JP2014200143A - Driving circuit and driving method for piezoelectric actuator, and measuring instrument for characteristic frequency - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a driving circuit and driving method for piezoelectric actuator and measuring instrument for characteristic frequency, suitable for easy measurement of characteristic frequency of a mechanical system without need of a sensing system for the mechanical system.SOLUTION: The driving circuit 10 is configured to be driven under a coupled state with a vibrator 30 along with a piezoelectric actuator 20, and includes: a differentiator 11 that differentiates a terminal-to-terminal voltage ν of the piezoelectric actuator 20; an amplifier 12 that amplifies an output of the differentiator 11 to L times; an amplifier 13 that amplifies the terminal-to-terminal voltage ν to R times; an adder 14 that adds output voltages of the amplifiers 12 and 13; and a V/I converter 15 that converts L(dν/dt)+Rν which is an output voltage of the adder 14 into an electric current i corresponding to the magnitude and supplies the electric current i to the piezoelectric actuator 20.

Description

  The present invention relates to a technique for driving a piezoelectric actuator that transmits a force to a mechanical system.

Conventionally, there is a method of identifying the natural frequency of a mechanical system from a resonance frequency by periodically changing an input voltage ν of a piezoelectric actuator such as a piezoelectric actuator. There is also a method of performing the same thing with an input current in consideration of circuit equations.
Further, there is a method in which the input voltage ν of the piezoelectric actuator is generated by positive feedback of the mechanical system speed, self-excited vibration is generated, and the natural frequency is identified from the response frequency. There is also a method of performing the same thing with an input current in consideration of circuit equations.
For example, Non-Patent Document 1 discloses a measurement in which a forced vibration is mechanically applied to a test piece (mechanical system), a resonance frequency (natural frequency) is measured, and a Young's modulus (longitudinal elastic modulus) is calculated from the resonance frequency. Method (resonance method) is disclosed.

"IIC REVIEW / 2010/4. No.43 P30-34 (IHI Inspection and Measurement Co., Ltd.)"

  However, in each of the above prior arts, the displacement or speed of the mechanical system must be sensed by some method, and a sensing system for the mechanical system is required. Such a sensing system increases the size of the apparatus and requires troublesome work such as initial setting during measurement.

For example, when the optical lever method is used as a sensing technique, it is necessary to align the optical axis of the laser for the optical lever method. This optical axis alignment has a high degree of difficulty especially in observation in liquid where the laser is refracted. In addition, we have a hard time dealing with noise from laser light sources. Further, the presence of the optical lever mechanism prevents the entire apparatus from being downsized. For this reason, since the device cannot be made highly rigid, it is easy to pick up noise, making it difficult to increase the sensitivity and resolution of the sensing function.
The present invention pays attention to the above-mentioned problems, and a piezoelectric actuator drive circuit suitable for easily measuring the natural frequency of a mechanical system without a sensing system for the mechanical system, a piezoelectric actuator driving method, and An object is to provide a natural frequency measuring device.

  [Mode 1] In order to achieve the above object, a drive circuit for a piezoelectric actuator according to mode 1 is for a piezoelectric actuator that drives the piezoelectric actuator in a state coupled with the mechanical system together with a piezoelectric actuator that transmits force to the mechanical system. A drive circuit for supplying a drive current i proportional to the inter-terminal voltage to the piezoelectric actuator based on the inter-terminal voltage ν of the piezoelectric actuator;

With such a configuration, it is possible to supply a drive current i proportional to the terminal voltage ν of the piezoelectric actuator to the piezoelectric actuator. As a result, the piezoelectric actuator generates an inter-terminal voltage ν corresponding to the drive current i, and transmits a force proportional to the inter-terminal voltage ν to the mechanical system.
Here, the piezoelectric actuator includes all actuators whose dynamics follow the piezoelectric basic formula. The same applies to Form 5 below.

[Mode 2] Furthermore, the piezoelectric actuator drive circuit according to mode 2 supplies the piezoelectric actuator with a drive current i represented by the following expression (1), in contrast to the configuration of mode 1.
i = L (dν / dt) + Rν (1)
In the above equation (1), L and R are the piezoelectric actuators including the driving circuit for the piezoelectric actuator, where the driving current i is the natural frequency of the mechanical system that is the natural frequency including the rigidity effect of the piezoelectric actuator. The feedback gain is set so that the electric system as the drive system has a current value at which self-oscillation occurs.

  With such a configuration, the drive current i shown in the above equation (1) in which the feedback gains L and R are set so that the electric system self-oscillates at the natural frequency of the mechanical system is supplied to the piezoelectric actuator. It is possible. As a result, the piezoelectric actuator generates an inter-terminal voltage ν corresponding to the drive current i shown in the above equation (1), and transmits a force proportional to the inter-terminal voltage ν to the mechanical system.

  [Mode 3] Furthermore, the piezoelectric actuator drive circuit according to mode 3 is different from the configuration of mode 2 in that the first amplifying unit that amplifies the inter-terminal voltage ν R times and the differential that differentiates the inter-terminal voltage ν. , A second amplifying unit that amplifies the output voltage of the differentiating unit L times, and a voltage V / that converts the sum of the output voltage of the first amplifying unit and the output voltage of the second amplifying unit into a current. And an output current of the V / I converter is supplied to the piezoelectric actuator as the drive current i.

  With such a configuration, the inter-terminal voltage ν can be amplified R times by the first amplifying unit, the inter-terminal voltage ν can be differentiated by the differentiating unit, and the second amplification The differential unit can amplify the differential result of the differential unit by L times. Furthermore, the current supply unit converts the sum of the output voltage of the first amplification unit and the output voltage of the second amplification unit into a current by the V / I conversion unit. The current supply unit can supply the output current of the V / I conversion unit as a drive current i to the piezoelectric actuator.

[Embodiment 4] Furthermore, the piezoelectric actuator drive circuit of Embodiment 4 has the following equation (2), which is the circuit equation of the electric system, and the equation of motion of the mechanical system, for the configuration of Embodiment 2 or 3. The feedback gains L and R are determined so that the expression (3) has one negative real number and two real part positive conjugate complex numbers as eigenvalues.
dν / dt- {1 / (C p -d 33 2 K a -L)} Rν = - {d 33 K a / (C p -d 33 2 K a -L)} dx / dt ··· (2 )
^{m (d 2 x / dt 2} ) + c (dx / dt) + (k + K a) x = d 33 K a ν ··· (3)

In the above equations (2) and (3), x is the displacement of the mechanical system, m is the mass of the mechanical system, k is the spring constant of the mechanical system, c is the damping constant of the mechanical system, C _p is the capacitance of the piezoelectric actuator, d ₃₃ is the piezoelectric constant of the piezoelectric actuator, K _a is expressed as K _a = A / (s ^E l), A is the cross-sectional area of the piezoelectric actuator, s ^E is the elastic compliance of the piezoelectric actuator, and l is the polarization direction of the piezoelectric actuator Is the thickness.
With such a configuration, the feedback gains L and R are set so that the above equations (2) and (3) have one negative real number and two real part positive conjugate complex numbers as eigenvalues. In addition, the drive current i shown in the above equation (1) can be supplied to the piezoelectric actuator.

  [Mode 5] On the other hand, in order to achieve the above object, the method for driving a piezoelectric actuator according to mode 5 is a drive for driving the piezoelectric actuator in a state coupled with the mechanical system together with the piezoelectric actuator for transmitting force to the mechanical system. A method of driving a piezoelectric actuator using a circuit, comprising: supplying a driving current i proportional to the inter-terminal voltage ν to the piezoelectric actuator based on the inter-terminal voltage ν of the piezoelectric actuator. .

[Mode 6] In order to achieve the above object, the natural frequency measurement device according to mode 6 detects the piezoelectric actuator drive circuit according to any one of modes 1 to 4 and the inter-terminal voltage ν. A voltage detection unit; and a natural frequency detection unit that detects a natural frequency of the mechanical system based on the inter-terminal voltage ν detected by the voltage detection unit.
With such a configuration, the voltage detector can detect the voltage ν between the terminals of the piezoelectric actuator, and the natural vibration detector can detect the natural frequency of the mechanical system based on the detected voltage ν between the terminals. It is possible to detect.

  As described above, according to the present invention, the drive current i proportional to the inter-terminal voltage ν is supplied to the piezoelectric actuator based on the inter-terminal voltage ν of the piezoelectric actuator. This allows the mechanical system to self-excited with a force proportional to the voltage ν between the terminals, so it is possible to easily detect the natural frequency of the mechanical system from the time change of the voltage ν between the terminals at that time. is there. That is, it is possible to eliminate the need for a system that senses the displacement and speed of the mechanical system for measuring the natural frequency of the mechanical system.

It is a figure which shows an example of the mechanical system model of the coupled mechanical system, a piezoelectric actuator, and a drive circuit. It is a block diagram which shows an example of the dynamics of the whole system. It is a figure which shows a root locus in case of "K _a 'ψ = -2". It is a figure which shows a root locus at the time of "K _a 'ψ = -0.1". It is a block diagram which shows the structure of the natural frequency measuring device which concerns on this embodiment. It is a flowchart which shows an example of the process sequence of a natural frequency detection process. It is a figure which shows an example of the result of having calculated numerically the displacement and speed of a mechanical system, and the voltage between terminals of a piezoelectric actuator using a known parameter.

  Embodiments of a piezoelectric actuator drive circuit, a piezoelectric actuator drive method, and a natural frequency measuring device according to the present invention will be described below with reference to the drawings. 1 to 6 are diagrams showing an embodiment of a piezoelectric actuator drive circuit, a piezoelectric actuator drive method, and a natural frequency measuring device according to the present invention.

(Constitution)
First, the configuration of a piezoelectric actuator drive circuit (hereinafter simply referred to as a drive circuit) according to the present embodiment will be described.
This drive circuit is a circuit that drives a piezoelectric actuator that transmits force to the mechanical system. Here, the piezoelectric actuator includes all actuators whose dynamics follow the piezoelectric basic formula. As specific examples, there are various types of piezoelectric actuators such as an actuator that operates with a Coulomb force acting between electric charges and an actuator that uses the inverse piezoelectric effect of a piezoelectric element.

In the present embodiment, such a drive circuit operates together with a piezoelectric actuator in a coupled state with a mechanical system (for example, a vibrating body such as a cantilever) that is a transmission target of the force of the piezoelectric actuator.
Specifically, the coupled mechanical system, piezoelectric actuator, and drive circuit can be represented as a mechanical system model shown in FIG. 1 with the mechanical system as an equivalent model of a “spring-mass-damper” system. Here, FIG. 1 is a diagram illustrating an example of a mechanical system model of a coupled mechanical system, a piezoelectric actuator, and a drive circuit.

As shown in FIG. 1, the mechanical system model includes a piezoelectric actuator and a drive circuit for a mechanical system having an object of mass m, a damper having a damping constant c, and a spring having a spring constant k. And connected in parallel.
With this configuration, when a force f is applied to the mechanical system by the piezoelectric actuator, the displacement x (vibration) of the mechanical system due to the force f also acts on the piezoelectric actuator and the drive circuit.

Here, a circuit equation of a drive system (hereinafter referred to as an electric system) of a piezoelectric actuator including such a drive circuit is represented by the following expression (4).
_{dv / dt + {d 33 K} a / (C p -d 33 2 K a)} (dx / dt) = {1 / (C p -d 33 2 K a)} i ··· (4)
In the above equation (4), ν is the voltage between the terminals of the piezoelectric actuator, C _p is the capacitance of the piezoelectric actuator, and d ₃₃ is the piezoelectric constant of the piezoelectric actuator. Further, K _a is expressed by “K _a = A / (s ^E l)”, A is a sectional area of the piezoelectric actuator, s ^E is an elastic compliance of the piezoelectric actuator, and l is a thickness of the piezoelectric actuator in the polarization direction. is there.

Hereinafter, the derivation method of the above equation (4) will be described.
First, the piezoelectric equation (piezoelectric basic equation) is expressed by the following equations (5) and (6).
D = εE + d ₃₃ T (5)
S = d ₃₃ E + s ^E T (6)
In the above formulas (5) and (6), D is electrical displacement, ε is dielectric constant, E is electric field, T is stress, and S is strain.

When the cross-sectional area A of the piezoelectric actuator is applied to both sides of the above equation (5) and the length (thickness in the polarization direction) l of the piezoelectric actuator is applied to both sides of the above equation (6), the following equations (7) and (8) It can be expressed as
Q = C _p ν + d ₃₃ f (7)
x = d ₃₃ ν + (1 / K _a ) f (8)

If f is deleted from the above equation (7) using the above equation (8), the following equation (9) is obtained.
^{_{Q = (C p -d 33 2}} K a) ν + d 33 K a x ··· (9)
When the above equation (9) is differentiated by time and arranged, the electric system equation shown in the following equation (10) is obtained.
dv / dt = {1 / ( C p -d 33 2 K a)} i- {d 33 K a / (C p -d 33 2 K a)} (dx / dt) ··· (10)
That is, the above equation (4) is obtained by moving the second term on the right side of the above equation (10) to the left side.

On the other hand, the equation of motion of the mechanical system is as shown in the following equation (11).
^{m (d 2 x / dt 2} ) + c (dx / dt) + (k + K a) x = d 33 K a ν ··· (11)
Hereinafter, a method for deriving the above equation (11) will be described.
The formula when an external force is applied to the mechanical system by the piezoelectric actuator is the following formula (12).
m (d ² x / dt ² ) + c (dx / dt) + kx = −f (12)
Then, the above expression (11) is derived by substituting the above expression (8) into the above expression (12).

Next, in the present embodiment, the current i flowing through the piezoelectric actuator is given by the following equation (13) using the terminal voltage ν of the piezoelectric actuator.
i = L (dν / dt) + Rν (13)
In the above equation (13), L and R are feedback gains. Although details will be described later, the mechanical system self-oscillates by appropriately setting the feedback gains L and R. The oscillation frequency at that time substantially matches the natural frequency of the mechanical system.
Here, the right side of the above equation (13) can be easily obtained from the inter-terminal voltage ν of the piezoelectric actuator and its differential value, and there is no need to measure the displacement and speed of the mechanical system.

Next, when the above equation (13) is substituted into the above equation (4), the following equation (14) is obtained.
dν / dt- {1 / (C p -d 33 2 K a -L)} Rν = - {d 33 K a / (C p -d 33 2 K a -L)} dx / dt ··· (14 )
When the above equation (13) is changed to the above equation (14), the dynamics of the entire system including the mechanical system, the piezoelectric actuator, and the drive circuit is governed by the above equation (11) and the above equation (14). It will be.

Specifically, the dynamics of the entire system can be expressed as a block diagram shown in FIG. 2, for example. FIG. 2 is a block diagram showing an example of the dynamics of the entire system.
As shown in FIG. 2, in the electrical system 1, the voltage ν between the terminals of the piezoelectric actuator output from the transmission element 1a is converted into a force f in the transmission element 1i, and this force f is transferred to the transmission element 2 of the mechanical system. Entered.

The output of the transfer element 2 corresponding to the input force f (mechanical displacement x) is electricity by the interaction due to the coupling via a transmission element 1b and 1c as a current i _x whose magnitude is proportional to the speed of the mechanical system Input to system 1.
On the other hand, in the present embodiment, the current i shown in the above equation (13) is supplied to the piezoelectric actuator, so the differential value dν / dt of the terminal voltage ν is multiplied by L through the differentiating unit 1e and the multiplying unit 1f. The voltage L (dν / dt) is input to the adder 1h. Further, a voltage Rν obtained by multiplying the inter-terminal voltage ν by R times is input to the adder 1h via the multiplier 1g. The adder 1h adds the input L (dν / dt) and Rν. In addition, the voltage resulting from the addition is converted into a current i and output.

A current i _x which is input from the mechanical system via a transmission element 1b and 1c, a current is input from the adding unit 1h i (corresponding to current shown in the above equation (13)), an adder 1d in FIG. 2 as shown, the current i _x is subtracted from the current i. Then, the subtraction result _{(i d = i-i x} ) is input to the transfer element 1a. In this manner, the piezoelectric actuator is driven by the current i _{d formed} by the sum of the component proportional to the inter-terminal voltage ν of the piezoelectric actuator and the component proportional to the first derivative of the inter-terminal voltage ν. At this time, the mechanical system self-oscillates by appropriately setting the feedback gains L and R.

(L, R setting range)
Next, an appropriate setting range of the feedback gains L and R will be described.
First, the above formula (11) and the above formula (14) are made dimensionless. At this time, the representative time is a cycle “T = {m / (k + K _a )} ^1/2 ”, the representative length is the maximum displacement X of the piezoelectric actuator, and the representative voltage is the voltage V when the maximum displacement X is applied.
The dimensionless equations and dimensionless parameters at this time can be calculated as in the following formulas (15) to (20).

R '= {T / (C p -d 33 2 K a -L)} R ··· (17)
_{K a '= {d 33 K} a / (C p -d 33 2 K a -L)} (X / V) ··· (18)
γ = c / (m (k + K _a )) ^1/2 (19)
_{ψ = d 33 K a V /} ((k + K a) X) ··· (20)
In the above equations (15) and (16), “·” attached to the upper part of the parameter x represents the first derivative of the dimensionless time T ^* , and “··” represents the second derivative of the dimensionless time T ^*. . For example, for the parameter x, the first derivative of the dimensionless time T ^* is “dx ₁ / dT ^* ”, and the second derivative is “d ² x ₁ / dT ^{* 2} ”. In the following description, * representing a dimensionless quantity is omitted.

  When the above equations (15) and (16) are written in the form of “(d / dt) x = Bx” using a matrix, the following equation (21) is obtained.

Here, if the matrix B of the above equation (21) has one negative real number and two real part positive conjugate complex numbers as eigenvalues, self-excited oscillation occurs. Therefore, the matrix B is coordinate-transformed to obtain a characteristic equation. Then, using the fact that the characteristic equation does not depend on the coordinate transformation, the coefficient comparison of the characteristic equation obtained by the coordinate transformation is performed.
If the matrix B has one real number and two conjugate complex numbers as eigenvalues, the matrix B is converted into a matrix as shown in the following equation (22) by coordinate conversion.

Here, in the above equation (22), if “a> 0, c <0”, a negative real number and a real complex positive conjugate complex number are eigenvalues.
The characteristic equation of the matrix B and the characteristic equation of the matrix after conversion are as shown in the following equations (23) and (24), respectively.
s ³ + (− R ′ + γ) s ² + (1−R′γ + K _a ′ ψ) s−R ′ = 0 (23)
s ³ + (− 2a−c) s ² + (a ² + b ² + 2ac) s−c (a ² + b ² ) = 0
... (24)

From the above equations (23) and (24), conditional expressions shown in the following equations (25) to (27) can be derived by coefficient comparison.
-R '+ γ = -2a-c (25)
1-R′γ + K _a ′ ψ = a ² + b ² + 2ac (26)
−R ′ = − c (a ² + b ² ) (27)
From the above equations (25) to (27), conditions for satisfying “a> 0, c <0” are considered.
First, the condition that satisfies “c <0” is satisfied. From the above equation (27), the right side is always positive if “c <0”. For this purpose, “R ′ <0” must be satisfied. I must.

Next, when b and R ′ are deleted from the above formulas (25) to (27), c is arranged and solved, the following formulas (28) and (29) are obtained.
c ² + {(2γa + γ ² −K _a 'ψ) / (γ + 2a)} c + 1 = 0 (28)

In order for c to be a negative real number, one item of the above formula (29) must be negative and the inside of the root of two items must be positive. Therefore, an inequality including a is obtained as the following expression (30).
(2γa + γ ² −K _a ′ ψ) / (γ + 2a)> 2 (30)
When the above equation (30) is further arranged by a, the following equation (31) is obtained.
a> (2γ−γ ² + K _a ′ ψ) / (2 (γ−2)) (31)

From the above equation (31), for a> 0, the following equation (32) must be established.
(2γ−γ ² + K _a ′ ψ) / (2 (γ−2))> 0 (32)
Considering that the attenuation coefficient γ is a constant in the range of “0 <γ <1”, in order to satisfy “a> 0”, the inequality shown in the following equation (33) is a condition.
-2γ + γ ² > K _a 'ψ (33)
Since the value of K _a 'is the variable by a differential feedback gain L, consider the setting range of L for satisfying the above equation (33).

Since “−2γ + γ ² <0”, the following expression (34) is established.
^{_{K a 'ψ = d 33 2}} K a 2 / {(C p -d 33 2 K a -L) (k + K a)} <- 2γ + γ 2 <0 ··· (34)
The condition of L from the above equation (34) is the following equation (35).
_{^{C p -d 33 2 K a <}} L <-d 33 2 K a 2 / {(- 2γ + γ 2) (k + K a)} + C p -d 33 2 K a ··· (35)

From the above equation (35), the allowable range of L is determined by the size of the following equation (36).
_{^{d 33 2 K a 2 / {}} (- 2γ + γ 2) (k + K a)} ··· (36)
Since the value that can be changed in the above equation (36) is “K _a = A / (s ^E l)”, the ratio of the length (the thickness in the polarization direction) 1 of the piezoelectric actuator to the cross-sectional area A is important. That is, if the cross-sectional area A of the piezoelectric actuator is increased as much as possible and the thickness l is decreased, the setting range of L can be widened.

Also, consider b, which is the size of the imaginary part of the eigenvalue. If c is deleted from the above equations (35) and (36) and b ² is noted, the following equation (37) can be written.
b ² = {a (3a−2R ′ + 2γ) −R′γ} + 1 + K _a ′ ψ (37)
Since “a> 0, R ′ <0, γ> 0”, the inside of the braces of the above formula (37) is always positive, and for any “a> 0”, “1 + K _a 'ψ> “0” is a sufficient condition for “b ² > 0, that is, always has a real root of a complex number”. Furthermore, in other words, since “a> 0” when “K _a 'ψ <−2γ + γ ² ”, “−1 <K _a ' ψ <−2γ + γ ² ” has a real complex positive conjugate complex number. It is a sufficient condition for.

Here, FIG. 3 is a diagram illustrating a root locus when “K _a ′ ψ = −2”. FIG. 4 is a diagram showing the root locus when “K _a 'ψ = −0.1”. 3 and 4, the horizontal axis is the real axis, and the vertical axis is the imaginary axis.
That is, the root locus when “K _a 'ψ <−1” is as shown in FIG. On the other hand, the root locus when “−1 <K _a 'ψ <−2γ + γ ² ” is as shown in FIG.

In the case of “K _a 'ψ <−1”, as shown in FIG. 3, it is in a buckled state while the gain is small, and a feedback gain of a certain level or more is required for self-oscillation. In other words, focusing on the value of the imaginary axis, as shown in FIG. 4, in the case of “−1 <K _a 'ψ <−2γ + γ ² ”, oscillation occurs at a frequency close to the natural frequency with a small feedback gain R ′. I understand what I can do. Therefore, for measurement, it is desirable to set L so as to take a range of “−1 <K _a 'ψ <−2γ + γ ² ”. Further, by setting an appropriate L, an appropriate R can be obtained from the above formulas (15), (17) and the like.

(Configuration of natural frequency measuring device)
Next, based on FIG. 5, the structure of the natural frequency measuring device to which the drive circuit equivalent to the said structure is applied is demonstrated.
Here, FIG. 5 is a block diagram showing a configuration of the natural frequency measurement device according to the present embodiment.
As shown in FIG. 5, the natural frequency measuring device 100 includes a drive circuit 10, a piezoelectric actuator 20, a vibrating body 30, a voltmeter 40, and a natural frequency detecting unit 50. . The drive circuit 10 is driven while being coupled to the vibrating body 30 together with the piezoelectric actuator 20.

The drive circuit 10 includes a differentiator 11 (corresponding to the differentiating unit 1e), amplifiers 12 and 13 (corresponding to the multiplying units 1f and 1g), an adder 14 (corresponding to the adding unit 1h), and a V / I converter 15 (Corresponding to the adding unit 1h).
The differentiator 11 time-differentiates the inter-terminal voltage ν of the piezoelectric actuator and outputs a differential value dν / dt to the amplifier 12.

The amplifier 12 amplifies dν / dt input from the differentiator 11 by L times. Then, the amplified voltage L (dν / dt) amplified by L times is output to the adder 14. This feedback gain L is set in advance to a value that takes a range of “−1 <K _a 'ψ <−2γ + γ ² ”.
The amplifier 13 amplifies the terminal voltage ν of the piezoelectric actuator R times. Then, the amplified voltage Rν amplified by R times is output to the adder 14. This feedback gain R is an appropriate value set based on an appropriate L set in advance.

The adder 14 adds the input L (dν / dt) and Rν. Then, the voltage “L (dν / dt) + Rν” as a result of the addition is output to the V / I converter 15.
The V / I converter 15 converts the input voltage “L (dν / dt) + Rν” into a current i proportional to the voltage “L (dν / dt) + Rν”. Then, this current i is output to the piezoelectric actuator 20. At this time, the piezoelectric actuator 20, the current i _x corresponding to the displacement x of the vibration member 30 shown by a broken line in FIG. 2 is input. Therefore, in practice, the current i _d obtained by subtracting the current i _x from the current i which is outputted from the V / I converter 15 is input to the piezoelectric actuator 20.

In this embodiment, the piezoelectric actuator 20 is composed of a piezo actuator. Such a piezoelectric actuator can use, for example, titanic acid / zirconic acid / lead (PZT) as a piezoelectric element.
The piezoelectric actuator 20 applies a force proportional to the terminal voltage ν, that is, a force f proportional to the current i _d to the vibrating body 30 in response to the supply of the current i _d from the drive circuit 10.

The vibrating body 30 is a measurement target of the natural frequency, and corresponds to, for example, a thing used as a probe such as a cantilever or a structure such as a building. In the present embodiment, the vibrating body 30 is a probe used in, for example, an AFM (Atomic Force Microscope).
In addition, the natural frequency measuring device 100, when the vibration body 30 that is a measurement target of the natural frequency is fixed like a probe (when the measurement target does not change) as in the present embodiment, the vibration body 30. It is set as the structure containing.

  On the other hand, when the measurement object is an arbitrary structure (when the measurement object changes), or when the object to be measured is required such as a building, the natural frequency measuring device 100 is used. The configuration does not include the vibrating body 30. In this case, for example, the force f of the piezoelectric actuator 20 is brought into contact with the measurement target to transmit the force f. In addition, when an arbitrary structure is a measurement target, feedback gains L and R that are gains of the amplifiers 12 and 13 can be tuned.

When the force f is applied from the piezoelectric actuator 20, the vibrating body 30 is displaced by a displacement amount x corresponding to the magnitude of the force f. In the present embodiment, since the feedback gains L and R are set to appropriate values, the vibrating body 30 eventually self-vibrates. Further, the displacement of the vibrating body 30 also acts on the piezoelectric actuator 20 and the drive circuit 10.
The voltmeter 40 measures the inter-terminal voltage ν of the piezoelectric actuator, and outputs the measured inter-terminal voltage ν to the natural frequency detector 50.

The natural frequency detection unit 50 detects the natural frequency (frequency) based on the time change of the inter-terminal voltage ν input from the voltmeter 40.
Each component of the drive circuit 10 and the natural frequency detection unit 50 may be configured only by hardware, may be configured only by software, or may be configured by a combination of hardware and software. May be.

In addition, the natural frequency measuring device 100 includes a computer system necessary for executing software when at least a part of the functions is realized on software.
Specifically, as a computer system, a CPU (Central Processing Unit) responsible for various controls and arithmetic processing, a RAM (Random Access Memory) responsible for work memory, and a dedicated program for realizing some of the above functions And a ROM (Read Only Memory) for storing data necessary for program execution and a data transmission bus for transmitting data to each component.

In the present embodiment, each function of the natural frequency detection unit 50 is configured to be realized by software. Therefore, the natural frequency measuring device 100 includes a computer system.
In the present embodiment, the voltmeter 40 performs A / D conversion on the measured analog inter-terminal voltage ν and inputs the analog voltage ν to the natural frequency detection unit 50 as a digital voltage value.
In the present embodiment, the amplifiers 12 and 13 may include a variable amplifier, and the feedback gains L and R may be adjusted to arbitrary values.

(Natural frequency detection processing)
Next, the processing procedure of the natural frequency detection process in the natural frequency detection unit 50 will be described with reference to FIG. FIG. 6 is a flowchart illustrating an example of a processing procedure of the natural frequency detection process. Note that the process of FIG. 6 is repeatedly executed at a preset cycle.
When the program stored in the ROM is executed by the CPU and the natural frequency detection process is started, first, as shown in FIG. 6, the process proceeds to step S100.
In step S <b> 100, the natural frequency detection unit 50 acquires the terminal voltage ν of the piezoelectric actuator 20 input from the voltmeter 40. Thereafter, the process proceeds to step S102.

  In step S102, the natural frequency detection unit 50 compares the inter-terminal voltage ν acquired in step S100 with a preset voltage threshold value. Then, it is determined whether or not the acquired inter-terminal voltage ν is equal to or higher than a voltage threshold value. Thereby, when it determines with the voltage ν between terminals being more than a voltage threshold value (Yes), it determines with the self-excited vibration having generate | occur | produced. Thereafter, the acquired inter-terminal voltage ν is stored in a time series in a memory such as a RAM (not shown), and a count value (a preset count variable value) is incremented by 1, and the process proceeds to step S104. On the other hand, when it is determined that the terminal voltage ν is less than the voltage threshold (No), it is determined that no self-excited vibration has occurred. Thereafter, the count value is cleared to the initial value and the inter-terminal voltage ν stored in the memory is erased, and the process proceeds to step S100.

When the process proceeds to step S104, the natural frequency detection unit 50 determines whether or not the count value is equal to or greater than a preset time threshold value. When it is determined that the count value is equal to or greater than the preset time threshold value (Yes), the process proceeds to step S106, and when it is determined that the count value is not (No), the series of processing ends.
When the process proceeds to step S106, the natural frequency detection unit 50 detects the natural frequency (frequency) based on the time change of the inter-terminal voltage ν stored in the memory. Thereafter, the series of processing is terminated. In the present embodiment, the detected natural frequency is stored in a memory and displayed on a display device (not shown).

(Operation)
Next, operation | movement of the natural frequency measuring device 100 of this embodiment is demonstrated.
When the power switch of each device constituting the natural frequency measuring device 100 is turned on, the voltage ν between the terminals of the piezoelectric actuator 20 is input to the differentiator 11, the amplifier 13 and the voltmeter 40, respectively. As a result, the differentiator 11 differentiates the input inter-terminal voltage ν and outputs the differentiated voltage dν / dt to the amplifier 12. The amplifier 12 amplifies the input voltage dν / dt to L times, and outputs the amplified voltage L (dν / dt) to the adder 14.

On the other hand, the amplifier 13 amplifies the inputted inter-terminal voltage ν R times, and outputs the amplified voltage Rν to the adder 14.
The adder 14 adds the input voltage L (dν / dt) and the voltage Rν, and outputs a voltage “L (dν / dt) + Rν” as a result of the addition to the V / I converter 15.
The V / I converter 15 converts the input voltage “L (dν / dt) + Rν” into a current i having a magnitude proportional to the voltage “L (dν / dt) + Rν”. Then, the converted current i is output to the piezoelectric actuator 20. In this case, current i, the current i _x corresponding to the displacement x of the vibrating body 30 from the piezoelectric actuator 20, is supplied to the piezoelectric actuator 20 as "i _d = i-i _x".

Thus, the piezoelectric actuator 20, a force f which is proportional to the terminal voltage ν corresponding to the input current i _d, give to the vibrating body 30.
In this way, a feedback loop is formed in which the voltage ν between the terminals of the piezoelectric actuator 20 is positively fed back and a current i (currently, current i _d ) proportional to the voltage ν between the terminals is supplied to the piezoelectric actuator 20. .
On the other hand, the voltmeter 40 measures the inter-terminal voltage ν of the piezoelectric actuator 20 and inputs the measured inter-terminal voltage ν to the natural frequency detector 50.

  The natural frequency detection unit 50 acquires the inter-terminal voltage ν input from the voltmeter 40, and accumulates the acquired inter-terminal voltage ν in the memory (step S100). Further, the acquired inter-terminal voltage ν is compared with a preset voltage threshold value, and it is determined whether or not the acquired inter-terminal voltage ν is equal to or higher than the voltage threshold value (step S102). If the natural frequency detection unit 50 determines that the inter-terminal voltage ν is equal to or higher than the voltage threshold based on this determination, it determines that self-excited vibration has occurred. Further, the natural frequency detection unit 50 adds 1 to the count value, and stores the acquired inter-terminal voltage ν in the memory in time series (Yes in step S102). On the other hand, if it is determined that the inter-terminal voltage ν is less than the voltage threshold, it is determined that no self-excited vibration has occurred. Further, the natural frequency detection unit 50 clears the count value and erases the inter-terminal voltage ν stored in the memory (No in step S102).

  If it is determined that the self-excited vibration has occurred, the natural frequency detection unit 50 next determines whether or not the count value is equal to or greater than the time threshold (step S104). When the natural frequency detection unit 50 determines that the count value is equal to or greater than the time threshold value based on this determination (Yes in step S104), the natural frequency detection unit 50 determines the natural frequency of the vibrating body 30 based on the time change of the inter-terminal voltage ν accumulated in the memory. The frequency is detected (step S106). The detected natural frequency is stored in a memory and displayed on a display device (not shown).

  As described above, in the piezoelectric actuator drive circuit 10 and the natural frequency measuring device 100 according to the present embodiment, the component proportional to the terminal voltage ν of the piezoelectric actuator 20 and the first derivative of the terminal voltage ν are proportional. A drive current i represented by the sum of the components can be supplied to the electrostatic actuator 20. At this time, the feedback gains L and R for generating the drive current i proportional to the inter-terminal voltage ν are set to values that satisfy the condition for self-oscillation of the mechanical system (vibrating body 30).

As a result, in the above-described configuration in which the electrical system (the drive circuit 10 and the piezoelectric actuator 20) and the mechanical system (vibrating body 30) are coupled, the natural frequencies of the two are made equal to each other at the natural frequency of the mechanical system. Can be self-oscillated.
Therefore, the natural frequency of the vibrating body 30 can be detected only by measuring the voltage ν between the terminals of the piezoelectric actuator 20. That is, the natural frequency of the mechanical system can be easily measured without a sensing system for sensing the displacement and speed of the mechanical system.

Here, in the above-described embodiment, the differentiator 1e and the differentiator 11 correspond to the differentiator, the multiplier 1g and the amplifier 13 correspond to the first amplifier, and the multiplier 1f and the amplifier 12 correspond to the second amplification. Corresponding to the part.
In the embodiment, the adder 1h, the adder 14, and the V / I converter 15 correspond to the V / I converter.
Moreover, in the said embodiment, the voltmeter 40 respond | corresponds to a voltage detection part, and the natural frequency detection part 50 respond | corresponds to a natural frequency detection part.

Next, an embodiment to which the piezoelectric actuator driving circuit and the piezoelectric actuator driving method according to the present invention are applied will be described with reference to FIG. FIG. 7 is a diagram illustrating an example of a result of numerical calculation of displacement and vibration speed of a mechanical system and voltage between terminals of a piezoelectric actuator using known parameters.
Specifically, in this example, the voltage between the terminals of the piezoelectric actuator and the displacement and speed of the mechanical system were obtained by numerical calculation using the parameter values shown in the following equations (38) to (46).

d ₃₃ = 4.72 × 10 ⁻¹⁰ [m / V] (38)
C _p = 6.91 × 10 ⁻⁹ [F] (39)
K _a = 2.2 × 10 ⁶ [N / m] (40)
T = 2π / 260 [1 / s] (41)
m = 0.00485 [kg] (42)
k = 2.83 × 10 ⁻⁶ [N / m] (43)
γ = 0.0063 (44)
L = 6.9101 × 10 ⁻⁸ [H] (45)
R = 0.65 × 10 ⁻¹⁰ [Ω] (46)

  The calculation results using the parameter values are as shown in FIG. In FIG. 7, the horizontal axis is the dimensionless time axis, the vertical axis is the axis corresponding to each dimensionless value, ○ in FIG. 7 is the terminal voltage, □ is the displacement, and x is the speed. is there. In the numerical calculation, initial values of displacement, speed, and voltage between terminals were set to displacement 0.5, speed 0, and voltage between terminals 0, respectively.

As shown in FIG. 7, the displacement, speed, and voltage between terminals gradually increase in amplitude as the dimensionless time increases. However, as shown in FIG. 7, the frequency (frequency) of the voltage between the terminals is different in phase with respect to the frequency of displacement or speed (frequency corresponding to the natural frequency of the mechanical system), but the same natural vibration. You can see that it is a number.
Based on the above, it is possible to detect the natural frequency of a mechanical system just as in the past by simply measuring the voltage between terminals using a voltmeter or the like without detecting displacement or speed using a mechanical sensing system. I understand what I can do.

(Modification)
In the above embodiment, the terminal voltage ν is differentiated and the differentiation result is amplified by L times, while the terminal voltage ν is amplified by R times, and these amplification results are added together. It was set as the structure converted into an electric current. That is, in the above-described embodiment, the terminal voltage ν is differentiated and amplified. However, the present invention is not limited to this structure. For example, another configuration may be employed such that the inter-terminal voltage ν is first converted into a current by a V / I converter, and the converted current is differentiated or amplified to generate the current i.

The above embodiments are preferable specific examples of the present invention, and various technically preferable limitations are given. However, the scope of the present invention is described in particular in the above description to limit the present invention. As long as there is no, it is not restricted to these forms. In the drawings used in the above description, for convenience of illustration, the vertical and horizontal scales of members or parts are schematic views different from actual ones.
Further, the present invention is not limited to the above-described embodiment, and modifications, improvements, and the like within the scope that can achieve the object of the present invention are included in the present invention.

  Since the present invention can eliminate the need for a sensing system that detects displacement and speed of a mechanical system, the apparatus can be miniaturized. Therefore, it is possible to reduce the size and weight of the device by making it portable, for example, when measuring the natural frequency of a measurement object that can not be measured unless it goes to the place where it exists, such as a building such as a bridge or a tunnel. To help. In addition, by measuring the natural frequency, it is possible to obtain various information such as the degradation state of the measurement target (appears as a change in the natural frequency). For example, the degradation state of structures, etc. It is also possible to apply as a device for detecting deterioration or the like.

  DESCRIPTION OF SYMBOLS 100 ... Natural frequency measuring device, 1 ... Electric system, 1a-1d, 1i ... Transmission element, 1e ... Differentiation part, 1f, 1g ... Multiplication part, 1h ... Addition part, 10 ... Drive circuit, 11 ... Differentiator, 12 , 13 ... Amplifier, 14 ... Adder, 15 ... V / I converter, 20 ... Piezoelectric actuator, 30 ... Vibrating body, 40 ... Voltmeter, 50 ... Natural frequency detector

Claims (6)

A piezoelectric actuator drive circuit for driving the piezoelectric actuator in a state coupled with the mechanical system together with the piezoelectric actuator for transmitting force to the mechanical system,
A piezoelectric actuator drive circuit, wherein a drive current i proportional to the inter-terminal voltage ν is supplied to the piezoelectric actuator based on the inter-terminal voltage ν of the piezoelectric actuator. The drive circuit for a piezoelectric actuator according to claim 1, wherein a drive current i represented by the following formula (1) is supplied to the piezoelectric actuator.
i = L (dν / dt) + Rν (1)
In the above equation (1), L and R are the piezoelectric actuators including the driving circuit for the piezoelectric actuator, where the driving current i is the natural frequency of the mechanical system that is the natural frequency including the rigidity effect of the piezoelectric actuator. The feedback gain is set so that the electric system as the drive system has a current value at which self-oscillation occurs. A first amplifier for amplifying the inter-terminal voltage ν by R times;
A differentiating unit for differentiating the terminal voltage ν;
A second amplifying unit for amplifying the output voltage of the differentiating unit L times;
A V / I converter that converts the sum of the output voltage of the first amplifier and the output voltage of the second amplifier into a current, and
The piezoelectric actuator drive circuit according to claim 2, wherein an output current of the V / I converter is supplied to the piezoelectric actuator as the drive current i. The following equation (2) that is the circuit equation of the electric system and the following equation (3) that is the equation of motion of the mechanical system are, as eigenvalues, one negative real number, two real-part positive conjugate complex numbers, and The drive circuit for a piezoelectric actuator according to claim 2 or 3, wherein the feedback gains L and R are set so as to have the following.
dν / dt- {1 / (C p -d 33 2 K a -L)} Rν = - {d 33 K a / (C p -d 33 2 K a -L)} dx / dt ··· (2 )
^{m (d 2 x / dt 2} ) + c (dx / dt) + (k + K a) x = d 33 K a ν
... (3)
In the above equations (2) and (3), x is the displacement of the mechanical system, m is the mass of the mechanical system, k is the spring constant of the mechanical system, c is the damping constant of the mechanical system, C _p is the capacitance of the piezoelectric actuator, d ₃₃ is the piezoelectric constant of the piezoelectric actuator, K _a is expressed as K _a = A / (s ^E l), A is the cross-sectional area of the piezoelectric actuator, s ^E is the elastic compliance of the piezoelectric actuator, and l is the polarization direction of the piezoelectric actuator Is the thickness. A method for driving a piezoelectric actuator using a drive circuit for driving the piezoelectric actuator in a state of being coupled to the mechanical system together with the piezoelectric actuator for transmitting force to the mechanical system,
The method for driving a piezoelectric actuator, comprising: a step of supplying a driving current i proportional to the voltage ν between the terminals to the piezoelectric actuator based on the voltage ν between the terminals of the piezoelectric actuator. A drive circuit for a piezoelectric actuator according to any one of claims 1 to 4,
A voltage detector for detecting the inter-terminal voltage ν;
And a natural frequency detector for detecting a natural frequency of the mechanical system based on the inter-terminal voltage ν detected by the voltage detector.

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