Tracking of Backbone Curves of Nonlinear Systems Using Phase-Locked-Loops

Péter, Simon; Riethmüller, Robin; Leine, Remco I.

doi:10.1007/978-3-319-29739-2_11

Cited by 14 publications

(17 citation statements)

References 20 publications

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“…This property remains valid as long as the frequency and amplitude ranges do not allow for internal resonances. 23 PLL controllers are designed in order to guarantee a given phase lag between the forcing excitation of a system and a reference signal (e.g., the system response: displacement, velocity). More precisely, a PLL adjusts the forcing excitation frequency (control command) in order to keep the phase lag to a preset value.…”

Section: Pll Controllermentioning

confidence: 99%

“…22,25 In the second configuration, setting the phase lag value at 0 or p/2 (depending on whether we measure the NNM velocity or displacement, respectively) allows for the tracking of the backbone curve (nonlinear phase resonance). 23 This latter configuration is used in the study.…”

Section: Pll Controllermentioning

confidence: 99%

“…The PLL controller consists of a phase detector, a proportional-integral-derivative controller (PID), and a voltage controlled oscillator (VCO) 23,34 (see Fig. 1).…”

Section: Pll Controllermentioning

confidence: 99%

“…In both experiments, frequency-time post-processing is performed to extract the amplitude-frequency curve (backbone curve) and the frequency-time curve (pitch glide) from the fundamental free vibration regime. The measurement of the backbone curve in the free vibration regime using the PLL setup set the first experiment (experiment A) a bit apart from the previous PLL backbone curve measurements 23,25 where the backbone curves were measured in forced regime. This a priori choice avoids thermal effects evidenced in Sec.…”

Section: Study Protocolmentioning

confidence: 99%

“…In the second continuation technique, which is used in this study, the tracking of the backbone is carried out in forced regime by setting the system at phase resonance using a phase-locked-loop (PLL) controller. [22][23][24][25] The forcing amplitude is set incrementally step by step and the forcing frequency is adjusted by the PLL in order to achieve the nonlinear phase resonance. The main advantage of continuation techniques is to directly obtain the backbone curve from forced regime rather than rely on the free vibration frequency-time analysis, which is performed with the NPR method.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Effects of internal resonances in the pitch glide of Chinese gongs

Jossic

Thomas

Denis

et al. 2018

The Journal of the Acoustical Society of America

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The framework of nonlinear normal modes gives a remarkable insight into the dynamics of nonlinear vibratory systems exhibiting distributed nonlinearities. In the case of Chinese opera gongs, geometrical nonlinearities lead to a pitch glide of several vibration modes in playing situation. This study investigates the relationship between the nonlinear normal modes formalism and the ascendant pitch glide of the fundamental mode of a xiaoluo gong. In particular, the limits of a single nonlinear mode modeling for describing the pitch glide in playing situation are examined. For this purpose, the amplitude-frequency relationship (backbone curve) and the frequency-time dependency (pitch glide) of the fundamental nonlinear mode is measured with two excitation types, in free vibration regime: first, only the fundamental nonlinear mode is excited by an experimental appropriation method resorting to a phase-locked loop; second, all the nonlinear modes of the instrument are excited with a mallet impact (playing situation). The results show that a single nonlinear mode modeling fails at describing the pitch glide of the instrument when played because of the presence of 1:2 internal resonances implying the nonlinear fundamental mode and other nonlinear modes. Simulations of two nonlinear modes in 1:2 internal resonance confirm qualitatively the experimental results.

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Section: Pll Controllermentioning

confidence: 99%

Section: Pll Controllermentioning

confidence: 99%

“…The PLL controller consists of a phase detector, a proportional-integral-derivative controller (PID), and a voltage controlled oscillator (VCO) 23,34 (see Fig. 1).…”

Section: Pll Controllermentioning

confidence: 99%

Section: Study Protocolmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Effects of internal resonances in the pitch glide of Chinese gongs

Jossic

Thomas

Denis

et al. 2018

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

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Characterization of Nonlinearities in a Structure Using Nonlinear Modal Testing Methods

Nagesh

Allemang

Phillips

2021

Nonlinear Structures &Amp; Systems, Volume 1

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Using phase-locked loop (PLL) controllers for obtaining frequency response curves (FRC) and backbone curves for nonlinear systems is gaining prominence. Such controllers deliberate a phase lag between the response obtained and the excitation provided. The use of such feedback controllers provides many advantages against traditional sine-sweep methods and helps better characterize nonlinear behavior of the test structure. This paper focuses on obtaining the nonlinear frequency response curves (FRC) and backbone curves of an isolated mode of a structural system exhibiting geometric nonlinearity. The capabilities of testing with such PLL controllers are highlighted and other important characteristics such as stability of the system are discussed. A qualitative comparison is provided between nonlinear modal testing using such feedback controllers as against other traditional methods such as sine-sweep methods.

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Challenges of Characterizing Geometric Nonlinearity of a Double-Clamped Thin Beam Using Nonlinear Modal Testing Methods

Nagesh

Allemang

Phillips

2021

Nonlinear Structures &Amp; Systems, Volume 1

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Phase-locked loop (PLL) controllers are increasingly employed for obtaining nonlinear frequency response curves (FRC) and backbone curves. Such controllers provide a specific phase lag between the response obtained and the excitation signal and isolate the nonlinear mode under consideration. The use of such feedback controllers provides many advantages against traditional sine-sweep methods and helps better characterize nonlinear behavior of dynamic systems. This paper briefly discusses about obtaining the nonlinear frequency response curves (FRC) and backbone curves of both symmetric and asymmetric modes of a double-clamped thin beam exhibiting geometric nonlinearity including a qualitative analysis such as stability and other prominent issues that arise during nonlinear modal testing particularly when the technique is applied to a thin and light structure. A comparison of nonlinear modal testing using PLL controllers as against other traditional methods such as sine-sweep methods is also demonstrated.

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Tracking of Backbone Curves of Nonlinear Systems Using Phase-Locked-Loops

Cited by 14 publications

References 20 publications

Effects of internal resonances in the pitch glide of Chinese gongs

Effects of internal resonances in the pitch glide of Chinese gongs

Characterization of Nonlinearities in a Structure Using Nonlinear Modal Testing Methods

Challenges of Characterizing Geometric Nonlinearity of a Double-Clamped Thin Beam Using Nonlinear Modal Testing Methods

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