# To stick or to slip: Lyapunov-based reset PID for positioning systems with Coulomb and Stribeck friction

Thursday 8th October, 2pm – 3pm

Luca Zaccarian, LAAS, CNRS, Toulouse, France

To stick or to slip: Lyapunov-based reset PID for positioning systems with Coulomb and Stribeck friction

Reset control systems for continuous-time plants were introduced in the 1950's by J.C. Clegg, then extended by Horowitz twenty years later and revisited using hybrid Lyapunov theory a few decades ago, to rigorously deal with the continuous-discrete interplay stemming from the reset laws. In this talk we overview a recent research activity where suitable reset actions induce stability and performance of PID-controlled positioning systems suffering from nonlinear frictional effects. With Coulomb-only effect, PID feedback produces a nontrivial set of equilibria whose asymptotic (but not exponential) stability can be certified by using a discontinuous Lyapunov-like function. With velocity weakening effects (the so-called Stribeck friction), the set of equilibria becomes unstable with PID feedback and the so-called hunting phenomenon'' (persistent oscillations) is experienced. Resetting laws can be used in both scenarios. With Coulomb friction only, the discontinuous Lyapunov-like function immediately suggests a reset action providing extreme performance improvement, preserving stability and increasing the convergence speed. With Stribeck, a more sophisticated set of logic-based reset rules recovers global asymptotic stability of the set of equilibria, providing an effective solution to the hunting instability. We will discuss the Lyapunov-based proofs with these hybrid laws, requiring nontrivial derivations, such as building semiglobal hybrid simulation models. The theoretical results will be illustrated by experiments carried out on an industrial nano-positioning system, showing the experimental advantages arising from our novel reset PID controllers.

BIO
Luca Zaccarian received the Laurea and the Ph.D. degrees from the University of Roma Tor Vergata (Italy) in 1995 and 2000, respectively. He has been Assistant Professor in control engineering at the University of Roma, Tor Vergata (Italy), from 2000 to 2006 and then Associate Professor. Since 2011 he is Directeur de Recherche at the LAAS-CNRS, Toulouse (France) and since 2013 he holds a part-time associate professor position at the University of Trento, Italy. Luca Zaccarian's main research interests include analysis and design of nonlinear and hybrid control systems, modeling and control of mechatronic systems. He has served in the organizing committee and TPC of several IEEE and IFAC conferences. He has been a member of the IEEE-CSS Conference Editorial Board and an associate editor for Systems and Control Letters and IEEE Transactions on Automatic Control. He is currently a member of the EUCA-CEB and an associate editor for the IFAC journal Automatica and for the European Journal of Control. He was a nominated member of the Board of Governors of the IEEE-CSS in 2014, and an elected member in 2017-2019. He was Student Activities Chair for the IEEE-CSS in 2015--2017 and is currently Associate Editor of Electronic Publications (Conference Information) for the IEEE-CSS. He was a recipient of the 2001 O. Hugo Schuck Best Paper Award given by the American Automatic Control Council. He is a fellow of the IEEE, class of 2016.

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