Self-excited oscillation under nonlinear feedback with time-delay

Chatterjee, Satyajit

doi:10.1016/j.jsv.2010.11.005

Cited by 49 publications

(21 citation statements)

References 20 publications

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“…By repeating the continuation scheme in Appendix A, the lobe diagram [39] is obtained and the stability boundary is located in Fig. 3.…”

Section: Linear Grinding Stabilitymentioning

confidence: 99%

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Non-linear analysis and quench control of chatter in plunge grinding

Yan

Wiercigroch

2015

International Journal of Non-Linear Mechanics

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“…By repeating the continuation scheme in Appendix A, the lobe diagram [39] is obtained and the stability boundary is located in Fig. 3.…”

Section: Linear Grinding Stabilitymentioning

confidence: 99%

“…4, perturbation method can be used for prediction of the grinding dynamics. Among several perturbation methods, we choose the method of multiple scales [39,43,33,35], which is begun by introducing perturbations to the system parameters:…”

Section: Appendix B Multiple Scales Analysismentioning

confidence: 99%

Non-linear analysis and quench control of chatter in plunge grinding

Yan

Wiercigroch

2015

International Journal of Non-Linear Mechanics

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“…Limit cycles model dynamical systems that exhibit self-sustained oscillations for some set of parameters. Thus, a self-excited system exhibits the property to generate steady state oscillations (limit cycles) even in the absence of external periodic forcing [1][2][3]. Some examples of dynamical systems that exhibit a self-excited oscillation are beating of a heart, rhythms in body temperature, hormone secretion, chemical reactions, vibrations in bridges and airplane wings, inverted pendulums, the Van der Pol oscillator, the Duffing oscillator, biped robots, etc.…”

Section: Introductionmentioning

confidence: 99%

Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC

et al. 2017

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This paper deals with the tracking approach of a self-generated stable limit cycle for an underactuated mechanical system: The Inertia Wheel Inverted Pendulum (IWIP). Such system is subject to unilateral constraints limiting its swing motion. It is known that an Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) can be employed to control such pendulum to its upright position. In this work, we briefly show first that the IWIP can generate a stable period-1 limit cycle through a Hopf bifurcation by varying some gain parameter of the IDA-PBC. Thus, such self-generated limit cycle is used as a reference trajectory, which is chosen to be tracked by the IWIP. To achieve the tracking problem, a supplementary control input is added. Such tracking problem is reformulated as an asymptotic stabilization of the tracking error. Our fundamental approach hinges mainly on the use of the S-procedure to introduce the unilateral constraints, and the Schur complement and the matrix inversion lemma to transform Bilinear Matrix Inequalities (BMI) into Linear Matrix Inequalities (LMI). Several simulations have been presented to corroborate the mathematical results and to show the efficiency of the proposed tracking scheme of the self-generated stable limit cycle of the controlled IWIP, even if it is subject to external disturbances, or in the presence of uncertainties in the friction parameters.

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“…As a result, chatter vibration is generated, and thus a wavy workpiece surface is produced. Traditionally, the regenerative machining dynamics has been investigated by using the regenerative chatter theory, which is mathematically described by delayed differential equations (DDEs) [6,7,15,17,24]. After the regenerative effect was first reported by Arnold [2], it has been used to study various machining chatter in turning [36], milling [19], drilling [15] and grinding [11].…”

Section: Natural Frequencies 1 Introductionmentioning

confidence: 99%

Regenerative chatter in self-interrupted plunge grinding

Yan

Wiercigroch

2016

Meccanica

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This paper investigates dynamics of regenerative chatter in self-interrupted plunge grinding with delayed differential equations (DDEs) and partial differential equations (PDEs). The DDEBIF-TOOL, a numerical simulation tool and the method of multiple scales are used to analyse stability and construct bifurcation diagrams. It was found out that in majority of cases, chatter is accompanied by a loss of contact. The loss of contact leaves uncut surface during the pass of grinding wheels, and thus the regeneration mechanism does not play a role. In that case, the delay used to represent the time span between two successive cuts should be multiple (double, triple, quadruple or higher). As a consequence, the chatter with losing contact cannot be accurately described by the DDEs with a fixed time delay. To address this problem, the PDEs are introduced to record the variation of workpiece profile. The PDEs are transformed into the ODEs by a Galerkin projection, and then the grinding dynamics is studied numerically. Solutions obtained from the DDEs and the PDEs are in a good agreement for a continuous grinding but there is a discrepancy for a self-interrupted cutting.

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Self-excited oscillation under nonlinear feedback with time-delay

Cited by 49 publications

References 20 publications

Non-linear analysis and quench control of chatter in plunge grinding

Non-linear analysis and quench control of chatter in plunge grinding

Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC

Regenerative chatter in self-interrupted plunge grinding

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