Time-delayed Autosynchronization Method Research Articles

Extended time-delay autosynchronization method for libration control of electrodynamic tether using Lorentz force

It is well known that the libration motion of the electrodynamic tether is unstable. Libration control of the electrodynamic tether system using the Lorentz force produced by current in the tether is studied. In the libration dynamic equation, the Lorentz force is virtually divided into two parts. One part takes the role of keeping the essential function of the electrodynamic tether system. The other part takes the role of controlling the libration motion. The control scheme of the Lorentz force is based on the extended time-delay autosynchronization method. In this scheme, the control current which is the control parameter is determined by real-time states of libration and angular velocities for delay time of previous periods. The validity of the control scheme proposed in this study is confirmed by numerical simulations in the case of circular orbit, elliptical orbit, orbit in the equatorial plane and noises existing in measuring the states of libration. The results show that the perturbed libration motions converge to the periodic solution with time growing in examples of circular orbit, elliptical orbit, and noises existing. The perturbed libration motion converges to an approximate periodic orbit in the example of equatorial orbit. The control current is in a reasonable range during the process of control, and converges to zero in the end. The curve of the current in the tether is continuous and smooth which can be easily achieved in an actual system.

Chaos Control of Fluctuations Caused by Flute Instability in Electron Cyclotron Resonance Plasma

Controlling chaos of density fluctuations observed in electron cyclotron resonance (ECR) plasma is carried out using the time-delayed auto synchronization (TDAS) method introduced by Pyragas. Since the TDAS method, which is a sort of feedback system, requires a feedback signal, the input power of microwaves for ECR discharge is modulated by signals of frequency (<30 kHz) based on the ion-saturation current indicating the electron density. Fluctuations caused by the flute instability reach the chaotic state when the microwave power is increased. It was found that when the TDAS method is applied to the chaotic state, the chaotic state transitions to the periodic state and the correlation dimension changes from a non integer value to an integer value.

Dynamical behavior of the motions associated with the nonlinear periodic regime in a laboratory plasma subject to delayed feedback

Time-delayed feedback is applied to the motions associated with the nonlinear periodic regime generated due to current-driven ion acoustic instability; this is a typical instability in a laboratory plasma, and the dynamical behavior is experimentally investigated using delayed feedback. A time-delayed autosynchronization method is applied. When delayed feedback is applied to the nonlinear periodic orbit, the periodic state changes to various motions depending on the control parameters, namely, the arbitrary time delay and the proportionality constant. Lyapunov exponents are calculated in order to examine the dynamical behavior.

Dynamical control of the chaotic state of the current-driven ion acoustic instability in a laboratory plasma using delayed feedback

Controlling chaos caused by the current-driven ion acoustic instability is attempted using delayed feedback, i.e., the time-delay auto synchronization (TDAS) method introduced by Pyragas [Phys. Lett. A 170, 421 (1992)] with flexibility. When the control parameter of the system Vm is increased, the current-driven ion acoustic instability is excited, and then, the system demonstrates chaotic oscillation in a certain range of the parameter. When the electronic circuit to control chaos based on the TDAS method is applied to the chaotic regime, the chaotic orbit changes to a periodic one maintaining the instability, that is, the chaotic state caused by the current-driven ion acoustic instability is well controlled using the TDAS method. Furthermore, it is shown that controlling chaos can be achieved when the delay time τ is chosen to be close to a fundamental frequency of the unstable periodic orbit embedding in the chaotic system.

Giant improvement of time-delayed feedback control by spatio-temporal filtering.

Control of spatio-temporal chaos by the time-delay autosynchronization method is improved by several orders of magnitude. Unstable time periodic patterns are efficiently stabilized if one employs filters and couplings which originate from the Floquet eigenvalue problem of the unstable orbit. We illustrate our scheme by an application to a globally coupled reaction-diffusion model which describes charge transport in semiconductor devices.

Control of chaotic solitons by a time-delayed feedback mechanism

We investigate a control of chaotic solitons using a modified time-delayed autosynchronization method. Numerical results for the maximal Lyapunov exponent are in very good agreement with analytical theory developed originally for low-dimensional systems. The control is most efficient when the spatial distribution of the control force is proportional to the kink translational mode. Observations of the motion of the kink center and the total power transmitted to the system lead to the same values of the maximal Lyapunov exponent.

Dynamical study and control of drift waves in a magnetized laboratory plasma

The various dynamical regimes of collisional drift waves in a magnetized plasma column are experimentally studied. These unstable low-frequency electrostatic waves are related with strong modulations of the ion and electron density. The angular velocity of the rotating plasma column is the control parameter of the dynamics: regular, chaotic and turbulent regimes are obtained. The spatial extension of the system allows for the occurrence of spatiotemporal chaos. The time-delay auto-synchronization method of controlling chaos [K. Pyragas, Phys. Lett. A 170, 421 (1992)] though purely temporal is successfully applied. A numerical study using coupled nonlinear oscillators exhibiting chaos is compared to the experimental results. The control method is tested on this model.

Control of the chaotic regimes of nonlinear drift-waves in a magnetized laboratory plasma

Nonlinear drift-waves are experimentally studied in a cylindrical magnetized laboratory plasma. Low-dimensional chaotic regimes are controled using the time-delay autosynchronization method [K. Pyragas, Phys. Lett. A 170, 421 (1992)]. A significant reduction of spectral width in the power spectrum is obtained.

Controlling chaos by negative feedback of subharmonic components

In this paper we present a control technique for stabilizing chaotic motion to periodic orbits in a ${\mathrm{CO}}_{2}$ laser with electro-optic feedback. The control method is based on negative feedback of subharmonic components of the laser intensity signal. A detailed analysis, performed using the four-level model for the ${\mathrm{CO}}_{2}$ laser, allows us both to reproduce the experimental features and to compare our method with the time-delayed autosynchronization method introduced by Pyragas [Phys. Lett. A 170, 421 (1992)].

Continuous control of ionization wave chaos by spatially derived feedback signals

In the positive column of a neon glow discharge, two different types of ionization waves occur simultaneously. The low-dimensional chaos arising from the nonlinear interaction between the two waves is controlled by a continuous feedback technique. The control strategy is derived from the time-delayed autosynchronization method. Two spatially displaced points of observation are used to obtain the control information, using the propagation characteristics of the chaotic wave.

Controlling the chaotic regime of nonlinear ionization waves using the time-delay autosynchronization method.

The chaotic regime of an unstable glow discharge is controlled using a continuous time-delay autosynchronization method. At a fixed location along the discharge tube, the electric field is chaotic within certain ranges of the discharge current. The control signal, built from the difference between the delayed signal and the real-time chaotic signal, leads to the stabilization of the discharge when applied to the control parameter (the discharge current).