Averaging of nonsmooth systems using dither

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

doi:10.1016/j.automatica.2005.12.012

Cited by 70 publications

(58 citation statements)

References 18 publications

(25 reference statements)

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“…The following averaging result follows from Theorem 3.1 in Iannelli et al (2006). It states conditions when the dithered system (10) can be approximated by the averaged system (11).…”

Section: Averagingmentioning

confidence: 99%

“…This finding is illustrated through a number of examples, by simulated models of DC/DC and three-phase converters as well as by two experimental setups of DC/DC converters. 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%

“…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%

“…In this section it is formulated a version of the main theorem in Iannelli et al (2006), which will provide the foundation for the subsequent analysis. The averaged system corresponding to the dithered system (10) is defined as…”

Section: Averagingmentioning

confidence: 99%

“…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. For instance, the averaging result in Iannelli et al (2006) requires the averaged system to be Lipschitz continuous, which, in the case of nonsmooth dynamics, in general means that the dither should have Lipschitz-continuous ADF.…”

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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“…The following averaging result follows from Theorem 3.1 in Iannelli et al (2006). It states conditions when the dithered system (10) can be approximated by the averaged system (11).…”

Section: Averagingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Averagingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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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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Robust impulsive control of motion systems with uncertain friction

Wouw

Leine

2011

Intl J Robust & Nonlinear

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SUMMARYIn this paper, we consider the robust set-point stabilization problem for motion systems subject to friction. Robustness aspects are particularly relevant in practice, where uncertainties in the friction model are unavoidable. We propose an impulsive feedback control design that robustly stabilizes the set-point for a class of position-, velocity-and time-dependent friction laws with uncertainty. Moreover, it is shown that this control strategy guarantees the finite-time convergence to the set-point which is a favorable characteristic of the resulting closed loop from a transient performance perspective. The results are illustrated by means of a representative motion control example.

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Averaging of nonsmooth systems using dither

Cited by 70 publications

References 18 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

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

Robust impulsive control of motion systems with uncertain friction

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Averaging of nonsmooth systems using dither

Cited by 70 publications

References 18 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

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

Robust impulsive control of motion systems with uncertain friction

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Product

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