Stability analysis of a noise control system in a duct by using delay differential equation

Haraguchi, Masakazu; Hu, Haiyan

doi:10.1007/s10409-008-0196-4

Cited by 5 publications

(3 citation statements)

References 13 publications

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“…where f (x, t) and g(x, t) represent the acoustic waves travelling downstream and upstream in the tube, respectively ( [5] and as in [20]). They are denoted as f i (t) and g i (t) in figure 1a, with the subscript i = 1, .…”

Section: Mathematical Model and Dynamic Stabilitymentioning

confidence: 99%

Predicting the secondary dynamic mode interference phenomenon in thermoacoustic instability control

Zalluhoglu

Olgaç

2016

Proc. R. Soc. A.

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This paper brings a novel mathematical perspective in assessing the rise of the secondary dynamic modes to prominence during the suppression of thermoacoustic instability. This phenomenon is observed by many earlier investigators; however, without a complete analytical reasoning. We consider a Rijke tube with both a passive Helmholtz resonator and an active feedback control to suppress instabilities. The core dynamics is represented as a linear time-invariant multiple time-delay system of neutral type. Parametric stability of the resulting infinite-dimensional dynamics is investigated using a recent analytical tool: cluster treatment of characteristic roots paradigm. This tool reveals the stability outlook of such systems exhaustively and non-conservatively in the parameter space of the system. First, we examine the stability with and without the Helmholtz resonator. We then select an unstable operation for the resonator-mounted Rijke tube, impose a time-delayed integral feedback control over it and reveal the stabilizing controller parameters using the cluster treatment of characteristic roots methodology. When high control gains are inappropriately selected, the new analytical procedure declares how the secondary dynamic modes of the system exhibit instability although the initially unstable mode is now stabilized. All of these stability assessments are cross-validated using experimental results from a laboratory-scale Rijke tube set-up.

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Section: Mathematical Model and Dynamic Stabilitymentioning

confidence: 99%

Predicting the secondary dynamic mode interference phenomenon in thermoacoustic instability control

Zalluhoglu

Olgaç

2016

Proc. R. Soc. A.

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“…With the introduction of hybrid systems and H ∞ theory, the system robustness to disturbances and plant uncertainties has been improved. The stability of closed loop feedback ANC in a duct system has also been considered with the effects of the dynamics of time-delay systems (Haraguchi and Hu, 2009). A delay differential equation was introduced for analyzing stability and the optimal distance between secondary path actuator and error sensor was obtained.…”

Section: Air Ductsmentioning

confidence: 99%

Active control of pressure pulsation in a switched inertance hydraulic system

Pan

Johnston

Hillis

2013

Proceedings of the Institution of Mechanical Engineers, Part I:

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The nature of digital hydraulic systems may cause pressure pulsation problems. For example, switched inertance hydraulic systems (SIHS), which are applied to adjust or control flow and pressure by a means that does not rely on dissipation of power, have noise problems due to the pulsed nature of the flow. An effective method to reduce the pulsation is important to improve system performance and increase efficiency. Although passive systems to reduce the noise have been shown to be effective in many situations, their attenuation frequency range is limited and they may be bulky. Furthermore, attenuation devices based on expansion chambers, accumulators or hoses are likely to be unsuitable for SIHS as they add compliance to the system and would impair the dynamic response. This thesis is concerned with issues relating to the development of an active noise canceller for attenuating the pressure pulsation which is caused primarily by pulsed flow from high-speed valves in SIHS.Active control methods are widely and successfully applied in the area of structureborne noise (SBN) and air-borne noise (ABN) cancellation. The idea is using the intentional superposition of waves to create a destructive interference pattern such that a reduction of the unwanted noise occurs. However, applications for fluid-borne noise (FBN) attenuation based on the 'Active noise control (ANC) principle' are rare due to the restriction of the hardware and experimental apparatus in previous researches.In this thesis, an adaptive controller has been developed for active control of pressure pulsation in hydraulic system. The principle of the adaptive LMS filter and details of the controller design are described and the implementation was carried out through simulation. The designed controller was applied on a vibration test rig initially prior to the hydraulic testing in order to investigate its advantages and limitations in practice.Extensive testing on a switched inertance hydraulic rig proved that the controller, which used a piezoelectric valve with fast response and good bandwidth, is effective and that it has several advantages over previous methods, being effective for low frequency cancellation, with a quick response, and is robust and versatile. II A novel method for the accurate measurement of unsteady flowrate in a pipe was proposed. This was applied and validated on a pipe, and was shown to give good results. This method solves the difficulty for measuring the unsteady flowrate currently by using easy-measured signals, such as pressures. It can be used widely for predicting the unsteady flowrate along the pipe. III ACKNOWLEDGEMENTS

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“…In practical applications, feedback loops are frequently used to reduce vibrations in continuum dynamical systems, which is an especially hard task if the internal damping is small like in acoustic systems (see, for example, [5,6]). Delay is an essential element in any feedback loop.…”

Section: Introductionmentioning

confidence: 99%

Exact stability chart of an elastic beam subjected to delayed feedback

Zhang

Stépàn

2016

Journal of Sound and Vibration

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a b s t r a c tThe stability of an elastic beam is studied when the beam is subjected to a longitudinal force governed by a feedback loop. The setup of the simplified mechanical model is motivated by a basic problem of electroacoustics. The corresponding governing equation is the 1D wave equation with delayed boundary conditions. By means of the D'Alembert solution, the system can be transformed into a delay differential equation of neutral type that includes two time delays. The intricate stability chart is constructed analytically in the parameter plane of the gain parameter and the ratio of the time delays. The complete chart extends the numerical results of the literature, while it also draws attention to the numerical difficulties of finite degree of freedom approximations and to the extreme sensitivity of the dynamics with respect to the time delay parameters of the system.

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Stability analysis of a noise control system in a duct by using delay differential equation

Cited by 5 publications

References 13 publications

Predicting the secondary dynamic mode interference phenomenon in thermoacoustic instability control

Predicting the secondary dynamic mode interference phenomenon in thermoacoustic instability control

Active control of pressure pulsation in a switched inertance hydraulic system

Exact stability chart of an elastic beam subjected to delayed feedback

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