Chaos Elimination Research Articles

Time-Delay Signature Elimination of Chaos in Semiconductor Lasers with Multimode Fiber Feedback

Time-Delay Signature Elimination of Chaos in Semiconductor Lasers with Multimode Fiber Feedback

Passive chaos suppression for the planar slider-crank mechanism with a clearance joint by attached vibro-impact oscillator

Chaotic dynamic behavior in clearance joints is the prominent nonlinear factor for multibody systems. This study presents a passive chaos suppression method to stabilize the planar slider-crank mechanism with a clearance joint. The strategy resorts to a vibro-impact oscillator attached to the slider. Primarily, the impact principle is employed to characterize the dynamics in clearance joints. The mathematical model of the integral system is conducted subsequently. The chaotic system behavior is evaluated by bifurcation analysis varying clearance size and crank speed. When the controller is activated, parametric optimizations of the stiffness, clearance coefficient, and particle mass are conducted to achieve optimum chaos elimination. Phase portraits, the largest Lyapunov exponent, and time-frequency distribution are evaluated. Numerical results illuminate that an adjusted oscillator can suppress the chaotic high-frequency composition of system response and help to maintain continuous contact between the joint elements. The results suggest applying the identical clearance size in the revolute joint and vibro-impact oscillator for fast optimization. Moreover, the method is still technology valid when considering different contact principles. Ultimately, a test platform is established to achieve some experimental validations.

Controlling Chaotic Vibrations of a Quarter-Car Model Excited by Road Surface Profile using Parametric Excitation.

Chaotic Vibrations are considered for a quarter-car model excited by the road surface profile. The equation of motion is obtained in the form of a classical Duffing equation and it is modeled with deliberate introduction of parametric excitation force term to enable us manipulate the behavior of the system. The equation of motion is solved using the Method of Multiple Scales. The steady-state solutions with and without the parametric excitation force term is investigated using NDSolve MathematicaTM Code and the nonlinear dynamical system’s analysis is by a study of the Bifurcations that are observed from the analysis of the trajectories, and the calculation of the Lyapunov. In making the system more strongly nonlinear the excitation amplitude value is artificially increased to various multiples of the actual value. Results show that the system’s response can be extremely sensitive to changes in the amplitude and the that chaos is evident as the system is made more nonlinear and that with the introduction of parametric excitation force term the system’s motion becomes periodic resulting in the elimination of chaos and the reduction in amplitude of vibration.

Variable Structure Controller for Chaos Elimination in a Single Ended Primary Inductance Converter

The paper attempts to off-set the circuit parasitics and the inherent switching nature of the power switch in a SEPIC (Single Ended Primary Inductance Converter) that eclipses its performance from theoretical predictions. The focus orients to design a control strategy that offers a chaotic free operation of the SEPIC. It envisages the use of a Variable Structure Control (VSC) strategy to irradiate the adverse effects of non-linear dynamics and assuage the operating range of the converter. The scheme projects the creation and elimination of this nonlinear property through time domain waveforms and phase portraits. The methodology underscores the theory to ensure an uniform rate of charging and discharging for the inductor current during the process of the converter operating the load. The scheme realizes the benefits of the mechanism through a correlation between the open and closed loop inductor current time domain waveform, with the help of adjustments in the parametric variations. The effort involves evaluating the performance using MATLAB simulation and experimental validation in a DSPIC (Digital signal peripheral interface controller) environment to illustrate its suitability for practical applications.

Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG.

Time delay signature (TDS) of a semiconductor laser subject to dispersive optical feedback from a chirped fibre Bragg grating (CFBG) is investigated experimentally and numerically. Different from mirror, CFBG provides additional frequency-dependent delay caused by dispersion, and thus induces external-cavity modes with irregular mode separation rather than a fixed separation induced by mirror feedback. Compared with mirror feedback, the CFBG feedback can greatly depress and even eliminate the TDS, although it leads to a similar quasi-period route to chaos with increases of feedback. In experiments, by using a CFBG with dispersion of 2000ps/nm, the TDS is decreased by 90% to about 0.04 compared with mirror feedback. Furthermore, both numerical and experimental results show that the TDS evolution is quite different: the TDS decreases more quickly down to a lower plateau (even background noise level of autocorrelation function) and never rises again. This evolution tendency is also different from that of FBG feedback, of which the TDS first decreases to a minimal value and then increases again as feedback strength increases. In addition, the CFBG feedback has no filtering effects and does not require amplification for feedback light.

Detection of Unstable Periodic Orbits and Chaos Control in a Passive Biped Model

Dynamic analysis of passive biped models plays a significant role both in understanding human locomotion and in developing humanoid robots. In this investigation, two chaos control algorithms based on linearization of Poincare map (OGY method) and artificial neural networks (ANNs) are utilized to control the motion of a passive biped model. To this end, the chaotic characteristics of the system are analyzed using several nonlinear dynamics tools such as Poincare map, bifurcation diagram, and Lyapunov exponents, and then, unstable periodic orbits (UPOs) of the system are detected. Detection of these orbits helps to extract a desired walking pattern and also is utilized for chaos elimination of the system. The robustness of the proposed ANN-based control algorithm is verified by applying toe-off impulses to the biped during the gait. Furthermore, the effect of network parameters on the biped walking performance is investigated to get design guidelines for the ANN-based controller.

Chaotic Motion of a Reentry Capsule During Descent into the Atmosphere

Conical-shaped reentry capsules with a spherical bottom and a displaced center of mass from the axis of symmetry are widely used in astronautics for payload delivery. In the case of control-system breakage, modern reentry capsules allow a successful landing to be carried out in an uncontrolled mode. At the same time, the aerodynamic features of this particular shape create preconditions for chaotic motion. This can lead to an overturn of the capsule, thus creating the risk of an accident. This article explores uncontrolled descent of the reentry capsule, with slight asymmetry, into the atmosphere. The system of differential equations describing uncontrollable descent of an asymmetric capsule in the atmosphere was recorded. Fast and slow variables were introduced. A simplified system of equations was obtained, describing the change of the spatial angle of attack. It was shown that chaotic motion can occur during the uncontrolled descent in the atmosphere. The algorithm of damping coefficient selection was developed on the basis of Melnikov’s method. Its application allows for the elimination of chaos in the whole descent trajectory, thus increasing the system reliability.

An analytical study of controlling chaotic dynamics in a spur gear system

In order to design and develop an optimal gear transmission system, it is important to control the occurrence of various types of nonlinear phenomena such as bifurcation and chaotic response. This paper describes a control system for elimination of the chaotic behaviors in a gear dynamic system. Analytical approach concerning the elimination of chaos in a gear system with applying the external control excitation is given by using Melnikov method. The numerical simulations are considered to check the validity of theoretical predictions, and also to investigate the efficiency of the proposed control system to eliminate the homoclinic bifurcation and chaos in nonlinear gear systems.

Multi-objective optimal backstepping controller design for chaos control in a rod-type plasma torch system using Bees algorithm

In this study, we propose an optimal backstepping controller for chaos control in a rod-type plasma torch system. The Bees algorithm is used to determine the optimal parameters for the backstepping controller by minimizing a multi-objective function. The objective function is a weighted sum of the integral of time multiplied absolute error and the squared control signal. Our simulation results demonstrate the greater effectiveness of the proposed controller for chaos elimination in a rod-type plasma torch system compared with a sliding mode controller and a backstepping controller tuned by particle swarm optimization.

Control of dry friction oscillator using semi-active magneto-rheological tuned liquid column damper

In this paper, first, the dynamic behavior of a nonlinear friction driven oscillator subjected to harmonic external excitations and supported by limited power supply is studied. Dynamic analysis of the system through the variation of excitation frequency reveals that the system has chaotic motion near the fundamental natural frequency. After analyzing the dynamic response of the system, the control of chaotic motion of this system using tuned liquid column dampers (TLCD) and magneto-rheological tuned liquid column damper (MR-TLCD) are analyzed. Time-delay feedback control strategy is used in order to have real-time semi-active vibration control of the block with MR-TLCD. Simulation results show the high performance of both of the proposed methods for chaos elimination and improving the system operation. It is also concluded that the system transient time in semi-active control using MR-TLCDs and based on the new proposed control strategy is less than conventional TLCDs.

Suppression of Chaotic Behavior in Duffing-holmes System using Back-stepping Controller Optimized by Unified Particle Swarm Optimization Algorithm

The nonlinear behavior analysis and chaos control for Duffing-Holmes chaotic system is discussed in this paper. In order to suppress the irregular chaotic motion, an optimal back-stepping controller is designed. The back-stepping method consists of parameters with positive values. The improper selection of the parameters leads to inappropriate responses or even may lead to instability of the system. In this paper, the Unified particle swarm optimization (UPSO) algorithm is utilized to determine the convenient and optimal values of the parameters. The minimized objective function via UPSO algorithm is a weighted sum of the Integral of Time multiplied Absolute Error (ITAE) and squared control signal. Fast control of chaos in a very short time and having more limited control signal for this purpose, are the great advantages of the proposed controller. Numerical simulations show the high performance of this method for chaos elimination in Duffing-Holmes system.

The Analysis of Optimal Chaos Suppression Conditions in Dissipative Non-Linear Oscillators with Parametric Uncertainty

In the work we present the method for the analysis of the optimal suppression peculiarities of chaotic behavior with or without parametric uncertainty. It is based on the task of optimal parameter correction. The solution for this situation is sought using Melnikov criterion. It allows revealing the connection between key parameters of the oscillator and finding the best way of chaos elimination.

Fuzzy logic combining controller design for chaos control of a rod-type plasma torch system

The nonlinear behavior analysis and chaos suppression control for a rod-type plasma torch system was discussed in the paper. The scenarios for the possible non-linear behavior in the plasma torch dynamics were also obtained with respect to the variation of system parameter μ via the numerical simulations, which might provide a guide for finding non-linear phenomena in the practical application of the plasma torch. From the bifurcation diagram, it shows that the plasma torch dynamics exit undesired chaotic behavior. In order to suppress the irregular chaotic motion, a fuzzy logic controller (FLC) that combines a sliding mode controller (SMC) and a state feedback controller (SFC) with guaranteed closed loop stability is designed. Each rule in this FLC has an SMC or an SFC in the consequent part. The role of the FLC is to schedule the final control under different antecedents. It is guaranteed that under the proposed control law, the rod-type plasma system with undesired chaotic motion can asymptotically stabilize to the unstable equilibrium point i.e. zero state. More importantly, the controller thus design can keep the advantages and remove the disadvantage of the two conventional controllers. Numerical simulations show the high performance of this method for chaos elimination in rod-type plasma torch system.

Chaos control in lateral oscillations of spinning disks via nonlinear feedback

In this paper the problem of chaos control in single mode lateral oscillations of spinning disks is studied. At first, using the harmonic balance method, one of the periodic orbits of system is evaluated. Then proposing a nonlinear feedback strategy a control law is presented for chaos elimination by tracking the mentioned periodic solution. It is shown that although the system is not input-state feedback linearizable, by defining an output signal and using the input–output linearization method, the objective of complete periodic orbit tracking is achieved. The sufficient condition for this purpose is presented, and the performance of proposed method is examined by numerical simulation.

Chaos control in AFM systems using nonlinear delayed feedback via sliding mode control

In this paper a nonlinear delayed feedback control is proposed to control chaos in an Atomic Force Microscope (AFM) system. The chaotic behavior of the system is suppressed by stabilizing one of its first-order Unstable Periodic Orbits (UPOs). At first, it is assumed that the system parameters are known, and a nonlinear delayed feedback control is designed to stabilize the UPO of the system. Then, in the presence of model parameter uncertainties, the proposed delayed feedback control law is modified via sliding mode scheme. The effectiveness of the presented methods is numerically investigated by stabilizing the unstable first-order periodic orbit of the AFM system. Simulation results show the high performance of the methods for chaos elimination in AFM systems.

Stabilizing unstable fixed points of chaotic maps via minimum entropy control

In this paper the problem of chaos control in nonlinear maps using minimization of entropy function is investigated. Invariant probability measure of a chaotic dynamics can be used to produce an entropy function in the sense of Shannon. In this paper it is shown that how the entropy control technique is utilized for chaos elimination. Using only the measured states of a chaotic map the probability measure of the system is numerically estimated and this estimated measure is used to obtain an estimation for the entropy of the chaotic map. The control variable of the chaotic system is determined in such a way that the entropy function descends until the chaotic trajectory of the map is replaced with a regular one. The proposed idea is applied for stabilizing the fixed points of the logistic and the Henon maps as some cases of study. Simulation results show the effectiveness of the method in chaos rejection when only the statistical information is available from the under-study systems.

Elimination of chaos in a multilongitudinal-mode, diode-pumped, 6-W continuous-wave, intracavity-doubled Nd:YAG laser

We present a new stability mechanism in an intracavity-doubled Nd:YAG laser oscillating in a multi-fundamental-longitudinal mode. Self-mode-locked oscillation, in which phases of the modes give the destructive interference between the sum and doubling components, leads to the low-noise operation of the diode-pumped, >6-W cw green laser, which we previously demonstrated [Opt. Lett. 21 1912 (1996)]. This phase-locked mode of operation would reduce the nonlinear output coupling and ultimately eliminate the chaotic amplitude fluctuation from the so-called green problem. The internally reflected green light at the end mirror has a significant effect on phase locking and elimination of noise through parametric processes.