Application of a method of averaging to the study of dithers in non-linear systems

Mossaheb, S.

doi:10.1080/00207178308933094

Cited by 52 publications

(31 citation statements)

References 11 publications

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“…The work by L. Iannelli and F. Vasca Shneydor, 1976Shneydor, , 1977. Similar results were obtained later using classical averaging theory (Mossaheb, 1983).…”

Section: Introductionsupporting

confidence: 76%

“…Eq. (4) is well defined except at possible discontinuity points of n. Thus, in the case in which n is continuous, the results of Zames and Shneydor (1976) and Mossaheb (1983) can be applied together with Eq. (4) to compute the averaged system.…”

Section: Averaged Systemmentioning

confidence: 99%

“…The result states that the dithered and the averaged systems have qualitatively the same behavior when the dither has sufficiently high frequency and an absolutely continuous amplitude distribution function with bounded derivative. The averaging theorem might be interpreted as an extension to nonsmooth feedback system of previous results, which were limited to Lipschitz-continuous systems (Zames & Shneydor, 1976Mossaheb, 1983).…”

Section: Introductionmentioning

confidence: 99%

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Averaging of nonsmooth systems using dither

et al. 2006

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It was shown by Zames and Shneydor and later by Mossaheb that a high-frequency 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. ᭧

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“…The work by L. Iannelli and F. Vasca Shneydor, 1976Shneydor, , 1977. Similar results were obtained later using classical averaging theory (Mossaheb, 1983).…”

Section: Introductionsupporting

confidence: 76%

Section: Averaged Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Averaging of nonsmooth systems using dither

et al. 2006

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“…Stability can be proven for a sufficiently high dither frequency by the use of the classical averaging theory, formerly developed by Zames and Shneydor [4], [5], [6] for continuous nonlinear systems. Other related works can be found in Mossaheb [7], Luigi Iannelli et al [8] and Lehman and Bass [9]. Their results showed that a sufficiently high frequency dither can reduce the limit cycles in the dithered system to a negligible ripple but exact conditions on the dither periods and amplitudes were not given.…”

Section: Introductionmentioning

confidence: 98%

Sinusoidal dither in a relay feedback system

Lim

Loh

2008

2008 American Control Conference

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Abstract-This paper examines the effect of a sinusoidal dither in a relay feedback system. The use of dither in achieving signal stabilization and quenching of limit cycles is well known in nonlinear systems. This paper shows that forced oscillations (FO) of higher frequencies will produce a lower amplitude and achieve a reduction in the amplitude of oscillations for dither periods below a certain value, T * f . The analytical expression and numerical value of T * f are obtained for first and second order plants. For higher order systems, a series of the delayed version of the Tsypkin Locus is used to identify T * f . For the desired frequency of FO, the required dither amplitude is determined accordingly. Simulation studies are presented to illustrate the results.

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“…Some other approaches exist in the literature. For example systems with smooth nonlinearity and smooth dither signal can be analyzed using powerful methods introduced in [8], [9], [10]. The smoothness assumptions are however often violated in practice [11]; for example, by nonsmooth static components such as switches and relays or by triangular and square wave dither signals.…”

Section: Introductionmentioning

confidence: 99%

Effects of dither shapes in nonsmooth feedback systems: experimental results and theoretical insight

Iannelli

Johansson²,

Jönsson³

et al.

42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)

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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.

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Application of a method of averaging to the study of dithers in non-linear systems

Cited by 52 publications

References 11 publications

Averaging of nonsmooth systems using dither

Averaging of nonsmooth systems using dither

Sinusoidal dither in a relay feedback system

Effects of dither shapes in nonsmooth feedback systems: experimental results and theoretical insight

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