Dither for smoothing relay feedback systems

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

doi:10.1109/tcsi.2003.815194

Cited by 45 publications

(42 citation statements)

References 25 publications

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“…The discrepancy between the averaged and the dithered dynamics indicated above have previously been discovered in simulations: limit cycles appeared in the dithered but not in the averaged system in an example in Iannelli et al (2003). The second example in next section shows that such discrepancy also can appear under experimental conditions.…”

Section: Article In Pressmentioning

confidence: 55%

“…The assumption on Lipschitz continuity posed by Zames and Shneydor is, however, often violated in practice; for example, that is the case for several power converters controlled using pulse width modulation. Results were recently obtained on averaging and stability for dithered systems with nonsmooth dynamics (Gelig & Churilov, 1998;Iannelli, Johansson, Jo¨nsson, & Vasca, 2003;Iannelli, Johansson, Jo¨nsson, & Vasca, 2006;Teel, Moreau, & Nesic, 2004). When the dynamics are nonsmooth, it seems like there is a considerably smaller class of dither signals that can be used, compared to the smooth case considered by Zames and Shneydor.…”

Section: Introductionmentioning

confidence: 99%

“…The results show the importance of some mathematical details behind the averaging theory: the sufficient conditions on the dither, first presented in Iannelli et al (2006), are rather tight, and disregarding them could have a dramatic effect on the accuracy of the averaging. It is also indicated how averaging can be used to infer rigorous practical stability of the dithered system by analyzing the simpler averaged system, cf., Gelig and Churilov (1998), Moreau and Aeyels (2000) and Iannelli et al (2003).…”

Section: Introductionmentioning

confidence: 99%

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Subtleties in the averaging of a class of hybrid systems with applications to power converters

Iannelli¹,

Johansson²,

Jönsson³

et al. 2008

Control Engineering Practice

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High-frequency dither signals are commonly used to implement modulation schemes in power electronics converters. These systems represent an interesting class of hybrid systems with external excitation. They have a rich dynamical behavior, which cannot be easily understood intuitively. Despite the common use of averaging techniques in power electronics, it was only recently proved that a dithered hybrid system can be approximated by an averaged system under certain conditions on the dither signal. Averaging and averaged models for various types of power converters are analyzed in the paper. It is shown that the averaged nonlinearity depends on the dither shape and that dither signals with Lipschitz-continuous averaged nonlinearities can be used to adapt the equivalent gain of power converters. Practical stability of the original dithered system can be inferred by analyzing a simpler averaged system. The main contribution of the paper is to show that the averaged and the dithered systems may have drastically different behavior if the assumptions of the recently developed averaging theory for dithered hybrid systems are violated. Several practical experiments and simulation examples of power electronics converters are discussed. They indicate that the conditions on the dither signal imposed by the averaging theory are rather tight. r

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Section: Article In Pressmentioning

confidence: 55%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Subtleties in the averaging of a class of hybrid systems with applications to power converters

Iannelli¹,

Johansson²,

Jönsson³

et al. 2008

Control Engineering Practice

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“…The study is motivated by applications in mechanical friction [6], such as stickslip drives [7], power electronics [8], such as pulse-width modulated converters [9], feedback systems [10] and quantized systems [11]. For instance, excitation signals are used for power electronics converters in order to ensure a finite and constant switching frequency and in relay feedback systems for quenching undesired oscillations such as limit cycles.…”

Section: Introductionmentioning

confidence: 99%

“…Averaging is a classical mathematical tool for analyzing time-scale separation in dynamical systems. Related work on averaging applied to discontinuous and hybrid system was recently presented in [7], [10], [14], while the case of Lipschitzcontinuous systems was thoroughly treated already in the 70's [13].…”

Section: Introductionmentioning

confidence: 99%

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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Robust H^∞fuzzy control design for dithered nonlinear large‐scale systems with multiple time delays

Hsiao

2018

Optim Control Appl Methods

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A novel approach is proposed in this study to stabilize nonlinear multiple time-delay (NMTD) large-scale systems via a composite of fuzzy controllers and dithers. Moreover, a delay-dependent stability criterion is derived from Lyapunov's direct method. According to this criterion and the decentralized control scheme, a set of model-based fuzzy controllers is synthesized to stabilize the NMTD large-scale system and the H ∞ control performance is achieved at the same time. If the designed fuzzy controllers cannot stabilize the NMTD large-scale system, a set of dithers (as the auxiliaries of fuzzy controllers) is simultaneously introduced to stabilize the NMTD large-scale system. Finally, a numerical example with simulations is provided to illustrate the concepts discussed throughout this paper. KEYWORDS delay-dependent stability criterion, dither, large-scale system, T-S fuzzy models Optim Control Appl Meth. 2019;40:203-225.wileyonlinelibrary.com/journal/oca HSIAO During the last decade, fuzzy control has been successfully applied to the control design of nonlinear systems (see other works 3,[9][10][11][12][13][14][15][16][17][18][19] and the references therein). In these papers, a so-called Takagi-Sugeno (T-S) fuzzy model was employed to approximate a nonlinear plant, and then, a fuzzy controller was designed to stabilize the T-S fuzzy model. All of them, however, neglect the modeling error between nonlinear systems and fuzzy models. The existence of modeling error may be a source of instability for control designs based on the assumption that the fuzzy model exactly matches the nonlinear plant. 20 Chen et al, 21 Cao and Frank, 20 Kiriakidis, 22 and Cao and Lin 23 recently proposed novel approaches to overcome the influence of modeling errors in the field of model-based fuzzy control for nonlinear systems.Furthermore, not only the stability but also the control performance of nonlinear systems is important issue for control design. The H ∞ control problem for nonlinear systems has received considerable attention over the last few years. 1,16,20,24,25 Hence, a fuzzy control design with guaranteed H ∞ control performance has been introduced for nonlinear large-scale system in this study.On the other hand, it has been long known that the injection of a high-frequency signal, known as a dither, into a nonlinear system may improve its performance (see other works [26][27][28][29][30][31][32][33][34][35] and the references therein). Better performance is viewed as less distortion in the system output, augmented stability, and quenching of limit cycles as well as jump phenomena. 30 A rigorous analysis of stability in a general nonlinear system with a dither control was given in Steinberg and Kadushin. 27 Later, Zames and Shneydor 28,29 considered a specific configuration of a system and provided a lower bond for the dither repetition frequency. Subsequently, Mossaheb 26 pointed out that the dither of sufficiently high frequency may result in output of the relaxed system and that of the dithered system as close as desir...

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Dither for smoothing relay feedback systems

Cited by 45 publications

References 25 publications

Subtleties in the averaging of a class of hybrid systems with applications to power converters

Subtleties in the averaging of a class of hybrid systems with applications to power converters

On the averaging of a class of hybrid systems

Robust H^∞fuzzy control design for dithered nonlinear large‐scale systems with multiple time delays

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Dither for smoothing relay feedback systems

Cited by 45 publications

References 25 publications

Subtleties in the averaging of a class of hybrid systems with applications to power converters

Subtleties in the averaging of a class of hybrid systems with applications to power converters

On the averaging of a class of hybrid systems

Robust H∞fuzzy control design for dithered nonlinear large‐scale systems with multiple time delays

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Product

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Robust H^∞fuzzy control design for dithered nonlinear large‐scale systems with multiple time delays