CN110906852B - Self-sensing method for output displacement of piezoelectric actuator - Google Patents

Self-sensing method for output displacement of piezoelectric actuator Download PDF

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CN110906852B
CN110906852B CN201911104119.2A CN201911104119A CN110906852B CN 110906852 B CN110906852 B CN 110906852B CN 201911104119 A CN201911104119 A CN 201911104119A CN 110906852 B CN110906852 B CN 110906852B
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piezoelectric actuator
displacement
operational amplifier
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CN110906852A (en
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崔玉国
聂志刚
马剑强
杨依领
王博文
谢启芳
应荣辉
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Ningbo University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
    • G01B7/02—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring length, width or thickness
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D5/00—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable
    • G01D5/12—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means
    • G01D5/14—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means influencing the magnitude of a current or voltage
    • G01D5/242—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means influencing the magnitude of a current or voltage by carrying output of an electrodynamic device, e.g. a tachodynamo

Abstract

The invention discloses a self-sensing method of output displacement of a piezoelectric actuator, which comprises an integrator for obtaining surface charge of a wafer of the piezoelectric actuator, wherein the integrator comprises an operational amplifier and an integrating capacitor, and the self-sensing expression of the output displacement delta of the piezoelectric actuator is as follows:
Figure DDA0002270748650000011
in the formula, deltaestFor self-sensing displacement of piezoelectric actuators, C, uoutRespectively, the integrating capacitance and the output voltage of the integrator, alpha is the charge-displacement coefficient, RPIs the insulation resistance of the piezoelectric actuator, u is the driving voltage applied to the piezoelectric actuator, QDAIs a dielectric absorption charge of the piezoelectric actuator wafer iBIASIs the bias current of the operational amplifier. The invention can eliminate the influence of the wafer leakage resistance in the piezoelectric actuator on the self-sensing precision without connecting a resistor in parallel with a feedback capacitor in the integrator; in addition, the dielectric absorption of the wafer in the piezoelectric actuator and the bias current of the operational amplifier forming the integrator are compensated, and the self-sensing precision of the output displacement of the piezoelectric actuator can be further improved.

Description

Self-sensing method for output displacement of piezoelectric actuator
Technical Field
The invention belongs to the technical field of nano positioning, relates to a piezoelectric actuator in a nano positioning system, and particularly relates to a self-sensing method for output displacement of the piezoelectric actuator.
Background
A piezoelectric actuator is an actuator capable of producing nanometer-scale motion accuracy and resolution. Compared with actuators in other forms such as electromagnetic type, magnetostriction type, electrostatic type, electrothermal type and shape memory alloy type, the piezoelectric actuator has the advantages of small volume, high rigidity, quick response, large output force, high displacement resolution, no heat generation, no noise and the like, and is widely applied to a nano positioning system. For example, a piezoelectric actuator is adopted to drive an x-y two-degree-of-freedom micro-displacement mechanism, so that an x-y two-degree-of-freedom micro-motion platform is formed, and the micro-motion platform can provide nanoscale x and y coordinates when a scanning tunnel microscope and an atomic force microscope are used for measuring the surface morphology of a microstructure; in MEMS micro-assembly and biomedical engineering, the micro-motion platform is combined with the micro-clamp to form a micro-assembly and micro-operation system, so that micro parts such as micro-shafts and micro-gears and micro parts such as micro-motors and micro-pumps can be picked up, transported and assembled, and cells can be captured and released.
In a nano positioning system, the displacement of a micro-motion mechanism (such as a micro-motion platform) needs to be sensed, and currently, a precise displacement sensor is mostly adopted for sensing, for example, a resistance strain gauge, an inductive sensor and a capacitive sensor are adopted for measuring the displacement of the micro-motion platform. These precision displacement sensors are expensive, making the costs of the micro positioning system high; in addition, in some nano positioning systems, such as micro-assembly and micro-operation systems, due to space limitation, the sensor cannot be installed, which increases the design difficulty of the system. In view of this, there are methods of obtaining displacement information of the piezoelectric actuator by using self-sensing (i.e. omitting a precise displacement sensor), mainly including bridge method and integrator method.
The principle of the bridge method is that the piezoelectric actuator is used as one bridge arm, the bridge is formed by the piezoelectric actuator and other three bridge arms, namely reference capacitance and series impedance, when the driving voltage does not act on the piezoelectric actuator, the bridge is balanced, under the action of the driving voltage, the bridge outputs voltage (namely sensing voltage), the voltage is in proportional relation with the driving voltage of the piezoelectric actuator, and as the displacement of the piezoelectric actuator is also in proportional relation with the driving voltage, the sensing voltage can be used for reflecting the displacement of the piezoelectric actuator. The bridge method has simple realization principle and circuit constitution, but has the following defects: this applies only to dynamic driving situations and not to static or low frequency driving situations, because: the piezoelectric ceramic wafer is not an ideal insulator, but has a certain leakage resistance, leakage current can be generated in the working process, the balance of the bridge can be damaged by the leakage current under the static or low-frequency condition, and the stability of the system can be deteriorated when the balance of the bridge is damaged; the sensing voltage is small compared to the driving voltage.
The principle of the integrator method is that a piezoelectric ceramic wafer forming a piezoelectric actuator deforms and is electrically polarized under the action of a driving voltage, so that electric charges in a proportional relation with the driving voltage are generated on the surface of the wafer, the displacement of the piezoelectric actuator is also in a proportional relation with the driving voltage, and further the displacement of the piezoelectric actuator is also in a proportional relation with the surface electric charges of the wafer, but the surface electric charges of the wafer cannot be directly obtained and need to be obtained through an integrator (namely, an integrating circuit), and the output voltage of the integrating circuit can reflect the displacement of the piezoelectric actuator. The integrator method is simple in implementation principle and circuit composition, the output voltage (namely, sensing voltage) of the integrator circuit reflecting the surface charge of the wafer is far larger than the sensing voltage of the bridge method, and the integrator circuit is suitable for static or low-frequency driving conditions and dynamic driving conditions. It can be seen that the integrator method has advantages over the bridge method. However, the current integrator method (such as the integrator method disclosed in patent ZL 201510515293.1) has the following disadvantages:
1) in order to eliminate the influence of leakage current generated by leakage resistance of the piezoelectric ceramic wafer on self-sensing precision, resistors are connected in parallel at two ends of a feedback capacitor in an integrator to meet the requirement of CP×RPC × R (the formula is a balance condition for eliminating chip leakage current, CP、RPRespectively a wafer in a piezoelectric actuatorC, R are the feedback capacitance and feedback resistance of the integrator, respectively), due to the leakage resistance R of the wafer in the piezoelectric actuatorPOften up to 1010Omega, so that the feedback resistance R of the integrator is 107The resistor with high resistance is difficult to purchase and is often realized by connecting a plurality of resistors in series; and, due to the leakage resistance R of the wafer in the piezoelectric actuatorPIs easily changed by the influence of the ambient temperature and humidity so as to satisfy CP×RPThe feedback resistance R of the integrator is also often adjusted, which makes the integrator method difficult to implement and the adjustment process is cumbersome.
2) The dielectric absorption of the wafer under voltage in a piezoelectric actuator is neglected. However, in practice, the piezoelectric ceramic wafer generates dielectric absorption under the action of voltage, and generates electric charge on the wafer surface, and the electric charge does not cause the piezoelectric actuator to generate output displacement, but causes an operational amplifier constituting the integrator to generate output voltage, and further reduces the self-sensing precision of the output displacement of the piezoelectric actuator.
3) The bias current of the operational amplifier constituting the integrator is ignored. In practice, however, any operational amplifier has a bias current that causes the output of the integrator, thereby reducing the self-sensing accuracy of the output displacement of the piezoelectric actuator.
Disclosure of Invention
The invention aims to provide a self-sensing method for outputting displacement of a piezoelectric actuator, which can improve the self-sensing precision without connecting a feedback capacitor in parallel with a resistor in an integrator when eliminating the influence of leakage current generated by a chip leakage resistor in the piezoelectric actuator on the self-sensing precision and on the basis of considering dielectric absorption generated by the chip in the piezoelectric actuator under the action of voltage and bias current of an operational amplifier forming the integrator.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for self-sensing output displacement of a piezoelectric actuator is characterized in that the piezoelectric actuator deforms under the action of a driving voltage u, when an output end of the piezoelectric actuator is not restrained, the deformation becomes output displacement delta of the piezoelectric actuator (shown in figures 1 and 2), the piezoelectric actuator deforms, and a wafer of the piezoelectric actuator is electrically polarized, so that electric charge Q (shown in figures 1 and 2) is generated on the surface of the wafer, information of the output displacement delta of the piezoelectric actuator is contained in the electric charge Q, and if the relation between Q and delta can be determined and Q can be obtained, delta can be obtained.
The relationship between δ and u and the relationship between Q and u can be clarified by the inverse piezoelectric effect and the dielectric effect of the piezoelectric material, respectively. According to the inverse piezoelectric effect, the output displacement δ of the piezoelectric actuator under the action of the driving voltage u can be expressed as:
δ＝au (1)
in the formula, a is a displacement-voltage coefficient.
And according to the dielectric effect of the dielectric medium (i.e. the electric polarization characteristic of the dielectric medium), the wafer surface charge Q of the piezoelectric actuator under the action of the driving voltage u can be expressed as:
Q＝Cpu (2)
in the formula, CpIs the capacitance of the piezoelectric actuator.
From (1) and equation (2), the relationship between Q and δ can be found as:
Q＝αδ (3)
wherein α ═ CpAnd a is a charge-displacement coefficient.
As can be seen from equation (3), the wafer surface charge of the piezoelectric actuator contains information of the output displacement of the piezoelectric actuator, and the output displacement of the piezoelectric actuator can be obtained by obtaining the wafer surface charge of the piezoelectric actuator, so that an external displacement sensor can be omitted, and the self-sensing of the output displacement of the piezoelectric actuator can be realized.
The wafer surface charge Q of the piezo actuator can be obtained by integrating the current through the wafer, and fig. 3 shows an integrating circuit (i.e., integrator) for obtaining the wafer surface charge of the piezo actuator. In fig. 3, the integrator includes an operational amplifier a, an integrating capacitor C, which functions to integrate the current flowing through the electro-actuator; the discharging circuit comprises a switch K and a current limiting resistor RkActing as a pair of integrating capacitors before each actuation of the piezoelectric actuatorC is discharged to ensure that the charge on C is zero.
In fig. 3, the positive electrode of the piezoelectric actuator is connected with the positive electrode of the power supply (the negative electrode of the power supply is grounded), and the negative electrode of the piezoelectric actuator is connected with the reverse end of the operational amplifier a (the same-direction end of the operational amplifier a is grounded); one end of the integrating capacitor C is connected with the reverse end of the operational amplifier A, and the other end of the integrating capacitor C is connected with the output end of the operational amplifier A; switch K and current limiting resistor RkAfter the serial connection, one end is connected with the inverting end of the operational amplifier A, and the other end is connected with the output end of the operational amplifier A.
In FIG. 3, the output voltage u of the operational amplifier AoutCan be expressed as:
Figure GDA0002895337460000041
wherein C is the integrating capacitor in the integrator, QCI is the current flowing through the integrating capacitor C and the piezo actuator PA, which is the charge on the integrating capacitor.
By substituting formula (3) for formula (4), it is possible to obtain:
Figure GDA0002895337460000042
from equation (5), the output voltage u of the operational amplifier AoutThe output displacement of the piezoelectric actuator can be reflected. Therefore, as long as u can be accurately obtainedoutThe precise self-sensing of the output displacement of the piezoelectric actuator can be realized. For this reason, it is necessary to consider the influence on the output voltage u of the operational amplifieroutThe factor of accuracy. These factors are mainly three:
1) the piezoelectric actuator is not an ideal insulator, the insulation resistance (the insulation resistance and the equivalent capacitance of the piezoelectric actuator are in parallel connection) of the piezoelectric actuator is not infinite, leakage current can be generated under the action of voltage, and the leakage current can also enable the operational amplifier to generate output voltage;
2) the piezoelectric ceramic material has dielectric absorption characteristics, so that charges are generated on the surface of the piezoelectric actuator wafer, and the charges can also enable the operational amplifier to generate output voltage;
3) the operational amplifier has a bias current that also causes the operational amplifier to generate an output voltage.
Considering the above three factors, the output voltage u of the operational amplifieroutCan be expressed as:
Figure GDA0002895337460000051
the last three terms on the right side of the middle sign in the equation (6) are output voltages of the operational amplifier caused by leakage current of the piezoelectric actuator, dielectric absorption charge on the surface of the wafer, and bias current of the operational amplifier. Wherein R isPBeing the insulation resistance, Q, of a piezoelectric actuatorDAIs a dielectric absorption charge of the piezoelectric actuator wafer iBIASIs the bias current of the operational amplifier.
According to equation (6), the self-sensing expression of the output displacement of the piezoelectric actuator can be obtained as follows:
Figure GDA0002895337460000052
in the formula, deltaestIs the self-sensing displacement of the piezoelectric actuator.
As can be seen from the formula (7), only alpha and R are recognizedP、QDA、iBIASTherefore, the self-sensing of the output displacement of the piezoelectric actuator can be realized. Alpha, RP、QDA、iBIASThe identification process of (1) is as follows.
1) Operational amplifier bias current iBIASSince the bias current of the operational amplifier is independent of the operational amplifier itself and the drive voltage u of the piezoelectric actuator, the bias current i of the operational amplifier is identifiedBIASIn the meantime, the output voltage u of the operational amplifier is acquired without applying a driving voltage (i.e., u is 0) to the piezoelectric actuatorout. Because the driving voltage of the piezoelectric actuator is zero, the output displacement delta and the leakage current u/R of the piezoelectric actuator are zeroPDielectric absorption charge QDAAre all zero, and then according to equation (6), operateOutput voltage u of amplifieroutCan be expressed as:
Figure GDA0002895337460000053
the simultaneous derivation of both sides of equation (8) can be obtained:
Figure GDA0002895337460000054
as shown in (9), the output voltage u of the operational amplifier is collected without the driving voltageoutThen i can be identifiedBIAS. Due to iBIASIs uoutIs thus iBIASThe identification result of (a) is accurate, and u needs to be alignedoutSeveral tens of consecutive seconds of acquisition are performed.
2) Piezoelectric actuator insulation resistor RPIs identified by
In identifying the insulation resistance R of a piezoelectric actuatorPIn this case, a constant drive voltage u is applied to the piezo actuator for several hundred seconds after the drive voltage has been applied (to eliminate the operational amplifier output voltage u)outDrift of) collecting the output voltage u of the operational amplifierout. Since dielectric absorption by the dielectric is only associated with transient charge and discharge processes, Q is the time ofDAIs zero, and the output voltage u of the operational amplifier is according to equation (6)outCan be expressed as:
Figure GDA0002895337460000061
the derivatives are simultaneously obtained on two sides of the equation (10), and since the output displacement delta of the piezoelectric actuator is a constant value, the derivative is zero, and then:
Figure GDA0002895337460000062
further, the insulation resistance of the piezoelectric actuator can be obtained as follows:
Figure GDA0002895337460000063
due to the bias current i of the operational amplifierBIASHas been recognized, the insulation resistance R of the piezoelectric actuator can be recognized from the formula (12)P. It can be seen that the output voltage u of the operational amplifier is collected only when the constant driving voltage is obtainedoutSo as to identify the insulation resistance R of the piezoelectric actuatorP。
3) Identification of charge-displacement coefficient alpha
As can be seen from equation (5), the charge-displacement coefficient α is the charge Q on the integrating capacitor C in the integratorC(i.e., Cu)out) The ratio of the output displacement δ of the piezoelectric actuator is:
Figure GDA0002895337460000064
then, in identifying the charge-displacement coefficient α, a stepped or sinusoidal voltage is applied to the piezoelectric actuator, the output displacement δ thereof is measured by a precision displacement sensor (the precision displacement sensor is used only in identifying the parameter and is not necessary for self-sensing), and the output voltage u of the operational amplifier is acquired at the same timeoutFurther, according to the formula (13), the charge-displacement coefficient α can be identified. In formula (13), uoutAnd δ may be obtained by taking the respective amplitudes.
4) Dielectric absorption charge Q on the surface of a chipDAIs identified by
As can be seen from the formula (4):
QC＝Q (14)
according to the formula (7), Q in the formula (14) can be obtainedCComprises the following steps:
QC＝αδest (15)
in the formula, deltaestCan be determined based on the identified parameters.
Q in the formula (14) is the charge (i.e. alpha delta) for causing the piezoelectric actuator to generate output displacement and the dielectric absorption charge QDAAnd (c) the sum, i.e.:
Q＝αδ+QDA (16)
further, it is possible to obtain:
QDA＝α(δest-δ)＝αΔδest (17)
in the formula, Δ δestFor self-sensing the displacement deltaestDifference from the measured displacement delta.
Dielectric absorption Q of dielectricsDAIn magnitude, can be represented by a first order transfer function between α Δ δ est and u, i.e.:
Figure GDA0002895337460000071
where s is a complex variable (i.e., a variable in the complex field), QDA(s) is a dielectrically absorbed charge QDAPull-type transformation of deltaest(s) is Δ δestU(s) is a pull-type transformation of u, k is the static sensitivity, and τ is the time constant.
Equation (18) can be further expressed as:
Figure GDA0002895337460000072
in the formula, Q* DA(s) is a dielectrically absorbed charge QDAPull type conversion QDARatio of(s) to charge-displacement coefficient α (i.e., Q)* DA(s)＝QDA(s)/α)，k*Is the ratio of k static sensitivity to the charge-displacement coefficient alpha (i.e., k)*＝k/α)。
As can be seen from the formula (19), as long as k is recognized*τ, Q can be recognized* DA(s), and thus the time domain Q can be identifiedDA. In the identification of k*And tau, applying step voltage to the piezoelectric actuator, measuring the output displacement delta of the piezoelectric actuator by the precise displacement sensor, and calculating delta according to the identified parametersestAnd further find the difference delta between the twoestDrawing Delta deltaestTime-dependent curve (i.e. delta. under the influence of the step voltage u)estResponse curve), Δ δestThe ratio of the steady state value of (a) to the steady state value of u is k*，ΔδestThe time to reach a steady state value of 63.2% is τ. Upon identification of Q* DAAfter(s), the Q can be obtained by performing inverse Ralstonian transformation on the obtained product* DATime domain response Q of(s)* DAFurther, Q can be obtainedDA。
Compared with the prior art, the invention has the advantages that:
1) when the influence of leakage current generated by wafer leakage resistance in the piezoelectric actuator on the self-sensing precision is eliminated, an output part caused by the wafer leakage current is reduced in the output voltage of the integrator instead of a mode of connecting resistors in parallel at two ends of a feedback capacitor in the integrator (namely, the balance condition for eliminating the wafer leakage current is not required to be met), so that the integrator method is easy to realize under the condition of improving the self-sensing precision of the output displacement of the electric actuator, and the process of repeatedly adjusting the balance is avoided;
2) the dielectric absorption generated by the wafer in the piezoelectric actuator under the action of voltage is considered, and then the output part caused by the dielectric absorption is reduced in the output voltage of the integrator, so that the self-sensing precision of the output displacement of the electric actuator is improved;
3) the bias current of an operational amplifier forming the integrator is considered, and then the output part caused by the bias current of the operational amplifier is subtracted from the output voltage of the integrator, so that the self-sensing precision of the output displacement of the piezoelectric actuator is further improved.
Drawings
FIG. 1 is a schematic diagram of a stacked piezoelectric actuator with displacement and charge generated by voltage;
FIG. 2 is a schematic diagram of a bimorph piezoelectric actuator generating displacement and charge under voltage;
FIG. 3 is a schematic diagram of the connection of a piezoelectric actuator to a self-sensing circuit;
FIG. 4 is a schematic diagram of the connection of a stacked piezoelectric actuator to a self-sensing circuit;
fig. 5 is a schematic diagram of the connection between the bimorph piezoelectric actuator and the self-sensing circuit.
Detailed Description
Embodiments of the present invention are described in further detail below with reference to the accompanying drawings.
First embodiment, as shown in fig. 1 and 4, a method for self-sensing output displacement of a piezoelectric actuator is that a stacked piezoelectric actuator deforms under a driving voltage u, and when an output end of the stacked piezoelectric actuator is unconstrained, the deformation becomes output displacement δ (shown in fig. 1) of the stacked piezoelectric actuator, and a wafer of the stacked piezoelectric actuator is electrically polarized while the stacked piezoelectric actuator deforms, so that a charge Q (shown in fig. 1) is generated on the surface of the wafer, and the charge Q contains information of the output displacement δ of the stacked piezoelectric actuator, and if a relationship between Q and δ can be determined and Q can be obtained, δ can be obtained.
The relationship between δ and u and the relationship between Q and u can be clarified by the inverse piezoelectric effect and the dielectric effect of the piezoelectric material, respectively. According to the inverse piezoelectric effect, the output displacement δ of the stacked piezoelectric actuator under the action of the driving voltage u can be expressed as:
δ＝au (1)
in the formula, a is a displacement-voltage coefficient.
According to the dielectric effect of the dielectric medium (i.e., the electric polarization characteristic of the dielectric medium), the wafer surface charge Q of the stacked piezoelectric actuator under the action of the driving voltage u can be expressed as:
Q＝Cpu (2)
in the formula, CpIs the capacitance of the stacked piezoelectric actuator.
From (1) and equation (2), the relationship between Q and δ can be found as:
Q＝αδ (3)
wherein α ═ CpAnd a is a charge-displacement coefficient.
As can be seen from equation (3), the wafer surface charge of the stacked piezoelectric actuator contains information of the output displacement of the stacked piezoelectric actuator, and the output displacement of the stacked piezoelectric actuator can be obtained as long as the wafer surface charge of the stacked piezoelectric actuator is obtained, so that an external displacement sensor can be omitted, and the self-sensing of the output displacement of the stacked piezoelectric actuator can be realized.
The wafer surface charge Q of the stacked piezoelectric actuator can be obtained by integrating the current flowing through the wafer, and fig. 4 shows an integrating circuit (i.e., an integrator) for obtaining the wafer surface charge of the stacked piezoelectric actuator. In fig. 4, the integrator includes an operational amplifier a and an integrating capacitor C, which is used to integrate the current flowing through the stacked piezoelectric actuator; the discharging circuit comprises a switch K and a current limiting resistor RkThe function of the piezoelectric actuator is to discharge the integrating capacitor C before driving the stacked piezoelectric actuator each time, so as to ensure that the charge on the capacitor C is zero.
In fig. 4, the positive electrode of the stacked piezoelectric actuator is connected to the positive electrode of the power supply (the negative electrode of the power supply is grounded), and the negative electrode of the stacked piezoelectric actuator is connected to the inverting terminal of the operational amplifier a (the inverting terminal of the operational amplifier a is grounded); one end of the integrating capacitor C is connected with the reverse end of the operational amplifier A, and the other end of the integrating capacitor C is connected with the output end of the operational amplifier A; switch K and current limiting resistor RkAfter the serial connection, one end is connected with the inverting end of the operational amplifier A, and the other end is connected with the output end of the operational amplifier A.
In FIG. 4, the output voltage u of the operational amplifier AoutCan be expressed as:
Figure GDA0002895337460000101
wherein C is the integrating capacitor in the integrator, QCFor the charge on the integrating capacitor, i is the current flowing through the integrating capacitor C and the stacked piezoelectric actuator PA.
By substituting formula (3) for formula (4), it is possible to obtain:
Figure GDA0002895337460000102
from equation (5), the output voltage u of the operational amplifier AoutThe output displacement of the stacked piezoelectric actuator can be reflected. Therefore, as long as u can be accurately obtainedoutCan realize the output displacement of the stacked piezoelectric actuatorFine self-perception of. For this reason, it is necessary to consider the influence on the output voltage u of the operational amplifieroutThe factor of accuracy. These factors are mainly three:
1) the stack type piezoelectric actuator is not an ideal insulator, the insulation resistance (the insulation resistance and the equivalent capacitance of the piezoelectric actuator are in a parallel connection relationship) of the stack type piezoelectric actuator is not infinite, leakage current can be generated under the action of voltage, and the leakage current can also enable the operational amplifier to generate output voltage;
2) the piezoelectric ceramic material has dielectric absorption characteristics, so that charges are generated on the surface of the stacked piezoelectric actuator wafer, and the charges can also enable the operational amplifier to generate output voltage;
3) the operational amplifier has a bias current that also causes the operational amplifier to generate an output voltage.
Considering the above three factors, the output voltage u of the operational amplifieroutCan be expressed as:
Figure GDA0002895337460000103
the last three terms on the right side of the middle sign in the equation (6) are output voltages of the operational amplifier caused by leakage current of the stacked piezoelectric actuator, dielectric absorption charge on the surface of the wafer, and bias current of the operational amplifier, respectively. Wherein R isPIs the insulation resistance, Q, of a stacked piezoelectric actuatorDAIs the dielectric absorption charge of a stacked piezoelectric actuator wafer iBIASIs the bias current of the operational amplifier.
According to the formula (6), the self-sensing expression of the output displacement of the stacked piezoelectric actuator can be obtained as follows:
Figure GDA0002895337460000111
in the formula, deltaestIs the self-sensing displacement of the stacked piezoelectric actuator.
As can be seen from the formula (7), only alpha and R are recognizedP、QDA、iBIASSo as to realize the stacking type pressingThe electric actuator outputs a self-sensing of displacement. Alpha, RP、QDA、iBIASThe identification process of (1) is as follows.
1) Operational amplifier bias current iBIASSince the bias current of the operational amplifier is related to the operational amplifier itself and not to the driving voltage u of the stacked piezoelectric actuator, the bias current i of the operational amplifier is identifiedBIASIn this case, the output voltage u of the operational amplifier is acquired without applying a drive voltage (that is, u is 0) to the stacked piezoelectric actuatorout. Because the driving voltage of the stacked piezoelectric actuator is zero, the output displacement delta and the leakage current u/R of the stacked piezoelectric actuator are zeroPDielectric absorption charge QDAAre all zero, and the output voltage u of the operational amplifier is according to equation (6)outCan be expressed as:
Figure GDA0002895337460000112
the simultaneous derivation of both sides of equation (8) can be obtained:
Figure GDA0002895337460000113
as shown in (9), the output voltage u of the operational amplifier is collected without the driving voltageoutThen i can be identifiedBIAS. Due to iBIASIs uoutIs thus iBIASThe identification result of (a) is accurate, and u needs to be alignedoutSeveral tens of consecutive seconds of acquisition are performed.
2) Piezoelectric actuator insulation resistor RPIs identified by
Insulation resistance R of stack-type piezoelectric actuator in identificationPIn the process, a constant drive voltage u is applied to the stack-type piezoelectric actuator for hundreds of seconds after the drive voltage is applied (to eliminate the output voltage u of the operational amplifier)outDrift of) collecting the output voltage u of the operational amplifierout. Since dielectric absorption by the dielectric is only associated with transient charge and discharge processes, Q is the time ofDAIs zero, and further according to equation (6),output voltage u of operational amplifieroutCan be expressed as:
Figure GDA0002895337460000121
the derivatives are simultaneously obtained at two sides of the formula (10), and since the output displacement delta of the stacked piezoelectric actuator is a constant value, the derivative is zero, and then:
Figure GDA0002895337460000122
further, the insulation resistance of the stacked piezoelectric actuator can be obtained as follows:
Figure GDA0002895337460000123
due to the bias current i of the operational amplifierBIASHas been identified, the insulation resistance R of the stacked piezoelectric actuator can be identified by the formula (12)P. It can be seen that the output voltage u of the operational amplifier is collected only when the constant driving voltage is obtainedoutSo as to identify the insulation resistance R of the piezoelectric actuatorP。
3) The charge-shift coefficient α is identified by equation (5), where the charge-shift coefficient α is the charge Q on the integrating capacitor C of the integratorC(i.e., Cu)out) The ratio of the output displacement δ of the stacked piezoelectric actuator is:
Figure GDA0002895337460000124
therefore, when the charge-displacement coefficient alpha is identified, step or sine wave voltage is applied to the stacked piezoelectric actuator, the output displacement delta of the stacked piezoelectric actuator is measured by a precision displacement sensor (the precision displacement sensor is only used for identifying parameters and is not necessary for self-sensing), and the output voltage u of the operational amplifier is acquired at the same timeoutFurther, according to the formula (13), the charge-bit can be identifiedThe coefficient of shift alpha. In formula (13), uoutAnd δ may be obtained by taking the respective amplitudes.
4) Dielectric absorption charge Q on the surface of a chipDAIs identified by
As can be seen from the formula (4):
QC＝Q (14)
according to the formula (7), Q in the formula (14) can be obtainedCComprises the following steps:
QC＝αδest (15)
in the formula, deltaestCan be determined based on the identified parameters.
Q in formula (14) is the charge (i.e. α δ) and the dielectric absorption charge Q for the stacked piezoelectric actuator to generate output displacementDAAnd (c) the sum, i.e.:
Q＝αδ+QDA (16)
further, it is possible to obtain:
QDA＝α(δest-δ)＝αΔδest (17)
in the formula, Δ δestFor self-sensing the displacement deltaestDifference from the measured displacement delta.
Dielectric absorption Q of dielectricsDAIn magnitude, can be represented by a first order transfer function between α Δ δ est and u, i.e.:
Figure GDA0002895337460000131
where s is a complex variable (i.e., a variable in the complex field), QDA(s) is a dielectrically absorbed charge QDAPull-type transformation of deltaest(s) is Δ δestU(s) is a pull-type transformation of u, k is the static sensitivity, and τ is the time constant.
Equation (18) can be further expressed as:
Figure GDA0002895337460000132
in the formula, Q* DA(s) is a dielectric absorption chargeQDAPull type conversion QDARatio of(s) to charge-displacement coefficient α (i.e., Q)* DA(s)＝QDA(s)/α)，k*Is the ratio of k static sensitivity to the charge-displacement coefficient alpha (i.e., k)*＝k/α)。
As can be seen from the formula (19), as long as k is recognized*τ, Q can be recognized* DA(s), and thus the time domain Q can be identifiedDA. In the identification of k*And tau, applying step voltage to the stacked piezoelectric actuator, measuring the output displacement delta of the stacked piezoelectric actuator by a precise displacement sensor, and calculating delta according to the identified parametersestAnd further find the difference delta between the twoestDrawing Delta deltaestTime-dependent curve (i.e. delta. under the influence of the step voltage u)estResponse curve), Δ δestThe ratio of the steady state value of (a) to the steady state value of u is k*，ΔδestThe time to reach a steady state value of 63.2% is τ. Upon identification of Q* DAAfter(s), the Q can be obtained by performing inverse Ralstonian transformation on the obtained product* DATime domain response Q of(s)* DAFurther, Q can be obtainedDA。
The second embodiment is similar to the first embodiment except that the piezoelectric actuator is a bimorph piezoelectric actuator, as shown in fig. 2 and 5.
While the preferred embodiments of the present invention have been illustrated, various changes and modifications may be made by one skilled in the art without departing from the scope of the invention.

Claims (3)

1. A self-sensing method for output displacement of a piezoelectric actuator comprises an integrator for obtaining surface charge of a wafer of the piezoelectric actuator, wherein the integrator comprises an operational amplifier and an integrating capacitor, and is characterized in that: the self-perception expression of the output displacement delta of the piezoelectric actuator is as follows:
Figure FDA0002895337450000011
in the formula (I), the compound is shown in the specification,δestis the self-sensing displacement of the piezoelectric actuator, C is the integrating capacitance in the integrator, uoutIs the output voltage of an operational amplifier A in the integrator, alpha is the charge-displacement coefficient, RPIs the insulation resistance of the piezoelectric actuator, u is the driving voltage applied to the piezoelectric actuator, QDAIs a dielectric absorption charge of the piezoelectric actuator wafer iBIASIs the bias current of the operational amplifier; the values of C and u are known;
iBIASthe value of (d) is obtained by collecting the output voltage u of the operational amplifier without applying a driving voltage to the piezoelectric actuator, i.e., with u equal to 0outFurther passing through the operation formula
Figure FDA0002895337450000012
Obtaining;
RPis to apply a constant drive voltage u to the piezoelectric actuator while acquiring the output voltage u of the operational amplifieroutFurther passing through the operation formula
Figure FDA0002895337450000016
Obtaining;
the value of alpha is to apply step or sine wave voltage to the piezoelectric actuator, measure the output displacement delta of the piezoelectric actuator through the precise displacement sensor and simultaneously acquire the output voltage u of the operational amplifieroutBy passing
Figure FDA0002895337450000014
Obtaining;
QDAis a pass operation formula
Figure FDA0002895337450000015
And Q* DA(s)＝QDAA and k*Obtained as k/α, in identifying k*And tau, applying step voltage to the piezoelectric actuator, measuring the output displacement delta of the piezoelectric actuator by the precise displacement sensor, and calculating delta according to the identified parametersestAnd further find the difference delta between the twoestDrawing Delta deltaestCurve of variation with time, deltaestThe ratio of the steady state value of (a) to the steady state value of u is k*，ΔδestThe time corresponding to the steady state value of 63.2% is tau; upon identification of Q* DAAfter(s), performing pull-type inverse transformation to obtain Q* DATime domain response Q of(s)* DAFurther, Q can be obtainedDA(ii) a s is a complex variable, Q* DA(s) is a dielectrically absorbed charge QDAPull type conversion QDARatio of(s) to the charge-displacement coefficient α, Δ δest(s) is Δ δestU(s) is a pull transform of u.
2. A method of self-sensing the output displacement of a piezoelectric actuator as claimed in claim 1, wherein: the piezoelectric actuator is a stacked piezoelectric actuator.
3. A method of self-sensing the output displacement of a piezoelectric actuator as claimed in claim 1, wherein: the piezoelectric actuator is a double-wafer type piezoelectric actuator.
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