Abstract:
A method to measure the vibrational characteristics of an oscillating system ( 1 ) uses a control system ( 6, 7   a,    7   b,    7   c ). 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 ( 7   a,    7   b,    7   c ). 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.

Description:
TECHNICAL FIELD 
       [0001]    The present invention relates to a method to measure the vibrational characteristics of an oscillating system using a control system, and to a corresponding device. 
       PRIOR ART 
       [0002]    Reference is made to the following prior-art documents: 
         [0003]    [1] R. M. Langdon, “Resonator sensors—a review,”  in Journal of Physics E: Scientific Instruments  18, vol. 18, no. 103, 1985. 
         [0004]    [2] C. Kharrat, E. Colinet, and A. Voda, “H∞ loop shaping control for pll-based mechanical resonance tracking in nems resonant mass sensors,” in  IEEE Sensors Conference,  2008, pp. 1135-1138 
         [0005]    [3] P. Rüst, D. Cereghetti, and J. Dual, “A viscometric chip for DNA analysis,”  Procedia Engineering , vol. 47, pp. 136-139, 2012, 26th European Conference on Solid-State Transducers, Eurosensor 2012. 
         [0006]    [4] J. Dual and O. O&#39;Reilly, “Resonant torsional vibrations: an application to dynamic viscometry,”  Archive of Applied Mechanics , vol. 63, no. 7, pp. 437-451, 1993. 
         [0007]    [5] U.S. Pat. No. 4,920,787 to J. Dual, M. Sayir, and J. Goodbread. 
         [0008]    [6] T. M. Stokich, D. R. Radtke, C. C. White, and J. L. Schrag, “An instrument for precise measurement of viscoelastic properties of low viscosity dilute macromolecular solutions at frequencies from 20 to 500 kHz,”  Journal of Rheology , vol. 38, no. 4, pp. 1195-1210, 1994. 
         [0009]    [7] C. Blom and J. Mellema, “Torsion pendula with electromagnetic drive and detection system for measuring the complex shear modulus of liquids in the frequency range 80-2500 Hz,”  Rheologica Acta , vol. 23, pp. 98-105, 1984. 
         [0010]    [8] J. R. Vig, “Temperature-insensitive dual-mode resonant sensors—a review,”  Sensors Journal, IEEE , vol. 1, no. 1, pp. 62-68, 2001. 
         [0011]    [9] J. Sell, A. Niedermayer, and B. Jakoby, “A digital pll circuit for resonator sensors,”  Sensors and Actuators A: Physical , vol. 172, no. 1, pp. 69-74, 2011. 
         [0012]    [10] A. Arnau, J. Garcia, Y. Jimenez, V. Ferrari, and M. Ferrari, “Improved electronic interfaces for at-cut quartz crystal microbalance sensors under variable damping and parallel capacitance conditions,”  Review of Scientific Instruments , vol. 79, no. 7, pp. 075110-075110-12, 2008. 
         [0013]    [11] H. Tjahyadi, F. He, and K. Sammut, “Multi-mode vibration control of a flexible cantilever beam using adaptive resonant control,”  Smart Materials and Structures , vol. 15, no. 2, p. 270, 2006. 
         [0014]    [12] J. Kutin, A. Smreĉnik, and I. Bajsić, “Phase-locking control of the coriolis meters resonance frequency based on virtual instrumentation,”  Sensors and Actuators A. Physical , vol. 104, no. 1, pp. 86-93, 2003. 
         [0015]    [13] C. Gökcek, “Tracking the resonance frequency of a series RLC circuit using a phase locked loop,” in  Proceedings of  2003  IEEE Conference on Control Applications,  2003, pp. 609-613. 
         [0016]    [14] D. Kern, T. Brack, and W. Seemann, “Resonance tracking of continua using self-sensing actuators,”  Journal of Dynamic Systems, Measurement, and Control , vol. 134, no. 5, p. 051004, 2012. 
         [0017]    [15] S. Park, C.-W. Tan, H. Kim, and S. K. Hong, “Oscillation control algorithms for resonant sensors with applications to vibratory gyroscopes,”  Sensors , vol. 9, no. 8, pp. 5952-5967, 2009. 
         [0018]    [16] U.S. Pat. No. 5,837,885 to J. Dual, J. Goodbread, K. Häusler and M. Sayir. 
         [0019]    [17] J. Gaspar, S. F. Chen, A. Gordillo, M. Hepp, P. Ferreyra, and C. Marqus, “Digital lock in amplifier: study, design and development with a digital signal processor,”  Microprocessors and Microsystems , vol. 28, no. 4, pp. 157-162, 2004 
         [0020]    Since the eigenfrequencies and damping parameters of an oscillating system are characteristic values which are dependent both on the system properties as well as on external influences, measuring these frequencies has led to the widespread principle of resonant sensors [1]. It has become a common technique in research as well as in industry to permanently track one resonance frequency using appropriate control structures. This allows to generate an output (i.e. the frequency or frequency change) which can be related to the desired physical quantity. Such applications can be found in quartz crystal microbalances or in micro electro mechanical systems (MEMS), for example as mass sensors [2] or as biosensors [3]. In the field of fluid characterization, the frequency tracking provides an efficient approach for the development of an on-line viscometer. This has been successfully realized by measuring the damping of a vibrating structure which is in contact with a fluid [4, 5]. All these applications can only track one single frequency. However, in many applications the investigation of more values is required, whether as investigation of frequency dependent behavior, as redundancy values to improve the measurement accuracy or as basis for compensation of errors. This can be achieved by consecutively tracking particular resonance frequencies of a continuous oscillator [6] or by simply using several oscillators [7]. Both methods, though, show several disadvantages. The former case limits the application to the detection of slowly changing processes, since the consecutive tracking is time consuming. On the other hand, the latter case does not ensure measuring the exact same condition (e.g. temperature), since the sensors are spatially separated and may have different properties. 
       SUMMARY OF THE INVENTION 
       [0021]    It is an object of the present invention to overcome these shortcomings of the prior art. 
         [0022]    In a first aspect, the present invention provides 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, said resonator being excited by said vibration exciter, the motion of said resonator being measured by said sensor, said control system using said sensor to control said motion of said resonator by said vibration exciter, said motion of said resonator being a superposition of at least two harmonic motions, said control system comprising at least two subcontrollers, said at least two harmonic motions being controlled independently by said at least two subcontrollers, respectively, and said harmonic motions being controlled by said subcontrollers simultaneously. 
         [0023]    The harmonic motions will in general have different frequencies. In other words, the invention proposes to track multiple frequencies of one single oscillator simultaneously with the aid of multiple separate subcontrollers. 
         [0024]    The method of the present invention can also be expressed as follows: 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 the resonator by said at least one vibration exciter;   measuring the motion of said resonator by said at least one sensor; and   operating said control system to control said motion of said resonator by said at least one vibration exciter, using said at least one sensor,   wherein said motion of said resonator is a superposition of at least two harmonic motions, in particular, harmonic motions having different frequencies,   wherein said control system comprises at least two subcontrollers, and   wherein said at least two harmonic motions are controlled independently by said at least two subcontrollers, said harmonic motions being controlled by said subcontrollers simultaneously.       
 
         [0031]    The subcontrollers are advantageously implemented as phase-locked loops. In other words, the subcontrollers are configured to keep a predetermined phase relationship between the harmonic excitation and the harmonic motion of the resonator in response to the harmonic excitation. 
         [0032]    Each of said harmonic motions preferably has a frequency close to (i.e., at or near) a resonance frequency of the resonator. Here, “close to a resonance frequency” is to be interpreted as being sufficiently close to a resonance frequency such that the slope of the phase response is sufficiently high and the amplitude of said harmonic motion is sufficiently high to be processed by said subcontroller. This can be formulated, e.g., as the frequency being in the range of ωε[ω res ±3Δω] where Δω is the bandwidth of the resonance, cf.  FIG. 1 . Advantageously, the resonance frequencies of the resonator are sensitive to properties of a fluid, being in contact with said resonator. In this manner, the method of the present invention can be employed to determine at least one property of a fluid that is in contact with the resonator. 
         [0033]    In exemplary embodiments, these properties may include the density and/or the viscosity and/or viscoelastic properties of the fluid. 
         [0034]    In particular, both density and viscosity of a fluid may be determined if at least one harmonic motion is a bending vibration of a resonator that is in contact with the fluid, and at least one other harmonic motion is a torsional oscillation of the same resonator. In [Wattinger, T. Modeling and experimental study of a flexural vibration sensor for density measurements. Diss. ETH No. 21938 Zurich, 2014, pages 69 to 70] the influence of Newtonian fluids on bending vibrations of a cylindrical structure was investigated. It was found that this influence of the fluid depends, in a first approximation, only on the density of the fluid, whereas the viscosity plays only a minor role (see Eq. 4.17 of the reference on pages 69-70). Therefore the simultaneous control of a bending vibration and of a torsional oscillation is an interesting concept for determining both the density and the viscosity of a fluid. By measuring the resonance frequency of the bending vibration, the density can be determined. The resonance frequency of the torsional oscillation depends on both density and viscosity; when density is known, viscosity can be determined. Separate transducers (vibration exciters) are advantageously employed to excite bending vibrations and torsional oscillations, respectively. However, many known sensors are sensitive to both bending vibrations and torsional oscillations, and it is advantageous to use a common sensor for measuring these two types of oscillations. 
         [0035]    Viscoelastic properties of a fluid may be determined by measuring a resonance frequency shift of at least one mode of the resonator due to the presence of the fluid, and by measuring a change of the damping of at least one mode of the resonator due to the presence of the fluid. A method for measuring the damping of a mode of the resonator is explained in more detail below. In the conference paper [Brack T., Dual J.: Multimodal torsional vibrations for the characterization of complex fluids.  Fluid Structure Interaction VII , Wit Transactions on the Built Environment, pp. 191-200, 2013], the relationship between resonance frequency ω and damping δ of a linear oscillator in contact with a linear viscoelastic fluid is described. In that paper, the following approximate relationships are presented: 
         [0000]      Δω n   2 =α n ·ρƒω res,n,0 ·(η′−η″)
 
         [0000]      Δδ n   2 =α n ·ρƒω res,n,0 ·(η′+η″)  (1)
 
         [0036]    Here, Δω n  is the shift of the resonance frequency ω res,n,0  of mode n due to the presence of the fluid, and Δδ n  is the change of the damping of mode n due to the presence of the fluid. The factor α n  is a mode-dependent sensor constant. The parameters η′ and η″ are the two components of the complex viscosity; they describe viscosity and elasticity of the fluid. These two quantities are frequency-dependent material properties. Assuming that the density ρ ƒ  of the fluid is known, the two parameters η′ and η″ can be determined by measuring the two parameters Δω n   2  and Δδ n   2 . 
         [0037]    Since η′ and η″ are frequency-dependent quantities, prior-art resonance sensors are only of limited use for characterizing viscoelastic fluids, as usually only a single frequency can be observed. By observing several frequencies simultaneously, the utility of resonance sensors for determining viscoelastic properties of fluids can be much increased. Because measurements can be performed very quickly, even dynamic changes of the viscoelastic properties can be determined at multiple frequencies. This has hitherto not been possible, neither with classical rheometers nor with resonance sensors. 
         [0038]    In other exemplary embodiments, the method of the present invention can be employed to determine the mass flow of a fluid through a resonator having a tube-like structure, as in a Coriolis mass flow meter. Coriolis mass flow meters are known per se. In a Coriolis mass flow meter, a fluid is passed through a flow tube, and a bending vibration of the flow tube is observed. The Coriolis forces on the fluid cause a position-dependent phase shift of the bending vibration. This phase shift is measured, and the mass flow can be derived from the phase shift. Furthermore, the density of the fluid can be determined by measuring the resonance frequency of the bending vibration, since the resonance frequency depends on the combined mass of the tube and the fluid contained in it. In summary, the vibration behavior of the resonator (including its resonance frequencies) is sensitive to the mass flow. By measuring several bending modes simultaneously, the precision of such mass flow and/or density measurements can be improved. By additionally exciting torsional oscillations, the viscosity of the fluid can additionally be determined. The bending modes and/or torsional oscillations are advantageously simultaneously controlled by the presently proposed method. 
         [0039]    In some embodiments, the vibration exciter(s) and the sensor(s) can be separate units. In other embodiments, a single transducer can act as both a vibration exciter and a sensor. For instance, an electromagnetic transducer can act both as an actuator for exciting vibrations and as a sensor for measuring the thus-excited vibrations. In such cases, it is advantageous if at least one of the phase-locked loops is implemented as a gated phase-locked loop containing at least one switch, in particular, as in patent U.S. Pat. No. 5,837,885, so as to enable a timewise separation of excitation and detection. In the alternative, some or all of the subcontrollers can have individual inputs connected to form a common input and have individual outputs, the individual outputs being connected to an adder having a common output, and the common input and/or the common output can be gated by switches. A gated implementation is particularly advantageous if a single transducer acts both as a vibration exciter and a sensor, but may be advantageous also in other contexts. 
         [0040]    In some embodiments, the subcontrollers are used with two different reference phase settings to measure the damping of the resonator in the vicinity of one resonance frequency. 
         [0041]    The subcontrollers may be used to measure the amplitudes of said harmonic motions. This is particularly useful in applications where the response of the resonator is non-linear. 
         [0042]    In a second aspect, the present invention provides a device for measuring the vibrational characteristics of an oscillating system, the device comprising said 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 vibration exciter for exciting a motion of the resonator,   the sensor being configured to measure said motion of the resonator,   the control system being configured to control the motion of the resonator via the vibration exciter using the 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 subcontrollers being configured to independently control one of said harmonic motions,   the subcontrollers being configured to control said harmonic motions simultaneously.       
 
         [0049]    As mentioned above, each of said subcontrollers can comprise a phase-locked loop. Each of said subcontrollers can be configured to control a harmonic motion that has a frequency close to (i.e., at or near) a resonance frequency of said resonator. Said resonator can have a plurality of resonance frequencies, said resonance frequencies being sensitive to properties of a fluid that is in contact with said resonator. Said fluid properties can include density and/or viscosity and/or viscoelastic properties of said fluid. In some embodiments, the resonator can be a tube-like structure, and its vibration behavior (including its resonance frequencies) can be sensitive to a mass flow of a fluid through said tube-like structure. At least one of the phase-locked loops can be a gated phase-locked loop containing at least one switch. In the alternative, some or all of the subcontrollers can have individual inputs connected to form a common input and can have individual outputs, the device can comprise an adder having inputs that are connected to the individual outputs of said subcontrollers and having a common output, and the device can comprise one or more switches for gating the common input and/or the common output. In some embodiments, said subcontrollers can be configured to operate with two different reference phase settings to measure the damping of the resonator. The subcontrollers can be configured to measure the amplitudes of said harmonic motions. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0050]    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: 
           [0051]      FIG. 1  shows steady state phase shift ΔΦ s  of a single degree of freedom oscillator around the resonance frequency ω res . 
           [0052]      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. 
           [0053]      FIG. 3  shows a control concept of the simultaneous excitation and control of multiple frequencies of an oscillating system. 
           [0054]      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. 
           [0055]      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 . 
           [0056]      FIG. 6  illustrates an oscillating system comprising a torsional resonator, electromagnetic excitation and optical readout.—a) Photo of the setup; b) Section view. 
           [0057]      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 . 
           [0058]      FIG. 8  is a diagram showing the time history of two frequencies starting at ƒ 1 ±10 Hz and developing so that the final phase shift values equal ΔΦ 1,2 =ΔΦ res ±α. (a) Simulation result; (b) Experimental result. 
           [0059]      FIG. 9  is a diagram showing experimentally determined phase shift curves of a torsional oscillator under the influence of fluids with different viscosities. 
           [0060]      FIG. 10  is a diagram showing viscosity determinations by measuring the resonance frequency shift with and without temperature compensation. 
       
    
    
     DETAILED DESCRIPTION 
       [0061]    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]. 
         [0062]    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. 
         [0063]    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). 
         [0064]    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 sys . The phase detector measures the phase shift y pd  between the output of the oscillating system y sys  and a possibly phase shifted reference signal y ref  of same frequency. A phase shifter  5  shifts the phase of the reference signal by −ΔΦ τ . By tuning the frequency of the VCO using the controller output y 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 sys  and y sys ) being equal to the predefined phase shift value −ΔΦ τ . 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 ΔΦ res ±α. This concept has been used in Patent U.S. Pat. No. 5,492,0787 and U.S. Pat. No. 5,837,885. 
         [0065]    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 . 
         [0066]    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 sys  and one to detect the output y 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. 
         [0067]    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.       
 
         [0072]    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 Σ i u sys,i . Consequently, the output of the oscillating system y sys  is a signal composed of the particular frequencies. Hence an effective frequency separation in each PLL is of utmost importance. 
         [0073]    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(ωt+ΔΦ) in steady state, both with a sine and cosine signal of the same frequency. Hence two reference signals cos(ωt) and sin(ωt) 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 ΔΦ is computed. The atan2 function is defined through 
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         [0074]    The APD acts as a very effective band-pass filter which enables the effective frequency separation. 
         [0075]    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. 
         [0076]    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 o =100 mm, an outer diameter of d o =9.5 mm and a wall thickness of t o =0.335 mm. The inner tube  12  measures length l i =135 mm, outer diameter d i =7 mm and wall thickness t 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. 
         [0077]    The operation of the invention is described in the following figures. 
         [0078]    In  FIG. 1 , the steady state phase shift ΔΦ s  between a harmonic excitation signal of frequency Ω and the response of the oscillating system is shown exemplarily in the region of the resonance frequency ω 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 Δω corresponding to the phase shift values of ΔΦ res ±α. 
         [0079]      FIG. 2  presents the phase-locked loop in conjunction with an oscillating system  1 . Both the excitation signal u sys  and the reference signals y ref  are created by the VCO  4 , whose frequency is varied by the output y ctri  of the controller  3 . The phase detector  2  closes the loop by detecting the phase shift y pd  of the system output and the phase shifted reference. 
         [0080]      FIG. 3  presents the concept of the multimode control. The particular PLLs  7   a ,  7   b ,  7   c  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. 
         [0081]      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 S 1  and S 2  the process alternates continuously between excitation (S 1  closed, S 2  open) and readout phase (S 1  open, S 2  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. 
         [0082]      FIG. 5  presents the working principle of the averaging phase detector. Due to the two multiplications  8   a  and  8   b  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. 
         [0083]      FIG. 6  shows the oscillating system  1  comprising the resonator, electromagnetic excitation and optical readout. The sensor design is shown in  FIG. 6 a    as a section view. The invention can be applied to every oscillating system that exhibits multiple vibration modes with separated resonance frequencies. 
         [0084]      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. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE I 
               
             
             
               
                   
               
               
                 Resonance frequencies ω 0  and damping ratio D of 
               
               
                 the torsional resonator in air at 22° C. 
               
             
          
           
               
                 Mode number 
                 ω 0  [Hz] 
                 D [10 −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 
               
               
                   
               
             
          
         
       
     
         [0085]    Possible Measurement Concepts: 
         [0086]    Concept 1: The simultaneous tracking of multiple resonance frequencies. This can be used in resonance sensors or to gain high efficiency in actuator applications. 
         [0087]    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 ):ΔΦ 1 =ΔΦ res,1 −α and ΔΦ res,2 +α. The achieved frequency difference Δf large =f(ΔΦ 2 )−f(ΔΦ 1 ) is a measure for the damping. Alternatively, one particular mode can be driven at two different phase shift values. 
         [0088]    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 
         [0000]    
       
         
           
             Δφ 
             = 
             
               
                 Δφ 
                 res 
               
               - 
               
                 
                   π 
                   4 
                 
                 . 
               
             
           
         
       
     
         [0000]    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. 
         [0089]    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 2 +Y 2 )}, where X and Y are the output signals of the low-pass filters  9   a  and  9   b , 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). 
         [0090]    Additional Explanations Concerning Concept 2 
         [0091]    The determination of damping is an important issue in many applications, especially in the field of viscometry. Two frequency values at known phase shifts ±α 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. 
         [0092]    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 ΔΦ 1 =ΔΦ res −α and ΔΦ 2 =ΔΦ res +α, respectively. 
         [0093]    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 α is advantageously set to 45°. 
         [0094]    In an example, the damping was increased by immersing the sensor in a calibration oil of constant dynamic viscosity η=8.18 mPas at 22° C. The damping of the first mode was therefore increased by a factor of 10 (Q 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 ω 3 dB =2π0.1 Hz. Obviously, the center frequencies ƒ 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 ƒ c ƒ i ±10 Hz. The controller parameters were adjusted as explained below, using a time constant of T c =2 sec. 
         [0095]      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. 
         [0096]    From the frequency difference Δf i  the damping can directly be calculated using the following equation: 
         [0000]    
       
         
           
             
               Q 
               i 
             
             = 
             
               
                 
                   ω 
                   
                     0 
                     , 
                     i 
                   
                 
                 
                   Δω 
                   i 
                 
               
                
               tan 
                
               
                   
               
                
               α 
             
           
         
       
     
         [0097]    Here, Δω i =2πΔƒ i  is the angular frequency difference of mode i, and ω 0,i  is the resonance frequency of mode i. 
         [0098]    Averaging Δf 1  over the last two seconds yielded a Q-Factor of 920, in very close agreement with simulation results. 
         [0099]    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 α, the more difficult the calculation of the Q-factor gets. 
         [0100]    Additional Explanations Concerning Concept 3 
         [0101]    The torsion angle Φ of a harmonically excited, linear torsional oscillator under the influence of a fluidic force F fluid  can be described by the differential equation 
         [0000]      {umlaut over (Φ)}( t )+2·δ·{dot over (Φ)}( t )+ω 0   2 ·Φ( t )= F   0  exp ( iΩt )+ F   fluid ,
 
         [0000]    wherein ω 0  is the resonance frequency and δ the exponential decay rate of the oscillator without fluid. Ω is the excitation frequency. The influence of a Newtonian fluid on a circular cross section can approximately be described by the force 
         [0000]        F   fluid   =−k (1 +i ){dot over (Φ)}( t ),
 
         [0000]    where k is the fluid influence factor that depends both on the density and the viscosity of the fluid. Hence F fluid  can be interpreted as an additional damping and mass. The steady-state phase shift between excitation force and coordinate Φ(t) is: 
         [0000]    
       
         
           
             Δφ 
             = 
             
               atan 
               ( 
               
                 
                   
                     
                       Ω 
                       2 
                     
                     · 
                     Ω 
                     · 
                     k 
                   
                   - 
                   
                     ω 
                     0 
                     2 
                   
                 
                 
                   Ω 
                    
                   
                     ( 
                     
                       k 
                       + 
                       
                         2 
                         · 
                         δ 
                       
                     
                     ) 
                   
                 
               
               ) 
             
           
         
       
     
         [0102]    Solving the equation for Ω at 
         [0000]    
       
         
           
             
               Δφ 
               = 
               
                 
                   - 
                   
                     3 
                     4 
                   
                 
                  
                 π 
               
             
             , 
           
         
       
     
         [0000]    one obtains: 
         [0000]    
       
         
           
             
               Ω 
                
               
                 ( 
                 
                   Δφ 
                   = 
                   
                     
                       - 
                       
                         3 
                         4 
                       
                     
                      
                     π 
                   
                 
                 ) 
               
             
             = 
             
               
                 - 
                 δ 
               
               + 
               
                 
                   1 
                   2 
                 
                  
                 
                   
                     
                       
                         4 
                          
                         
                           δ 
                           2 
                         
                       
                       + 
                       
                         4 
                          
                         
                           ω 
                           0 
                           
                             2 
                              
                             
                                 
                             
                           
                         
                       
                     
                   
                   . 
                 
               
             
           
         
       
     
         [0103]    This expression is independent of the fluid influence factor k. Therefore the frequency that belongs to a phase shift of 
         [0000]    
       
         
           
             
               - 
               
                 3 
                 4 
               
             
              
             π 
           
         
       
     
         [0000]    is inaepenaent or tne properties of the fluid. 
         [0104]    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 
         [0000]    
       
         
           
             Δφ 
             = 
             
               
                 Δφ 
                 res 
               
               - 
               
                 
                   π 
                   4 
                 
                  
                 
                   
                     ( 
                     
                       dash 
                        
                       
                         - 
                       
                        
                       dotted 
                        
                       
                           
                       
                        
                       line 
                     
                     ) 
                   
                   . 
                 
               
             
           
         
       
     
         [0105]    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. 
         [0106]    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. 
         [0107]    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.