scholarly journals Dynamic Analysis of a High-Static-Low-Dynamic-Stiffness Vibration Isolator with Time-Delayed Feedback Control

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Yong Wang ◽  
Shunming Li ◽  
Chun Cheng ◽  
Xingxing Jiang
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Multiple Scales ◽  
Dynamic Stiffness ◽  
Primary Resonance ◽  
Feedback Gain ◽  
Vibration Isolator ◽  
Controlled System ◽  
Effects Of Feedback ◽  
Isolation Performance

This paper proposes the time-delayed cubic velocity feedback control strategy to improve the isolation performance of High-Static-Low-Dynamic-Stiffness (HSLDS) vibration isolator. Firstly, the primary resonance of the controlled HSLDS vibration isolator is obtained by using multiple scales method. The equivalent damping ratio and equivalent resonance frequency are defined to study the effects of feedback gain and time delay on the primary resonance. The jump phenomenon analysis of the controlled system without and with time delay is investigated by using Sylvester resultant method and optimization method, respectively. The stability analysis of the controlled system is also considered. Then, the 1/3 subharmonic resonance of the controlled system is studied by using multiple scales method. The effects of feedback gain and time delay on the 1/3 subharmonic resonance are also presented. Finally, force transmissibility is proposed to evaluate the performance of the controlled system and compared with an equivalent linear passive vibration isolator. The results show that the vibration amplitude of the controlled system around the resonance frequency region decreases and the isolation frequency band is larger compared to the equivalent one. A better isolation performance in the high frequency band can be achieved compared to the passive HSLDS vibration isolator.

scholarly journals Cubic Velocity Feedback Control of High-Amplitude Vibration of a Nonlinear Plant to a Primary Resonance Excitation

2007 ◽  
Vol 14 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Li Jun ◽  
Shen Rongying ◽  
Hua Hongxing
Keyword(s):  
Feedback Control ◽  
Multiple Scales ◽  
Primary Resonance ◽  
High Amplitude ◽  
Resonance Excitation ◽  
Feedback Gain ◽  
Response Curves ◽  
Power Requirement ◽  
Velocity Feedback ◽  
Nonlinear Plant

High-amplitude response suppression of the primary resonance of a nonlinear plant under cubic velocity feedback control is investigated. By means of the multiple scales method, two equations on the amplitude and phase of the response of the nonlinear system are obtained and the force-response and frequency-response curves are shown. The stability analyses for the open- and closed-loop responses of the system are carried out and the performance of the control strategy is investigated. The instantaneous power requirement of the control law is also examined. It can be demonstrated that appropriate choice for the feedback gain can greatly reduce the response amplitude of the primary resonance and completely eliminate the multiple responses. Finally the perturbation solutions are verified with numerical simulations.

scholarly journals Vertical Vibration Control of Cold Rolling Mill’s Rolls Based on Time-delay Feedback Control Method

2018 ◽  
Vol 153 ◽  
pp. 06005
Author(s):  
Dongxiao Hou
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Cold Rolling ◽  
Rolling Mill ◽  
Control Method ◽  
Primary Resonance ◽  
Vertical Vibration ◽  
Resonance Amplitude ◽  
Feedback Control Method ◽  
Delay Feedback Control

In this paper, a two degree of freedom nonlinear vertical vibration equation of the cold rolling mill with the dynamic rolling force was established, then the delay feedback control method was introduced into the equation to controlled the vertical vibration of the system. The amplitude-frequency equations of primary resonance of system was carried out by using the multi-scale method, and the resonance characteristics of different parameters of delay feedback control method were obtained by adopting the actual parameters of rolling mill. It is found that the size of the resonance amplitude value was effectively controlled and the resonance region and jumping phenomenon of the system were eliminated by selecting the appropriate time-delay parameters combination, which provides an effective theoretical reference for solving mill vibration problems.

Resonances of a Nonlinear Single-Degree-of-Freedom System with Time Delay in Linear Feedback Control

2010 ◽  
Vol 65 (5) ◽  
pp. 357-368 ◽  
Author(s):  
Atef F. El-Bassiouny ◽  
Salah El-Kholy
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Feedback Control ◽  
Fixed Points ◽  
Multiple Scales ◽  
Degree Of Freedom ◽  
Linear Feedback ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Subharmonic Resonances

The primary and subharmonic resonances of a nonlinear single-degree-of-freedom system under feedback control with a time delay are studied by means of an asymptotic perturbation technique. Both external (forcing) and parametric excitations are included. By means of the averaging method and multiple scales method, two slow-flow equations for the amplitude and phase of the primary and subharmonic resonances and all other parameters are obtained. The steady state (fixed points) corresponding to a periodic motion of the starting system is investigated and frequency-response curves are shown. The stability of the fixed points is examined using the variational method. The effect of the feedback gains, the time-delay, the coefficient of cubic term, and the coefficients of external and parametric excitations on the steady-state responses are investigated and the results are presented as plots of the steady-state response amplitude versus the detuning parameter. The results obtained by two methods are in excellent agreement

The design of negative stiffness spring for precision vibration isolation using axially magnetized permanent magnet rings

2019 ◽  
Vol 25 (19-20) ◽  
pp. 2667-2677 ◽  
Author(s):  
Zhenhua Zhou ◽  
Shuhan Chen ◽  
Dun Xia ◽  
Jianjun He ◽  
Peng Zhang
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Design Procedure ◽  
Air Gap ◽  
Negative Stiffness ◽  
Linear Component ◽  
Vibration Isolator ◽  
Stiffness Characteristic ◽  
Isolation Performance

A negative stiffness element is always employed to generate high-static–low-dynamic stiffness characteristic of the vibration isolator, reduce the resonance frequency of the isolator, and improve the vibration isolation performance under low and ultra-low frequency excitation. In this paper, a new compact negative stiffness permanent magnetic spring (NSPMS) that is composed of two axial-magnetized permanent magnetic rings is proposed. An analytical expression of magnetic negative stiffness of the NSPMS is deduced by using the Coulombian model. After analyzing the effect of air-gap width, air-gap position, height difference between the inner ring and outer ring on the negative stiffness characteristic, a design procedure is proposed to realize the negative stiffness characteristic with a global minimum linear component and uniformity stiffness near the equilibrium position. Finally, an experimental prototype is developed to validate the effectiveness of the NSPMS. The experimental results show that combining a vibration isolator with the NSPMS in parallel can lower the natural frequency and improve the isolation performance of the isolator.

DELAY-INDUCED BIFURCATIONS IN A NONAUTONOMOUS SYSTEM WITH DELAYED VELOCITY FEEDBACKS

2004 ◽  
Vol 14 (08) ◽  
pp. 2777-2798 ◽  
Author(s):  
JIAN XU ◽  
PEI YU
Keyword(s):  
Control System ◽  
Time Delay ◽  
Feedback Control ◽  
Periodic Solutions ◽  
Stability Boundary ◽  
Primary Resonance ◽  
Perturbation Approach ◽  
Feedback Control System ◽  
Trivial Equilibrium ◽  
Functional Differential

This paper investigates the bifurcations due to time delay in the feedback control system with excitation. Based on an self-sustained oscillator, the delayed velocity feedback control system is proposed. For the case without excitation, the stability of the trivial equilibrium is discussed and the condition under which the equilibrium loses its stability is obtained. This leads to a critical stability boundary where Hopf bifurcation or periodic solutions may occur. For the case with excitation, the main attention is focused on the effect of time delay on the obtained periodic solution when primary resonance occurs in the system under consideration. To this end, the control system is changed to be a functional differential equation. Functional analysis is carried out to obtain the center manifold and then a perturbation approach is used to find periodic solutions in a closed form. Moreover, the unstable regions for the limit cycles are also obtained, predicting the occurrence of some complex behaviors. Numerical simulations are employed to find the routes leading to quasi-periodic motions as the time delay is varied. It has been found that: (i) Time delay can be used to control bifurcations; and (ii) time delay can be applied to generate bifurcations. This indicates that time delay may be used as a "switch" to control or create complexity for different applications.

scholarly journals Bifurcation Based-Delay Feedback Control Strategy for a Fractional-Order Two-Prey One-Predator System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Shuai Li ◽  
Chengdai Huang ◽  
Xinyu Song
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Feedback Gain ◽  
Controlled System ◽  
Delay Feedback Control ◽  
Feedback Control Strategy ◽  
System With Time Delay ◽  
Theoretical Results ◽  
Predator System

The issue of bifurcation control for a novel fractional-order two-prey and one-predator system with time delay is dealt with in this paper. Firstly, the characteristic equation is investigated by picking time delay as the bifurcation parameter, and some conditions for the appearance of Hopf bifurcation are obtained. It is shown that time delay can give rise to periodic oscillations and each order has an important impact on the occurrence of Hopf bifurcation for the controlled system. Then, it is illustrated that the control result is obviously influenced by the feedback gain. It is also noted that the inception of the bifurcation can be postponed if the feedback gain decreases. Finally, two simulation examples are carried out to verify the chief theoretical results.

Dynamics and Realization of a Feedback-Controlled Nonlinear Isolator With Variable Time Delay

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Xiuting Sun ◽  
Feng Wang ◽  
Jian Xu
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Nonlinear Vibration ◽  
Time Delays ◽  
Vibration Suppression ◽  
Multiple Scales ◽  
Nonlinear Resonance ◽  
Variable Time Delay ◽  
Frequency Bands ◽  
Variable Time

In this paper, time-delayed feedback (TD-FB) control is introduced for a nonlinear vibration isolator (NL-VI), and the isolation effectiveness features are investigated theoretically and experimentally. In the feedback control loop, compound control with constant and variable time delays is considered. First, a stability analysis is conducted to determine the range of control parameters for stable zero equilibrium without excitation. Next, the nonlinear resonance frequency and the nonlinear vibration attenuation are studied by the method of multiple scales (MMS) to demonstrate the mechanism of TD-FB control. The results of the nonlinear vibration performances show that large variable time delays can improve the vibration suppression. Additionally, the mechanism for the time delay is not only to tune the equivalent stiffness and damping but also to induce effective isolation bandgap at high frequency. Therefore, the variable time delay is assumed as the function of frequency to meet different requirements at different frequency bands. The relevant experiment verifies the improvement of designed variable time delay on isolation performances in different frequency bands. Due to the improvement of isolation performances by compound time delay feedback control on nonlinear systems, it can be applied in the fields of ships, flexible structure in aerospace and aviation.

scholarly journals Stabilization of Linear Sampled-Data Systems by a Time-Delay Feedback Control

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
F. Ricardo García ◽  
Baltazar Aguirre ◽  
Rodolfo Suárez
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Sufficient Conditions ◽  
Sampling Period ◽  
Fixed Time ◽  
Feedback Gain ◽  
Data Systems ◽  
Sampled Data ◽  
Sampled Signal ◽  
Time Invariant

We consider one-dimensional, time-invariant sampled-data linear systems with constant feedback gain, an arbitrary fixed time delay, which is a multiple of the sampling period and a zero-order hold for reconstructing the sampled signal of the system in the feedback control. We obtain sufficient conditions on the coefficients of the characteristic polynomial associated with the system. We get these conditions by finding both lower and upper bounds on the coefficients. These conditions let us give both an estimation of the maximum value of the sampling period and an interval on the controller gain that guarantees the stabilization of the system.

Stability and perturbation analysis of a one-degree-of-freedom doubly clamped microresonator with delayed velocity feedback control

2017 ◽  
Vol 24 (15) ◽  
pp. 3454-3470 ◽  
Author(s):  
Jianxin Han ◽  
Qichang Zhang ◽  
Wei Wang ◽  
Gang Jin ◽  
Baizhou Li
Keyword(s):  
Feedback Control ◽  
Perturbation Analysis ◽  
Stability Condition ◽  
Multiple Scales ◽  
Dynamic Properties ◽  
Stable Region ◽  
Feedback Gain ◽  
Velocity Feedback ◽  
Dc Voltage ◽  
Stability Chart

In this paper, a study on a doubly clamped microresonator actuated by two symmetrical electrodes is carried out to investigate its dynamic properties with delayed velocity feedback control. A stability chart of the linearized system depicting delay time versus feedback gain is drawn first, which is actually nonperiodic. Moreover, stability switches do exist in this system. Then, the method of multiple scales is used to determine the existence, stability and dynamic properties of small amplitude vibration in the neighborhood of different equilibrium positions. It is shown that the stability condition via perturbation analysis overestimates the system stable region. The delayed stability condition via linearized analysis is more suitable for stability estimation. The following analytical and numerical results are presented to investigate frequency responses and frequency/damping trimming properties with various system and control parameters. Moreover, explicit formulas for optimum direct current (DC) voltage and equivalent natural frequency, corresponding to an approximate linear-like state, are deduced, respectively. Two typical design sketches depicting the initial gap width versus DC voltage are drawn with different beam lengths and thicknesses. Finally, a case study is carried out to verify the correctness of our analytical results about linear-like state prediction and frequency/damping trimming.

Vibration Suppression of a Saturation Control System Using Delayed Feedback Control

2012 ◽  
Vol 226-228 ◽  
pp. 82-86
Author(s):  
Yan Ying Zhao
Keyword(s):  
Feedback Control ◽  
Analytical Solutions ◽  
Vibration Suppression ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Single Mode ◽  
Original System ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Saturation Control

In the present paper, the delayed feedback control is applied to suppress the amplitude of the vibration of a beam. The method of multiple scales is employed to obtain the analytical solutions when the primary resonance and 1:2 internal resonance occur simultaneously. The predictions from analytical solutions agree with the numerical simulations well. The analytical results show that the amplitude of the beam of the saturation control is much larger than its amplitude of the single-mode motion. The effects of the delayed feedback control on amplitude of the beam are investigated when the original system is in the saturation control. There is a tunable range of the delay could be used to suppress the amplitude of the beam for a fixed value of the gain. The amplitude of the beam can be suppressed from 0.20 to 0.10 when the gain and the delay are chosen appropriate values.

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