Corner-Impact Bifurcations: A Novel Class of Discontinuity-Induced Bifurcations in Cam-Follower Systems

Osorio, Gustavo; Bernardo, Mario di; Santini, Stefania

doi:10.1137/060666433

Cited by 36 publications

(12 citation statements)

References 21 publications

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“…Furthermore, they arise as Poincaré maps of piecewise-smooth systems of differential equations, particularly near sliding bifurcations [7,8] and near so-called corner collisions [9,10].…”

Section: Introductionmentioning

confidence: 99%

Shrinking point bifurcations of resonance tongues for piecewise-smooth, continuous maps

Simpson

Meiss

2009

Nonlinearity

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Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark-Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a distinctive lens-chain (or sausage) shape in two-parameter bifurcation diagrams. We give a symbolic description of a class of "rotational" periodic solutions that display lenschain structures for a general N -dimensional map. We then unfold the codimensiontwo, shrinking point bifurcation, where the tongues have zero width. A number of codimension-one bifurcation curves emanate from shrinking points and we determine those that form tongue boundaries.

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“…Furthermore, they arise as Poincaré maps of piecewise-smooth systems of differential equations, particularly near sliding bifurcations [7,8] and near so-called corner collisions [9,10].…”

Section: Introductionmentioning

confidence: 99%

Shrinking point bifurcations of resonance tongues for piecewise-smooth, continuous maps

Simpson

Meiss

2009

Nonlinearity

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“…Then, via coordinate transformations similar to those given in [26], we may assume the border-collision bifurcation occurs at the origin, x = 0, when a parameter, µ, is zero, and that to order l the switching manifold is simply the plane e T 1 x = 0. In this paper we are not concerned with effects due to a nonsmooth switching manifold (for studies of various piecewise-smooth systems involving a non-differentiable switching manifold, see, for instance, [21,27,28,29]). For this reason we assume l is sufficiently large to not affect local dynamics and for simplicity assume the switching manifold is exactly the plane e T 1 x = 0.…”

Section: Formulization Of the Codimension-two Point And Setupmentioning

confidence: 99%

Simultaneous border-collision and period-doubling bifurcations

Simpson

Meiss

2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that with sufficient nondegeneracy conditions, a locus of period-doubling bifurcations emanates nontangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. In the case that the map is one-dimensional local dynamics is completely classified; in particular, we give conditions that ensure chaos.

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“…To solve the tracking phase, we adopted the soft landing control (SLC) strategy previously presented in [22], and to solve the destabilizing phase (i), the goal of this paper, we propose for the first time a control algorithm for destabilizing the engine valve (at engine key-on) exploiting only the engine valve position. Moreover, strongly nonlinear dynamics are exhibited by resulting closed loop system, which are also here analyzed and collected in a closed loop bifurcation diagram, which in turn is used to tune the control gains [25,26]. In fact to initiate the valve motion, it is enough to tune also the initial condition of the integrator (i.e.…”

Section: Introductionmentioning

confidence: 99%

Valve Position‐based Control at Engine Key‐on of an Electro‐mechanical Valve Actuator for Camless Engines: A Robust Controller Tuning Via Bifurcation Analysis

Velasco¹,

Gaeta²

2015

Asian Journal of Control

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Electro-mechanical valve actuators (EMVA) formed by two opposed electromagnets and two balanced springs are appealing solutions to implement advanced combustion concepts for camless engines. A crucial control problem for this valve actuator regards the first valve lift manoeuvre (termed 'first catching') to be rapidly performed after each insertion of the engine ignition key, when the EMVA rests at middle position where electromagnets offer low control authority. The control problem is challenging due to system nonlinear behavior. Mathematically, the EMVA system can be assumed to be a spring-mass impacting system affected by a non-smooth friction force and a dynamic saturated magnetic force. In this work an effective valve position-based first catching control strategy is proposed to control the strongly nonlinear system. Bifurcation analysis and parameter space simulations are used to study the closed-loop system behavior and to tune the controller gains as well. The effectiveness of the control approach is validated through numerical simulations of a highly predictive dynamic model of the valve actuator developed by authors in a previous work.

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Corner-Impact Bifurcations: A Novel Class of Discontinuity-Induced Bifurcations in Cam-Follower Systems

Cited by 36 publications

References 21 publications

Shrinking point bifurcations of resonance tongues for piecewise-smooth, continuous maps

Shrinking point bifurcations of resonance tongues for piecewise-smooth, continuous maps

Simultaneous border-collision and period-doubling bifurcations

Valve Position‐based Control at Engine Key‐on of an Electro‐mechanical Valve Actuator for Camless Engines: A Robust Controller Tuning Via Bifurcation Analysis

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