Feedback control of limit cycles: a switching control strategy based on nonsmooth bifurcation theory

Angulo, Fabiola; Bernardo, Mario di; Fossas, Enric; Olivar, Gerard

doi:10.1109/tcsi.2004.841595

Cited by 23 publications

(15 citation statements)

References 12 publications

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“…In contrast, Angulo et al [18] exploits suitably designed near-grazing interactions for feedback stabilization of system limit cycles. It would certainly be interesting to explore formulations of these approaches within a traditional control framework, including addressing issues of robustness [19][20][21][22][23].…”

Section: Discussionmentioning

confidence: 99%

Control of near‐grazing dynamics and discontinuity‐induced bifurcations in piecewise‐smooth dynamical systems

Misra

Dankowicz

2009

Intl J Robust & Nonlinear

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SUMMARYThis paper develops a rigorous control paradigm for regulating the near-grazing bifurcation behavior of limit cycles in piecewise-smooth dynamical systems. In particular, it is shown that a discrete-in-time linear feedback correction to a parameter governing a state-space discontinuity surface can suppress discontinuity-induced fold bifurcations of limit cycles that achieve near-tangential intersections with the discontinuity surface. The methodology ensures a persistent branch of limit cycles over an interval of parameter values near the critical condition of tangential contact that is an order of magnitude larger than that in the absence of control. The theoretical treatment is illustrated with a harmonically excited damped harmonic oscillator with a piecewise-linear spring stiffness as well as with a piecewise-nonlinear model of a capacitively excited mechanical oscillator.

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Section: Discussionmentioning

confidence: 99%

Control of near‐grazing dynamics and discontinuity‐induced bifurcations in piecewise‐smooth dynamical systems

Misra

Dankowicz

2009

Intl J Robust & Nonlinear

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“…The controlled second order system was found to have nine different solution sets. Limit cycles analysis for systems controlled by switch controllers using different methods, can be found in Angulo et al [5], Flieller et al [3], diBernardo-Camlibel [4] and X.-S. Yang-G. Chen [20]. In this paper the converter is modelled as a third order switched system and controlled by switch surfaces making the set of possible solutions even richer.…”

Section: Introductionmentioning

confidence: 99%

Two types of limit cycles of a resonant converter modelled by a three-dimensional system

Melin¹,

Hultgren

Lindström³

2008

Nonlinear Analysis: Hybrid Systems

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“…The case with g ¼ 21=2 is considered in [3]. Other examples of grazing and sliding bifurcations with nonlinear leading-order terms occur in power converters and in nonsmooth sliding-mode controls ( [1], [5], [6]). In [19] the map in (1) was considered in the discontinuous case with g .…”

Section: Introductionmentioning

confidence: 99%

“…As in [11] and [13] we consider system (1) for positive values of the parameter m, and for any m . 0 the transformation ðx; a; b; mÞ !…”

Section: Introductionmentioning

confidence: 99%

Border collision and fold bifurcations in a family of one-dimensional discontinuous piecewise smooth maps: divergence and bounded dynamics

Makrooni

Khellat

Gardini

2015

Journal of Difference Equations and Applications

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In this work we continue the study of a family of 1D piecewise smooth maps, defined by a linear function and a power function with negative exponent, proposed in engineering studies. The range in which a point on the right side is necessarily mapped to the left side, and chaotic sets can only be unbounded, has been already considered. In this work we are characterizing the remaining ranges, in which more iterations of the right branch are allowed and in which divergent trajectories occur. We prove that in some regions a bounded chaotic repellor always exists, which may be the only nondivergent set, or it may coexist with an attracting cycle. In another range, in which divergence cannot occur, we prove that unbounded chaotic sets always exist. The role of particular codimension-two points is evidenced, associated with fold bifurcations and border collision bifurcations (BCBs), related to cycles having the same symbolic sequences. We prove that they exist related to the border collision of any admissible cycle. We show that each BCB, each fold bifurcation and each homoclinic bifurcation is a limit set of infinite families of other BCBs.

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Feedback control of limit cycles: a switching control strategy based on nonsmooth bifurcation theory

Cited by 23 publications

References 12 publications

Control of near‐grazing dynamics and discontinuity‐induced bifurcations in piecewise‐smooth dynamical systems

Control of near‐grazing dynamics and discontinuity‐induced bifurcations in piecewise‐smooth dynamical systems

Two types of limit cycles of a resonant converter modelled by a three-dimensional system

Border collision and fold bifurcations in a family of one-dimensional discontinuous piecewise smooth maps: divergence and bounded dynamics

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