Numerical analysis of the friction-induced oscillator of Duffing's type with modified LuGre friction model

Pikunov, Danylo; Stefański, Andrzej

doi:10.1016/j.jsv.2018.10.003

Cited by 21 publications

(7 citation statements)

References 27 publications

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“…To overcome this obstacle, a novel method has recently been presented in [14], which estimates the Jacobian matrix by a truncated Taylor series expansion with small orthogonal perturbations. The spectrum of Lyapunov exponents has been estimated from that numerical method in [15] to analyze the stability of a nonlinear mass-on-belt system. It is shortly summarized as follows: Consider a discretization in time given by the set {t i |i = 1, .…”

Section: Numerical Estimation Of the Lyapunov Exponentsmentioning

confidence: 99%

“…A Duffing's type oscillator has been studied analytically in [11] in order to obtain expressions for stick-slip and pure-slip vibration amplitudes and frequencies. An estimation method for the spectrum of Lyapunov Exponents (LE)s proposed by [14] is employed in [15] to analyze the stability of a discontinuous MoB system. To avoid computing and analyzing the behavior in the time domain, some indicators of instabilities have been proposed in the literature, such as Kolmogorov entropy [16], correlation dimension [17] and sticking time [18].…”

Section: Introductionmentioning

confidence: 99%

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Surrogate model approach for investigating the stability of a friction-induced oscillator of Duffing’s type

Fuhg

Fau

2019

Nonlinear Dyn

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Parametric studies for dynamic systems are of high interest to detect instability domains. This prediction can be demanding as it requires a refined exploration of the parametric space due to the disrupted mechanical behavior. In this paper, an efficient surrogate strategy is proposed to investigate the behavior of an oscillator of Duffing's type in combination with an elasto-plastic friction force model. Relevant quantities of interest are discussed. Sticking time is considered using a machine learning technique based on Gaussian processes called kriging. The largest Lyapunov exponent is proposed as an efficient indicator of non-regular behavior. This indicator is estimated using a perturbation method. A dedicated adaptive kriging strategy for classification called MiVor is utilized and appears to be highly proficient in order to detect instabilities over the parametric space and can furthermore be used for complex response surfaces in multi-dimensional parametric domains.

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Section: Numerical Estimation Of the Lyapunov Exponentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Surrogate model approach for investigating the stability of a friction-induced oscillator of Duffing’s type

Fuhg

Fau

2019

Nonlinear Dyn

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“…The nonlinear friction may lead to large steady state error or limit cycles in low velocity regime [27]. Several models have been proposed to describe the friction phenomena, such as the classic nonlinear model, Karnopp model, Dahl Model, LuGre model and so on [27][28][29]. However, all the above mentioned friction models are discontinuous due to the sign function of velocity, which is not desired in high performance control system.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Sliding Mode Based Position Tracking Control for PMSM Drive System With Desired Nonlinear Friction Compensation

et al. 2020

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The output feedback position tracking control of permanent-magnet synchronous motor (PMSM) drive system is addressed in this paper. In order to obtain a differentiable disturbance theoretically, a continuous differentiable model is employed to model the nonlinear friction, and the desired velocity, rather than the measured or estimated velocity, is used in the friction compensation. Then, based on the desired friction compensation model, the reaching law based sliding mode controller is designed to make the position tracking error as small as possible in the presence of model uncertainties and load disturbance, and the gain of the reaching law is online tuned to adapt the variations of the controlled system. Moreover, a nonlinear extended state observer (NESO) is designed to simultaneously estimate the unmeasured states and unknown disturbance to guarantee the finite time stability of the proposed controller, and the designed NESO is proven to be exponentially stable and has zero estimation errors theoretically. Simulations and experimental results are given to verify the effectiveness of the proposed control scheme.

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“…There are many numerical methods of computing Lyapunov exponents, e.g., Wolf method, Rosenstein method, Kantz method, method based on neural network modification, synchronization method, and others, see [1][2][3][4][5][6]. There are two main approaches to numerical assessment in the literature: with known motion equations and a time series approach.…”

Section: Introductionmentioning

confidence: 99%

“…Appl. 2019, 24, x FOR PEER REVIEW 2 of 15 of computing the full spectrum of Lyapunov exponents is presented in [3], the calculation of the largest Lyapunov exponent is given in [5,6], and the determination of the spectrum of Lyapunov exponents can be found in [7]. From a practical point of view, Lyapunov exponents are used in various fields of science, such as: rotor systems [8], electricity systems [9], aerodynamics [10].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov Exponents of Early Stage Dynamics of Parametric Mutations of a Rigid Pendulum with Harmonic Excitation

Śmiechowicz

Loup

Olejnik

2019

MCA

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This paper considers three dynamic systems composed of a mathematical pendulum suspended on a sliding body subjected to harmonic excitation. A comparative dynamic analysis of the studied parametric mutations of the rigid pendulum with inertial suspension point and damping was performed. The examined system with parametric mutations is solved numerically, where phase planes and Poincaré maps were used to observe the system response. Lyapunov exponents were computed in two ways to classify the dynamic behavior at relatively early stage of forced responses using two proven methods. The results show that with some parameters three systems exhibit a very similar dynamic behavior, i.e., quasi-periodic and even chaotic motions. Math. Comput. Appl. 2019, 24, 90 2 of 15 the full spectrum of Lyapunov exponents is presented in [3], the calculation of the largest Lyapunov exponent is given in [5,6], and the determination of the spectrum of Lyapunov exponents can be found in [7].From a practical point of view, Lyapunov exponents are used in various fields of science, such as: rotor systems [8], electricity systems [9], aerodynamics [10]. The Parametric Pendulum and Its Mutations

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Numerical analysis of the friction-induced oscillator of Duffing's type with modified LuGre friction model

Cited by 21 publications

References 27 publications

Surrogate model approach for investigating the stability of a friction-induced oscillator of Duffing’s type

Surrogate model approach for investigating the stability of a friction-induced oscillator of Duffing’s type

Adaptive Sliding Mode Based Position Tracking Control for PMSM Drive System With Desired Nonlinear Friction Compensation

Lyapunov Exponents of Early Stage Dynamics of Parametric Mutations of a Rigid Pendulum with Harmonic Excitation

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