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arxiv: 2512.03236 · v2 · pith:PVOYQUVFnew · submitted 2025-12-02 · ⚛️ physics.flu-dyn

Real-Time Adaptive Feedback Control of a Supersonic Dual-Stream Jet

Melissa Yeung , Yiyang Sun This is my paper

Pith reviewed 2026-05-21 18:37 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords adaptive controlsupersonic jetdynamic mode decompositionfeedback controlvortex suppressionshear layer instabilityresonant tone
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The pith

Adaptive feedback control using real-time dynamic mode decomposition suppresses the resonant tone in a supersonic dual-stream jet while leaving the mean flow largely unchanged.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that online dynamic mode decomposition can build a continuously updated linear model of the jet flow from sensor snapshots, which then drives an adaptive controller to target the high-frequency tone produced by vortex shedding in the mixing layer. This matters because the tone and associated shock train are persistent noise and structural issues in supersonic jets, and the method works without elaborate actuation hardware or precise sensor positioning. The controller remains effective even when actuator limits are imposed, and in that restricted case it actually improves suppression by repeatedly stabilizing the shear layer instability for short periods. Statistical checks confirm that the tone arises from intermittent low-pressure events that the control largely removes.

Core claim

Adaptive control applied via online DMD to a Mach 1.6 core and Mach 1.0 bypass supersonic jet efficiently targets the resonant tone with minimal disturbance to mean features. The framework is insensitive to sensor placement, and under actuator constraints the restricted controller achieves greater vortex suppression by repeated transitory stabilization of the shear layer instability. Intermittent low-pressure events drive the characteristic frequency and are largely suppressed.

What carries the argument

Online dynamic mode decomposition, which estimates the system dynamics as a locally linear evolution from continuously updated snapshot matrices of sensor measurements, enabling real-time feedback control.

If this is right

  • The resonant tone is suppressed efficiently with little change to the mean flow features.
  • The control performance holds across different sensor locations, supporting practical actuator placement.
  • Imposing actuator constraints produces stronger vortex suppression through repeated short-term stabilization of the shear layer.
  • Intermittent low-pressure events that generate the tone frequency are largely eliminated by the feedback action.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same real-time modeling approach could be tested on other supersonic or transonic flows where vortex shedding creates unwanted tones.
  • Scaling the method to full-scale engine exhausts would require checking how actuator power limits interact with the stabilization effect.
  • Connecting the low-pressure event statistics to acoustic far-field measurements could quantify noise reduction in decibels.

Load-bearing premise

The flow dynamics can be represented accurately enough in real time as a locally linear system estimated from sensor snapshot matrices, and this model stays useful even when actuator constraints are applied.

What would settle it

Experimental measurements showing that the resonant tone amplitude remains comparable before and after the adaptive controller is turned on, or that mean flow features such as velocity profiles change substantially under control.

Figures

Figures reproduced from arXiv: 2512.03236 by Melissa Yeung, Yiyang Sun.

Figure 1
Figure 1. Figure 1: (a) Illustration of a generic three-stream engine [1]. (b) Nozzle configuration. topic of study over the past decade with joint experimental [2, 3, 4, 5] and computational efforts [6, 7, 8, 9, 10]. A signature high-frequency tone of approximately 34 kHz is detected in the far-field acoustics, which originates from the instability generated by the mixing of the core and bypass streams. Various flow control … view at source ↗
Figure 2
Figure 2. Figure 2: Computational domain and flow configuration with nozzle geometry in gray. NE = Nozzle exit. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) AFC schematic with actuation surface indicated in blue. (b) Online DMD sensor configurations. To ensure the dynamical model is informed by the appropriate flow dynamics, various sensor configurations (SC) are considered, as shown in figure 3(b). SC1 follows both the shock-induced separation near the nozzle lip and the splitter plate shear layer, and SC2 aims to detect the vortex-induced pressure waves … view at source ↗
Figure 4
Figure 4. Figure 4: (a) Method of event identification and signal reconstruction. (b-c) Closer view of events. 3 Results In this section, the baseline flow features of the dual-stream jet are presented. Then, adaptive control is implemented using online DMD. The supersonic flow under the influence of adaptive control is compared with open-loop steady￾blowing control. Finally, restrictions on the control method are explored an… view at source ↗
Figure 5
Figure 5. Figure 5: Instantaneous (a) and mean (b) flow fields for baseline case. 3.1.2 Spectral analysis of flow unsteadiness The vortex shedding originating from the splitter plate trailing edge gives rise to the characteristic frequency (i.e., resonant tone) of the flow. The frequency spectrum is first examined using the power spectral density (PSD) of the pressure time series at two point probes, denoted P1 and P2 in figu… view at source ↗
Figure 6
Figure 6. Figure 6: (a) PSD∗ for the baseline flow. (b) SPOD spectra with leading modes at the resonant tone. resonant tone StDh = 3.28. It is observed that the cause of the high-energy resonant tone is concentrated within the splitter plate shedding, and this instability largely dominates the baseline flow. 3.2 Adaptive Control of Jet Flow Using Online DMD Adaptive control using online DMD is first explored without constrain… view at source ↗
Figure 7
Figure 7. Figure 7: Spectrogram of the actuation signal for adaptive control introduced at ( [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a)Instantaneous and mean flow fields for all adaptive control cases. (b-c) Closer view near the SPTE. 3.2.2 Reduced unsteadiness through adaptive control Actuation-induced changes are characterized by the momentum introduced by the controller, surface loading along the aft-deck plate, thrust coefficient, and the pressure spectra through P2, and are shown collectively in figure 9 for all adaptive control c… view at source ↗
Figure 9
Figure 9. Figure 9: Momentum coefficient, change in surface loading, thrust coefficient, and PSD [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Constrained adaptive control with uk/cref = ±1.0. (a) Control signal with P2 spectrogram. (b) Representa￾tive instantaneous and mean flow fields [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Constrained adaptive control with uk/cref = ±0.3. (a) Control signal with P2 spectrogram. (b) Representa￾tive instantaneous and mean flow fields. While the mean shock structure and location appears similar to that of uk/cref = ±1.0, the relative strength of the shocks are stronger for subsonic actuation. This is due to the fact that subsonic blowing is insufficient in weakening the primary shock, and only… view at source ↗
Figure 12
Figure 12. Figure 12: (a) Momentum coefficient, change in surface loading, thrust coefficient, and (b) PSD∗ for constrained control cases. Baseline thrust coefficient is CT = 0.732. 3.4 Tone Contribution of Intermittent Events and Statistical Analysis To investigate the contribution of intermittent events to the dominant tone, the pressure time series through P2 is reconstructed, as shown in figure 4(a). In this region, it is … view at source ↗
Figure 13
Figure 13. Figure 13: (a) Optimal ξ for signal reconstruction. (b) PSD∗ of the original and reconstructed signals. A power spectral density of the original and reconstructed signal for the baseline case is presented in figure 13(b). The reconstructed is performed in three ways. The full reconstruction is carried out as described in Section 2.4. The cases with Λi/pPRMS < 0 and Λi/pPRMS > 0 correspond to reconstructions based so… view at source ↗
Figure 14
Figure 14. Figure 14: PDF of the event amplitudes Λi for unconstrained control with (a) ψ = 0◦ , (b) ψ = 30◦ , and (c) constrained control. sensor configurations are explored, where each measures the instantaneous pressure fluctuations. It is found that online DMD-based control is not sensitive to the sensor placements, but rather the actuation angle. Adaptive feedback control with an unconstrained controller frequency at soni… view at source ↗
Figure 15
Figure 15. Figure 15: State evolution through time and online DMD estimation of ( [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
read the original abstract

Adaptive control is applied to a supersonic dual-stream jet flow comprised of Mach 1.6 core and Mach 1.0 bypass streams that mix to form a supersonic shear layer. The vortices shed are the source of a high-frequency tone that persists throughout the flow. The intricate flow dynamics motivates the need for an elaborate and efficient actuation system to suppress the tone and weaken the propagating shock train. The present work utilizes online dynamic mode decomposition, which estimates the system dynamics as a locally linear evolution. Snapshot matrices are constructed using sensor measurements, facilitating economical and real-time computations, which are continuously updated and used in a feedback control model. Adaptive control is found to efficiently target the resonant tone with little disturbance to the mean features. The framework is not sensitive to sensor placements, enabling actuator design under physically realizable spatial locations in practical implementation. To reflect physical limitations, constraints are imposed on the controller model. It is found that the restricted controller yields greater vortex suppression due to repeated transitory stabilization of the shear layer instability. Statistical analysis reveals intermittent low-pressure events are responsible for the characteristic frequency, which are largely suppressed by adaptive feedback control.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript applies real-time adaptive feedback control to a Mach 1.6/1.0 dual-stream supersonic jet using online dynamic mode decomposition (DMD) to construct continuously updated, locally linear models from sensor snapshot matrices. The approach targets suppression of the high-frequency resonant tone generated by shed vortices in the shear layer while imposing actuator constraints; the restricted controller is reported to achieve greater vortex suppression via repeated transitory stabilization of the shear-layer instability, with minimal disturbance to mean flow features. Statistical analysis identifies intermittent low-pressure events as the source of the tone, which are largely suppressed under control. The framework is claimed to be insensitive to sensor placement.

Significance. If the results hold, the work demonstrates a computationally economical, real-time adaptive control method suitable for complex supersonic flows with nonlinear features such as shock trains. Strengths include the emphasis on physically realizable actuator constraints, the reported insensitivity to sensor locations, and the mechanistic insight linking suppression to repeated shear-layer stabilization. These elements could support practical jet-noise mitigation strategies in aerospace applications.

major comments (2)
  1. [online DMD and control synthesis sections] The central claim that the restricted controller produces greater vortex suppression through repeated transitory stabilization rests on the online DMD model remaining sufficiently accurate under actuator limits. The manuscript provides no quantitative assessment of closed-loop prediction error, model fidelity, or deviation from local linearity once constraints are enforced (see the description of the feedback control model and results on vortex suppression). In a flow with propagating shocks and nonlinear instability growth, this omission leaves the reported mechanism unsecured.
  2. [statistical analysis and results sections] The statistical analysis linking the resonant tone to intermittent low-pressure events and their suppression requires explicit metrics (e.g., event frequency, amplitude distributions, or error bars on suppression percentages) to substantiate the claim that adaptive control largely eliminates these events without altering mean features.
minor comments (2)
  1. Clarify the precise definition and detection criteria for the 'intermittent low-pressure events' in the statistical analysis, including any thresholding or windowing parameters used.
  2. Ensure all flow-field and spectral figures explicitly label controlled versus baseline cases and include quantitative scales for vortex or pressure fluctuations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and positive review of our manuscript. We address each major comment below in detail and will revise the manuscript to incorporate additional quantitative support where indicated.

read point-by-point responses

  1. Referee: [online DMD and control synthesis sections] The central claim that the restricted controller produces greater vortex suppression through repeated transitory stabilization rests on the online DMD model remaining sufficiently accurate under actuator limits. The manuscript provides no quantitative assessment of closed-loop prediction error, model fidelity, or deviation from local linearity once constraints are enforced (see the description of the feedback control model and results on vortex suppression). In a flow with propagating shocks and nonlinear instability growth, this omission leaves the reported mechanism unsecured.

    Authors: We agree that explicit quantification of model accuracy under constraints would strengthen the mechanistic interpretation. In the revised manuscript we will add a new subsection presenting closed-loop prediction error metrics, specifically the time-averaged L2 norm of the residual between online DMD one-step predictions and measured sensor states during controlled operation, as well as the evolution of the DMD eigenvalue magnitudes to monitor deviation from local linearity. These diagnostics will be computed over multiple actuation cycles and compared against the unconstrained case. The repeated transitory stabilization mechanism is directly supported by the observed phase-locked reduction in vortex passage frequency and the corresponding attenuation of the dominant shear-layer DMD mode; the added error analysis will confirm that the locally linear models remain adequate for control synthesis even when actuator saturation is active. revision: yes

  2. Referee: [statistical analysis and results sections] The statistical analysis linking the resonant tone to intermittent low-pressure events and their suppression requires explicit metrics (e.g., event frequency, amplitude distributions, or error bars on suppression percentages) to substantiate the claim that adaptive control largely eliminates these events without altering mean features.

    Authors: We accept this suggestion for improved statistical rigor. The revised manuscript will include quantitative metrics in the statistical analysis section: (i) event frequency defined as the number of low-pressure excursions (pressure below -0.5 in normalized units) per unit time, (ii) probability density functions of event amplitudes for both uncontrolled and controlled cases, and (iii) error bars on suppression percentages obtained from ensemble statistics over non-overlapping time windows. These additions will be placed alongside the existing time-averaged profiles to demonstrate that the intermittent events responsible for the tone are largely eliminated while mean flow quantities remain statistically unchanged within the reported uncertainty. revision: yes

Circularity Check

0 steps flagged

No significant circularity; control performance evaluated independently on measured flow quantities

full rationale

The paper applies online DMD to build a locally linear model from continuously updated sensor snapshot matrices and then synthesizes an adaptive feedback controller with actuator constraints. Performance is reported via direct statistical measures on the flow field (resonant tone amplitude, vortex suppression, low-pressure event frequency) rather than any quantity defined by the DMD fit itself. No load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior author work are invoked; the derivation chain consists of standard data-driven estimation followed by separate closed-loop evaluation against physical observables. The central claims therefore do not reduce to their inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on standard assumptions from fluid dynamics and control theory rather than new postulates.

axioms (1)
  • domain assumption Flow evolution can be locally approximated as linear over short time windows for DMD-based modeling.
    Invoked when constructing snapshot matrices and estimating system dynamics for real-time control.

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Lean theorems connected to this paper

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    Relation between the paper passage and the cited Recognition theorem.

    online dynamic mode decomposition, which estimates the system dynamics as a locally linear evolution. Snapshot matrices are constructed using sensor measurements... Adaptive control is found to efficiently target the resonant tone

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Reference graph

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