scholarly journals Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Wen-Qing Zhang ◽  
Jie Li ◽  
Kun Zhang ◽  
Peng Cui
Keyword(s):  
Control System ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Feedback Control ◽  
Magnetic Flux ◽  
Critical Value ◽  
Feedback Control System ◽  
Maglev System ◽  
Period Solution ◽  
Period Motion

Nonlinear properties of magnetic flux feedback control system have been investigated mainly in this paper. We analyzed the influence of magnetic flux feedback control system on control property by time delay and interfering signal of acceleration. First of all, we have established maglev nonlinear model based on magnetic flux feedback and then discussed hopf bifurcation’s condition caused by the acceleration’s time delay. The critical value of delayed time is obtained. It is proved that the period solution exists in maglev control system and the stable condition has been got. We obtained the characteristic values by employing center manifold reduction theory and normal form method, which represent separately the direction of hopf bifurcation, the stability of the period solution, and the period of the period motion. Subsequently, we discussed the influence maglev system on stability of by acceleration’s interfering signal and obtained the stable domain of interfering signal. Some experiments have been done on CMS04 maglev vehicle of National University of Defense Technology (NUDT) in Tangshan city. The results of experiments demonstrate that viewpoints of this paper are correct and scientific. When time lag reaches the critical value, maglev system will produce a supercritical hopf bifurcation which may cause unstable period motion.

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 Dynamics of the disparity vergence fusion sustain component

2019 ◽  
Vol 12 (4) ◽  
Author(s):  
John L. Semmlow ◽  
Chang Yaramothu ◽  
Tara L. Alvarez
Keyword(s):  
Control System ◽  
Time Delay ◽  
Feedback Control ◽  
Slow Component ◽  
Strong Support ◽  
Low Frequency ◽  
Oscillatory Behavior ◽  
Feedback Control System ◽  
Frequency Spectra ◽  
Frequency Components

The stereotypical vergence response to a step stimulus consists of two dynamic components: a high velocity fusion initiating component followed by a slower component that may mediate sustained fusion.  The initial component has been well-studied and is thought to be controlled by an open-loop mechanism. Less is known about the slow, or fusion sustaining component except that it must be feedback controlled to achieve the positional precision of sustained fusion.  Given the delays in disparity vergence control, a feedback control system is likely to exhibit oscillatory behavior.  Vergence responses to 4 deg step changes in target position were recorded in eight subjects. The slow component of each response was isolated manually using interactive graphics and the frequency spectrum determined.  The frequency spectra of all isolated slow vergence movements showed a large low frequency peak between 1.0 and 2.0 Hz and one or more higher frequency components.  The higher frequency components were found to be harmonics of the low frequency oscillation.  A feedback model of the slow component was developed consisting of a time delay, an integral/derivative controller and an oculomotor plant based on Robinson’s model.  Model simulations showed that a direction dependent asymmetry in the derivative element was primarily responsible for the higher frequency harmonic components. Simulations also showed that the base frequencies are primarily dependent on the time delay in the feedback control system. The fact that oscillatory behavior was found in all subjects provides strong support that the slow, fusion sustaining component is mediated by a feedback system.

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