delayed feedback
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2021 ◽  
pp. 231-239
Aleksandr Andreev ◽  
Olga Peregudova

In this paper, the trajectory tracking control problem of a robot manipulator with cylindrical joints is considered by means of a nonlinear PD controller taking into account the delayed feedback structure. The conclusion about stability of a closed-loop system is obtained on the basis of the development of the direct Lyapunov method in the study of the stability property for a non-autonomous functional differential equation by constructing a Lyapunov functional with a semi-definite time derivative.

Yong Guo ◽  
Chuanbo Ren

In this paper, the mechanical model of two-degree-of-freedom vehicle semi-active suspension system based on time-delayed feedback control with vertical acceleration of the vehicle body was studied. With frequency-domain analysis method, the optimization of time-delayed feedback control parameters of vehicle suspension system in effective frequency band was studied, and a set of optimization method of time-delayed feedback control parameters based on “equivalent harmonic excitation” was proposed. The time-domain simulation results of vehicle suspension system show that compared with the passive control, the time-delayed feedback control based on the vertical acceleration of the vehicle body under the optimal time-delayed feedback control effectively broadens the vibration absorption bandwidth of the vehicle suspension system. The ride comfort and stability of the vehicle under random road excitation are significantly improved, which provides a theoretical basis for the selection of time-delayed feedback control strategy and the optimal design of time-delayed feedback control parameters of vehicle suspension system.

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Huijian Zhu ◽  
Lijie Li

In this paper, the influence of delayed feedback on the unified chaotic system from the Sprott C system and Yang system is studied. The Hopf bifurcation and dynamic behavior of the system are fully studied by using the central manifold theorem and bifurcation theory. The explicit formula, bifurcation direction, and stability of the periodic solution of bifurcation are given correspondingly. The Hopf bifurcation diagram and chaotic phenomenon are also analyzed by numerical simulation to prove the correctness of the theory. It shows that this delay control can only be applied to the hidden chaos with two stable equilibria.

2021 ◽  
Sovan Sundar Dasgupta

Abstract In non-ideal vibratory system, the excitation is a nonlinear function of system response. The dynamic behavior of such system is often characterized by an energy source with limited power. The study of instability phenomena in non-ideal rotor driven through a non-ideal energy source is of considerable current interest. The non-ideal rotor system often gets destabilized on exceeding a critical input power near the resonance. This kind of instability is termed as Sommerfeld effect marked with nonlinear jump phenomena. This paper investigates the attenuation of nonlinear jump phenomena and numerical study of bifurcations of a non-ideal unbalanced rotor system with internal damping using time delayed feedback via active magnetic bearings. The results show that the time delay indeed plays a critical role on the suppression of the jump phenomena. Following, some new insights are also revealed through a numerical study of saddle node, Hopf and trans-critical bifurcations with time delay as a bifurcation parameter. The transient analysis confirms the results obtained analytically through the steady-state consideration.

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