Parameter impulse control of chaos in crystal growth process

Zhou, Zi-Xuan; Grebogi, Celso; Ren, Hang

doi:10.1016/j.jcrysgro.2021.126079

Cited by 8 publications

(4 citation statements)

References 34 publications

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“…We compare the single direction impulse control with the bi-directional impulse control. The equation of the controlled system for the single impulse control method is defined in [2]. The method applies one negative impulse per period.…”

Section: A the Effectiveness Of The Bi-directional Impulse Control Methodsmentioning

confidence: 99%

“…For a practice system in which the state variables cannot be measured and the manipulated variable is firmly restricted, such as the FSRL system, the parameter impulse control is the a appropriate control method. Hence, a single directional parameter impulse control was proposed to perturb the rotation speed in [2]. However, there is a drawback in that method.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, for a functioning plant, the control of chaos is not a trivial task under such restrictive constraints. The periodic single impulse control is a candidate for the FRSL system [2]. However, there exists a significant weak point in that control method.…”

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confidence: 99%

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Bi-directional impulse chaos control in crystal growth

Zhou

Ren

Grebogi

2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Mono-silicon crystals, free of defects, are essential for the Integrated Circuit industry. Chaotic swing in the flexible shaft rotating-lifting (FSRL) system of the mono-silicon crystal puller causes harm to the quality of the crystal and must be suppressed in the crystal growth procedure. From the control system viewpoint, the constraints of the FSRL system can be summarized as not having measurable state variables for state feedback control, and only one parameter is available to be manipulated, namely, the rotation speed. From the application side, an additional constraint is that the control should affect the crystallization physical growth process as little as possible. These constraints make the chaos suppression in the FSRL system to be a challenging task. In this work, the analytical periodic solution of the swing in the FSRL system is derived using perturbation analysis. A bi-directional impulse control method is then proposed for suppressing chaos. This control method does not alter the average rotation speed. It is thus optimum regarding the crystallization process as compared with the single direction impulse control. The effectiveness and robustness of the proposed chaos control method to parameters uncertainties are validated by the simulations.

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Section: A the Effectiveness Of The Bi-directional Impulse Control Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bi-directional impulse chaos control in crystal growth

Zhou

Ren

Grebogi

2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Therefore, lots of efforts were given to eliminate or control chaos in the systems, which led to the seminal work of chaos control in 1990, namely, the OGY control [2]. After the OGY method, time-delay feedback [3], linear feedback [4], [5], impulse control [6], [7], and others, were reported to control chaos.…”

Section: Introductionmentioning

confidence: 99%

Chaos Generation With Impulse Control: Application to Non-Chaotic Systems and Circuit Design

Tian

Grebogi

Ren

2021

IEEE Trans. Circuits Syst. I

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Chaos has been successfully applied in many fields to improve the performance of engineering systems, such as communication, vibration compact, and mixing. Generating chaos from originally non-chaotic systems is a relevant topic because of potential applications. In this work, the impulse control is shown to generate chaos from non-chaotic system. Using nonchaotic Chen system as an example, we prove by analytical and numerical methods that chaos is indeed generated. The features of the chaos generated by impulse control are analysed using Lyapunov exponents, bifurcation diagram, power spectrum, Poincaré mapping and Kaplan-Yorke dimension. Furthermore, we demonstrate the chaotic attractor generation by impulse control using a circuit experiment. The last but not minor point is that the existence of topological horseshoe is given by rigorous computer-aided proof.

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