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For the chaotic motion control of a single-degree-of-freedom vibro-impact system with soft constraint, two-parameter cooperative intelligent optimal control method based on LRS-QPSO (i.e., Local Rotational Search Quantum Particle Swarm Optimization) algorithm optimization SVM (i.e., Support Vector Machines) was proposed. Firstly, in the parameter plane (ω,ζ), the motion distribution of the system and the change of the maximum Lyapunov exponent is obtained by numerical simulation, and the correlation between parameters change and the transition from chaotic motion to periodic motion is analyzed. Secondly, by introducing ω and ζ into the construction of the input variables of the SVM controller, a chaotic motion two-parameter cooperative intelligent optimal control strategy is proposed to meet the requirements of expected control objectives. Therefore, by the virtue of nonlinear mapping characteristics of SVM, the combined effects of ω and ζ on the dynamic state transition of the system can be reflected in the output variables of the controller. Finally, with single parameter ω and single parameter ζ as the research object, the bifurcation diagram, Lyapunov exponential spectrum, and controlled periodic motion orbit diagram are analyzed, and the advantages of two-parameter cooperative intelligent optimal control are compared and analyzed. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study of the nonlinear characteristics of an axially moving string. An experimental system with a simple configuration, which is similar to a practical application, was built. Two laser sensors were used to monitor the vertical and horizontal vibrations of the moving string under different conditions. Using the Hilbert-Huang transform method, the detailed results of a typical measured data series, which include intrinsic mode decomposition, Hilbert spectrum and marginal spectrum, are introduced. For comparison, marginal spectra for almost all test cases are also given. Based on the results, several observed nonlinear phenomena, which include whirling motion, resonances, quasiperiodical and a beating motion, torus doublings and one chaotic motion, are presented. The quantitative nonlinear vibrating details and the observed rich behaviors help explain the great complexity of a single moving string. [ABSTRACT FROM AUTHOR]

Axially translating beams are widely seen in engineering applications. An active vibration control strategy based on a modified fuzzy sliding mode control is developed for controlling and stabilizing the motion of the beam. Geometric nonlinearity of the beam is considered. In the development of the control strategy, the governing equation of the beam is transformed into a multi-dimensional dynamic system with the Galerkin method of 6th order. An active control strategy is developed corresponding to the dynamic system, such that the control strategy can be used for multi-dimensional systems. Numerical simulations are performed with application of the control strategy developed. The effectiveness of the active control strategy is demonstrated in controlling and stabilizing the chaotic motion of the translating beam. [ABSTRACT FROM PUBLISHER]

In this study, various nonlinear dynamic analysis techniques are employed to reveal the rich nonlinear phenomena of an electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamic problems. The Lyapunov exponent method is employed to show the occurrence of chaotic motion and to verify the numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented. [ABSTRACT FROM PUBLISHER]

This investigation confirms and controls chaotic motion in a permanent magnet synchronous motor (PMSM) system in electric vehicles. Complex nonlinear behaviors may be observed over a range of parameter values in the bifurcation diagram. The method of the Lyapunov exponent is adopted to identify the onset of chaotic motion and verify the analysis. Finally, a technique for effectively controlling a chaotic PMSM system will be offered. It involves applying an external input, called a dither signal, to the system. Some simulation results are presented to demonstrate the feasibility of the developed approach. [ABSTRACT FROM AUTHOR]

In most situations, the high performance of permanent magnet synchronous motors (PMSMs) depends on an absence of chaos; consequently, suppressing chaos becomes quite important. Therefore, this study confirms the chaotic motion and then applies synchronization to a chaotic PMSM system to control chaos. Rich dynamics of the PMSM system are studied using a bifurcation diagram, phase portraits, a Poincaré map, frequency spectra and Lyapunov exponents. First, the largest Lyapunov exponent is estimated using synchronization to identify periodic and chaotic motions. Next, complex nonlinear behaviors are thoroughly observed throughout a range of parameter values in the bifurcation diagram. Finally, a proposed continuous feedback control method based on synchronization characteristics eliminated chaotic oscillations. Numerical simulations are utilized to verify the feasibility and efficiency of the proposed control technique. [ABSTRACT FROM PUBLISHER]