The generalization of equal-peak method for delay-coupled nonlinear system

Meng, Hao; Sun, Xiuting; Xu, Jian; Wang, Feng

doi:10.1016/j.physd.2020.132340

Cited by 20 publications

(6 citation statements)

References 37 publications

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“…In case of digital control, the states of the system are measured with a given sampling frequency, and the corresponding mathematical model leads to a discrete time system [9,13]. However, when the sampling time is small compared to the data processing and transmission time, continuous time delay description can be applied, which leads to delay differential equations (DDE) [21,32]. Similar DDE models are used in case of human-controlled machines [12].…”

Section: Introductionmentioning

confidence: 99%

Delay-induced bifurcations in collocated position control of an elastic arm

Szaksz

Stépàn

2021

Nonlinear Dyn

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The interference of the elasticity of a single robotic arm and the unavoidable time delay of its position control is analysed from nonlinear vibrations viewpoint. The simplified mechanical model of two blocks and a connecting spring considers the first vibration mode of the arm, while the collocated proportional-derivative (PD) control uses the state of the first block only and actuates also there. It is assumed that the relevant nonlinearity is the saturation of the delayed control force. The linear stability analysis proves that stabilizable and non-stabilizable parameter regions follow each other periodically even for large spring stiffnesses and for tiny time delays. Hopf bifurcation calculation is carried out after an infinite-dimensional centre manifold reduction, and closed-form algebraic expressions are given for the amplitudes of the emerging oscillations. These results support the experimental tuning of the control gains since the parameters of the arising and often unexpected self-excited vibrations can serve as a guide for this practical procedure.

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Section: Introductionmentioning

confidence: 99%

Delay-induced bifurcations in collocated position control of an elastic arm

Szaksz

Stépàn

2021

Nonlinear Dyn

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“…Dai and Zhao 32 studied the negative stiffness time-delay feedback control dynamic vibration absorber, which greatly reduces the amplitude and widens the effective vibration reduction frequency band. Meng et al 33 designed a time-delay vibration absorbing system based on the optimization criterion of equal-peak property, which effectively suppressed the vibration peak of the system. Wu et al 34 applied time-delay feedback control to vehicle suspension, which can greatly suppress harmonic excitation.…”

Section: Introductionmentioning

confidence: 99%

Effect of time-delay feedback control on vehicle seat vibration reduction and suspension performance

Zhang

Ren

et al. 2022

Journal of Low Frequency Noise, Vibration and Active Control

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To reduce seat vibration caused by uneven road surfaces, the time-delay feedback control into the seat suspension system was introduced and an active seat suspension control method based on time-delay feedback was proposed in this paper. A three-degree-of-freedom (3-DOF) suspension model with time-delay feedback control was established. The time-delay independent stability region and critical stability curve of the system were derived using the method of characteristic root and stability switching. The effect of feedback control parameters on system vibration was investigated in the stability region. The seat acceleration (SA), body acceleration (BA), suspension dynamic deflection (SDD), and tire dynamic displacement (TDD) were used as multi-objective optimization functions and the optimal values of feedback control parameters were obtained based on the particle swarm algorithm (PSO) with above optimization functions. The numerical simulation was conducted to validate the proposed model. The simulated results show that the time-delay feedback control can significantly suppress the vibration response of the seat and effectively improve the suspension performance under different road excitation compared with the passive suspension. It can be seen that the active seat suspension with time-delay control significantly improve ride comfort and handling stability of the vehicle, which can be used as a reference for the active control technology of vehicle suspension.

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“…In recent years, lots of nonlinear mechanical oscillators have been developed due to the application-driven theoretical and experimental studies. Several comprehensive reviews can serve as guides how to utilize various of nonlinear oscillators for vibration isolation [19][20][21][22][23][24][25], vibration absorption [26][27][28][29] and energy harvesting [30][31][32][33][34][35][36], and for other applications.…”

Section: Introductionmentioning

confidence: 99%