Synthesis of a hybrid control algorithm for chaotifying mechanical systems

IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Chaos Solitons & Fractals Pub Date : 2024-10-30 DOI:10.1016/j.chaos.2024.115670
Swapnil Mahadev Dhobale, Shyamal Chatterjee
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Abstract

This paper presents a novel hybrid control algorithm for inducing chaos in a limit cycle oscillator by chaotically varying suitable parameters within the chosen bounds. A discrete chaotic map governs the parameter variation at the predetermined Poincaré section. A cubic polynomial mapping is used to obtain the continuous variation between two consecutive crossings at the Poincaré section. A resonant controller with acceleration feedback is designed to implement the proposed control algorithm in a mechanical system with a single degree of freedom. This controller generates a limit cycle at the desired frequency and amplitude. The next step involves using a modified Pomeau-Manneville (PM) map to achieve the chaotification of the limit cycle, which yields a flat Fast Fourier Transform (FFT) of the response within a given bandwidth. The proposed control strategy not only chaotifies the system but also regulates desired response characteristics, such as amplitude, frequency band, chaoticity and power spectral distributions. This is believed to be the first attempt to control the desired characteristics of chaotic response in the case of continuous-time systems. Experiments with an electromagnetic actuator validate the simulation results.
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混沌化机械系统混合控制算法的合成
本文提出了一种新颖的混合控制算法,通过在所选范围内混沌改变合适的参数,在极限周期振荡器中诱导混沌。离散混沌映射控制着预定波恩卡莱截面处的参数变化。立方多项式映射用于获得波恩卡莱截面上两个连续交叉点之间的连续变化。为了在单自由度机械系统中实施所提出的控制算法,我们设计了一个带有加速度反馈的谐振控制器。该控制器能以所需的频率和振幅产生一个极限周期。下一步是使用修改后的波莫-曼内维勒(PM)图实现极限周期的混沌化,从而在给定带宽内获得响应的平滑快速傅立叶变换(FFT)。所提出的控制策略不仅能使系统混沌化,还能调节所需的响应特性,如振幅、频带、混沌度和功率谱分布。这是首次尝试在连续时间系统中控制混沌响应的理想特性。电磁致动器的实验验证了模拟结果。
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来源期刊
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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