Dither shape in the averaging of switched systems

Iannelli, Luigi; Johansson, Karl Henrik; Jönsson, Ulf; Vasca, Francesco

doi:10.23919/acc.2004.1384784

Cited by 5 publications

(11 citation statements)

References 15 publications

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“…For trapezoidal dither, the assumptions of the averaging result in [15] are not fulfilled. In fact, the approximation error between the dithered system and the smoothed system may not tend to zero in this case, as was indicated by a theoretical example in [20]. In the following, we show that the DC motor application supports these conclusions: the system is stabilized with sawtooth dither, while it is not with trapezoidal or square wave dither.…”

Section: Resultssupporting

confidence: 68%

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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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Section: Resultssupporting

confidence: 68%

“…In this paper we will illustrate these phenomena by new experimental results followed by a theoretical explanation that the authors have recently rigorously proved and generalised to a wider class of nonlinear systems in [20].…”

Section: Preliminariesmentioning

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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show abstract

“…Proof: This was proven for the case of periodic excitation signals in [12]. All details for the generalization to F -repetitive signals is given in [15].…”

Section: Averaging Theoremmentioning

confidence: 99%

“…Remark 2: Signals that fulfill the assumption on the amplitude distribution function include periodic triangular and sawtooth signals, while square wave signals have discontinuous amplitude distribution function, see [10], [12].…”

Section: B Excitation Signalmentioning

confidence: 99%

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On the averaging of a class of hybrid systems

Iannelli

Johansson

Jönsson

et al. 2004

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)

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Abstract-Modeling abstraction and time-scale 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 high-frequency 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.

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Input-to-state stability for a class of hybrid dynamical systems via averaging

Wang

Nešić

Teel

2011

Math. Control Signals Syst.

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Input-to-state stability (ISS) properties for a class of time-varying hybrid dynamical systems via averaging method are considered. Two definitions of averages, strong average and weak average, are used to approximate the time-varying hybrid systems with time-invariant hybrid systems. Closeness of solutions between the timevarying system and solutions of its weak or strong average on compact time domains is given under the assumption of forward completeness for the average system. We also show that ISS of the strong average implies semi-global practical (SGP)-ISS of the actual system. In a similar fashion, ISS of the weak average implies semi-global practical derivative ISS (SGP-DISS) of the actual system. Through a power converter example, we show that the main results can be used in a framework for a systematic design of hybrid feedbacks for pulse-width modulated control systems.

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Dither shape in the averaging of switched systems

Cited by 5 publications

References 15 publications

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

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

On the averaging of a class of hybrid systems

Input-to-state stability for a class of hybrid dynamical systems via averaging

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