Simultaneous phase control of multiple frequencies of multi-degree-of-freedom systems

Brack, Tobias; Vujanic, Robin; Dual, Jürg

doi:10.1177/1077546316644366

Cited by 4 publications

(5 citation statements)

References 28 publications

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“…The output signals are added together and form the excitation signal of the oscillating system. Consequently, the input signal of each PLL is composed of multiple frequencies, hence an effective extraction of the specific frequency is required inside each PLL (Brack et al 2018).…”

Section: Control Methods For Continuous Measurementmentioning

confidence: 99%

Simultaneous and continuous measurement of shear elasticity and viscosity of liquids at multiple discrete frequencies

2018

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This paper presents the extension of the classical torsional resonance viscometer towards the characterization of linear viscoelastic fluids. By simultaneously tracking multiple resonance frequencies, shear viscosity and elasticity can be monitored at multiple discrete frequencies at the same time. The proposed method is applied to the well-established sensor design of a simple rod-like structure, hence enabling a robust and versatile measurement system that can be used in different applications, such as in-line measurement or hand-held devices. In order to simultaneously control different resonance frequencies, multiple independent phase-locked loops are used, of which each subsystem is responsible for one natural vibration. An analytical description of the relationship between measurement parameters and physical fluid parameters is presented that is valid both for Newtonian and linear viscoelastic fluids. Consequently, calibration of the sensor is possible using Newtonian fluids only. To demonstrate the sensor, viscoelastic polymer and surfactant solutions are investigated at five frequencies between 2 kHz and 20 kHz. Additionally, the test fluids are characterized by means of a classical rotational rheometer (low frequency range) and diffusing-wave spectroscopy (high frequency range). The comparison of all methods shows very good agreement and validates the application of the sensor as resonant rheometer for viscoelastic fluids.

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Section: Control Methods For Continuous Measurementmentioning

confidence: 99%

Simultaneous and continuous measurement of shear elasticity and viscosity of liquids at multiple discrete frequencies

2018

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“…With a feedback-based actuation system, the excitation signal can be arbitrarily placed on the desired phase condition. In order to extract the damping ratio of a system in addition to exciting the resonator at its resonance frequency (phase condition ΔΦ=−π/2), it is required to superpose additional frequency components [6]. Suitably this added frequency components are chosen according to (2), with B being the bandwidth of the resonator and (4) denoting the required phase condition for these two frequencies.…”

Section: Signal Modelmentioning

confidence: 99%

“…When exciting the resonator at frequencies f0, f1 and f2 simultaneously, these frequencies can not be directly measured as they are very close to each other. Separating these frequencies by means of band pass filters [6] in such a case is a very challenging task. The quite small bandwidth (|f2−f1|<0.5rad/normals at its minimum) of the resonator demands an comparable bandwidth of the channel selection filters.…”

Section: Signal Modelmentioning

confidence: 99%

High Precision Vibration-Type Densitometers Based on Pulsed Excitation Measurements

Rechberger

Amsuss

Rossegger

et al. 2019

Sensors

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Glass flexural resonators have established themselves as one of the de-facto standard methods for measuring the density of liquids in a laboratory environment. The core of this sensor is a U-Tube measuring cell whose oscillator’s resonance frequency changes with the mass of the liquid within the tube. This relationship can be used to derive the density of liquids in a fast and reliable way. In order to achieve the highest accuracy for the density measurement multiple physical effects (e.g., damping due to viscosity effects) need to be taken into account. For a reliable correction, additional measurements are required. The pulsed excitation method is able to produce these additional parameters along with a superior measurement performance compared to previous techniques.

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“…1, which is challenging for resonance tracking techniques based solely on phase information. Since the phase in not unique, multiple equilibria arise, which alternate between stable and unstable modes [27,18,28,17]. The points in Fig.…”

Section: Siso System With Non-monotonic Phasementioning

confidence: 99%

“…This is the case even for linear SISO systems, if the phase difference between the input and output signal is non-monotonic. This problem has been pointed out for piezoelectric actuators and multi-degree-of-freedom system, where a resonance and an anti-resonance frequency are present [27,18,28,17].…”

Section: Introductionmentioning

confidence: 99%

Model-based resonance tracking of linear systems

Vasileiou

2018

Preprint

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This paper develops a recursive algorithm for tracking resonance frequency shifts of linear timevarying systems corrupted by additive white Gaussian noises, in real time. So far, automatic resonance tracking is limited to non-model-based designs that rely solely on the phase difference between a selected input and output of the system. Instead, we propose a transformation of the system into a complex-valued representation, which allows to abstract the resonance shifts as an exogenous disturbance acting on the excitation frequency, perturbing it from the natural frequency of the plant. The resonance tracking problem is then split in two tasks; identifying the frequency disturbance and solving an optimization problem to determine the excitation frequency. The design of the resonance tracker is therefore simplified, due to the application of well-established techniques. We discuss the stability of the proposed scheme, even in cases that seriously challenge the current phasebased approaches, like non-monotonic phase differences and multiple-input multiple-output systems. Numerical simulations further demonstrate the performance of the resonance tracking scheme.Keywords resonance • frequency tracking • time-varying systems • complex variables • closed-loop identification.

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Simultaneous phase control of multiple frequencies of multi-degree-of-freedom systems

Cited by 4 publications

References 28 publications

Simultaneous and continuous measurement of shear elasticity and viscosity of liquids at multiple discrete frequencies

Simultaneous and continuous measurement of shear elasticity and viscosity of liquids at multiple discrete frequencies

High Precision Vibration-Type Densitometers Based on Pulsed Excitation Measurements

Model-based resonance tracking of linear systems

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