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14
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.
An Overview on Averaging for Pulsemodulated Switched Systems
, 2011
"... 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. In this paper we overview the few formal approaches proposed in the li ..."
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Cited by 6 (4 self)
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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. In this paper we overview the few formal approaches proposed in the literature to deal with the averaging of nonsmooth systems. The dithering, the phasor dynamics and the hybrid framework techniques are recast and compared by considering pulsemodulated switched linear systems as the common modeling platform.
On the Averaging of a Class of Hybrid Systems
, 2004
"... Modeling abstraction and timescale separation in the design of complex systems often leads to hybrid dynamics. Discontinuities in the continuous evolution of a hybrid system may however create difficulties in the formal analysis, as well as in numerical simulation and verification. Here we study a ..."
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Cited by 3 (2 self)
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Modeling abstraction and timescale separation in the design of complex systems often leads to hybrid dynamics. Discontinuities in the continuous evolution of a hybrid system may however create difficulties in the formal analysis, as well as in numerical simulation and verification. Here we study a class of hybrid systems that are excited by highfrequency external signals. These systems arise in the modeling of switched power converters, mechanical systems with friction and quantized systems. For a quite general class of excitation signals, an averaging result is shown stating that the hybrid system can be approximated by a Lipschitzcontinuous system. The approximation is in the order of the maximal repetition interval of the excitation signal.
Input to State Stability of Pulse Width Modulated Control Systems
"... Results on stability and inputtostate stability in pulsewidth modulated (PWM) control systems are presented. The results are based on a recent generalization of two time scale stability theory to di#erential equations with disturbances. In particular, averaging theory for systems with disturbance ..."
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Cited by 1 (0 self)
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Results on stability and inputtostate stability in pulsewidth modulated (PWM) control systems are presented. The results are based on a recent generalization of two time scale stability theory to di#erential equations with disturbances. In particular, averaging theory for systems with disturbances is used to establish the results. The nonsmooth nature of PWM systems is accommodated by working with upper semicontinuous setvalued maps, locally Lipschitz inflations of these maps, and locally Lipschitz parameterizations of locally Lipschitz setvalued maps. 1
PRACTICAL STABILITY AND LIMIT CYCLES OF DITHERED RELAY FEEDBACK SYSTEMS
"... relay feedback systems. ..."
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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.
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"... stability conditions for semiquasiZsource inverters: switched and averaged models ..."
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stability conditions for semiquasiZsource inverters: switched and averaged models