JP3318689B2 - Driving method of piezoelectric ceramic actuator - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a piezoelectric ceramic actuator for converting electric energy into mechanical energy such as displacement or force, and more particularly, to a driving method of a piezoelectric ceramic actuator for reducing hysteresis generated at the time of the displacement. .

[0002]

2. Description of the Related Art Conventionally, an actuator is used in a precision positioning device such as an XY table. As an ordinary actuator, an electromagnetic actuator including a voice coil motor, a pulse motor, and the like is generally used.

On the other hand, in recent years, positioning accuracy, response speed,
In order to respond to demands for improvements in characteristics such as power consumption,
The adoption of a piezoelectric ceramic actuator that is superior in characteristics to an electromagnetic actuator is being studied.

[0004] This piezoelectric ceramic actuator is a device utilizing the electric-field-induced strain of piezoelectric ceramics, and generally has a structure in which electrodes and ceramics are laminated. In addition, the piezoelectric ceramic is a polycrystalline material obtained by subjecting a ceramic fine powder of a piezoelectric material to molding and sintering, and then performing a polarization process. Therefore, rotation of a crystal axis (referred to as domain rotation) occurs by applying a voltage. . For this reason, a large strain is generated in the piezoelectric ceramics, and the displacement-voltage characteristic becomes non-linear under the influence of the rotation of the crystal axis, showing a large hysteresis.

However, the piezoelectric ceramic actuator is very suitable due to its minute displacement characteristics, particularly for applications where positioning is performed with high accuracy.

[0006]

In the case of the above-described piezoelectric ceramic actuator, when driven by a voltage, it is difficult to perform precise displacement control due to the influence of hysteresis.

Therefore, in practice, the piezoelectric ceramic actuator is driven to the target position by detecting the current position using a position detecting sensor and calculating the deviation from the target position. To drive this deviation amount, it is necessary to use a feedback control circuit.

However, if a dedicated feedback control circuit is used to drive the actuator by the amount of the deviation, the cost of the entire piezoelectric ceramic actuator driving device increases.

On the other hand, it has been proposed to employ a charge driving method as a driving method of a piezoelectric ceramic actuator having no hysteresis. This charge amount driving method is effective for driving by pulse or AC,
There is a disadvantage that stable control cannot be obtained with DC drive.

Further, even when a LiNbO ₃ piezoelectric single crystal is used as the piezoelectric material, a piezoelectric actuator having no hysteresis can be obtained without causing domain rotation.

However, in this case, the piezoelectric constant of the LiNbO ₃ piezoelectric single crystal is one order of magnitude smaller than that of the piezoelectric ceramic actuator, and therefore, there is a disadvantage that the amount of displacement of the piezoelectric actuator becomes too small.

SUMMARY OF THE INVENTION The present invention has been made to solve such a problem, and a technical problem of the present invention is to provide a method of driving a piezoelectric ceramic actuator capable of performing DC driving and reducing hysteresis of displacement-voltage characteristics. To provide.

[0013]

According to the present invention, there is provided a method of applying a DC voltage to a piezoelectric ceramic actuator to generate mechanical energy, and obtaining a displacement of the piezoelectric ceramic actuator by the mechanical energy.
A method for driving a piezoelectric ceramic actuator is provided in which nonlinear amplification of an input voltage is performed with reference to the nonlinearity of displacement with respect to a DC voltage, and an output voltage obtained as a result of the nonlinear amplification is applied to the piezoelectric ceramic actuator as a DC voltage. Can be

[0014]

Generally, a piezoelectric ceramic actuator exhibits a non-linear displacement with respect to a DC input voltage. Therefore, in the present invention, the nonlinear drive voltage is combined with the input voltage, and then the piezoelectric ceramic actuator is driven with the nonlinear output voltage, so that the displacement of the piezoelectric ceramic actuator is linear or pseudo-linear with respect to the input voltage. To be able to.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The driving method of a piezoelectric ceramic actuator according to the present invention will be described in detail with reference to the drawings.

First, the outline of the driving method of the present invention will be briefly described. In this driving method, mechanical energy is generated by applying a DC voltage, and the input voltage is nonlinearly amplified so that the amount of displacement of the piezoelectric ceramic actuator that displaces minutely becomes linear with respect to the input voltage. The non-linear output voltage obtained by the non-linear amplification is applied to the piezoelectric ceramic actuator. Thereby, the piezoelectric ceramic actuator can be driven in a state where the hysteresis is reduced.

FIG. 1 is a flowchart showing the basic operation of this driving method. In this driving method,
First, when an input voltage is applied (step S1), a nonlinear amplifier provided in a power supply circuit or the like performs nonlinear voltage amplification on the input voltage (step S2). As a result, a non-linear output voltage is obtained (step S3). Therefore,
Thereafter, the piezoelectric ceramic actuator is driven according to the non-linear output voltage (step S4). That is, this driving method is characterized by performing nonlinear amplification.

Next, the driving method of the piezoelectric ceramic actuator of the present invention will be specifically described with reference to several embodiments.

[0019] In the non-linear increase width is according to the driving method of (Example 1) Example 1, as an initial stage, the measured nonlinear displacement amount [delta] ₁ of the piezoelectric ceramic actuator with respect to the input voltage V _1, the non-linear displacement [delta] ₁ Equation 18

(Equation 18) Is approximated by a linear n-th order equation relating to the input voltage V ₁ , and a, b, c,..., N, which are intrinsic parameters of the ceramic actuator, are determined by the least square method.

[0020] Also, as a function of the input voltages V ₁ and output voltage V ₂ for a linear displacement of the piezoelectric actuator relative to the input voltages V _1, Formula 19 the output voltage V ₂ at the time of the booster

[Equation 19] Indicated by Further, where the input of the maximum output voltage when the voltage V ₁ is a maximum value V _1MAX as V _2MAX, number 20 formula the output voltage V ₂ at the time of buck

(Equation 20) Indicated by Subsequently, the displacement amount δ ₂ of the piezoelectric ceramic actuator is calculated using the output voltage V ₂ as shown in Equation 21.

(Equation 21) Expressed by Thereafter, Formula 19 and number 20 Expressions and were placed into each of several 21 Formula, and the number 22 Formula synthesis type of displacement [delta] ₂ at the time of each organized boosted by V ₁

(Equation 22) And the combined equation of the displacement amount δ ₂ at the time of step-down is expressed by Equation 23.

(Equation 23) Get as. Next, the intrinsic parameters a, b, c, of the piezoelectric ceramic actuator obtained by the above-mentioned least square method are described.
.., に are determined so that the second-order and higher-order polynomials related to Equations 22 and 23 are approximated by a series of pseudo-linear functions. Here, if the second and subsequent polynomials of the input voltage V ₁ in Equations 22 and 23 are equivalent by a pseudo-linear function, the displacement δ ₂ of the piezoelectric ceramic actuator is linear with respect to the input voltage V ₁ . Become. Therefore, the intrinsic parameters a, b, c,
Using the values of..., N, the functions f ₂ (•), f ₃ (•),.
The gains α, β, γ, and nonlinear gain of the nonlinear amplification are set so that the value of f _n (·) becomes equal to the coefficient of the series term of the pseudo-linear function.
.., Ξ may be determined.

FIG. 2 shows the results of actual measurement of the nonlinear displacement δ ₁ of the piezoelectric ceramic actuator with respect to the input voltage V ₁ in the initial stage of this driving method. From Figure 2, the piezoceramic actuator is seen to exhibit a non-linear displacement with respect to the input voltage V _1. Here, counterclockwise hysteresis occurs. Therefore, next to synthesize nonlinear driving voltage to the input voltage V _1.

[0022] Figure 3 shows the result of measurement of output voltage V ₂ to the input voltages V ₁ according to the intermediate stage of the driving method. From Figure 3, the output voltage V ₂ is seen to exhibit a non-linear displacement with respect to the input voltage V _1. Here, clockwise hysteresis occurs. Further, this nonlinear output voltage V ₂ is applied to the piezoelectric ceramic actuator.

FIG. 4 shows the measured results of the displacement δ ₂ of the piezoelectric ceramic actuator with respect to the input voltage V ₁ in the latter stage of the driving method. From FIG.
By applying a non-linear output voltage V ₂ as shown in FIG. 3 in the piezoelectric ceramic actuator, the piezoelectric ceramic actuator is seen that the linear displacement amount [delta] ₂ with respect to the input voltage V ₁ is obtained.

Hereinafter, a linear drive device employing the drive method of the present invention will be described together with a method of manufacturing the components thereof. First, as a piezoelectric ceramic actuator,
A multi-layer piezoelectric actuator of the type utilizing electric field induced strain in the laminating direction by laminating a plurality of piezoelectric ceramic thin plates each having a thickness of 100 [μm] and electrodes with a length of 18 [mm]. Was manufactured.

On the other hand, as another piezoelectric ceramic actuator, bending deformation of a plate is used by bonding a thin metal plate in a sandwich shape with two piezoelectric ceramic plates having a thickness of 250 [μm] and a metallized surface. A type of piezoelectric bimorph actuator was manufactured.

Next, with respect to the piezoelectric ceramic actuators of these two specifications, the dimensions [mm] and the displacement [μ
m] / rated voltage [V], and the difference between the amount of displacement between the step-up and the step-down when a voltage of 50% of the rated voltage generated in the process of applying the rated voltage is applied. The value divided by the amount is defined as 50% hysteresis [%].
Each characteristic was measured. Table 1 shows the measurement results.

[0027]

[Table 1]

Subsequently, the driving method of the present invention was applied to the piezoelectric ceramic actuators of these two specifications by using a driving device as shown in FIG. 5 (the main part thereof is shown as a non-linear driving voltage output circuit). That is, first measurement calculation machine prepared out of the driving voltage output circuit by (personal computer), a non-linear displacement [delta] ₁ is measured for the input voltage V _1, the number 18 Expressions specific parameters a respective piezoelectric ceramic actuator, b , C,..., N are calculated by the least squares method. However, the calculation for this drive is
In consideration of the contribution rate to the displacement amount, the simplification of the calculation, the simplification of the configuration of the drive voltage output circuit, and the like, in practice, it is sufficient to expand the equations (18) to (22) to the quartic equations. .

Next, in order to make the output voltage V ₂ to the piezoelectric ceramic actuator non-linear with respect to the input voltage V ₁ , the equations correspond to the second, third and fourth order terms of equations (19) and (20). Output values are obtained from the three-stage multipliers of the drive voltage output circuit, respectively, and further added and synthesized. The combined output value becomes the output voltage V _2.

Further, the quadratic, 3
The gain adjustment for making the coefficients of the fourth and fourth order terms equal to the coefficients of the series term of the quasi-linear function is performed by the resistors R ₁ connected in series to the respective multipliers and the resistors R ₁
Each performed by a parallel connection circuit including a variable resistor R ₂ connected in parallel with each series-connected operational amplifier Op, and thereto.

Table 2 shows that various characteristics of the displacement amount [μm] / rated voltage [V] and 50% hysteresis [%] are actually measured for a piezoelectric ceramic actuator of two specifications assuming such a drive. This shows the result of the measurement.

[0032]

[Table 2]

As is clear from the comparison between Tables 1 and 2, according to the driving method of the piezoelectric ceramic actuator according to the present invention, the value of displacement / rated voltage [V] does not change.
It can be seen that the magnitude of the 50% hysteresis becomes very small.

[0034] In the non-linear increase width is according to the driving method of (Example 2) Example 2, an initial stage, the measured nonlinear displacement amount [delta] ₁ of the piezoelectric ceramic actuator with respect to the input voltage V _1, the non-linear displacement [delta] ₁ Equation 24

(Equation 24) Is approximated by a linear cubic equation relating to the input voltage V ₁ , and a, b, and c, which are intrinsic parameters of the ceramic actuator, are determined by the least square method.

[0035] Also, as a function of the input voltages V ₁ and output voltage V ₂ for a quasilinear form the displacement amount of the piezoelectric actuator relative to the input voltages V _1, at the time of boosting the number of output voltage V ₂ 25
formula

(Equation 25) Indicated by Further, where the input of the maximum output voltage when the voltage V ₁ is a maximum value V _1MAX as V _2MAX, during the step-down number 26 formula the output voltage V ₂

(Equation 26) Indicated by Subsequently, the displacement amount δ ₂ of the piezoelectric ceramic actuator is calculated by using the output voltage V _{2 according} to Equation 27.

[Equation 27] Expressed by Thereafter, the equations (25) and (26) are respectively substituted into the equations (27), and the combined equations of the displacement δ ₂ at the time of boosting are arranged by V ₁ and the equations (28) are obtained.

[Equation 28] And the combined equation of the displacement δ ₂ at the time of step-down is expressed by Equation 29

(Equation 29) Get as. Next, the intrinsic parameters a, b, c, of the piezoelectric ceramic actuator obtained by the above-mentioned least square method are described.
.., Ξ are determined so that the second-order and higher-order polynomials relating to Expressions 28 and 29 are approximated by a series of pseudo-linear functions. Here, if the second and subsequent polynomials of the input voltage V ₁ in Equations 28 and 29 are equivalent by a pseudo-linear function, the displacement δ ₂ of the piezoelectric ceramic actuator is linear with respect to the input voltage V ₁ . Become. Therefore, functions f ₂ (•), f ₃ (•),..., F
₉ The values of the gains α, β, and γ of the nonlinear amplification may be determined so that the value of (•) becomes equal to the coefficient of the series term of the pseudo-linear function.

FIG. 6 shows the measurement results of the nonlinear displacement δ ₁ of the piezoelectric ceramic actuator with respect to the input voltage V ₁ in the initial stage of the driving method according to the second embodiment.
From FIG. 6, it can be seen that the piezoelectric ceramic actuator is the first embodiment
Similarly if (see FIG. 2) of, shows a non-linear displacement with respect to the input voltage V _1, moreover it can be seen that caused the counterclockwise hysteresis. Therefore, next to synthesize nonlinear driving voltage to the input voltage V _1.

[0037] Figure 7 shows the result of measurement of output voltage V ₂ to the input voltages V ₁ according to the intermediate stage of the driving method. From Figure 7, the output voltage V _2, like the case of Example 1 (see FIG. 3) shows a non-linearity with respect to the input voltage V _1, it can be seen that cause clockwise hysteresis.
Further, this nonlinear output voltage V ₂ is applied to the piezoelectric ceramic actuator.

[0038] Figure 8 inputs the output voltage V ₂ voltages V ₁
The displacement amount δ of the piezoelectric ceramic actuator with respect to the input voltage V ₁ in the latter stage of the driving method approximated by the cubic expression
₂ shows the measurement results. From FIG. 8, when a nonlinear output voltage V ₂ as shown in FIG. 7 is applied to the piezoelectric ceramic actuator, the piezoelectric ceramic actuator has a substantially linear (pseudo-linear) displacement δ _{2 with} respect to the input voltage V ₁ . Is obtained.

(Embodiment 3) In Embodiment 3, in order to further simplify the nonlinear drive voltage output circuit and reduce the cost,
In the driving method according to the second embodiment, the third-order terms of Expressions 25 and 26 are omitted, and the output voltage V ₂ is increased by Expression 30 when boosting.

[Equation 30] In the step-down operation, the output voltage V ₂ is calculated by Equation 31.

(Equation 31) Then, the displacement amount δ ₂ of the piezoelectric ceramic actuator is expressed by Expression 32 using the output voltage V _2.

(Equation 32) Then, the equations (30) and (31) are substituted into the equation (32), and the displacement amount δ at the time of boosting is rearranged by V _1.
Formula 33 of the composite formula of ₂

[Equation 33] And the combined equation of the displacement δ ₂ at the time of step-down is expressed by Equation 34.

(Equation 34) Then, using the values of the intrinsic parameters a, b, and c of the voltage ceramic actuator obtained by the above-mentioned least square method, the second and subsequent polynomials of Expressions 33 and 34 are converted into a series of pseudo-linear functions. The values of the gains α and β are determined so as to be approximated. Here, if the second and subsequent polynomials of the input voltage V ₁ in Equations 33 and 34 are equivalent by a pseudo-linear function, the displacement δ ₂ of the piezoelectric ceramic actuator becomes pseudo-linear with respect to the input voltage V ₁ . Becomes Therefore, the functions f ₂ (·) and f ₂ are calculated using the values of the intrinsic parameters a, b and c of the piezoelectric ceramic actuator which are known by the least square method.
The values of the gains α and β of the nonlinear amplification may be determined so that the values of ₃ (•),..., F ₆ (•) are equal to the coefficients of the series term of the pseudo-linear function.

Also in the piezoelectric ceramic actuator to which the driving method of the third embodiment is introduced, in the initial stage, the input voltage V ₁ exhibits a nonlinear displacement similar to that shown in FIG. 6, and a counterclockwise hysteresis is generated. together with the stage shows the non-linearity output voltage V ₂ was approximated in FIG. 7 with respect to the input voltage V _1, it was found to cause clockwise hysteresis.

FIG. 9 shows that the output voltage V ₂ is equal to the input voltage V ₁ .
The input voltage V _{1 in} the later stage of the driving method approximated by the following equation
Shows the result of measurement of the displacement amount [delta] ₂ of the piezoelectric ceramic actuator for. From FIG. 9, if the nonlinear output voltage V ₂ similar to FIG. 7 is applied to the piezoelectric ceramic actuator at a later stage, a quasi-linear displacement amount δ ₂ with respect to the input voltage V ₁ is obtained in the piezoelectric ceramic actuator. It turns out that it is possible.

FIGS. 10 and 11 show a method for applying the driving methods of the second and third embodiments to the piezoelectric ceramic actuator of two specifications having various characteristics shown in Table 1 described in the first embodiment. 1 shows a driving device (a non-linear driving voltage output circuit of a main part thereof). In these drives, first measurement processor that prepared out of the driving voltage output circuit by (personal computer), a non-linear displacement [delta] ₁ is measured for the input voltage V _1, unique in each of the piezoelectric ceramic actuator having 24 formula Parameters a, b,
c is calculated by the least squares method.

Next, in order to make the output voltage V ₂ to the piezoelectric ceramic actuator non-linear with respect to the input voltage V ₁ , the output value corresponding to the third order term of the equations (25) and (26), Output values corresponding to the quadratic terms of Expression 31 are obtained from the multipliers of the respective drive voltage output circuits, and are subsequently added and synthesized. Here the combined output value at is the output voltage V ₂ of each drive unit. Furthermore, Equation 28, Equation 2
Each multiplier performs a gain adjustment for making the coefficients of the second-order and third-order terms of Equation 9 and the coefficients of the second-order terms of Equations 33 and 34 equal to the coefficients of the series term of the pseudo-linear function. conducted a resistor R ₁ connected in series, in parallel circuit including the resistors R op Op which are respectively connected in series _1, and a variable resistor R ₂ that this was connected in parallel, respectively.

Table 3 shows that the driving described in the second and third embodiments was performed to measure various characteristics of the displacement / rated voltage and the 50% hysteresis for the piezoelectric ceramic actuators of the two specifications described above. It shows the results.

[0045]

[Table 3]

From the comparison between Tables 1 and 3, it is clear that Example 2 was obtained.
Further, according to the piezoelectric ceramic actuator driving method according to the third embodiment, it is found that there is no large change in the value of the displacement amount / applied voltage, and the magnitude of the 50% hysteresis becomes sufficiently small.

[0047]

As described above, according to the driving method of the piezoelectric ceramic actuator of the present invention, a non-linear output voltage is obtained by synthesizing a non-linear voltage with a DC input voltage. Drives the piezoelectric ceramic actuator, the amount of displacement of the piezoelectric ceramic actuator can be made linear with respect to the input voltage. Further, according to the driving method of the present invention, there is an extraordinary advantage that the hysteresis of the displacement-voltage characteristic can be reduced without using any special feedback control means. Furthermore, in the case of the driving method of the present invention, the number of dimensions of the polynomial required for nonlinear amplification is suppressed to a minimum in consideration of effectiveness, so that a driving device capable of sufficiently suppressing hysteresis is provided at low cost. Become like

[Brief description of the drawings]

FIG. 1 is a flowchart showing a basic operation according to a driving method of a piezoelectric ceramic actuator of the present invention.

FIG. 2 shows an input voltage V according to the driving method of the first embodiment of the present invention.
Shows the measured results of the nonlinear displacement amount [delta] ₁ of the piezoelectric ceramic actuator for _1.

FIG. 3 shows an input voltage V according to the driving method of the first embodiment of the present invention.
Shows the result of measurement of output voltage V ₂ for _1.

FIG. 4 shows an input voltage V according to the driving method of the first embodiment of the present invention.
Shows the result of measurement of the linear displacement of [delta] ₂ of the piezoelectric ceramic actuator for _1.

FIG. 5 shows a driving device (its nonlinear driving voltage output circuit) using the driving method according to the first embodiment of the present invention.

FIG. 6 shows an input voltage V according to the driving method according to the second embodiment of the present invention.
Shows the measured results of the nonlinear displacement amount [delta] ₁ of the piezoelectric ceramic actuator for _1.

FIG. 7 shows an input voltage V according to the driving method according to the second embodiment of the present invention.
Shows the result of measurement of output voltage V ₂ for _1.

FIG. 8 shows an input voltage V according to the driving method according to the second embodiment of the present invention.
Shows the result of measurement of the linear displacement of [delta] ₂ of the piezoelectric ceramic actuator for _1.

FIG. 9 shows an input voltage V according to the driving method of the third embodiment of the present invention.
Shows the result of measurement of the linear displacement of [delta] ₂ of the piezoelectric ceramic actuator for _1.

FIG. 10 illustrates a driving device (its non-linear driving voltage output circuit) using the driving method according to the second embodiment of the present invention.

FIG. 11 shows a driving device (its nonlinear driving voltage output circuit) using the driving method according to the third embodiment of the present invention.

──────────────────────────────────────────────────続 き Continuation of the front page (72) Inventor Jiangwei 1-12 Kameoka Residence, 68 Kameoka-cho, Aoba-ku, Sendai City, Miyagi Prefecture (56) References JP-A-3-256375 (JP, A) JP-A-61- 256774 (JP, A) JP-A-6-104501 (JP, A) (58) Fields investigated (Int. Cl. ⁷ , DB name) H01L 41/09

Claims (5)

(57) [Claims] 1. A method of applying a DC voltage to a piezoelectric ceramic actuator to generate mechanical energy, and obtaining a displacement of the piezoelectric ceramic actuator by the mechanical energy, wherein a non-linearity of the displacement with respect to the DC voltage is referred to. A method of driving a piezoelectric ceramic actuator, comprising: performing nonlinear amplification of an input voltage; and applying an output voltage obtained as a result of the nonlinear amplification to the piezoelectric ceramic actuator as the DC voltage. 2. The method of driving a piezoelectric ceramic actuator according to claim 1, wherein the nonlinear amplification compensates for the nonlinearity. 3. The method for driving a piezoelectric ceramic actuator according to claim 2, wherein the nonlinear amplification is obtained by actually measuring a nonlinear displacement δ ₁ of the piezoelectric ceramic actuator with respect to the input voltage V ₁ , and calculating the nonlinear displacement δ _1. Equation 1 Is approximated by a linear n following equation for the input voltages V _1, shown in, and a is an inherent parameter of the piezoelectric ceramic actuator wherein, b, c, ..., and determines a minimum square method to n, piezoelectric [2 number] output voltage V ₂ of the equation (2) is the output voltage V ₂ at the booster as a function of the input voltages V ₁ to linear with respect to the input voltages V ₁ the displacement of the ceramic actuator On the other hand, the maximum output voltage when the input voltage V ₁ reaches the maximum value V _1MAX is _set as V _2MAX , and the output voltage V ₂ is used in step-down when the voltage is stepped down. On the other hand, the displacement amount δ ₂ of the piezoelectric ceramic actuator is expressed by the following equation (4) using the output voltage V _2. After that, Expression 2 and Expression 3 are respectively expressed by Expression 4.
Substituting into the equation and rearranging it by V ₁ , the composite equation of the displacement amount δ ₂ at the time of boosting is expressed by the following equation (5). And the combined equation of the displacement amount δ ₂ at the time of step-down is expressed by the following equation (6). After that, the intrinsic parameters a, b, c, of the piezoelectric ceramic actuator obtained by the least squares method are further obtained.
.., Ξ are determined so that the second-order and higher-order polynomials related to Equations (5) and (6) are approximated by a series of pseudo-linear functions. A method for driving a piezoelectric ceramic actuator. 4. The method of driving a piezoelectric ceramic actuator according to claim 2, wherein the nonlinear amplification is obtained by actually measuring a nonlinear displacement δ ₁ of the piezoelectric ceramic actuator with respect to the input voltage V ₁ , and calculating the nonlinear displacement δ _1. Is given by Equation 7 Is approximated by a linear cubic expression relating to the input voltage V ₁ , and a, b, and c, which are intrinsic parameters of the piezoelectric ceramic actuator, are determined by the least square method. output voltage V ₂ for a quasilinear form an amount relative to the input voltages V ₁
At the time of boosting as a function of the input voltage V _1.
2 is expressed by Equation 8 On the other hand, the maximum output voltage when the input voltage V ₁ reaches the maximum value V _1MAX is set to V _2MAX , and the output voltage V ₂ is used in step-down when the voltage is stepped down. On the other hand, the displacement amount δ ₂ of the piezoelectric ceramic actuator is expressed by the following equation (10) using the output voltage V _2. After that, Expression 8 and Expression 9 are respectively expressed by Expression 1.
Substituting into Equation 0 and organizing it by V ₁ , the combined equation of the displacement δ ₂ at the time of boosting is given by Equation 11 And the composite equation of the displacement amount δ ₂ at the time of step-down is given by
Equation 12 Then, using the values of the intrinsic parameters a, b, and c of the piezoelectric ceramic actuator obtained by the least square method, the second-order and higher-order polynomials of the equations (11) and (12) are pseudo-linear functions. Wherein the values of the gains α, β, and γ are determined so as to approximate the series of the piezoelectric ceramic actuator. 5. The driving method for a piezoelectric ceramic actuator according to claim 4, wherein the third-order terms of the equations (8) and (9) are omitted in the nonlinear amplification, and the output voltage V ₂ is reduced at the time of boosting. Equation 13 In the step-down operation, the output voltage V ₂ is calculated by the following equation (14). Then, the displacement amount δ ₂ of the piezoelectric ceramic actuator is expressed by the following equation (15) using the output voltage V _2. After that, the expression (13) and the expression (14) are substituted into the expression (15), and the combined expression of the displacement δ ₂ at the time of boosting is arranged by V ₁ to obtain the expression (16). And the combined equation of the displacement δ ₂ at the time of step-down is expressed by the following equation (17). Then, using the values of the intrinsic parameters a, b, and c of the voltage ceramic actuator obtained by the least square method, the second and subsequent polynomials of Expressions 16 and 17 are transformed into a series of pseudo-linear functions. A method for driving a piezoelectric ceramic actuator, wherein the values of the gains α and β are determined so as to approximate