CHAOTIFICATION OF A NONLINEAR VIBRATION ISOLATION SYSTEM BY DUAL TIME DELAYED FEEDBACK CONTROL

2013 ◽  
Vol 23 (06) ◽  
pp. 1350096 ◽  
Author(s):  
YINGLI LI ◽  
DAOLIN XU ◽  
YIMING FU ◽  
JIAXI ZHOU
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Vibration Isolation ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Stable Region ◽  
Control Parameters ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Time Delayed Feedback

Line spectrum of noise radiated from machinery vibrations of underwater vehicles is one of the most harmful signals that expose the characteristics of vehicles and locations. In order to distort the features and restrain the intensity of the line spectra, we attempt to chaotify the vibration system by time delay control. To avoid blindly numerical testing of the control parameters, stability of a two-dimensional vibration isolation floating raft system with two time-delayed feedback control is studied in this paper, aiming to provide guidance for chaotification. The system with dual equal time delay is investigated by the generalized strum method and the polynomial eigenvalues are adopted to analyze the stability of the controlled vibration isolation system with two unequal time delays. The critical control gains and delays for stability switches are obtained. By adjusting the control parameters beyond stable region, it is feasible to chaotify the system. Numerical simulations are conducted to compare the effect of two time delay with different control parameters and different control scheme to complicate the vibration isolation system.

Research on vibration reduction of semi-active suspension system of quarter vehicle based on time-delayed feedback control with body acceleration

2021 ◽  
pp. 146134842110518
Author(s):  
Yong Guo ◽  
Chuanbo Ren
Keyword(s):  
Feedback Control ◽  
Delayed Feedback ◽  
Suspension System ◽  
Delayed Feedback Control ◽  
Vehicle Body ◽  
Vehicle Suspension ◽  
Vertical Acceleration ◽  
Control Parameters ◽  
Vehicle Suspension System ◽  
Time Delayed Feedback

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.

Responses and energy transmissibility of a viscoelastic isolation system with a power-form restoring force under delayed feedback control

2015 ◽  
Vol 23 (14) ◽  
pp. 2291-2306 ◽  
Author(s):  
Dongmei Huang ◽  
Wei Xu ◽  
Wenxian Xie ◽  
Wei Liu
Keyword(s):  
Feedback Control ◽  
Frequency Response ◽  
Vibration Isolation ◽  
Multiple Scales ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Restoring Force ◽  
Isolation System ◽  
Feedback Parameter ◽  
Dynamical Behaviors

In this paper, combination of cubic nonlinearity and time delay is designed to improve the performance of a viscoelastic isolation system with a power-form restoring force. By the method of multiple scales, the amplitude-frequency response, stability, backbone curve and energy transmissibility are considered. More specifically, three nonlinear cubic delayed feedback control methodologies are examined: position, velocity and acceleration delayed feedback. It is found that the viscoelastic damping coefficient can induce multi-valued response, especially frequency island phenomenon. In this regard, the isolation system indicates the softening behavior for under-linear restoring force and hardening behavior for over-linear restoring force. And equivalent damping and jump avoidance condition are first proposed to interpret the effect of feedback control loop on dynamical behaviors. Furthermore, with the purpose of improving the stability and reducing the vibration, suitable feedback parameter pairs are determined by the frequency response together with stability conditions. Finally, the vibration isolation property is predicted based on energy transmissibility in different cases. Results show that the strategy proposed in this paper is practicable and feedback control parameters are significant factors to alter dynamical behaviors, and more importantly, to improve the isolation effectiveness for the viscoelastic isolation system.

BIFURCATION, CHAOS AND THEIR CONTROL IN A TIME-DELAY DIGITAL TANLOCK LOOP

2013 ◽  
Vol 23 (08) ◽  
pp. 1330029 ◽  
Author(s):  
TANMOY BANERJEE ◽  
BISHWAJIT PAUL ◽  
B. C. SARKAR
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Parameter Space ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Convergence Time ◽  
Stable Phase ◽  
Bifurcation And Chaos ◽  
Global Parameter ◽  
Time Delayed Feedback

This paper reports the detailed parameter space study of the nonlinear dynamical behaviors and their control in a time-delay digital tanlock loop (TDTL). At first, we explore the nonlinear dynamics of the TDTL in parameter space and show that beyond a certain value of loop gain parameter the system manifests bifurcation and chaos. Next, we consider two variants of the delayed feedback control (DFC) technique, namely, the time-delayed feedback control (TDFC) technique, and its modified version, the extended time-delayed feedback control (ETDFC) technique. Stability analyses are carried out to find out the stable phase-locked zone of the system for both the controlled cases. We employ two-parameter bifurcation diagrams and the Lyapunov exponent spectrum to explore the dynamics of the system in the global parameter space. We establish that the control techniques can extend the stable phase-locked region of operation by controlling the occurrence of bifurcation and chaos. We also derive an estimate of the optimum parameter values for which the controlled system has the fastest convergence time even for a larger acquisition range. The present study provides a necessary detailed parameter space study that will enable one to design an improved TDTL system.

TIME-DELAYED FEEDBACK CONTROL OF TIME-DELAY CHAOTIC SYSTEMS

2003 ◽  
Vol 13 (01) ◽  
pp. 193-205 ◽  
Author(s):  
XINPING GUAN ◽  
CAILIAN CHEN ◽  
HAIPENG PENG ◽  
ZHENGPING FAN
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Error Control ◽  
Chaotic Systems ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Control Technique ◽  
Time Delayed Feedback

This paper addresses time-delayed feedback control (DFC) of time-delay chaotic systems. To extend the DFC approach to time-delay chaotic system, alter having been successfully used in chaotic systems without time-delays, the standard feedback control (SFC) method is firstly employed to show the main control technique in this paper based on one error control system. Then sufficient conditions for stabilization and tracking problems via DFC are derived from the results based on SFC. Also, the systematic and analytic controller design method can be obtained to stabilize the system to an unstable fixed point and to tracking an unstable periodic orbit, respectively. Some numerical examples are provided to demonstrate the effectiveness of the presented method.

Stochastic Stability of Mathieu-Van Der Pol System with Delayed Feedback Control

2011 ◽  
Vol 105-107 ◽  
pp. 132-138
Author(s):  
Chang Shui Feng ◽  
Shuang Lin Chen
Keyword(s):  
Time Delay ◽  
Lyapunov Exponent ◽  
Feedback Control ◽  
Lyapunov Stability ◽  
Original System ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Control Force ◽  
Van Der Pol ◽  
Time Delayed Feedback

The asymptotic Lyapunov stability with probability one of Mathieu-Van der Pol system with time-delayed feedback control under wide-band noise parametric excitation is studied. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged Itô stochastic differential equations for the system are derived by using the stochastic averaging method and the expression for the Lyapunov exponent of the linearized averaged Itô equations is derived. It is inferred that the Lyapunov exponent so obtained is the first approximation of the largest Lyapunov exponent of the original system, and the asymptotic Lyapunov stability with probability one of the original system can be determined approximately by using the Lyapunov exponent. Finally, the effects of time delay in feedback control on the Lyapunov exponent and the stability of the system are analyzed. The theoretical results are well verified through digital simulation.

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