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13
On periodicity of solutions for thermocontrol problems with hysteresistype switches
 SIAM J. Math. Anal
, 2009
"... Abstract. Mathematical models of thermocontrol processes occurring in chemical reactors and climate control systems are considered. In the models under consideration, the temperature inside a domain is controlled by a thermostat acting on the boundary. The feedback is based on temperature measuremen ..."
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Abstract. Mathematical models of thermocontrol processes occurring in chemical reactors and climate control systems are considered. In the models under consideration, the temperature inside a domain is controlled by a thermostat acting on the boundary. The feedback is based on temperature measurements performed by thermal sensors inside the domain. The solvability of the corresponding nonlinear nonlocal problems and the periodicity of solutions are studied.
Dither for smoothing relay feedback systems
 IEEE Trans. on Circuits and SystemsI: Fundamental Theory and Applications
, 2003
"... Dither signals are commonly used for compensating nonlinearities in feedback systems in electronics and mechanics. The seminal works by Zames and Shneydor and more recently by Mossaheb present rigorous tools for systematic design of dithered systems. Their results rely however on a Lipschitz assumpt ..."
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Dither signals are commonly used for compensating nonlinearities in feedback systems in electronics and mechanics. The seminal works by Zames and Shneydor and more recently by Mossaheb present rigorous tools for systematic design of dithered systems. Their results rely however on a Lipschitz assumption on the nonlinearity and thus do not cover important applications with discontinuities. The aim of this thesis is to provide some ideas and tools on how to analyse and design dither in nonsmooth systems. In particular, it is shown that a dithered relay feedback system can be approximated by a smoothed system. Guidelines are given for tuning the amplitude and the period time of the dither signal, in order to stabilize the nonsmooth system. Stability results based on Popovlike and ZamesFalb criteria jointly with some Linear Matrix Inequalities are proposed. Moreover it is argued that in dithered relay feedback systems the shape of dither signals is relevant for stabilization. Some peculiar behaviours of relay feedback systems dithered with a particular class of dither signals are presented. When the dither signal is a square wave, the dithered system can exhibit an asymmetric periodic orbit, though the smoothed system is asymptotically stable. We even show an example in which, by using a trapezoidal dither signal, both systems have a stable oscillation, but the period time for the oscillation of the smoothed system is different from the one of the dithered system. Finally some engineering applications are presented in order to show the usefulness of techniques and results discussed in the thesis. Thesis Supervisor: Franco Garofalo, Professor of Automatic Control Thesis Supervisor: Francesco Vasca, Associate Professor of Automatic Control Acknowledgements Yes, ...it's fina...
ON THE ROBUSTNESS OF PERIODIC SOLUTIONS IN RELAY FEEDBACK SYSTEMS
 15TH TRIENNIAL WORLD CONGRESS, BARCELONA, SPAIN
"... Structural robustness of limit cycles in relay feedback systems is studied. Motivated by a recent discovery of a novel class of bifurcations in these systems, it is illustrated through numerical simulation that small relay perturbations may change the appearance of closed orbits dramatically. It i ..."
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Structural robustness of limit cycles in relay feedback systems is studied. Motivated by a recent discovery of a novel class of bifurcations in these systems, it is illustrated through numerical simulation that small relay perturbations may change the appearance of closed orbits dramatically. It is shown analytically that certain stable periodic solutions in relay feedback systems are robust to relay perturbations.
PERIODIC SOLUTIONS OF PARABOLIC PROBLEMS WITH HYSTERESIS ON THE BOUNDARY
"... (Communicated by HansOtto Walther) Abstract. We consider a parabolic problem with discontinuous hysteresis on the boundary, arising in modelling various thermal control processes. By reducing the problem to an infinite dynamical system, sufficient conditions for the existence and uniqueness of a p ..."
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(Communicated by HansOtto Walther) Abstract. We consider a parabolic problem with discontinuous hysteresis on the boundary, arising in modelling various thermal control processes. By reducing the problem to an infinite dynamical system, sufficient conditions for the existence and uniqueness of a periodic solution are found. Global stability of the periodic solution is proved. 1. Introduction. Hysteresis
Dynamics of a hysteretic relay oscillator with periodic forcing
, 2009
"... The dynamics of a hysteretic relay oscillator with simple harmonic forcing is studied in this paper. Even though there are no bounded solutions in the absence of forcing, periodic excitation gives rise to more complex responses including periodic, quasiperiodic and chaotic behavior. A Poincaré map i ..."
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The dynamics of a hysteretic relay oscillator with simple harmonic forcing is studied in this paper. Even though there are no bounded solutions in the absence of forcing, periodic excitation gives rise to more complex responses including periodic, quasiperiodic and chaotic behavior. A Poincaré map is introduced to facilitate mathematical analysis. Families of periodone solutions are determined as fixed points of the Poincaré map. These represent coexisting subharmonic responses. Conditions on the amplitude and frequency of the forcing for the existence of periodic solutions have been obtained. Linear stability analysis reveals that these solutions can be classified as centers or saddles. The presence of higher periodic, quasiperiodic motions together with homoclinic and heteroclinic tangles imply the existence of chaotic solutions. 1
Local Stability of Limit Cycles for TimeDelay RelayFeedback Systems
"... [15] S. M. Guo, L. S. Shieh, G. Chen, and C. F. Lin, “Effective chaotic orbit ..."
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[15] S. M. Guo, L. S. Shieh, G. Chen, and C. F. Lin, “Effective chaotic orbit
AND CONTROL
"... This new textbook is a breath of fresh air in the market of books devoted to probability and random processes. The book lives up to its ambition of setting a new standard for a modern, computerbased treatment of the subject. Despite the issues discussed above, I fully recommend its use in undergrad ..."
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This new textbook is a breath of fresh air in the market of books devoted to probability and random processes. The book lives up to its ambition of setting a new standard for a modern, computerbased treatment of the subject. Despite the issues discussed above, I fully recommend its use in undergraduate and firstyear graduate courses.