Method and device for multiple-frequency tracking of oscillating systems

Abstract

A method to measure the vibrational characteristics of an oscillating system (1) uses a control system (6, 7a, 7b, 7c). The oscillating system comprises a resonator, at least one vibration exciter and at least one sensor. The resonator is excited by the vibration exciter, and the motion of the resonator is measured by the sensor. The control system uses the sensor to control the motion of the resonator by the vibration exciter. The motion of the resonator is a superposition of at least two harmonic motions, and the control system comprises at least two subcontrollers (7a, 7b, 7c). Each harmonic motion is controlled independently by one of the subcontrollers. The harmonic motions are controlled by the subcontrollers simultaneously. A corresponding device is also disclosed.

Claims

1. A method to measure the vibrational characteristics of an oscillating system using a control system, said oscillating system comprising a resonator, at least one vibration exciter and at least one sensor, the method comprising: exciting said resonator by said at least one vibration exciter, measuring a motion of said resonator by said at least one sensor, operating said control system to control said motion of said resonator by said at least one vibration exciter, based on sensor output received from said at least one sensor, wherein said motion of said resonator is a superposition of at least two harmonic motions, wherein said control system comprises at least two subcontrollers, wherein each of said at least two harmonic motions is controlled independently by one of said at least two subcontrollers, said at least two harmonic motions being controlled by said at least two subcontrollers simultaneously.

2. The method according to claim 1, wherein said at least two subcontrollers are phase-locked loops.

3. The method according to claim 1, wherein each of said at least two harmonic motions has a frequency close to a resonance frequency of said resonator.

4. The method according to claim 1, wherein resonance frequencies of said resonator are sensitive to properties of a fluid, being in contact with said resonator.

5. The method according to claim 4, wherein said fluid properties are the density and viscosity of said fluid.

6. The method according to claim 4, wherein said fluid properties are viscoelastic properties of said fluid.

7. The method according to claim 1, wherein the resonator is a tube-like structure and said resonator's resonance frequencies are sensitive to the mass flow of a fluid through said tube-like structure.

8. The method according to claim 1, wherein a single transducer acts as the at least one vibration exciter and the at least one sensor.

9. The method according to claim 2, wherein at least one of said phase-locked loops is a gated phase-locked loop containing at least one switch.

10. The method according to claim 1, wherein some or all of said at least two subcontrollers have individual inputs connected to form a common input and have individual outputs which are connected to an adder having a common output, and wherein the common input and/or the common output are gated by switches.

11. The method according to claim 1, wherein said at least two subcontrollers are used with two different reference phase settings to measure the damping of the resonator.

12. The method according to claim 1, wherein said at least two subcontrollers are used to measure amplitudes of said at least two harmonic motions.

13. A device comprising an oscillating system and a control system, said oscillating system comprising a resonator, at least one vibration exciter and at least one sensor, the resonator being coupled to the at least one vibration exciter for exciting a motion of the resonator, the at least one sensor being configured to measure said motion of the resonator, the control system being configured to control the motion of the resonator via the at least one vibration exciter, based on sensor output received from the at least one sensor, wherein the motion of the resonator is a superposition of at least two harmonic motions, the control system comprising at least two subcontrollers, each of said at least two subcontrollers being configured to independently control one of said at least two harmonic motions, the at least two subcontrollers being configured to control said at least two harmonic motions simultaneously.

14. The device according to claim 13, wherein each of said at least two subcontrollers comprises a phase-locked loop.

15. The device according to claim 13, wherein each of said at least two subcontrollers is configured to control a harmonic motion that has a frequency close to a resonance frequency of said resonator.

16. The device according to claim 13, wherein said resonator has a plurality of resonance frequencies, said resonance frequencies being sensitive to properties of a fluid that is in contact with said resonator.

17. The device according to claim 16, wherein said fluid properties are density and viscosity of said fluid.

18. The device according to claim 16, wherein said fluid properties are viscoelastic properties of said fluid.

19. The device according to claim 16, wherein the resonator is a tube-like structure, and said resonance frequencies are sensitive to a mass flow of a fluid through said tube-like structure.

20. The device according to claim 13, wherein a single transducer acts as the at least one vibration exciter and the at least one sensor.

21. The device according to claim 14, at least one of said phase-locked loops is a gated phase-locked loop containing at least one switch.

22. The device according to claim 13, wherein some or all of said at least two subcontrollers have individual inputs connected to form a common input and have individual outputs, wherein the device comprises an adder having inputs that are connected to the individual outputs of said at least two subcontrollers and having a common output, and wherein the device comprises one or more switches for gating the common input and/or the common output.

23. The device according to claim 13, where said at least two subcontrollers are configured to operate with two different reference phase settings to measure the damping of the resonator.

24. The device according to claim 13, where said at least two subcontrollers are configured to measure amplitudes of said at least two harmonic motions.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Preferred embodiments of the invention are described in the following with reference to the drawings, which are for the purpose of illustrating the present preferred embodiments of the invention and not for the purpose of limiting the same. In the drawings:

(2) FIG. 1 shows steady state phase shift .sub.s of a single degree of freedom oscillator around the resonance frequency .sub.res.

(3) FIG. 2 shows the setup of a phase-locked loop in combination with an oscillating system. The elements of the PLL are framed by the dashed line.

(4) FIG. 3 shows a control concept of the simultaneous excitation and control of multiple frequencies of an oscillating system.

(5) FIG. 4 shows a control concept of the simultaneous excitation and control of multiple frequencies of an oscillating system. By alternating between excitation and readout phase only one single transducer is necessary.

(6) FIG. 5 shows a block diagram of an averaging phase detector, consisting of two multiplications 8, two low-pass filters 9 and an atan2 function block 10.

(7) FIG. 6 illustrates an oscillating system comprising a torsional resonator, electromagnetic excitation and optical readout.a) Photo of the setup; b) Section view.

(8) FIG. 7 is a diagram showing an experimental result of the simultaneous tracking of five resonance frequencies of the oscillating system depicted in FIG. 6.

(9) FIG. 8 is a diagram showing the time history of two frequencies starting at f.sub.110 Hz and developing so that the final phase shift values equal .sub.1,2=.sub.res. (a) Simulation result; (b) Experimental result.

(10) FIG. 9 is a diagram showing experimentally determined phase shift curves of a torsional oscillator under the influence of fluids with different viscosities.

(11) FIG. 10 is a diagram showing viscosity determinations by measuring the resonance frequency shift with and without temperature compensation.

DETAILED DESCRIPTION

(12) It is beneficial to track multiple frequencies of one single oscillator simultaneously. The multi-mode control has become an object of research in the field of crystal oscillators to overcome accuracy problems [8] or as compensation of the parasitic capacitance of piezoelectric crystals [9,10]. Multi-mode techniques are also used to actively damp several vibration modes of a structure [11].

(13) Based on the integration of an oscillator in a phase-locked loop (PLL), which has been successfully investigated by numerous research groups [2,12-15], the present invention claims a novel control concept that allows the simultaneous tracking of multiple frequencies of an oscillating system. These frequencies could be the resonance frequencies or any other frequencies that lie near the resonance value. The PLL could also be used in a gated fashion as described in patent U.S. Pat. No. 5,837,885.

(14) In every linear oscillating system, the stationary phase shift between a harmonic excitation and the response signal is an amplitude independent and unique function around the resonance frequency, as it is shown in FIG. 1. It is therefore beneficial to use the phase shift to control the exciting frequency to maintain the system at resonance or at any other state that is related to a specific phase shift value. This can be achieved by the integration of the oscillating system with a phase-locked loop (PLL).

(15) A conventional PLL is shown in the dashed box of FIG. 2. It consists of a phase detector 2, a controller 3 (often denoted as filter) and a voltage controlled oscillator (VCO) 4. The VCO generates a periodic signal (e.g. square, triangle or harmonic wave) whose frequency follows the frequency of the incoming signal of the PLL, leaving a certain phase difference as controller offset. Hence the conventional PLL takes a frequency modulated signal as input and returns the modulation signal as output. There is no oscillating system within the feedback. But since the functionality of the PLL bases upon the phase detection between two harmonic signals, it can be used in conjunction with an oscillating system 1 as shown in the block diagram in FIG. 2. The periodic VCO output is led to the oscillating system as excitation u.sub.sys. The phase detector measures the phase shift y.sub.pd between the output of the oscillating system y.sub.sys and a possibly phase shifted reference signal y.sub.ref of same frequency. A phase shifter 5 shifts the phase of the reference signal by .sub.t . By tuning the frequency of the VCO using the controller output y.sub.ctrl, the excitation frequency is varied until the controller input is zero, which is related to the phase shift of the oscillating system (i.e. phase shift between u.sub.sys and y.sub.sys) being equal to the predefined phase shift value .sub.t . This system can be used to actively track the resonance frequency or any other frequency that is related to a unique phase shift value. The damping can be measured by extracting the frequencies that are related to the phase shift values of .sub.res. This concept has been used in Patent U.S. Pat. No. 5,492,0787 and 5,837,885.

(16) Oscillating systems might exhibit multiple vibration modes, each with a specific resonance frequency. If the resonance frequencies are clearly separated, the modes have almost no interaction. Hence every single mode can be regarded as an independent one degree of freedom system. Therefore multiple frequency bands exist where the phase shift shows the behavior described in FIG. 1.

(17) The present invention describes a method that enables the simultaneous control of multiple frequencies by means of the described phase-locked loop method. Independent of the number of controlled frequencies, only two transducers are necessary, one to generate the excitation u.sub.sys and one to detect the output y.sub.sys. If the system is used in a gated fashion as in U.S. Pat. No. 5,837,885, only one transducer can be used alternately as sensor or actuator.

(18) This enables a variety of novel possibilities in measurement instrumentation, especially in the field of fluid characterization. For example: Viscometry. The tracking of one frequency is a common method in industrial viscometry applications. The tracking of multiple frequencies increases the accuracy of such devices. Rheology. In this field a lot of instruments have been investigated that aim to characterize a fluid at several frequencies. The necessary data is up to now only consecutively accessible. The presented invention enables to gather all information simultaneously. General resonance sensor methods. The use of multiple frequencies can also be used to compensate for unwanted influences, for example due to temperature effects. Simultaneous measurements of several different fluid properties, each of which might influence the different modes to various degrees. A rod can be used in a bending mode and a torsional mode in a fluid, where density and viscosity are influencing the resonance frequency and damping in different ways.

(19) For the simultaneous tracking of multiple frequencies a parallel arrangement of multiple PLLs 7 can be used, each generating a periodic single-frequency signal as illustrated in FIG. 3. The output signals of the particular PLLs are added together in an adder 6 and form the multi-frequency excitation signal .sub.iu.sub.sys,i. Consequently, the output of the oscillating system y.sub.sys is a signal composed of the particular frequencies. Hence an effective frequency separation in each PLL is of utmost importance.

(20) Using a special kind of phase detector, namely a digital averaging phase detector (APD) in each PLL, one can combine this task and the phase detection. The APD is used in various applications e.g. in digital lock-in amplifiers [17]. The working principle is shown in FIG. 5. The APD multiplies its input signal, which can be described by A sin(t+) in steady state, both with a sine and cosine signal of the same frequency. Hence two reference signals cos(t) and sin(t) are necessary. After the multiplications 8 a low-pass filter 9 follows, whose cutoff frequency is much smaller than the exciting frequency. Performing the atan2 function 10 using the output signals of the low-pass filters, the phase difference is computed. The atan2 function is defined through

(21) $\mathrm{atan}2\left(y,x\right)=\{\begin{array}{cc}\arctan \left(\frac{y}{x}\right),& x>0\\ \arctan \left(\frac{y}{x}\right)+,& y0,x<0\\ \arctan \left(\frac{y}{x}\right)-,& y<0,x<0\\ +\frac{}{2},& y>0,x=0\\ -\frac{}{2},& y<0,x=0\\ \mathrm{undefined},& y=0,x=0\end{array}$

(22) The APD acts as a very effective band-pass filter which enables the effective frequency separation.

(23) While the use of an APD for frequency separation and phase detection is advantageous, it is not the only possibility. For instance, instead of an APD, any of the following may be used: (a) A conventional band pass filter followed by any kind of conventional phase detector (computationally expensive and well-suited only if frequencies are sufficiently well separated); or (b) a so-called single-point discrete Fourier transform (DFT), i.e., a variant of a DFT that computes only a single spectral component, the most important single-point DFT algorithm being the Goertzel Algorithm.

(24) The mechanical resonator which is used as oscillating system can be a torsional resonator originally used for viscosity measurements. FIG. 6 shows a torsional resonator 100 that is composed of two hollow cylinders. The outer cylinder 11 is fixed at one end to the body 14 and represents the part that is in contact with a fluid. It is closed at the end with an end piece 13, to which a second tube 12 is fixed. The second tube 12 leads inside the outer tube 11 back into the body 14. On top of tube 12 a permanent magnet 15 is mounted. Using a coil system 16 that is arranged around the magnet position, the excitation moment is applied electromagnetically. The movement is detected optically using a single-point laser vibrometer 17. Alternatively the same transducer can be used for the detection using a gated PLL as disclosed in U.S. Pat. No. 5,837,885. The laser beam points on the inner cylinder 12, whereas the position is selected to be as near as possible to the excitation. The outer tube 11 has a length of l.sub.o=100 mm, an outer diameter of d.sub.o=9.5 mm and a wall thickness of t.sub.o=0.335 mm. The inner tube 12 measures length l.sub.i=135 mm, outer diameter d.sub.i=7 mm and wall thickness t.sub.i=0.45 mm. Experimental results, depicted in FIG. 7, show the effective simultaneous control of the first five resonance frequencies of the system. The control loop is implemented on a TMS320C6747 floating point digital signal processor (DSP) from Texas Instrument which is integrated in the OMAP-L137 Evaluation Module from Spectrum Digital.

(25) The operation of the invention is described in the following figures.

(26) In FIG. 1, the steady state phase shift .sub.s between a harmonic excitation signal of frequency and the response of the oscillating system is shown exemplarily in the region of the resonance frequency .sub.res. The depicted situation represents a linear single degree of freedom oscillator and also continuous oscillating systems with many resonance frequencies, as long as these resonance frequencies are well separated. The slope of the curve is related to the damping of the system (i.e. of the particular vibration mode), characterized by the frequency difference corresponding to the phase shift values of .sub.res.

(27) FIG. 2 presents the phase-locked loop in conjunction with an oscillating system 1. Both the excitation signal u.sub.sys and the reference signals y.sub.ref are created by the VCO 4, whose frequency is varied by the output y.sub.ctri of the controller 3. The phase detector 2 closes the loop by detecting the phase shift y.sub.pd of the system output and the phase shifted reference.

(28) FIG. 3 presents the concept of the multimode control. The particular PLLs 7a, 7b, 7c etc. are of the same structure as the PLL in FIG. 2. The phase detectors are designed such that they extract the phase shift only at one particular frequency. These frequencies are the known excitation frequencies. A single line in the figure represents a harmonic signal containing a single frequency, a double line represents the signal, where multiple frequencies are superimposed.

(29) FIG. 4 presents the concept of the multimode control used in a gated fashion. The functionality remains the same, but the gated PLL uses the same transducer alternately for excitation or readout (see patent U.S. Pat. No. 5,837,885). By means of two switches S1 and S2 the process alternates continuously between excitation (S1 closed, S2 open) and readout phase (S1 open, S2 closed). The timing of the switches has to be adapted to the processed frequencies. Also a waiting time might be introduced between the excitation and readout phases.

(30) FIG. 5 presents the working principle of the averaging phase detector. Due to the two multiplications 8a and 8b of the system output with a sine and cosine signal of the same frequency (which is known since it is the VCO frequency) it is possible to extract the phase shift at that particular frequency. The requirements on the low-pass filters 9 are low, since they only have to attenuate the component of double excitation frequency resulting from the multiplication.

(31) FIG. 6 shows the oscillating system 1 comprising the resonator, electromagnetic excitation and optical readout. The sensor design is shown in FIG. 6a as a section view. The invention can be applied to every oscillating system that exhibits multiple vibration modes with separated resonance frequencies.

(32) FIG. 7 depicts the experimental results. The graph shows the development of five frequencies of the torsional oscillator in air at 22 C. The frequencies, damping and resonance phase shift values of the torsional oscillator are given in Table I below. The frequencies start at 0.1% below the resonance value and develop simultaneously to the exact resonance values within 1 second. The resonance values have been measured before by means of traditional methods. The control process starts at t=3 sec, the frequency values are represented as relative values, with the particular resonance frequency as reference.

(33) TABLE-US-00001 TABLE I Resonance frequencies .sub.0 and damping ratio D of the torsional resonator in air at 22 C. Mode number .sub.0 [Hz] D [10.sup.5] 1 2588.95 5.33 2 5588.51 5.25 3 11190.01 10.08 4 13918.81 7.37 5 19269.07 5.48
Possible Measurement Concepts:

(34) Concept 1: The simultaneous tracking of multiple resonance frequencies. This can be used in resonance sensors or to gain high efficiency in actuator applications.

(35) Concept 2: Method for the fast and exact determination of the damping which uses the simultaneous control of the phase shift values of two different modes (denoted by the subscripts 1 and 2):.sub.1=.sub.res,1 and .sub.res,2+. The achieved frequency difference f.sub.large=f(.sub.2)f(.sub.1) is a measure for the damping. Alternatively, one particular mode can be driven at two different phase shift values.

(36) Concept 3: When using a torsional oscillator that is clamped at one end and surrounded by a fluid, it can be shown that the fluid influence is very weak at

(37) $={}_{\mathrm{res}}-\frac{}{4}.$
This fact enables to measure the properties of the oscillator itself even if a fluid is present, which could be used for temperature measurements. During multi-mode control this feature can be used as temperature reference.

(38) Concept 4: The APD is also capable to extract the amplitude of the input signal by using the formulation A=2{square root over (X.sup.2+Y.sup.2)}, where X and Y are the output signals of the low-pass filters 9a and 9b, respectively. Therefore the presented invention enables also the simultaneous control of the vibration amplitudes of the oscillator which is very useful in the field of rheology (in rheology, the system response is generally non-linear and therefore depends on the excitation amplitude).

(39) Additional Explanations Concerning Concept 2

(40) The determination of damping is an important issue in many applications, especially in the field of viscometry. Two frequency values at known phase shifts around the resonance are needed to calculate the damping or, equivalently, the Q-factor of a specific mode. These two frequency values are usually evaluated one after another by consecutively changing the reference phase. Using the presently proposed method one can obtain the damping value directly by controlling the two required frequency values simultaneously. This is called direct damping measurement in what follows. In contrast to the simultaneous resonance tracking, the frequencies that have to be processed correspond in this case to the same vibration mode. Hence they will be very close together, depending on the resonance frequency and damping ratio of the investigated mode, which puts high demands on the APD.

(41) Since the system is assumed to be linear, the superposition principle holds, and it is therefore possible to excite one mode with a two-frequency signal, of which the frequencies follow the phase shift target of .sub.1=.sub.res and .sub.2=.sub.res+, respectively.

(42) In contrast to the simultaneous tracking of multiple resonances, in the present application the two frequencies are not well separated. It has therefore to be ensured that the frequency separation works properly nonetheless. This can be achieved by maximizing the frequency difference, hence is advantageously set to 45.

(43) In an example, the damping was increased by immersing the sensor in a calibration oil of constant dynamic viscosity =8.18 mPas at 22 C. The damping of the first mode was therefore increased by a factor of 10 (Q.sub.fluid=920). However, the two frequencies were still very close-by, which required a relatively high-order filter. The filters were therefore implemented as 2nd order Butterworth low-pass filter with .sub.3 dB=20.1 Hz. Obviously, the center frequencies f.sub.c of the filters should initially be set so that the two frequencies do not have the same value during the process. In the present example, the initial center frequencies were set to f.sub.cf.sub.i10 Hz. The controller parameters were adjusted as explained below, using a time constant of T.sub.c=2 sec.

(44) FIG. 8 shows simulation and experimental result of the frequency tracking for the direct damping measurement. The frequencies reached the final value after approximately four seconds and were stable with only small variations.

(45) From the frequency difference f.sub.i the damping can directly be calculated using the following equation:

(46) $Q_i=\frac{{}_{0,i}}{{}_i}\tan$

(47) Here, .sub.i=2f.sub.i is the angular frequency difference of mode i, and .sub.0,i is the resonance frequency of mode i.

(48) Averaging f.sub.1 over the last two seconds yielded a Q-Factor of 920, in very close agreement with simulation results.

(49) The result shows that the method is generally capable to separate frequencies even if they lie very close together, which can be used for the direct damping measurement. However, the closer the frequencies come together, whether due to low damping or a small , the more difficult the calculation of the Q-factor gets.

(50) Additional Explanations Concerning Concept 3

(51) The torsion angle of a harmonically excited, linear torsional oscillator under the influence of a fluidic force F.sub.fluid can be described by the differential equation
{umlaut over ()}(t)+2.Math..Math.{dot over ()}(t)+.sub.0.sup.2.Math.(t)=F.sub.0 exp(it)+F.sub.fluid,
wherein .sub.0 is the resonance frequency and the exponential decay rate of the oscillator without fluid. is the excitation frequency. The influence of a Newtonian fluid on a circular cross section can approximately be described by the force
F.sub.fluid=k(1+i){dot over ()}(t),
where k is the fluid influence factor that depends both on the density and the viscosity of the fluid. Hence F.sub.fluid can be interpreted as an additional damping and mass. The steady-state phase shift between excitation force and coordinate (t) is:

(52) $=\mathrm{atan}\left(\frac{{}^2.Math..Math.k-{}_0^2}{\left(k+2.Math.\right)}\right)$

(53) Solving the equation for at

(54) $=-\frac{3}{4},$
one obtains:

(55) $\left(=-\frac{3}{4}\right)=-+\frac{1}{2}\sqrt{4{}^2+4{}_0^2}.$

(56) This expression is independent of the fluid influence factor k. Therefore the frequency that belongs to a phase shift of

(57) $-\frac{3}{4}$
is inaepenaent or tne properties of the fluid.

(58) This is illustrated in FIG. 9, which shows experimentally determined phase shift curves of a torsional oscillator under the influence of fluids with different viscosities. Due to parasitic phase shifts, the resonance is at a phase shift of approximately 175 (dashed line). Relative to the phase shift at resonance, the phase shift independent of k is at

(59) $={}_{\mathrm{res}}-\frac{}{4}\left(\mathrm{dash}\text{-}\mathrm{dotted}\mathrm{line}\right).$

(60) The frequency at which this phase shift occurs can be used to determine influences on the sensor that are not caused by the fluid, even when the sensor is in contact with the fluid.

(61) When fluids are characterized, usually the sensor responses in the presence and in the absence of the fluid are compared. Therefore it is very important that the reference (sensor response in the absence of the fluid) does not change during the measurements. In particular, the sensor response depends on the temperature of the sensor. The method outlined above can be used to determine the sensor temperature during the measurement of the fluid. While the fluid temperature and the sensor temperature are somewhat correlated, they are not necessarily the same.

(62) This method is particularly interesting if viscosity is not determined via measuring the damping, but via measuring the resonance frequency. This is illustrated in FIG. 10, which shows viscosity determinations by measuring the resonance frequency shift with and without temperature compensation. Temperature was determined by observing the first mode at around 2590 Hz, while viscosity was determined by measuring the frequency shift of the second mode at around 5590 Hz. Without temperature compensation, a determination of viscosity via measuring the resonance frequency is virtually impossible.