD student in Automatic Control, University of Sannio, "Limit cycles computation via complementarity models", co-tutor prof. Luigi Iannelli.
Gianluca Angelone, PhD in Automatic Control, University of Sannio, "Steady-state analysis for switched electronic systems through complementarity", co-tutor prof. Luigi Iannelli.
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
Maurizio Zoppi, LS Ingegneria dell'Automazione, ottobre 2011, "Complementary model and minimum energy control for switched capacitor converters", 110 e lode, co-relatore ing. Gianluca Angelone.
V. Sessa, L. Iannelli, F. Vasca, "Mixed Linear Complementarity Problems for the Analysis of Limit Cycles in Piecewise Linear Systems", 51st IEEE Conference on Decision and
Control, Maui, Hawaii, December 2012, p. 1023-1028.
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, http://www.springer.com/engineering/control/book/978-1-4471-2884-7.
L. Iannelli, F. Vasca, G. Angelone, "Computation of Steady State Oscillations in Power Converters Through Complementarity", IEEE Transactions on Circuits and Systems, vol. 58, no. 6, June 2011, p. 1421-1432.
L. Iannelli, F. Vasca, V. Sessa, "Computation of Limit Cycles in Lur'e Systems", American Control Conference, San Francisco, California, USA, June 2011, p. 1402-1407.
G. Angelone, F. Vasca, L. Iannelli, "Linear Complementarity Models for Steady-state Analysis of Pulse-width Modulated Switched Electronic Systems", 19th Mediterranean Conference on Control and Automation, Corfu, Greece, June 2011, p. 400-405.
R. Iervolino, L. Iannelli, F. Vasca, "Absolute Stability of Lur'e Systems: a Complementarity and Passivity Approach", 49th IEEE Conference on Decision and Control, Atlanta, Georgia, December 2010, p. 2420-2425.
F. Vasca, M. K. Camlibel, L. Iannelli, R. Frasca, "A new perspective for modeling power electornics converters: complementarity framework", IEEE Transactions on Power Electronics, vol. 24, no. 2 , February 2009, p. 456-468.
L. Iannelli, F. Vasca, "Cyclic Steady State Behavior of Switched Electronic Systems", 48th IEEE Conference on Decision and Control, Shangai, China, December 2009, p. 6549-6554.
F. Vasca, L. Iannelli, G. Angelone, "Steady State Analysis of Power Converters via a Complementarity Approach", European Control Conference, Budapest, Hungary, August 2009, p. 3587-3592.
L. Iannelli, F. Vasca, "Computation of Limit Cycles and Forced Oscillations in Piecewise Linear Feedback Systems Through a Complementarity Approach", 47th IEEE Conference on Decision and Control, Cancun, Mexico, December 2008, p. 1169-1174.
L. Iannelli, F. Vasca, "Analysis of Periodic Solutions in Piecewise Linear Feedback System via a Complementarity Approach", IFAC World Conference, Seoul, Korea, June 2008.
F. Vasca, L. Iannelli, K. Camlibel, "A New Perspective in Power Converters Modeling: Complementarity Systems", 38th IEEE Power Electronics Specialists Conference, Orlando, Florida, June 2007, p. 1817-1823.
L. Iannelli, F. Vasca, K. Camlibel, "Complementarity and Passivity for Piecewise Linear Feedback Systems", 45th IEEE Conference on Decision and Control, San Diego, CA, December 2006, p. 4212-4217.