Воздействие гармонического сигнала на генератор квазипериодических колебаний Анищенко-Астахова

A harmonic effect on a modified Anishchenko-Astakhov generator capable of demonstrating two-frequency quasi-periodic oscillations in the autonomous mode is considered. The possibility of doubling the three-frequency tori in a non-autonomous system is shown. The possibility of the effect of chaos suppression by an external signal is demonstrated, which leads not only to periodic, but also to quasi-periodic modes when the influence amplitude exceeds a certain threshold.

Fixed-Time Synergetic Control-Based Chaos Suppression for Eighth-Order IFOCIM Drive System

This paper investigates chaos suppression in widely used indirect field oriented controlled induction machine (IFOCIM) drive system using fixed-time synergetic control method. The complex eighth-order IFOCIM drive system shows chaotic oscillations during a specific range of the integral gain of the PI speed controller. The conventional synergetic control method is improved by employing the fixed-time theory, the characteristics of the designed controller are chattering free and the convergence time is limited within a fixed-time upper bound depending on the controller parameters. The fixed-time synergetic control method is used to converge a selected macro variable to the origin within the fixed time upper bound. The controller can stabilize the chaotic system dynamics in a good way within a short time.

Study on Nonlinear Dynamics and Chaos Suppression of Active Magnetic Bearing Systems Based on Synchronization

This study employed a variety of nonlinear dynamic analysis techniques to explore the complex phenomena associated with a nonlinear mathematical model of an active magnetic bearing (AMB) system. The aim was to develop a method with which to assume control over chaotic behavior. The bifurcation diagram comprehensively explicates rich nonlinear dynamics over a range of parameter values. In this study, we examined the complex nonlinear behaviors of AMB systems using phase portraits, Poincaré maps, and frequency spectra. Furthermore, estimates of the largest Lyapunov exponent based on the properties of synchronization confirmed the occurrence of chatter vibration indicative of chaotic motion. Thus, the proposed continuous feedback control approach based on synchronization characteristics eliminates chaotic oscillations. Finally, some simulation results demonstrated the feasibility and efficiency of the proposed control scheme.

Accelerated Adaptive Backstepping Control of the Chaotic MEMS Gyroscope by Using the Type-2 Sequential FNN

In this paper, we propose an accelerated adaptive backstepping control algorithm based on the type2 sequential fuzzy neural network (T2SFNN) for the microelectromechanical system (MEMS) gyroscope with deadzone and constraints. Firstly, the mathematical model of the MEMS gyroscope is established to perform dynamical analyses and controller design. Then, the phase diagrams and Lyapunov exponents are presented to reveal its chaotic oscillation, which is harmful to system stability. In order to suppress oscillations derived from chaos and deadzone, an accelerated adaptive backstepping controller is proposed wherein an adaptive auxiliary is established to compensate the influence of nonsymmetric deadzone on stability performance, along with the T2SFNN designed to approximate unknown functions of dynamic systems. Furthermore, the speed function is introduced to accelerate convergence speed of the control system, and the problem of complex term explosion in traditional backstepping is successfully solved by a secondorder tracking differentiator. Finally, simulation results show that the proposed control scheme can guarantee asymptotic convergence of all signals in the closedloop system, as well as satisfying states constraints and fulfilling the purposes of chaos suppression and accelerated convergence.

Chaos Suppression in a Pendulum Equation through Parametric Excitation with Phase Shift for Ultra-Subharmonic Resonance

Under ultra-subharmonic resonance, we investigate the chaos suppression of pendulum equation by using Melnikov methods, and get the conditions of suppressing chaos for homoclinic and heteroclinic orbits, respectively. At the same time, we give some numerical simulations including the bifurcation diagrams of system and corresponding phase diagrams, and observe that the chaos behaviors of system may be suppressed to period-n(n ∈ Z+) orbits by adjusting the value of Ψ. Although our results are only necessary, not sufficient. Numerical simulations show that our method is effect in suppressing chaos for this case.

Chaos Suppression via Integrative Time Delay Control

A general strategy for suppressing chaos in chaotic Burke–Shaw system using integrative time delay (ITD) control is proposed, as an example. The idea of ITD is that the feedback is integrated over a time interval. Physically, the chaotic system responds to the average information it receives from the feedback. The main feature of integrative is that the stability of the chaotic system occurs over a wider range of the space parameters. Controlling chaotic systems with ITD has not been discussed before as far as we know. Stability and the existence of Hopf bifurcation are studied which demonstrate that the switch stability occurs at critical values of the time delay. Employing the normal form theory and center manifold argument, an explicit formula is derived to determine the stability and the direction of the bifurcating periodic solutions. Numerically, the bifurcation diagram and the eigenvalues of the corresponding characteristic equations are computed to supply a clear interpretation for suppressing chaos via ITD. Furthermore, ITD method is compared with the time delayed feedback (TDF) control numerically. This comparison shows that the stability area with ITD is larger than TDF which demonstrates the feasibility and effectiveness of the ITD. Other examples of chaotic systems can be similarly investigated.