Two-parameter dynamics of an autonomous mechanical governor system with time delay

AbstractIn this paper, we propose a novel dynamical system with time delay to describe the outbreak of 2019-nCoV in China. One typical feature of this epidemic is that it can spread in the latent period, which can therefore be described by time delay process in the differential equations. The accumulated numbers of classified populations are employed as variables, which is consistent with the official data and facilitates the parameter identification. The numerical methods for the prediction of the outbreak of 2019-nCoV and parameter identification are provided, and the numerical results show that the novel dynamic system can well predict the outbreak trend so far. Based on the numerical simulations, we suggest that the transmission of individuals should be greatly controlled with high isolation rate by the government.

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Stability and Stabilization of the Fractional-order Power System with Time Delay

IEEE Transactions on Circuits & Systems II Express Briefs ◽

10.1109/tcsii.2021.3069323 ◽

2021 ◽

pp. 1-1

Author(s):

Zhongming Yu ◽

Yue Sun ◽

Xin Dai

Keyword(s):

Time Delay ◽

Power System ◽

Fractional Order ◽

Stability And Stabilization ◽

System With Time Delay

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Nonlinear vibrations and time delay control of an extensible slowly rotating beam

Nonlinear Dynamics ◽

10.1007/s11071-020-06079-3 ◽

2020 ◽

Author(s):

Jerzy Warminski ◽

Lukasz Kloda ◽

Jaroslaw Latalski ◽

Andrzej Mitura ◽

Marcin Kowalczuk

Keyword(s):

Time Delay ◽

Control Strategies ◽

Vibration Reduction ◽

Least Action ◽

Active Elements ◽

Principle Of Least Action ◽

Second Mode ◽

Delay Control ◽

Speed Range ◽

System With Time Delay

AbstractNonlinear dynamics of a rotating flexible slender beam with embedded active elements is studied in the paper. Mathematical model of the structure considers possible moderate oscillations thus the motion is governed by the extended Euler–Bernoulli model that incorporates a nonlinear curvature and coupled transversal–longitudinal deformations. The Hamilton’s principle of least action is applied to derive a system of nonlinear coupled partial differential equations (PDEs) of motion. The embedded active elements are used to control or reduce beam oscillations for various dynamical conditions and rotational speed range. The control inputs generated by active elements are represented in boundary conditions as non-homogenous terms. Classical linear proportional (P) control and nonlinear cubic (C) control as well as mixed ($$P-C$$ P - C ) control strategies with time delay are analyzed for vibration reduction. Dynamics of the complete system with time delay is determined analytically solving directly the PDEs by the multiple timescale method. Natural and forced vibrations around the first and the second mode resonances demonstrating hardening and softening phenomena are studied. An impact of time delay linear and nonlinear control methods on vibration reduction for different angular speeds is presented.

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