{"title":"Synthesis of a hybrid control algorithm for chaotifying mechanical systems","authors":"Swapnil Mahadev Dhobale, Shyamal Chatterjee","doi":"10.1016/j.chaos.2024.115670","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos Solitons & Fractals","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0960077924012220","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
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.
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.