HK1083533B - A system for calibrating a drive signal in a coriolis flowmeter - Google Patents

Description

System for calibrating drive signal of Coriolis flowmeter

Technical Field

The present invention relates to a device for measuring a property of a material flowing through, for example, a Coriolis mass flowmeter device. More particularly, the present invention relates to calibrating a driver secured to a conduit so as to excite the conduit only in a desired vibration mode. Still more particularly, the present invention relates to determining a drive signal that causes a driver to vibrate a conduit in a desired vibration mode.

Background

It is known to use Coriolis effect flow meters to measure mass flow and other information for a material flowing through a conduit within the meter. Typical Coriolis flowmeters are disclosed in U.S. patent 4,109,524, filed 1978, 8-29, 1985, patent 4,491,025, filed 1985, 1-1, and patent re.31.450, filed 1982, 11, by j.e. smith et al. These meters have one or more conduits of either straight or curved configuration. Each conduit in a Coriolis mass flowmeter has a set of natural vibration modes, which may be a simple bending type, a torsional type, or a combination of types. Each conduit is driven to oscillate at resonance with one of a plurality of natural vibration modes. Material flows into the meter from a connecting line at the inlet of the meter, through one or more conduits, and out of the meter at the outlet side of the meter. The natural vibration modes of vibrating a material filling a system can be determined in the art by combining the conduit mass and the material flowing within the conduit.

When no material flows through the flowmeter, all points along the conduit oscillate with the same phase or with a small initial fixed phase shift that can be corrected due to the applied driving force. As the material flows, the Coriolis force causes each point along the vibrating conduit to have a different phase. The phase on the inlet side of the conduit lags the driver while the phase on the outlet side of the conduit leads the driver. The sensor is placed on the catheter (or catheters) to generate a sinusoidal signal representative of the motion of the catheter (or catheters). The signals output from the sensors are processed to determine the phase difference between the signals. The phase difference between the two sensor signals is proportional to the mass flow rate of the substance through the conduit (or conduits).

The primary component of each Coriolis flowmeter and each vibrating tube densitometer is the drive or excitation system. The drive system, which is operable to apply a periodic physical force to the conduit, which causes the conduit to oscillate, includes a drive mechanism mounted on the conduit (or conduits) and a drive circuit for generating a drive signal to operate the drive mechanism. A typical drive mechanism includes one of many known devices, such as a magnet mounted on one catheter and a coil mounted on the other catheter in an opposed relationship to the magnet.

The drive circuit continuously applies a periodic drive signal to the drive mechanism. The drive signal is typically a sine wave or a square wave. In a typical magnetic coil drive mechanism, a periodic drive signal causes the coil to generate an alternating magnetic field. The alternating magnetic field of the coil and the constant magnetic field created by the magnetic force cause the flow conduit to vibrate in a sinusoidal pattern. It will be understood by those skilled in the art that any device that converts an electrical signal into a mechanical force is suitable for use in applications such as actuators (see U.S. patent 4,777,833 issued to Carpenter and assigned to Micro Motion, Inc). Also, it is not necessary to use a sinusoidal signal. Any periodic signal is also suitable as a driver signal. (see U.S. patent 5,009,109 issued to Kalotay et al and assigned to Micro Motion, Inc.).

For a dual tube meter, a typical mode that a Coriolis meter can typically be driven to vibrate, although this is not the only mode, is a first out of phase bending mode. The bending mode of the first guided phase is the fundamental resonant bending mode in which the two conduits of the dual tube Coriolis flowmeter vibrate in opposite phase. However, this is currently not the only mode of vibration in the vibrating structure of a Coriolis flowmeter. Higher vibration modes may also be excited in some catheters. For example, a first out-of-phase twist mode may be excited as a result of the material flowing through the vibrating conduit and subsequent Coriolis forces induced by the flowing material. Other higher modes of vibration that can be excited include in-phase bending and transverse modes of vibration.

Hundreds of vibrational modes can be excited in a Coriolis flowmeter driven in a first out of phase bending mode. Even within a relatively narrow frequency range near the first out of phase bending mode, there are at least several additional vibration modes that may be excited by the drive system. In addition to the multiple modes that can be excited by the driver, undesirable vibration modes can also be excited due to external vibrations of the flow meter. For example, the vicinity of machinery in a production line may produce vibrations that may excite unwanted vibration modes in a Coriolis flowmeter.

The drive system is capable of exciting additional and undesirable vibration modes because the drive mechanism is not ideal. The drive system includes a drive circuit that generates a command signal and a driver mechanism that converts the received command signal into a force. Ideally the actuator mechanism is linear and the mechanism will produce a force that is linearly related to the command signal. However, for various reasons, the relationship between the command signal applied to the actuator and the force generated by the actuator is non-linear. Manufacturing tolerances require that the driver elements be placed symmetrically on the catheter. Any resulting non-linearity causes distortion under the driving force that occurs as a force applied to the structure at a harmonic of the original drive signal. The drive system is configured to apply a drive signal to the driver that applies sufficient force to the conduit(s) to cause them to vibrate in the desired vibration mode. However, where the driver is not ideal, the force applied to the conduit(s) is not ideal and the force may be generated at higher frequencies. These high frequency forces can excite other unwanted structural modes.

The applied eccentric force may excite multiple vibration modes within some conduits. In this way, the Coriolis flowmeter is driven to oscillate or resonate in a desired vibrational mode, such as a first out-of-phase bending mode, effectively having a conduit (or conduits) that oscillates in many other modes in addition to the desired mode. Driving the meter to oscillate in different modes other than the first out-of-phase bending mode produces the same phenomenon with multiple excited vibration modes including the intended vibration mode.

The eccentric force exerted by the conduit on the driver is a particular problem if the devices, such as Coriolis flowmeters, are not balanced. The devices are balanced when vibrations within the devices cancel each other, generating a zero-sum device vibration. When the vibrations do not cancel each other, the devices are not balanced. This applies a force to the system. A typical dual conduit device, such as a dual conduit Coriolis flowmeter, is balanced in that the two conduits vibrate in opposite phase to each other, which counteracts the relative vibration. However, the unbalanced device lacks such a conduit: it vibrates in the opposite direction so that the vibrational forces from the catheter can be cancelled.

The non-uniformity can cause significant coupling between the surrounding environment and the conduit. This coupling increases the structural dynamic impact of the surrounding environment and can cause undesirable vibration modes excited by harmonic forces applied by the driver to the conduit. It is therefore desirable to have a driver in a non-uniform device that applies a force that excites only the desired vibration modes.

For the foregoing reasons, there is a need for drive circuitry for vibrating a conduit in a device for measuring the conduit driving vibrations in a flow meter to reduce undesirable vibration modes excited by the driver oscillating the conduit.

Disclosure of Invention

It is an object of the present invention to address the above-mentioned problems, and others, and to provide a system for calibrating a drive signal, and to advance the art. To measure a characteristic of a substance flowing through a conduit, the calibration system of the present invention determines an appropriate drive signal for a driver secured to the conduit. The drive signal causes the driver to apply a force that vibrates the conduit in the desired vibration mode. By determining the appropriate drive signal, the harmonic forces applied to the catheter by the driver will be reduced. This increases the amount of vibration in the desired vibration mode and decreases the amount of vibration in the undesired vibration mode. The reduction of vibration in undesirable vibration modes can substantially reduce the noise floor to which the flow meter is exposed. Amplifying the desired response and reducing noise will allow more accurate measurements of characteristics such as mass flow rate. Furthermore, the repeatability of the measurements is improved.

To calibrate the appropriate drive signal, a sensor, such as an accelerometer, is affixed to the catheter proximate the driver. A computer or digital processor excites the driver with a broadband noise signal. This causes the drive to apply a band-limited noise force to the conduit and sensor for measuring the motion of the vibrating structure at the drive. The digital processor receives data regarding the structural action output from the sensor. The digital processor uses the data to generate a dynamic pattern of the structure and drivers. The digital processor uses the dynamic mode to determine a drive signal that will cause the driver to apply a force to the conduit that will vibrate the conduit in the desired vibration mode.

In one embodiment, the digital processor outputs results to a display or the like, and conventional analog driver circuitry coupled to the driver is configured to generate appropriate drive signals. In this preferred embodiment, a conventional driver circuit can be configured by setting a reference voltage in the driver circuit.

In an alternative embodiment, the electronic gauge comprises a digital signal processor that controls the drive signals applied to the driver. When a digital signal processor is used in an electronic meter, calibration is periodically performed by the digital signal processor to adjust the drive signal as the configuration of the device dynamically changes. This is done by periodically vibrating the conduit of the driver. The vibration data is then stored in a memory. The stored data is used with the current vibration data to detect new device configuration dynamics and determine new drive signals.

According to the present invention, there is provided a method for calibrating a drive signal applied to a driver, the drive signal causing the driver to oscillate at least one flow tube in a flow measurement device for measuring a characteristic of a substance flowing in the at least one flow tube, the method comprising the steps of: vibrating the at least one flow tube with the driver; measuring vibration of the at least one flow tube in response to vibrating the flow tubes; the method is characterized by comprising the following steps: detecting physical characteristics of the apparatus and the driver from the measured vibration of the at least one flow tube; determining a driving signal for the driver according to the detection result of the physical characteristic; and applying the determined drive signal to the driver to oscillate the at least one flow tube in the desired vibration mode.

Another aspect is the step of storing a measure of said vibration of said at least one flow tube, wherein said step of detecting said physical characteristic of said apparatus further comprises the steps of:

combining the current vibration measurement with the stored vibration measurement to determine the physical characteristic;

another aspect includes the step of setting a reference voltage in a drive signal circuit in response to the determined drive signal to cause the drive signal circuit to generate the drive signal;

another aspect further comprises the step of periodically repeating the method for calibrating the drive signal;

another aspect is where the step of detecting physical characteristics of the driver and device includes the step of simulating the dynamics of the driver and device based on the measured vibrations.

Another aspect further comprises the step of modifying the drive circuit to generate said drive signal.

Another aspect is that the step of determining the drive signal comprises the steps of:

calculating coefficients of a functional polynomial representing a relationship between a drive signal and a force applied to the catheter;

determining coefficients of an inverse function polynomial of the function representing the relationship between the drive signal and the force; and

adding the command level of the drive signal to the inverse function to determine the drive signal.

The present invention also provides an electronic meter for a flow measurement device for measuring a property of a substance, the device having at least one flow tube for receiving the substance, a driver for vibrating the at least one flow tube, a plurality of transducers for measuring the vibration of the at least one flow tube at points along the flow tube, the electronic meter including a drive circuit for applying a drive signal to the driver to cause the driver to oscillate the at least one flow tube, and a circuit for measuring the property of the substance flowing through the at least one flow tube, the electronic meter further comprising: a first circuit for receiving signals output from said sensor and detecting physical characteristics of said device and said driver based on said measured vibration of said at least one flow tube; and a second circuit responsive to receipt of the signal for determining a drive signal for causing the driver to oscillate the at least one flow tube in a desired vibration mode based on physical characteristics of the apparatus and the driver.

Another aspect further includes a memory for storing vibration measurements of the at least one flow tube.

Another aspect is that the first circuit further comprises circuitry for combining a current vibration measurement with the stored vibration measurement for determining the physical characteristic.

Another aspect includes a reference voltage provided in the drive signal circuit, the reference voltage being set to a level for generating the drive signal in response to determining the drive signal to cause the drive signal circuit to generate the drive signal.

Another aspect includes a timing circuit for periodically repeating the drive signal calibration.

Another aspect is that the first circuit includes analog circuitry for simulating the dynamics of the device and driver based on the measured vibrations.

Another aspect is the second circuit comprising:

circuitry for calculating coefficients of a functional polynomial representing a relationship between a drive signal and a force applied to the conduit;

circuitry for determining coefficients of an inverse function polynomial of the function representing the relationship between the drive signal and the force; and

circuitry for adding a command signal of the current drive signal to the inverse function to determine the drive signal.

The present invention also provides a product for calibrating a drive signal applied to a driver to cause the driver to oscillate at least one flow tube in a flow measurement device for measuring a property of a substance flowing through the at least one flow tube, the product comprising: instructions for instructing a processor to: receiving a signal output from a sensor affixed to the at least one flow tube measuring vibration of the at least one flow tube, and detecting physical characteristics of the device and driver based on the measured vibration of the at least one flow tube, and determining a drive signal based on the physical characteristics of the device and driver that causes the driver to oscillate the at least one flow tube in a desired vibration mode; and a medium readable by the processor for storing the instructions.

Another aspect is that the instructions further comprise instructions for instructing the processor to apply the drive signal to the driver to oscillate the at least one flow tube in the desired vibration mode.

Another aspect is that the instructions further comprise instructions for instructing the processor to store the vibration measurements of the at least one flow tube in a memory.

Another aspect is that the instructions that cause the processor to detect the physical characteristics of the device and drive further comprise:

instructions for instructing the processor to read the measurements from the memory and to combine the current vibration measurements with the stored vibration measurements for use in determining the physical characteristic.

Another aspect is that the instructions further comprise:

instructions for instructing the processor to provide a drive signal circuit reference voltage responsive to the determined drive signal to cause the drive signal circuit to generate the drive signal.

Another aspect is that the instructions further comprise instructions for instructing the processor to periodically repeat the drive signal calibration.

Another aspect is that the instructions for detecting the physical characteristics of the device and driver include instructions for instructing the processor to simulate the dynamics of the device and driver as a function of the measured vibrations.

Another aspect is that the instructions for instructing the processor to determine the drive signal comprise:

instructions for instructing the processor to calculate coefficients of a function polynomial representing a relationship between a drive signal and a force applied to the catheter, determine coefficients of an inverse function polynomial of the function representing the relationship between the drive signal and the force, and add a command signal of the drive signal to the inverse function to determine the drive signal.

Drawings

The above and other features of the drive signal calibration system can be understood from a reading of the detailed description and the accompanying drawings:

FIG. 1 illustrates a Coriolis mass flowmeter incorporating the drive signal calibration system of the present invention;

FIG. 2 shows an electronic gauge for use in the drive signal calibration system of the present invention;

FIG. 3 illustrates a drive circuit for generating a drive signal for exciting a desired vibration mode as determined by the drive signal calibration system;

FIG. 4 shows a processing unit for performing drive signal calibration;

FIG. 5 shows a block diagram of a second embodiment of the electronic gauge 20 using a digital transmitter;

FIG. 6 shows a graph of conduit vibration oscillated by an ideal drive system;

FIG. 7 shows a graph of conduit vibration oscillated by a typical non-ideal drive system;

FIG. 8 shows a graph of the actual vibration of a catheter oscillated by a drive system with a calibrated drive signal;

FIG. 9 shows a flow chart of a method for calibrating a drive signal;

FIG. 10 shows a flow chart of the processing performed by the digital processor for drive signal calibration; and

FIG. 11 shows additional details of the cells 906& 1007.

Detailed Description

Total Coriolis flowmeter-FIG. 1

FIG. 1 illustrates a typical Coriolis flowmeter 5 including a Coriolis meter component 10 and an electronic meter 20. The electronic meter 20 is connected to the meter component 10 via leads 100 for providing density, mass flow rate, volume flow rate and aggregate mass flow information on the path 26. The construction of a Coriolis flowmeter is described, although it will be understood by those skilled in the art that the present invention may be practiced in conjunction with any device having a vibrating conduit for measuring a characteristic of a material flowing through the conduit. A second example of such a device is a vibrating tube densitometer which does not have the additional measurement capability that can be provided by a Coriolis mass flowmeter.

The meter assembly 10 includes a pair of process connections, such as flanges 101 and 101', a manifold 102, and conduits 103A and 103B. Connected to conduits 103A and 103B are driver 104, accelerometer 190, and sensors 105 and 105'. Struts 106 and 106 'are used to determine the axis W and W' of oscillation of each conduit.

When flow meter 5 is inserted into a piping system (not shown) for transporting the process material being measured, the material enters meter assembly 10 through flange 101, passes through manifold 102 (where the material enters conduits 103A and 103B directly), flows through conduits 103A and 103B, and returns to manifold 102, where the material exits meter assembly 10 via flange 101'.

Conduits 103A and 103B are selected and properly mounted on manifold 102 so that they each have substantially the same mass distribution, inertia about bending axes W-W and W '-W', and instantaneous modulus of elasticity. The conduits 103A-103B extend outwardly from the manifold in a substantially parallel manner.

The conduits 103A-103B are driven by the driver 104 in an opposite phase about their respective bending axes W and W' and in a first out of phase resonant bending mode known as a flow meter. The driver 104 comprises any one of a number of well known devices, such as a magnet mounted on the conduit 103A and a counter-acting coil mounted on the conduit 103B, with alternating current flowing through the magnet and coil for vibrating both conduits. The electronic meter 20 applies a suitable drive signal to the driver 104 via the lead 110.

Sensors 105 and 105' are placed on opposite ends of at least one of the conduits 103A and 103B to measure the oscillation of the conduits. As the conduits 103A-103B vibrate, the sensors 105 and 105' generate first and second velocity signals. First and second rate signals are applied to the conductive lines 111 and 111'. An acceleration sensor 105 "is affixed to the conduit proximate to the driver 104 and generates an acceleration signal responsive to oscillations of the conduits 103A and 103B. An acceleration signal is applied to the wire 111 "to indicate the vibration of the flow tubes 103A and 103B.

The electronic meter 20 receives first and second sensor rate signals and driver rate signals appearing on the leads 111, 111', and 111 ", respectively. The electronic meter 20 processes the first and second velocity signals to calculate mass flow rate, density, or other characteristics of the material passing through the meter component 10. The electronic meter 20 applies the calculated information on path 26 to a utilization device (not shown), such as a digital signal processing unit (see fig. 4).

It is known to those skilled in the art that Coriolis flowmeters 5 are smaller in construction than vibrating tube densitometers. Vibrating tube densitometers also use a vibrating tube through which a liquid flows or, in the case of a simple type of densitometer, in which the liquid is held. Vibrating tube densitometers also use a drive system for exciting the conduit to vibrate. A typical vibrating tube densitometer utilizes only one feedback signal because density measurement requires only frequency measurement and no phase measurement. The description of the invention herein applies equally to vibrating tube densitometers. Those skilled in the art will appreciate that Coriolis flowmeters have two feedback signals available, whereas vibrating tube densitometers have only one feedback signal typically available. Thus, in order for the present invention to be applicable to a vibrating tube densitometer, it is only necessary to provide an additional feedback signal in the vibrating tube densitometer. Moreover, it will be apparent to those skilled in the art that the following inventive steps and methods may be used in any apparatus for measuring properties of a substance by vibrating a conduit.

Electronic measuring instrument-figure 2

Fig. 2 shows further details of the electronic measuring instrument 20. The electronic meter 20 includes a characteristic measurement circuit 30, and a flow tube drive circuit 40. The characteristic measurement circuit 30 is one of many known circuits for calculating a material characteristic, such as the mass flow rate of a material as it passes through the vibrating conduits 103A-103B, based on a phase difference between two points of the vibrating conduit. Characteristic measurement circuit 30 produces an output on conductor 26 for use with a device (not shown). The means of use may be, for example, a display and a digital processing unit as shown in fig. 4. The details of characteristic measurement circuit 30 are well known to those skilled in the art and are not a part of the present invention. Typical information regarding the characteristic measurement circuit 30 for determining the mass flow rate of a substance is disclosed by Smith, U.S. Pat. No. RE31,450, published 11/29 1983 and assigned to Micro Motion, Inc, or Zoloc, U.S. Pat. No. 4,879,911, published 11/14 1989 and assigned to Micro Motion, Inc, or Zoloc, U.S. Pat. No. 5,231,884, published 8/3 1993 and assigned to Micro Motion, Inc.

In the flow meter drive circuitry, the drive circuit 40 receives a feedback signal from the left sensor 105 on path 41. As described in more detail in connection with fig. 3, the drive circuitry applies a drive signal on path 110 to drive coil 104. Those skilled in the art will appreciate that existing drive systems may choose to use the right sensor as feedback for the drive circuit 40. Also, some existing drive systems may use the sum of the two sensor signals as a feedback signal for the drive circuit 40.

Drive circuit 40-FIG. 3

Fig. 3 shows further details of the drive circuit 40. Drive circuit 40 receives a feedback signal on path 41 from one of the many transducers of the flow meter and adjusts the amplitude of the transducer signal to apply a drive signal on path 110 to driver 104. Note that some existing drive systems sum the signals of the two sensors and process the summed signal to generate the drive signal. Drive circuit 40 receives signals from sensor 105 on path 41. The sensor signal is passed through a rectifier 300 and an integrator 301. The signal output from the integrator 301 represents the average amplitude of the sensor signal 105. The average amplitude signal is applied to an amplitude control 302. Amplitude control 302 compares the average amplitude signal from integrator 301 with a reference voltage V_ref. If the average amplitude is below the reference voltage, multiplier 303 amplifies the sensor signal and applies the amplitude adjusted sensor signal to path 305. Power amplifier 304 amplifies the amplitude adjusted sensor signal 105 to produce the final drive signal to be fed back to driver 104 on path 110. Thus, the drive circuit 40 maintains a relatively constant magnitude drive signal. The details of the existing control circuit 40 are well known to those skilled in the Coriolis electronic flowmeter art and are not a part of the present invention. See us 5009109 for a more detailed discussion of further embodiments of the drive circuit 40.

Digital processing Unit-FIG. 4

Fig. 4 shows a digital processing unit 400 for executing instructions that provide the drive signal calibration of the present invention. The digital processing unit 400 has a processor 401 for executing instructions stored in a memory for performing applications such as the drive signal calibration of the present invention. The processor 401 may be a conventional processor, microprocessor, or serial processor coupled together to perform a series of instructions.

Processor 401 is connected to memory bus 402 to read instructions and data from, and write data to, the memory. Random Access Memory (RAM)412 is a volatile memory connected to memory bus 402 by path 411. The RAM412 stores instructions currently being executed by the processor 401 and data required to complete the instructions. Read Only Memory (ROM)414 is connected to memory bus 402 by path 413. ROM414 stores configuration and operating system information required by processor 401 in order to execute system routines that allow processor 400 to implement applications.

The processor 401 is also connected to an input/output ("I/O") bus 403. The I/O bus 403 connects the processor 401 and the peripheral devices for allowing the processor 401 to send and receive data to and from the peripheral devices. Some typical devices connected to the I/O bus include, but are not limited to, a memory 422, a display 424, I/O devices 426, and I/O devices 428. Memory 422 is coupled to I/O bus 403 by path 421 and stores data and application instructions that can be executed by processor 401. An example of the memory 422 is a magnetic disk, from which data can be read and to which data can be written. A display 424 is connected to I/O bus 403 via path 423, which is a driver connected device capable of receiving data output from processor 401 and displaying the data in a manner understood by a user. For example, the display 424 may be a monitor and video card connected to the bus. The display 424 may also be a device for providing audible sound based on received data.

I/O device 426 is connected to I/O bus 403 by path 425. I/O devices 426 are devices used to receive input data or output data to a user or other machine. Some examples of I/O devices 426 include, but are not limited to, a keyboard, a mouse, a Local Area Network (LAN) connection, a modem, or the like. The I/O device 428 is connected to the I/O bus 403 via path 413 and in the preferred embodiment is an I/O device that receives data output from the electronic meter 20 via path 26. The I/O device 428 converts data received over the path 26 into data that can be recognized by the processor 401.

Digital signal processor of electronic measuring instrument 20-figure 5

Alternatively, the electronic meter connected to the electronic meter 20 instead of the digital processing unit 400 may be a digital signal processor. Fig. 5 shows the elements of the electronic measuring instrument 20, wherein the electronic measuring instrument 20 is a digital signal processor. Paths 111 and 111' transmit left and right rate signals from the flow meter assembly 10 to the electronic meter 20. An analog-to-digital (a/D) converter 503 in the electronic meter 20 receives the rate signal. a/D converter 503 converts the left and right rate signals to digital signals that can be used by processor 501 and sends the digital signals on path 513 to I/O bus 510. The I/O bus 510 transmits the digital signal to the processor 501. The drive signals are sent to digital-to-analog (D/A) converter 502 over I/O bus 510 and path 512. The analog signal from D/a converter 502 is sent to driver 104 through path 110. The path 26 is connected to an I/O bus 510 and transmits signals to input and output devices (not shown) that allow the electronic gauge 20 to receive data from and transmit data to an operator.

Processor 501 reads instructions from Read Only Memory (ROM)520 via path 521 for performing various functions of the flow meter, including, but not limited to, calculating mass flow rate of the material, calculating volumetric flow rate of the material, and calculating density of the material. Data and instructions to perform various functions are stored in a random access processor (RAM) 530. Processor 501 performs read and write operations to RAM memory 530 via path 531.

Basic principle of drive signal calibration

The present invention is a system for calibrating drive signals in a device such as a Coriolis flowmeter 5. The calibrated drive signal is applied to the driver such that the driver applies a force to the conduit to cause the conduit to vibrate in the desired vibration mode. The calibration of the drive signal may be done before the device in the line starts to operate or may be done periodically when the device measures a characteristic of the substance flowing through the line.

To calibrate the drive signals, a mathematical model of the Coriolis flowmeter 5 must be generated. For purposes of discussion, it is assumed that the system of the Coriolis flowmeter 5 is non-linear and time invariant. In such systems, the relationship between the input and output does not change over time. The following equation gives the most common way to mathematically model a non-linear, time invariant system:

y＝g(x，r)； (2)

wherein:

x is the system state;

r ═ the input to the system (drive signal);

y is the output of the system; and

f and g are functions describing the system functionality.

Equations 1 and 2 are too general to be used to determine the required inputs that can produce the desired output, which may be, for example, that the conduits 103A-103B vibrate in a desired vibration mode. A more specific form of mathematical model is selected among the information about the system in which the Coriolis flowmeter 5 is used. The flow meter model is divided into two subsystems, one representing the mechanical structure of the flow meter and the other representing the driver placed on the structure. It is known that mechanical structures can be accurately modeled by an ideal linear system. A non-ideal driver applies a driving force to the structure. The driver subsystem is modeled as a non-linear function. For the Coriolis flowmeter 5, the following standard state space equations were chosen to model the system:

y＝Cx+Df_α(r)； (4)

wherein:

a, B, C, D is a matrix that models the structural dynamics of the Coriolis flowmeter element 10;

f_α(r) is a function of the relationship between the analog drive command signal and the force generated by the driver;

r is the driver signal.

From equations 3 and 4, it can be seen that f_α(r) inverse function (f)_α ^-1(r)) will compensate for the non-linearity of the system so that the force applied to the conduits 103A and 103B is in timeIs linear in the desired vibration mode within the desired range. f. of_αThe precise form of (r) is unknown. Approximation f_α ^-1One method of (r) is with respect to a hypothetical polynomial, as shown in equation 5 below.

f_a ^-1(r)＝α₀+α₁r+α₂r²+α₃r³+α₄r⁴+…… (5)

Wherein alpha is₀…α₄Are unknown constants.

Used as approximation f_α ^-1The order of the polynomial of (r) is determined by the non-linear characteristic given by the system in the range of r (command signal) values used to drive the flow meter. To calibrate the drive signal, f is determined_α ^-1(r) the drive signal is set to f_α ^-1(r); the last dynamic system becomes:

x＝Ax+Bf_α(f_α ^-1(r))≈Ax+Br； (6)

wherein (f)_α ^-1(r)) is a correction factor; (7)

therefore, to calibrate the drive signal, α must be determined for a particular driver₀L ∈ {0, 1, 2, 3, … }. For purposes of the present discussion, f is approximated by the following polynomial_α(r)：

f_a(f)＝β₀+β₁*r+β₂*r²+β₃*r³+… (8)

For clarity, the third order polynomial shown is adjusted, and different order polynomials can be adjusted to fit the data, if desired. Thus, equations 3 and 4 can be rewritten as:

y＝Cx+D(β₀+β₁*r+β₂r²+β₃r³) (10)

and finally, the step of,

y＝Cx+[Dβ₁；Dβ₂；Dβ₃]·[r，r²…r³]^T (10B)

equations 10A and 10B may be viewed as dynamic equations for a multi-input dynamic system, where the input is equivalent to each term of a polynomial, [ r, r²，r³]. Standard multiple-input system identification methods can be used to determine all variables associated with a dynamic system. In 1987, EnglewoodCliffs, PTR Prentice Hall, Lennart Lijung, N.JPart 2 of system identification: user' s Theory of the inventionA detailed description of a technique for estimating the parameters in equations 10A and 10B is included.

Once the variables of the dynamic system are determined,the inverse function (correction factor) f must be determined_α ^-1(r) of (A). The inverse function exists because the driver 104 has a non-linearity that is monotonic over the normal operating range of a device such as the Coriolis flowmeter 5. Determining an inverse function f_α ^-1One way of (r) is to fit a polynomial to the inverse function, such that equation f_α(r)·f_α ^-1(r) ═ 1. However, other methods may be used to determine the inverse function.

The following is an example of calibrating a drive signal applied to driver 104 such that driver 104 vibrates conduits 103A-103B in a desired vibration pattern. Assume that driver 104 is modeled by the following equation:

f_α(r)＝r+.5r²+.3r³ (11)

the discrete structure model of the Coriolis flowmeter 5 in this example is a second order system defined by the following equations 12, 13, 14, and 15:

C＝[1 0] (14)

D＝0 (15)

the first step is to apply a band limiting clutter noise command signal to the Coriolis flowmeter 5 driver using a signal generator and read the output data from the accelerometer 190. Next, the order of the polynomial used to adjust the non-linearity is estimated. There are many free terms in the order of the selected polynomial. If the selected order is too high, the terms associated with the higher order will be small and can be ignored. Thus, a fifth order polynomial is selected. For each term in the polynomial, an input to the system model is generated, changing this single input system to one with multiple virtual inputs (physical drive commands are consistent with the sum of all the individual elements).

Each input is consistent with a different term of the polynomial, as in equation 8. These inputs are the vector r, r²，r³，r⁴，r⁵]. The model parameters are estimated using standard MIMO identification techniques. The terms in the B matrix are the coefficients of a non-linear polynomial. See reference 1 which discusses various techniques for estimating these parameters.

Once the model is determined, the B matrix is examined. As seen in equation 10A, the B matrix will constitute a column vector proportional to the coefficients of the polynomial. The polynomial coefficient estimate β is generated by completely separating equation (10A) through the first column β.

In this example, the signal of the noise generator is set to a signal-to-noise ratio of 40 dB. Then a fifth order polynomial is used for f consistent with the drive signal_α(r), the following results were produced:

f_α(r)＝.9987＊r+.5002＊r²+.2998＊r³.0003＊r⁴+0.0000＊r⁵ (16)

when comparing equations 11 and 16, it is apparent that the system accurately characterizes the non-linearity of the drive. The next step is to process the adjusted function f of equation 16_α(r) determining the inverse function (correction factor) f_α ^-1(r) of (A). There are many different ways in which the calibration factor can be found. The method used here is to estimate the adjusted function over a range of r values, equation 16. r value and f_αThe (r) values are inverted and a least squares method is used to fit another polynomial to its inverse. In 1980, Monterey, Brooks/Cole publishing company, Ward Cheney and David Kincaid, Calif.,Numerical Mathematics and Computingthe least squares approach used is discussed. In a preferred embodiment, a 10 th order polynomial is adapted to the inverse function.

The correction factor is used to determine the calibrated drive signal of equation (5) for application to the driver 104. The calibrated drive signal is determined from evaluating the inverse function on the command signal without calibration. The calibrated command signal is then applied to the driver 104. FIG. 7 shows conduit vibration in a Coriolis flowmeter in which the drive signals are not calibrated. A first spike 701 at approximately 125Hz represents vibration in a first bending vibration mode. The first spike 701 represents the desired vibration mode in a preferred embodiment of the present invention. 702 and 703 represent the vibration portions caused by the non-linear actuators. These portions are at 250 and 375Hz, respectively. FIG. 6 is a graph showing the vibration of conduits 103A-103B when a desired drive signal has been applied to driver 104 in a preferred exemplary embodiment. It can be seen that in the vibration frequency range, only the spike 601, which is the first bending vibration mode that is the desired vibration mode in the preferred embodiment of the invention, appears at about 125 Hz.

FIG. 8 shows a graph of the vibrations of conduits 103A-103B caused by a calibrated drive signal applied to driver 104 in a second embodiment. In this embodiment, the calibrated drive signal does not extinguish all harmonics of the desired vibration mode. Instead, the calibrated drive signal reduces the final harmonic signal by a factor greater than 50 dB.

The peak 801 is a peak indicating vibration in a desired vibration mode, i.e., the first bending vibration mode. The peaks 802 and 807 represent vibrations at harmonics of the desired vibration mode. Comparing fig. 8 and 6, it is apparent that the calibrated drive signal causes the conduit to vibrate at a number of harmonics, which is greater in number than if the conduit was driven without the calibrated signal. However, the level of each harmonic is reduced by more than 50dB, which is consistent with a reduction of more than a factor of 100dB, and can be easily filtered from the received signal.

Method of vibrating drive signals for a Coriolis flowmeter 5-fig. 9

FIG. 9 shows a flow chart of a method 900 of completing a calibration step for a drive signal of a Coriolis flowmeter 5. Method 900 begins with step 901 of vibrating conduits 103A-103B. As mentioned above, in explaining the calibration process, in a preferred exemplary embodiment, the catheters 103A-103B are vibrated by applying clutter noise to the driver 104. In step 902, vibrations of the conduits 103A-103B are measured from the vibrating conduit. The measurement values are received in step 903. The measurements include data from the accelerometer 190 and the sensor 105 and 105'. The measurement data is stored in a memory or other storage device for later calibration of the drive signal in step 904.

A dynamic model of the Coriolis flowmeter 5 is generated in step 905 from the measurements obtained in step 903. The dynamic model may be generated using only the measurements from step 903, or using the measurement data received and stored in step 903. In step 906, the dynamic model of the Coriolis flowmeter 5 generated in step 905 is used to determine the appropriate drive signals to apply to the driver 104 to vibrate the conduit in the desired vibration mode. In step 907, the drive circuit is configured such that the desired drive signal is used for the driver 104. One way to vary the drive signal is to vary a reference voltage in the drive circuit. In other words, the digital signal processor can store the appropriate voltage to the memory and apply that voltage to the driver 104 when needed.

In decision step 908, a determination is made as to whether the method 900 is repeated periodically. If the method 900 is not repeated periodically for recalibration of the drive signal, the method 900 ends. Otherwise, the method 900 is repeated again starting with step 901. The idea of the periodic repeating method 900 is to periodically calibrate the drive signal in order to adjust the drive signal to compensate for any changes in the dynamics of the system caused by component losses within the Coriolis flowmeter 5.

Procedure for calibration by a digital processor-FIG. 10

Fig. 10 shows a process 1000 of steps performed by a processor, such as the processing unit 400 or the digital signal processor 500, to complete the method 900 shown in fig. 9. The instructions stored in the memory coupled to the processor include instructions executed by the processor to perform the steps of process 1000. Writing an executable application for completing the steps of process 1000 is left to those skilled in the art.

Process 1000 begins with step 1001 of generating a drive signal. As mentioned above, in the preferred embodiment, the drive signal generated is a clutter. In step 1002, the generated signals are stored for use in generating a structural dynamic model of the Coriolis flowmeter 5. Subsequently, the generated driving signal is transmitted to the driver 104 in step 1003. The driver 104 vibrates the conduits 103A-103B in response to the received drive signal. The accelerometer 190 and sensor 105 and 105' measure the vibration of the conduits 103A-103B from the driver 104 vibrating the flow tube and send the measured data to the transmitter.

In step 1004, the processor receives measurement data from the accelerometer 190 and the sensor 105 and 105'. In step 1005, the processor stores the data in a memory coupled thereto in response to the received measurement data. A model of the structural dynamics of the Coriolis flowmeter 5 is generated in step 1006 from the measurement data received in step 1004. The dynamic model may be generated from only the data received in step 1004, or may be generated from the data received in step 1004 and previously measured data stored in memory.

In step 1006, the dynamic model generated in step 1005 is used to determine appropriate drive signals for driver 104 such that driver 104 vibrates conduits 103A-103B in a desired vibration mode. A possible exemplary procedure for determining a suitable drive signal is provided below. The drive circuitry is altered in step 1007 to provide the appropriate drive signal as determined in step 1006. One way to be able to vary the drive signal is to vary the reference voltage in the drive circuit. In other words, the digital signal processor can store the appropriate voltage to the memory and apply that voltage to the driver 104 when needed.

In decision step 1008, a determination is made whether process 1000 is repeated periodically. If process 1000 is not periodically repeated for recalibration of the drive signal, process 1000 ends. Otherwise, the processor starts a counter and waits for a predetermined amount of time to arrive at step 1010. After the predetermined amount of time has been reached, process 1000 begins again with step 1001. The idea of the periodically repeating process 1000 is to periodically calibrate the drive signal in order to adjust the drive signal to compensate for any changes in the dynamics of the system due to component losses within the Coriolis flowmeter 5.

Exemplary Process or method of determining an appropriate drive Signal-FIG. 11

FIG. 11 further discloses details of elements 906 and 1007 and illustrates an exemplary process 1100 or method of determining an appropriate drive signal for driver 104 to vibrate conduits 103A-103B in a desired vibration mode as described above. The process 1100 begins at step 1101 in which a dynamic model generated from vibration measurement data is used to calculate the coefficients of a polynomial function that models the forces applied to the conduits 103A-103B from the drive signals. Once the coefficients of the polynomial function are determined, the coefficients of the inverse function may be determined in step 1102 using the coefficients of the force determined in step 1101. The drive command signal is added to a polynomial representing the inverse function in step 1103 in order to determine the appropriate drive command for the driver 104. Process 1100 ends after step 1103.

Summary of the invention

As described, the present invention relates to calibration of Coriolis flowmeters, and more particularly, to calibration of associated drive signals.

The Coriolis flowmeter includes at least one conduit, and the example Coriolis flowmeter shown in fig. 1 includes two conduits, such as conduits 103A and 103B. The conduit is vibrated by a drive signal applied to a driver secured to the conduit. The actuator is a physical structure that may include a magnet and a reaction coil. The drive signal 110 is in the form of a periodic wave, such as a sine wave, and is provided by the electronic gauge 20, see also fig. 1. The drive signal of the described embodiment is a sine wave with a frequency of 125 hertz (Hz), although other periodic wave shapes of the drive signal may also be used. Measurements of the material flowing through the flow meter, such as mass flow rate, mass density, and others, are derived from sensor signals emitted from the conduit. The measured value is determined from the frequency deviation and the phase deviation of the drive signal as the substance flows through the flowmeter.

Accurate measurement of the material flowing through the meter is necessary for the drive signal to be calibrated. However, there are inaccurate measurements due to structural variations in the conduit and in the drive through a single flow meter. The structural changes produce unwanted, non-linear responses, such as drive signal harmonics. The drive signal harmonics raise the noise floor and vibrate the catheter in an unexpected manner, which produces inaccurate measurements.

The described invention solves the problem of unwanted drive signal harmonics by a novel method of using the output a priori information for the drive signal. First, a Coriolis flowmeter is characterized by applying a test drive signal to its driver, which is a practical physical structure. The accelerometer then collects data about the vibrations produced in the flow tube by the test drive signal. This system can be characterized as a single input-single output system with a transfer function equivalent to the input-distributed output. The state space equations for a Coriolis flowmeter system can be written to include the inputs, outputs, and structural characteristics of each individual flowmeter. This state space equation can be written as:

y＝Cx+Df_α(r)，

where A, B, C and D are state space matrices forming coefficients representing each individual flowmeter structural parameter, f_A(r) is a polynomial function representing the drive signal, as shown in equations 1 and 2 above.

The conversion from a single input-single output system to a multiple input-single output system can be formed by constructing a plurality of inputs from the original signal as terms of a predetermined number of polynomials. E.g., a multi-input signal comprising high order parts is generated from a single signal, e.g. in sinusoidal form,

f_A(r)＝αsin(2πft)，

where α is a scalar, f is frequency, t is time, and the order of the polynomial must be predetermined. The multiple inputs to the system being produced by the number of terms of the desired polynomial, e.g.

f_A(r)＝αsin(2πft)+α²sin(2πft)²+α³sin(2πft)³+…+αⁿsin(2πft)ⁿ

Although the order of any polynomial may be chosen, for the purposes of the present invention, it may be determined that a fifth order polynomial is sufficient because the higher order portions have negligible effect on the overall system. Because the inputs characterized by the plurality of input signals and the output signal of the Coriolis flowmeter system are now known, the system can be characterized by its transfer function. The state space matrices a, B, C and D can be solved by converting the transfer function into its controllable canonical form. Similar techniques are well known to those skilled in the art and may be found in such references as the Lennart Lijing reference mentioned earlier.

Once the system is characterized by its transfer function, the state space matrices A, B, C and D are constructed into a controllable canonical form, as is well known to those skilled in the art. From a controllable canonical form, the coefficients of the B matrix are used to construct a signal compensator. This signal compensator is rewritten as follows:

y＝Cx+D(β₀+β₁r+β₂r²+β₃r³+β₃r⁴+β₃r⁵)，

where now the beta coefficients are represented by the coefficients of the B matrix in the previously mentioned controllable canonical form, r is still the input signal.

Once the β coefficient is determined, the drive signal is input into the system. The output produces a new set of data. The new output data is a curve fitted using a least squares algorithm, as is also well known to those skilled in the art. The least squares curve fit produces a polynomial of a predetermined order. Once the polynomial is generated, an inverse of the polynomial may be calculated and a non-test drive signal estimated for the inverse polynomial.

To illustrate, a test signal consisting of broadband noise is input to a Coriolis flowmeter. A second order system is predetermined, which is sufficient for an example. When writing the transfer function into a controllable canonical form, state space matrices a, B, C and D can be generated:

C＝[1 0]

D＝0

a drive signal consisting of a 125Hz sine wave with a signal-to-noise ratio (SNR) of 40 decibels (dB) was used in the system. The drive signal is arranged in the form of a polynomial function of the form:

f_A(r)＝r+0.5r²+0.3r³

where r is the drive signal as shown in equation 11. The coefficients of the signal are based on heuristic data of the actual flow meter output with nonlinear harmonic components and are used here as an example only. The above functions are applied to the state space configuration parameters of known Coriolis flowmeters as shown in equations 1 and 2. A Power Spectrum Display (PSD) representing the output data of the accelerometer reveals the resulting drive signal harmonics as shown in fig. 7. The output data is a curve fitted using a least squares algorithm in the form of a fifth order polynomial function. The least squares algorithm generates a polynomial function:

f_A(r)＝.9987＊r+.5002＊r²+.2998＊r³-.0003＊r⁴+0.0000＊r⁵

as shown in equation 8. Calculating the fitting curve f_AThe inverse polynomial function of (r). The inverse polynomial function is stored in a memory located in an electronic meter, such as electronic meter 20 in fig. 1. The inverse polynomial function is applied to the drive signal by evaluating the inverse polynomial function with the sampled values of the drive signal. For example, a sample of the drive signal is input to the inverse polynomial function, and the result is an output sample representing the compensated sample of the drive signal. The overall process results in a reduction in the amplitude of the drive signal harmonics, as shown by the PSD of fig. 8.

Previously, the drive signal harmonics were of sufficient amplitude to unexpectedly vibrate the Coriolis flow tube. While this novel approach as taught substantially reduces the amplitude of the drive signal harmonics at a point that is nearly negligible. Although the results may be different, the above example effectively reduces the drive signal harmonics by more than 20dB, and no harmonics by more than 0 dB.

Claims (24)

1. A method for calibrating a drive signal applied to a driver that causes the driver to oscillate at least one flow tube in a flow measurement device for measuring a characteristic of a substance flowing in the at least one flow tube, the method comprising the steps of:

vibrating the at least one flow tube with the driver;

measuring vibration of the at least one flow tube in response to vibrating the flow tubes; the method is characterized by comprising the following steps:

detecting physical characteristics of the apparatus and the driver from the measured vibration of the at least one flow tube; determining a drive signal for the driver based on the detection result of the physical characteristic, and

applying the determined drive signal to the driver to oscillate the at least one flow tube in the desired vibration mode.

2. The method of claim 1, wherein the flow measurement device is a flow meter and the method is used to calibrate a drive signal to be applied to a driver of the flow meter, the method characterized by the steps of:

applying a first signal to said driver to vibrate said at least one flow tube;

measuring vibration of the at least one flow tube and the driver in response to vibrating the at least one flow tube while the first signal is applied to the driver;

determining a physical vibration characteristic from said vibration measurements of said at least one flow tube while said first signal is applied to said driver, the physical vibration characteristic including any undesirable physical characteristics of said flow meter having said flow tube and said driver;

determining a correction factor for the determined physical vibration characteristic;

determining a drive signal to be applied to the driver using the determined physical vibration characteristic and the correction factor; and

applying the determined drive signal to the driver to oscillate the at least one flow tube in a desired vibration mode that compensates for the undesirable physical characteristic.

3. The method of claim 1, further comprising the steps of:

storing a measurement of the vibration of the at least one flow tube.

4. The method of claim 3, wherein said step of detecting said physical characteristic of said device further comprises the steps of:

combining the current vibration measurement with the stored vibration measurement to determine the physical characteristic.

5. The method of claim 1, further comprising the steps of: setting a reference voltage in a drive signal circuit in response to the determined drive signal to cause the drive signal circuit to generate the drive signal.

6. The method of claim 1, further comprising the steps of: the method for calibrating the drive signal is repeated periodically.

7. The method of claim 1, wherein said step of detecting physical characteristics of said driver and device comprises the steps of: simulating the dynamics of the driver and device from the measured vibrations.

8. The method of claim 1, further comprising the steps of: the drive circuit is altered to generate the drive signal.

9. The method of claim 1, wherein said step of determining said drive signal comprises the steps of:

calculating coefficients of a functional polynomial representing a relationship between the drive signal and a force applied to the at least one flow tube;

determining coefficients of an inverse function polynomial of the function representing the relationship between the drive signal and the force; and

adding a command signal of the drive signal to the inverse function to determine the drive signal.

10. An electronic meter for a flow measurement device for measuring a property of a substance, said device having at least one flow tube for receiving the substance, a driver for vibrating said at least one flow tube, a plurality of transducers for measuring the vibration of said at least one flow tube at points along said flow tube, said electronic meter including a drive circuit for applying a drive signal to said driver to cause said driver to oscillate said at least one flow tube, and a circuit for measuring the property of the substance flowing through said at least one flow tube, said electronic meter further comprising:

a first circuit for receiving signals output from said sensor and detecting physical characteristics of said device and said driver based on said measured vibration of said at least one flow tube; and

second circuitry responsive to receipt of the signal for determining a drive signal for causing the driver to oscillate the at least one flow tube in a desired vibration mode based on physical characteristics of the apparatus and the driver.

11. The electronic meter of claim 10, further comprising: a memory for storing vibration measurements of the at least one flow tube.

12. The electronic meter of claim 11, wherein the first circuit further comprises: circuitry for combining a current vibration measurement with the stored vibration measurement for use in determining the physical characteristic.

13. The electronic meter of claim 10, further comprising: a reference voltage provided in the drive signal circuit, the reference voltage being set to a level for generating the drive signal in response to determining the drive signal, to cause the drive signal circuit to generate the drive signal.

14. The electronic meter of claim 10, further comprising: a timing circuit for periodically repeating the calibration of the drive signal.

15. The electronic meter of claim 10, wherein the first circuit comprises: an analog circuit for simulating the dynamics of the device and driver from the measured vibrations.

16. The electronic meter of claim 10, wherein the second circuit comprises:

circuitry for calculating coefficients of a functional polynomial representing a relationship between the drive signal and a force applied to the at least one flow tube;

circuitry for determining coefficients of an inverse function polynomial of the function representing the relationship between the drive signal and the force; and

circuitry for adding a command signal of the current drive signal to the inverse function to determine the drive signal.

17. A product for calibrating a drive signal applied to a driver to cause the driver to oscillate at least one flow tube in a flow measurement device for measuring a property of a substance flowing through the at least one flow tube, the product comprising:

means for receiving a signal output from a sensor affixed to the at least one flow tube measuring vibration of the at least one flow tube,

means for detecting physical characteristics of the apparatus and driver based on the measured vibration of the at least one flow tube, an

Means for determining a drive signal that causes the driver to oscillate the at least one flow tube in a desired vibration mode based on physical characteristics of the apparatus and the driver.

18. The article of manufacture of claim 17, further comprising:

means for applying the drive signal to the driver to oscillate the at least one flow tube in a desired vibration mode.

19. The article of manufacture of claim 17, further comprising:

means for storing the vibration measurements of the at least one flow tube in a memory.

20. The article of manufacture of claim 19, wherein said means for detecting said physical characteristics of said device and driver further comprises:

means for instructing a processor to read said measurements from said memory and to combine the current vibration measurements with said stored vibration measurements for use in determining said physical characteristic.

21. The article of manufacture of claim 17, further comprising:

means for providing a reference voltage for a drive signal circuit to cause the drive signal circuit to generate the drive signal in response to the determined drive signal.

22. The article of manufacture of claim 17, further comprising:

means for periodically repeating the calibration of the drive signal.

23. The article of manufacture of claim 17, wherein the means for detecting the physical characteristics of the device and driver comprises:

means for simulating the dynamics of the device and driver from the measured vibrations.

24. The product of claim 17, wherein the means for determining the drive signal comprises:

means for calculating coefficients of a function polynomial representing a relationship between a drive signal and a force applied to the at least one flow tube, determining coefficients of an inverse function polynomial of the function representing the relationship between the drive signal and the force, and adding a command signal of the drive signal to the inverse function to determine the drive signal.