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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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Cited by 7 (5 self)
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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...
Averaging of nonsmooth systems using dither
, 2006
"... It was shown by Zames and Shneydor and later by Mossaheb that a highfrequency dither signal of a quite arbitrary shape can be used to narrow the effective nonlinear sector of Lipschitz continuous feedback systems. In this paper, it is shown that also discontinuous nonlinearities of feedback systems ..."
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Cited by 6 (2 self)
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It was shown by Zames and Shneydor and later by Mossaheb that a highfrequency dither signal of a quite arbitrary shape can be used to narrow the effective nonlinear sector of Lipschitz continuous feedback systems. In this paper, it is shown that also discontinuous nonlinearities of feedback systems can be narrowed using dither, as long as the amplitude distribution function of the dither is absolutely continuous and has bounded derivative. The averaged system is proven to approximate the dithered system with an error of the order of dither period.
Analysis of dither in relay feedback systems
 in Proc. of IEEE Conference on Decision and Control, Las Vegas
, 2002
"... Dither signals provide an effective way of compensating for nonlinearities in control systems. 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 nonlinear ..."
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Cited by 2 (2 self)
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Dither signals provide an effective way of compensating for nonlinearities in control systems. 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. This paper presents initial results on how to analyze and design dither in nonsmooth systems. In particular, it is shown that a dithered relay feedback system can be approximated by a smoothed system obtained through an averaging approach. Guidelines are given for tuning the amplitude and the period time of the dither signal, in order to stabilize the nonsmooth system. 1
PRACTICAL STABILITY AND LIMIT CYCLES OF DITHERED RELAY FEEDBACK SYSTEMS
"... relay feedback systems. ..."
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Dither in Systems with Hysteresis
, 1995
"... : This paper deals with differential inclusion containing an hysteresis nonlinearity and two inputs: a control input and a dither input of high frequency. Conditions are introduced under which its solution admits asymptotic behavior when the dither frequency goes to infinity. According to asymptotic ..."
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: This paper deals with differential inclusion containing an hysteresis nonlinearity and two inputs: a control input and a dither input of high frequency. Conditions are introduced under which its solution admits asymptotic behavior when the dither frequency goes to infinity. According to asymptotic growth of the dither amplitude, two different behaviors appear: the nonlinearity is smoothed (resp. quenched) if the velocities induced by the dither are asymptotically bounded (resp. unbounded). Convergence results for finite and infinite time intervals are given, and linked with the averaging principle. The case of bounded dithering velocities is of interest in a mechanical context, where hysteresis is used to model dry friction. A very interesting feature is that the averaged hysteresis operator may be linearized for small velocities. The hypotheses on the dither include periodicity, F repetitiveness and (asymptotic) almostperiodicity. Keywords: hysteresis operators, differential in...
Conditions on the dither shape in the averaging of switched systems
, 2003
"... It was shown by Zames and Shneydor that a highfrequency dither of a quite arbitrary shape can be used to smooth the effective nonlinear sector of Lipschitz continuous feedback systems. Here it is shown that also systems with discontinuous nonlinearities can be smoothed using dither signals, as lon ..."
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It was shown by Zames and Shneydor that a highfrequency dither of a quite arbitrary shape can be used to smooth the effective nonlinear sector of Lipschitz continuous feedback systems. Here it is shown that also systems with discontinuous nonlinearities can be smoothed using dither signals, as long as the amplitude distribution function of the dither is Lipschitz continuous.
Dip. di Informatica e
"... Abstract — Dither signals are commonly used to compensate for nonlinearities in feedback systems in electronics and mechanics. Recently, theoretical results were proposed for the analysis of a particularly interesting class of nonsmooth systems, namely relay feedback systems with triangular dither. ..."
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Abstract — Dither signals are commonly used to compensate for nonlinearities in feedback systems in electronics and mechanics. Recently, theoretical results were proposed for the analysis of a particularly interesting class of nonsmooth systems, namely relay feedback systems with triangular dither. In this paper the class of dither signals is enlarged by considering square and trapezoidal dither: it is shown how the dither shape affects the behavior of nonsmooth feedback systems, differently from the case of dither in Lipschitz continuous systems. Experimental results support this fact and a theoretical insight is given in order to explain the phenomena. I.