Strange nonchaotic and chaotic attractors in a self-excited thermoacoustic oscillator subjected to external periodic forcing

Guan, Yu; Murugesan, Meenatchidevi; Li, Larry K.B.

doi:10.1063/1.5026252

Cited by 60 publications

(25 citation statements)

References 67 publications

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“…The prototypical thermoacoustic system under study consists of a laminar conical premixed flame in a tube combustor subjected to external acoustic forcing. Figure 1 shows the experimental set-up, which is identical to that of our recent studies on periodic thermoacoustic oscillations (Guan et al 2018(Guan et al , 2019a and which is modelled after the numerical set-up of Kashinath et al (2018). The system has four main components: a stainless steel burner (inner diameter, ID: 16.8 mm; length: 800 mm), a quartz tube combustor with double open ends (ID: 44 mm; length: L = 860 mm), an acoustic decoupler (ID: 180 mm; length: 200 mm) and a loudspeaker for acoustic forcing.…”

Section: Experimental Set-up and Data Analysismentioning

confidence: 88%

“…Balusamy et al (2015) applied similar off-resonance forcing to a swirl-stabilized turbulent premixed combustor and found additional synchronization dynamics, such as frequency pushing and pulling as well as phase locking, slipping, drifting and trapping -the latter a partially synchronous feature defined by frequency locking without phase locking (Li & Juniper 2013c). For high forcing amplitudes, Guan et al (2018) found that a synchronized system can transition out of synchronization and into strange non-chaotic and chaotic states, behaving in line with the Afraimovich & Shilnikov (1991) theorem for the collapse of a phase-locked torus.…”

Section: Forced Synchronization Of Periodic Oscillationsmentioning

confidence: 97%

“…In thermoacoustics, open-loop forcing has been shown to be able to weaken periodic self-excited oscillations in various combustion systems, ranging from the simple Rijke tube (Reynolds numbers of Re ∼ 10 3 with natural frequencies of f 1 ∼ 10 2 Hz; Guan, Murugesan & Li 2018;Kashinath et al 2018;Guan et al 2019a;Mondal, Pawar & Sujith 2019) to turbulent premixed combustors (Re ∼ 10 4 , f 1 ∼ 10 2 Hz; Bellows, Hreiz & Lieuwen 2008;Balusamy et al 2015). A recurring theme of these studies has been the application of periodic acoustic forcing to periodic thermoacoustic oscillations, accompanied by an examination of the nonlinear dynamics en route to and beyond the synchronization boundaries.…”

Section: Forced Synchronization Of Periodic Oscillationsmentioning

confidence: 99%

“…When unforced, this thermoacoustic system can exhibit a variety of nonlinear self-excited states -including period-1 limit cycles, quasiperiodicity and chaosdepending on the equivalence ratio and the flame position within the combustor (Guan et al 2018(Guan et al , 2019a. As this study focuses on the open-loop control of ergodic T 2 quasiperiodic oscillations ( § 1.4), we apply forcing to a quasiperiodic state 396 Y.…”

Section: Experimental Set-up and Data Analysismentioning

confidence: 99%

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Forced synchronization of quasiperiodic oscillations in a thermoacoustic system

et al. 2019

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In self-excited combustion systems, the application of open-loop forcing is known to be an effective strategy for controlling periodic thermoacoustic oscillations, but it is not known whether and under what conditions such a strategy would work on thermoacoustic oscillations that are not simply periodic. In this study, we experimentally examine the effect of periodic acoustic forcing on a prototypical thermoacoustic system consisting of a ducted laminar premixed flame oscillating quasiperiodically on an ergodic $\mathbb{T}^{2}$ torus at two incommensurate natural frequencies, $f_{1}$ and $f_{2}$. Compared with that of a classical period-1 system, complete synchronization of this $\mathbb{T}_{1,2}^{2}$ system is found to occur via a more intricate route involving three sequential steps: as the forcing amplitude, $\unicode[STIX]{x1D716}_{f}$, increases at a fixed forcing frequency, $f_{f}$, the system transitions first (i) to ergodic $\mathbb{T}_{1,2,f}^{3}$ quasiperiodicity; then (ii) to resonant $\mathbb{T}_{1,f}^{2}$ quasiperiodicity as the weaker of the two natural modes, $f_{2}$, synchronizes first, leading to partial synchronization; and finally (iii) to a $P1_{f}$ limit cycle as the remaining natural mode, $f_{1}$, also synchronizes, leading to complete synchronization. The minimum $\unicode[STIX]{x1D716}_{f}$ required for partial and complete synchronization decreases as $f_{f}$ approaches either $f_{1}$ or $f_{2}$, resulting in two primary Arnold tongues. However, when forced at an amplitude above that required for complete synchronization, the system can transition out of $P1_{f}$ and into $\mathbb{T}_{1,2,f}^{3}$ or $\mathbb{T}_{2,f}^{2}$. The optimal control strategy is to apply off-resonance forcing at a frequency around the weaker natural mode ($f_{2}$) and at an amplitude just sufficient to cause $P1_{f}$, because this produces the largest reduction in thermoacoustic amplitude via asynchronous quenching. Analysis of the Rayleigh index shows that this reduction is physically caused by a disruption of the positive coupling between the unsteady heat release rate of the flame and the $f_{1}$ and $f_{2}$ acoustic modes. If the forcing is applied near the stronger natural mode ($f_{1}$), however, resonant amplification can occur. We then phenomenologically model this $\mathbb{T}_{1,2}^{2}$ thermoacoustic system as two reactively coupled van der Pol oscillators subjected to external sinusoidal forcing, and find that many of its synchronization features – such as the three-step route to $P1_{f}$, the double Arnold tongues, asynchronous quenching and resonant amplification – can be qualitatively reproduced. This shows that these features are not limited to our particular system, but are universal features of forced self-excited oscillators. This study extends the applicability of open-loop control from classical period-1 systems with just a single time scale to ergodic $\mathbb{T}^{2}$ quasiperiodic systems with two incommensurate time scales.

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Section: Experimental Set-up and Data Analysismentioning

confidence: 88%

Section: Forced Synchronization Of Periodic Oscillationsmentioning

confidence: 97%

Section: Forced Synchronization Of Periodic Oscillationsmentioning

confidence: 99%

Section: Experimental Set-up and Data Analysismentioning

confidence: 99%

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Forced synchronization of quasiperiodic oscillations in a thermoacoustic system

et al. 2019

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“…Afterwards, several numerical studies have demonstrated the existence of SNAs in systems such as pendulum [5], Duffing oscillator [6], logistic map [7], Henon map [8], and circular map [9].The experimental discovery of SNA was reported by Ditto et al[10] in a quasiperiodically forced system with a buckled magnetoelastic ribbon. In subsequent years, there have been several experimental observations of SNAs in practical systems [11][12][13][14][15]; however, all these studies presented the necessity of having quasiperiodic forcing to generate SNAs. Contrary to these studies, Negi et al [16] showed theoretically that the need of quasiperiodic forcing is not mandatory for the creation of SNAs, and it could happen in naturally driven systems as well without the need of external forcing.…”

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confidence: 99%

Strange nonchaos in self-excited singing flames

Premraj¹,

Pawar²,

Kabiraj³

et al. 2020

EPL

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We report the first experimental evidence of strange nonchaotic attractor (SNA) in the natural dynamics of a self-excited laboratory-scale system. In the previous experimental studies, the birth of SNA was observed in quasiperiodically forced systems; however, such an evidence of SNA in an autonomous laboratory system is yet to be reported. We discover the presence of SNA in between the attractors of quasiperiodicity and chaos through a fractalization route in a laboratory thermoacoustic system. The observed dynamical transitions from order to chaos via SNA is confirmed through various nonlinear characterization methods prescribed for the detection of SNA.Coupled nonlinear systems exhibit various kinds of dynamical behaviours including periodic, quasiperiodic, and chaotic oscillations [1,2]. Among these dynamics, one of the commonly observed state in quasiperiodically driven nonlinear systems is a strange nonchaos. Although strange nonchaotic attractors (SNAs) show similarity to chaotic attractors by having a fractal geometrical structure, SNAs are insensitive to initial conditions unlike the chaotic attractors [3]. Grebogi et al. [4] was the first to report the possibility of SNAs in the system of quasiperiodically forced map. Afterwards, several numerical studies have demonstrated the existence of SNAs in systems such as pendulum [5], Duffing oscillator [6], logistic map [7], Henon map [8], and circular map [9].The experimental discovery of SNA was reported by Ditto et al.[10] in a quasiperiodically forced system with a buckled magnetoelastic ribbon. In subsequent years, there have been several experimental observations of SNAs in practical systems [11][12][13][14][15]; however, all these studies presented the necessity of having quasiperiodic forcing to generate SNAs. Contrary to these studies, Negi et al. [16] showed theoretically that the need of quasiperiodic forcing is not mandatory for the creation of SNAs, and it could happen in naturally driven systems as well without the need of external forcing. Recently, Lindner et al. [17] showed the observation of SNAs in the natural system of a pulsating star KIC 5520878 network. However, to the best of our knowledge, there has not been a single experimental evidence of SNA reported in self-driven laboratory systems until now.Most of the recent studies are focused on identifying the routes to generate SNAs [3,12,18]. The mechanisms for the onset of SNAs are usually classified into three types as: (i) Heagy-Hammel route -the SNAs emerges during the collision of a period doubled torus with its own unstable parent [19], (ii) fractalization route -the truncated torus gets wrinkled and forms SNAs without any interaction with the parent torus [20], and (iii) type-III intermittency route -SNAs occur when the torus doubling bifurcation is controlled by sub-harmonic bifurcations [6]. Another possibility for the occurrence of SNAs is through crisis-induced intermittency, wherein the collision of the wrinkled torus with the boundary results in sudden widening of the attra...

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Proximal policy optimization‐based controller for chaotic systems

Yau,

Kuo,

Luan

et al. 2023

Intl J Robust & Nonlinear

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Deep reinforcement learning (DRL) algorithms are suitable for modeling and controlling complex systems. Methods for controlling chaos, a difficult task, require improvement. In this article, we present a DRL‐based control method that can control a nonlinear chaotic system without any prior knowledge of the system's equations. We use proximal policy optimization (PPO) to train an agent. The environment is a Lorenz chaotic system, and our goal is to stabilize this chaotic system as quickly as possible and minimize the error by adding extra control terms to the chaotic system. Therefore, the reward function accounts for the total triaxial error. The experimental results demonstrated that the trained agent can rapidly suppress chaos in the system, regardless of the system's random initial conditions. A comprehensive comparison of different DRL algorithms indicated that PPO is the most efficient and effective algorithm for controlling the chaotic system. Moreover, different maximum control forces were applied to determine the relationship between the control forces and controller performance. To verify the robustness of the controller, random disturbances were introduced during training and testing, and the empirical results indicated that the agent trained with random noise performed better. The chaotic system has highly nonlinear characteristics and is extremely sensitive to initial conditions, and DRL is suitable for modeling such systems.

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Strange nonchaotic and chaotic attractors in a self-excited thermoacoustic oscillator subjected to external periodic forcing

Cited by 60 publications

References 67 publications

Forced synchronization of quasiperiodic oscillations in a thermoacoustic system

Forced synchronization of quasiperiodic oscillations in a thermoacoustic system

Strange nonchaos in self-excited singing flames

Proximal policy optimization‐based controller for chaotic systems

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