CN110868193B - A Self-Sensing Method for Output Displacement and Output Force of Piezoelectric Actuator - Google Patents

Abstract

The invention discloses a self-perception method for output displacement and output force of a piezoelectric actuator, comprising an integrator for obtaining the surface charge of a piezoelectric actuator wafer. The self-perception expression of the output force of the piezoelectric actuator is:

The self-sensing expression of the output displacement δ of the piezoelectric actuator under the action of external force and voltage is:

Among them, F _est , δ _est , δ _{fee_est} , k _p , C _p , R _P , u, Q _DA are the self-perceived force, self-perceived displacement, self-perceived no-load displacement, stiffness, capacitance, and insulation of the piezoelectric actuator, respectively Resistance, driving voltage, and dielectric absorption charge; C and u _out are the integral capacitance and output voltage of the integrator, respectively; α is the charge-force coefficient; i _BIAS is the bias current of the operational amplifier. The invention can eliminate the influence of the leakage resistance of the piezoelectric actuator on the self-sensing precision without adding a parallel resistance to the feedback capacitor in the integrator; and compensate for the dielectric absorption of the piezoelectric actuator and the bias current, and can further Improve the self-sensing accuracy of the output displacement and output force of the piezoelectric actuator.

Description

A Self-Sensing Method for Output Displacement and Output Force of Piezoelectric Actuator

technical field

The invention belongs to the technical field of nano-positioning, and relates to a piezoelectric actuator in a nano-positioning system, in particular to a self-sensing method for output displacement and output force of a piezoelectric actuator.

Background technique

Piezoelectric actuators are actuators capable of producing nanometer-scale motion precision and resolution. Compared with other forms of actuators such as electromagnetic, magnetostrictive, electrostatic, electrothermal, and shape memory alloy, piezoelectric actuators have the advantages of small size, high stiffness, fast response, large output force, high displacement resolution, It has the advantages of no heat and no noise, so it is widely used in nanopositioning systems. For example, the use of stacked piezoelectric actuators (consisting of multi-layer piezoelectric ceramic wafers mechanically connected in series and electrically connected in parallel) is used to drive the flexible hinge mechanism type tool holder, thereby forming a fast servo tool system to realize micro-precision machining in ultra-precision machining. Feed; using stacked piezoelectric actuators to drive flexible hinge mechanism clamps and using cantilever beam piezoelectric actuators (made by bonding a single-layer piezoelectric ceramic wafer with yellow bronze or beryllium bronze, that is, single wafer type) Piezoelectric actuator; or two layers of piezoelectric ceramic wafers are bonded to the two surfaces of yellow bronze or beryllium bronze respectively, that is, bimorph piezoelectric actuator) as a clamp finger, and then constitute a piezoelectric micro clamp. In MEMS micro-assembly, micro-components such as micro-shafts and micro-gears, as well as micro-components such as micro-motors and micro-pumps, are picked, transported, assembled, etc., as well as micro-operations such as capturing and releasing cells in biomedical engineering.

In the above nanopositioning systems, it is necessary to sense both the magnitude of the output displacement of the micro-movement mechanism and the magnitude of its output force. For example, when using a fast servo tool holder for ultra-precision machining, it is often necessary to sense the feed amount and feed force of the tool holder to ensure that the feed amount and feed force are appropriate. Serious friction and wear will occur between the workpiece and the tool, which will reduce the machining accuracy and machining quality; if it is too small, it will reduce the machining efficiency. During the working process of micro-assembly and micro-manipulator, it is necessary to sense the output displacement of the fingers of the micro-clamp to facilitate its control and avoid collision with the micro-object; at the same time, it is also necessary to sense and control the output force of the fingers , so that the output force is appropriate, otherwise, if the output force is too small, the micro-object will fall off, and if the output force is too large, the micro-object will be damaged.

At present, most of the precision sensors (such as resistance strain gauges, inductive sensors, and capacitive sensors) are used to sense the output displacement and output force of the micro-movement mechanism in the nanopositioning system. These precision sensors are expensive, which increases the cost of nanopositioning systems; in addition, in nanopositioning systems such as micro-assembly and micro-manipulation, due to space constraints, sensors are often unable to be installed, which increases the difficulty of system design. In order to reduce the cost and design difficulty of the nanopositioning system, there are also methods of self-sensing (ie, eliminating the need for precision sensors) to obtain the information of the output displacement and output force of the piezoelectric actuator, mainly including the bridge method and the integrator method.

The principle of the bridge method is to use the piezoelectric actuator as a bridge arm, and form a bridge together with the other three bridge arms—the reference capacitor and the series impedance. When the driving voltage does not act on the piezoelectric actuator, the bridge is balanced. Under the action of voltage, the bridge will output a voltage (that is, sense voltage), which is proportional to the driving voltage of the piezoelectric actuator. Since the output displacement and output force of the piezoelectric actuator are also proportional to the driving voltage, it can be used Sensing the voltage to reflect the output displacement and output force of the piezoelectric actuator. The realization principle and circuit structure of the bridge method are simple, but it has the following shortcomings: it is only suitable for dynamic driving, not for static or low-frequency driving. This is because: piezoelectric ceramic chips are not ideal insulators, but there are certain If the leakage resistance is high, leakage current will be generated during the working process. The leakage current will destroy the balance of the bridge under static or low frequency conditions. When the balance of the bridge is destroyed, the stability of the system will be deteriorated. Compared with the driving voltage , the sensed voltage is small.

The principle of the integrator method is that under the action of the driving voltage, the piezoelectric ceramic wafer constituting the piezoelectric actuator is deformed and electrically polarized at the same time, and then a charge proportional to the driving voltage is generated on the surface of the wafer. The output displacement and output force are also proportional to the driving voltage, and then the output displacement and output force of the piezoelectric actuator are also proportional to the surface charge of the wafer, but the surface charge of the wafer cannot be obtained directly, and needs to be obtained by an integrator (ie, an integrating circuit). , the output voltage of the integrating circuit can reflect the output displacement and output force of the piezoelectric actuator. The realization principle and circuit structure of the integrator method are also relatively simple. The output voltage of the integrator circuit reflecting the surface charge of the wafer (that is, the sensed voltage) is much larger than the sensed voltage of the bridge method, and it is not only suitable for static or low-frequency driving conditions, but also for dynamic driving situation. It can be seen that the integrator method has more advantages than the bridge method. But the current integrator method (such as the integrator method disclosed in patent ZL201510515293.1) still has the following shortcomings:

1) In order to eliminate the influence of the leakage current generated by the leakage resistance of the piezoelectric ceramic chip on the self-sensing accuracy, a parallel resistance is provided to both ends of the feedback capacitor in the integrator to satisfy C _P × R _P =C × R (the formula is Eliminate the balance condition of wafer leakage current, C _P and R _P are the capacitance and leakage resistance of the wafer in the piezoelectric actuator, respectively, and C and R are the feedback capacitance and feedback resistance of the integrator respectively). The leakage resistance R _P often reaches more than 10 ¹⁰ Ω, so that the feedback resistance R of the integrator must reach more than 10 ⁷ Ω. It is difficult to buy such a high resistance resistor, and it often needs to be realized by multiple series; The leakage resistance R _P of the chip in the electric actuator is easily changed by the influence of ambient temperature and humidity, so in order to satisfy C _P × R _P =C × R, the feedback resistance R of the integrator should also be adjusted frequently, which makes the integrator It is difficult to realize the method, and the adjustment process is cumbersome.

2) The dielectric absorption generated by the wafer in the piezoelectric actuator under the action of voltage is ignored. But in fact, the piezoelectric ceramic chip will produce dielectric absorption under the action of voltage, thereby generating charge on the surface of the chip. This charge will not cause the piezoelectric actuator to generate output displacement and output force, but will cause the calculation of the integrator. The amplifier generates an output voltage, which in turn reduces the self-sensing accuracy of the output displacement and output force of the piezoelectric actuator.

3) The bias current of the operational amplifier that constitutes the integrator is ignored. But in fact, any operational amplifier has a bias current, which will cause the output of the integrator, thereby reducing the self-sensing accuracy of the output displacement and output force of the piezoelectric actuator.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a method for eliminating the influence of the leakage current generated by the leakage resistance of the chip in the piezoelectric actuator on the self-sensing accuracy, without requiring parallel resistances between the two ends of the feedback capacitor in the integrator, and considering A self-sensing method for piezoelectric actuator output displacement and output force to improve self-sensing accuracy based on the dielectric absorption generated by the chip in the piezoelectric actuator under the action of voltage and the bias current of the operational amplifier that constitutes the integrator .

The technical solution adopted by the present invention to solve the above technical problems is: a self-sensing method for output displacement and output force of a piezoelectric actuator, comprising an integrator for obtaining the surface charge of the piezoelectric actuator wafer, the integrator comprising an operational amplifier and Integrating capacitor, the positive pole of the piezoelectric actuator is connected to the positive pole of the power supply, the negative pole of the power supply is connected to the ground, the negative pole of the piezoelectric actuator is connected to the reverse terminal of the operational amplifier, the non-inverting terminal of the operational amplifier is connected to the ground, and one end of the integrating capacitor is connected to the reverse terminal of the operational amplifier. The other end is connected to the output end of the operational amplifier. This method is that the piezoelectric actuator will deform δ under the action of the external force F and the driving voltage u (as shown in Figure 1 and Figure 2). The wafer in the piezoelectric actuator is electrically polarized, thereby generating a charge Q on the surface of the wafer (as shown in Figure 1 and Figure 2), which includes the output displacement δ of the piezoelectric actuator and the output force (its size). The same as the external force, the direction is opposite to the external force) information of F, if the relationship between δ and F, u and between Q and F, u can be determined, and Q can be obtained, then δ, F can be obtained.

The relationship between δ and F and u and the relationship between Q and F and u can be obtained by the first piezoelectric fundamental equation. According to the basic piezoelectric equation of the first kind, the relationship between Q and F and u can be expressed as:

Q=αF+C _p u (1)

In the formula, α is the charge-force coefficient, and C _p is the capacitance of the piezoelectric actuator.

According to the basic piezoelectric equation of the first kind, the relationship between δ and F and u can be expressed as:

In the formula, k _p is the stiffness of the piezoelectric actuator, and λ is the displacement-voltage coefficient.

It can be seen from equation (1) that the surface charge of the piezoelectric actuator contains the information of the output force of the piezoelectric actuator. Since the driving voltage of the piezoelectric actuator is known, as long as the surface charge of the piezoelectric actuator is obtained, The output force of the piezoelectric actuator can be obtained, and the external force sensor can be omitted to realize the self-sensing of the output force of the piezoelectric actuator.

The wafer surface charge Q of the piezoelectric actuator can be obtained by integrating the current flowing through the wafer. Figure 3 shows the integrating circuit (ie, the integrator) for obtaining the wafer surface charge of the piezoelectric actuator. In Fig. 3, the integrator includes an operational amplifier A and an integrating capacitor C, which are used to integrate the current flowing through the piezoelectric actuator; the discharge loop includes a switch K and a current limiting resistor R _k , which are used for each drive voltage Discharge the integral capacitor C before the electric actuator to ensure that the charge on C is zero.

In Figure 3, the positive pole of the piezoelectric actuator is connected to the positive pole of the power supply (the negative pole of the power supply is grounded), and the negative pole of the piezoelectric actuator is connected to the reverse terminal of the operational amplifier A (the same-direction terminal of the operational amplifier A is grounded); the integrating capacitor C One end is connected to the reverse end of the operational amplifier A, and the other end is connected to the output end of the operational amplifier A; the switch _K and the current limiting resistor Rk are connected in series, and then one end is connected to the reverse end of the operational amplifier A, and the other end is connected to the output end of the operational amplifier A.

In Figure 3, the output voltage u _out of operational amplifier A can be expressed as:

In the formula, C is the integrating capacitor in the integrator, Q _C is the charge on the integrating capacitor, and i is the current flowing through the integrating capacitor C and the piezoelectric actuator PA.

Substituting equation (1) into equation (3), we can get:

It can be known from equation (4) that the output voltage u _out of the operational amplifier A can reflect the output force of the piezoelectric actuator. Therefore, as long as u _out can be obtained accurately, the precise self-sensing of the output force of the piezoelectric actuator can be realized. To this end, it is necessary to consider the factors that affect the accuracy of the output voltage u _out of the operational amplifier. These factors mainly include the following three aspects:

1) Piezoelectric actuators are not ideal insulators, and their insulation resistance (which is in parallel with the equivalent capacitance of piezoelectric actuators) is not infinite. Under the action of voltage, a leakage current will be generated, which will also cause the operational amplifier to generate The output voltage;

2) The piezoelectric ceramic material has dielectric absorption properties, which will generate electric charge on the surface of the piezoelectric actuator wafer, and this electric charge will also cause the operational amplifier to generate an output voltage;

3) The operational amplifier has a _bias current i _BIAS , which also causes the operational amplifier to generate an output voltage.

Considering the above three factors, the output voltage u _out of the operational amplifier can be expressed as:

The last three terms on the right side of the equation (5) are respectively the output voltage of the operational amplifier caused by the leakage current of the piezoelectric actuator, the dielectric absorption charge on the wafer surface, and the bias current of the operational amplifier. Among them, R _P is the insulation resistance of the piezoelectric actuator, Q _DA is the dielectric absorption charge of the piezoelectric actuator wafer, and i _BIAS is the bias current of the operational amplifier.

According to formula (5), the self-perceived expression of the output force of the piezoelectric actuator can be obtained as:

In the formula, F _est is the self-sensing force of the piezoelectric actuator.

It can be seen from equation (6) that as long as α, R _P , Q _DA , and i _BIAS are identified, the self-sensing of the output force of the piezoelectric actuator can be realized. The identification process of α, R _P , Q _DA , and i _BIAS is as follows.

1) Identification of the bias current i _BIAS of the operational amplifier Since the bias current of the operational amplifier is related to the operational amplifier itself, and has nothing to do with the driving voltage u of the piezoelectric actuator, when identifying the bias current i _BIAS of the operational amplifier, the When no driving voltage is applied to the piezoelectric actuator (ie, u=0), the output voltage u _out of the operational amplifier is collected. Since the driving voltage of the piezoelectric actuator is zero, its output force F, leakage current u/R _P , and dielectric absorption charge Q _DA are all zero, and then according to equation (5), the output voltage u _out of the operational amplifier can be expressed as for:

Taking the derivative of both sides of equation (7) at the same time, we can get:

It can be known from (8) that i _BIAS can be identified as long as the output voltage u _out of the operational amplifier under no driving voltage is collected. Since i _BIAS is the slope of u _out , the identification result of i _BIAS is accurate, and u _out needs to be collected continuously for several tens of seconds.

2) Identification of piezoelectric actuator insulation resistance R _P

When identifying the insulation resistance R _P of the piezoelectric actuator, a constant driving voltage u is applied to the piezoelectric actuator under no-load (that is, the piezoelectric actuator is not constrained, F=0), and the driving voltage is applied for several hundred seconds. Then (to eliminate the drift of the output voltage u _out of the operational amplifier), the output voltage u _out of the operational amplifier is collected. Since the dielectric absorption of the dielectric is only related to the instantaneous charging and discharging process, Q _DA is zero at this time, and then according to equation (5), the output voltage u _out of the operational amplifier can be expressed as:

Calculate the derivative of both sides of equation (9) at the same time. Since the output force F of the piezoelectric actuator is a constant value, its derivative is zero, so it can be obtained:

Furthermore, the insulation resistance of the piezoelectric actuator can be obtained as:

Since the bias current i _BIAS of the operational amplifier has been identified, the insulation resistance R _P of the piezoelectric actuator can be identified by equation (11). It can be seen that as long as the output voltage u _out of the operational amplifier under a constant driving voltage is collected, the insulation resistance R _P of the piezoelectric actuator can be identified.

3) Identification of charge-force coefficient α It can be known from formula (1) that the charge-force coefficient α is the ratio of the chip surface charge of the piezoelectric actuator to the force under the action of the external force F, and the chip surface charge of the piezoelectric actuator is It is the same as the charge Q _C (ie Cu _out ) on the integrating capacitor C in the integrator, and then according to equation (4), the charge-force coefficient α can be expressed as:

Therefore, when identifying the charge-force coefficient α, in the case of u=0 (that is, no driving voltage is applied to the piezoelectric actuator), a dynamic standard force is applied to the piezoelectric actuator (such as applying a step force or a step force through a weight). The sine wave force is applied through the exciter. The reason for applying the dynamic force is that the piezoelectric ceramic has leakage resistance, and its surface charge will leak out quickly under static conditions; At this time, the piezoelectric actuator acts on the external force, that is, the output force of the piezoelectric actuator is equal to the step force generated by the weight to the piezoelectric actuator or the piezoelectric actuator exerted by the exciter. The sine wave force of , is F). At the same time, the output voltage u _out of the operational amplifier is collected, and then according to the formula (12), the charge-force coefficient α can be identified. In Equation (12), u _out and F only need to take their respective amplitudes.

4) Identification of the dielectric absorption charge Q _DA on the wafer surface

It can be known from formula (3) that:

Q _C = Q (13)

According to formula (6), QC in _formula (13) can be obtained as:

Q _C = αF _est (14)

In the formula, F _est can be calculated according to the identified parameters.

And Q in formula (13) is the sum of the wafer surface charge (ie αF) and the dielectric absorption charge Q _DA of the piezoelectric actuator under the action of external force, namely:

Q=αF+ _QDA (15)

And thus get:

Q _DA = α(F _est -F) = αΔF _est (16)

The dielectric absorption Q _DA of the dielectric can be represented by the first-order transfer function between αΔF _est and u in magnitude, namely:

where k is the static sensitivity and τ is the time constant.

Equation (17) can be further expressed as:

In the formula, Q ^* _DA (s) = Q _DA (s)/α, k ^* = k/α, where s is a complex variable, Q _DA (s) is the pull-type transformation of the dielectric absorption charge Q _DA , ΔF _est (s) is the pull transform of ΔF _est , u(s) is the pull transform of u, k is the static sensitivity, and τ is the time constant.

It can be known from equation (18) that as long as k ^* and τ are identified, Q ^* _DA (s) can be identified, and then the time domain Q _DA can be identified. When identifying k ^* and τ, in the case of u=0 (that is, no driving voltage is applied to the piezoelectric actuator), a step force is applied to the piezoelectric actuator through the weight, according to the size between the action force and the reaction force. The relationship between equal and opposite directions, at this time, the force acting on the outside world by the piezoelectric actuator, that is, the output force of the piezoelectric actuator is equal to the step force generated by the weight on the piezoelectric actuator, both of which are F. At the same time, the acquisition operation The output voltage u _out of the amplifier, F _est is obtained according to the identified parameters, and then the difference between F _est and F ΔF _est is obtained, and the curve of ΔF _est changing with time (that is, the response curve of ΔF _est under the action of weights) is drawn. ), the ratio of the steady state value of ΔF _est to the steady state value of the force generated by the weight is k ^* , and the time corresponding to ΔF _est reaching 63.2% of the steady state value is τ. After identifying Q ^* _DA (s), perform inverse Laplace transform on it, and then the time domain response Q ^* _DA of Q ^* _DA (s) can be obtained, and then Q _DA can be obtained.

The above is the self-sensing method of the output force of the piezoelectric actuator under the simultaneous action of external force and voltage, and the self-sensing method of the output displacement of the piezoelectric actuator under the simultaneous action of external force and voltage is given below. It can be seen from equation (2) that the output displacement of the piezoelectric actuator is the displacement generated by only the external force (u=0) (that is, the first term on the right side of the equation (2)) and the voltage (F=0) only. The sum of displacements (that is, the second term on the right side of the equation (2)). In the first term on the right side of the equation (2), the external force F has been obtained by the self-sensing method (that is, F _est in equation (6)), and the stiffness k _p of the piezoelectric actuator can be obtained by u=0 (that is, no When the piezoelectric actuator applies driving voltage), the ratio of the standard force (for example, can be generated by weights) and the displacement of the piezoelectric actuator under the action of the force can be identified, so that the piezoelectric actuator can be obtained when only external force is applied. output displacement.

The second term on the right side of the equal sign of equation (2) is given below, that is, the self-sensing method of the output displacement of the piezoelectric actuator under the action of voltage at no load. When the external force acting on the piezoelectric actuator is zero, equations (1) and (2) can be expressed as:

Q=C _p u (19)

δ=λu (20)

According to (19) and (20), the relationship between Q and δ can be obtained as:

Q=βδ (21)

In the formula, β=C _p /λ, and β is the charge-displacement coefficient.

It can be seen from equation (20) that when the piezoelectric actuator is only under the action of voltage, the surface charge of its wafer contains the information of its no-load output displacement. As long as the surface charge of the piezoelectric actuator is obtained, the pressure can be obtained. No-load output displacement of electric actuators.

Similar to the acquisition of the wafer surface charge in the self-sensing force, when the self-sensing piezoelectric actuator has no-load output displacement, the wafer surface charge Q is also acquired by the integrator (as shown in Figure 3). In Figure 3, when the piezoelectric actuator is only under the action of voltage, the output voltage u _out of the operational amplifier A can be expressed as:

Substituting equation (20) into equation (21), we can get:

Considering the leakage resistance, dielectric absorption, and bias current of the piezoelectric actuator, the output voltage u _out of the operational amplifier in Figure 3 can be expressed as:

Furthermore, the self-sensing expression of the output displacement of the piezoelectric actuator under the action of voltage at no-load can be obtained as:

It can be seen from equation (24) that as long as β, R _P , Q _DA , and i _BIAS are identified, the self-sensing of the output displacement of the piezoelectric actuator under the action of voltage at no-load can be realized. Among them, i _BIAS , R _P , and Q _DA have been identified during self-awareness. The identification process of β is given below.

It can be seen from equation (22) that the charge-displacement coefficient β is the ratio of the charge Q _C (ie Cu _out ) on the integrating capacitor C in the integrator to the output displacement δ of the piezoelectric actuator, namely:

Therefore, when identifying the charge-displacement coefficient β, in the case of F=0 (that is, no external force is applied to the piezoelectric actuator), a step or sine wave voltage is applied to the piezoelectric actuator, and its output is measured by a precision displacement sensor. Displacement δ (the precision displacement sensor is only used in identifying parameters, not necessary for self-sensing), while collecting the output voltage u _out of the operational amplifier, and then according to formula (25), the charge-displacement coefficient β can be identified. In Equation (25), u _out and δ can take their respective amplitudes.

In addition, Q _DA can also be identified by the measured no-load displacement and self-perceived no-load displacement. This identification method is given below.

According to formula (24), QC in _formula (13) can be obtained as:

Q _C = βδ _{fee_est} (27)

In the formula, δ _{fee_est} can be calculated according to the identified parameters.

And Q in equation (13) is the sum of the electric charge (ie βδ) that makes the piezoelectric actuator produce no-load output displacement and the dielectric absorption charge Q _DA , namely:

Q=βδ+ _QDA (28)

And thus get:

Q _DA = β(δ _{fee_est} -δ) = βΔδ _{fee_est} (29)

The dielectric absorption Q _DA of the dielectric can be represented by the first-order transfer function between αΔδ _{fee_est} and u in magnitude, namely:

where k is the static sensitivity and τ is the time constant.

Equation (29) can be further expressed as:

In the formula, Q ^* _DA (s)= _QDA /α, k ^* =k/α.

It can be known from equation (30) that as long as k ^* and τ are identified, Q ^* _DA (s) can be identified, and then Q _DA can be identified. When identifying k ^* and τ, a step voltage is applied to the piezoelectric actuator, the output displacement δ of the piezoelectric actuator is measured by a precision displacement sensor, δ _{fee_est} is obtained according to the identified parameters, and then the difference between the two is obtained. Δδ _{fee_est} , draw the curve of Δδ _{fee_est changing} with time (that is, the response curve of Δδ _{fee_est} under the action of step voltage u), the ratio of the steady-state value of Δδ _{fee_est} to the steady-state value of u is k ^* , Δδ _{fee_est} reaches steady state. The time corresponding to the state value of 63.2% is τ. After identifying Q ^* _DA (s), perform inverse Laplace transform on it, and then the time domain response Q ^* _DA of Q ^* _DA (s) can be obtained, and then Q _DA can be obtained.

After obtaining the self-perceived displacement δ _{fee_est} of the piezoelectric actuator under the action of voltage at no-load, the self-perceived displacement δ _est of the piezoelectric actuator under the action of external force and voltage can be expressed as:

In this way, the self-perception of the output displacement and output force of the piezoelectric actuator is realized. The above equations (6) and (31) are the self-perceived expressions of the output displacement and output force of the piezoelectric actuator, respectively.

Compared with the prior art, the advantages of the present invention are:

1) When eliminating the influence of the leakage current generated by the chip leakage resistance in the piezoelectric actuator on the self-sensing accuracy, it is not by adding parallel resistances to both ends of the feedback capacitor in the integrator (that is, it is not necessary to meet the balance of eliminating chip leakage current. Condition), but in the output voltage of the integrator, the output part caused by the leakage current of the wafer is subtracted, so that the integrator method is easy to realize under the condition of improving the self-sensing accuracy of the output displacement and output force of the electric actuator. And avoid the process of repeatedly adjusting the balance;

2) Considering the dielectric absorption generated by the chip in the piezoelectric actuator under the action of voltage, and then in the output voltage of the integrator, the output part caused by the dielectric absorption is subtracted, and the output displacement of the electric actuator is improved. and self-perceived accuracy of output force;

3) The bias current of the operational amplifier that constitutes the integrator is considered, and the output part caused by the bias current of the operational amplifier is subtracted from the output voltage of the integrator, which further improves the output displacement and output of the piezoelectric actuator. Self-perceived accuracy of force.

Description of drawings

Figure 1 is a schematic diagram of the displacement and charge generated by the stacked piezoelectric actuator under the action of external force and voltage;

Figure 2 is a schematic diagram of the displacement and charge generated by the bimorph piezoelectric actuator under the action of external force and voltage;

Fig. 3 is the connection schematic diagram of piezoelectric actuator and self-sensing circuit;

4 is a schematic diagram of the connection between the stacked piezoelectric actuator and the self-sensing circuit;

FIG. 5 is a schematic diagram of the connection between the bimorph piezoelectric actuator and the self-sensing circuit.

Detailed ways

The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

Embodiment 1, as shown in FIG. 1 and FIG. 4, a self-sensing method for output displacement and output force of a piezoelectric actuator, including an integrator for obtaining the surface charge of the piezoelectric actuator wafer, and the integrator includes an operational amplifier and Integrating capacitor, the positive pole of the piezoelectric actuator is connected to the positive pole of the power supply, the negative pole of the power supply is connected to the ground, the negative pole of the piezoelectric actuator is connected to the reverse terminal of the operational amplifier, the non-inverting terminal of the operational amplifier is connected to the ground, and one end of the integrating capacitor is connected to the reverse terminal of the operational amplifier. The other end is connected to the output end of the operational amplifier. This method is that the piezoelectric actuator of the stacked piezoelectric actuator will deform under the action of the external force F and the driving voltage u (as shown in Figure 1). At the same time of deformation, the wafer in the stacked piezoelectric actuator will be electrically polarized, thereby generating a charge Q on the surface of the wafer (as shown in Figure 1), which includes the output displacement of the stacked piezoelectric actuator. If the relationship between δ and F, u and between Q and F, u can be determined, and Q can be obtained, then the δ, F.

The relationship between δ and F and u and the relationship between Q and F and u can be obtained by the first piezoelectric fundamental equation. According to the basic piezoelectric equation of the first kind, the relationship between Q and F and u can be expressed as:

Q=αF+C _p u (1)

In the formula, α is the charge-force coefficient, and C _p is the capacitance of the stacked piezoelectric actuator.

According to the basic piezoelectric equation of the first kind, the relationship between δ and F and u can be expressed as:

In the formula, k _p is the stiffness of the piezoelectric actuator, and λ is the displacement-voltage coefficient.

It can be seen from equation (1) that the surface charge of the stacked piezoelectric actuator contains the information of the output force of the piezoelectric actuator. Since the driving voltage of the stacked piezoelectric actuator is known, it is only necessary to obtain the stacked piezoelectric actuator. The chip surface charge of the piezoelectric actuator can obtain the output force of the stacked piezoelectric actuator, thereby eliminating the need for an external force sensor and realizing the self-sensing of the output force of the stacked piezoelectric actuator.

The wafer surface charge Q of the stacked piezoelectric actuator can be obtained by integrating the current flowing through the wafer. Figure 4 shows the integrating circuit (ie, 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 are used to integrate the current flowing through the stacked piezoelectric actuator; the discharge loop includes a switch K and a current limiting resistor R _k , which are used to integrate the current flowing through the stacked piezoelectric actuator; Discharge the integral capacitor C before driving the stacked piezoelectric actuator to ensure that the charge on C is zero.

In Figure 4, the positive pole of the stacked piezoelectric actuator is connected to the positive pole of the power supply (the negative pole of the power supply is grounded), and the negative pole of the stacked piezoelectric actuator is connected to the reverse terminal of the operational amplifier A (the same-direction terminal of the operational amplifier A). Ground); one end of the integrating capacitor C is connected to the reverse end of the operational amplifier A, and the other end is connected to the output end of the operational amplifier A; the switch K and the current limiting resistor R _k are connected in series, and one end is connected to the reverse end of the operational amplifier A, and the other end is connected to the operational amplifier A Amplifier A's output.

In Figure 4, the output voltage u _out of operational amplifier A can be expressed as:

In the formula, C is the integrating capacitor in the integrator, Q _C is the charge on the integrating capacitor, and i is the current flowing through the integrating capacitor C and the stacked piezoelectric actuator PA.

Substituting equation (1) into equation (3), we can get:

It can be known from equation (4) that the output voltage u _out of the operational amplifier A can reflect the output force of the stacked piezoelectric actuator. Therefore, as long as u _out can be obtained accurately, the precise self-sensing of the output force of the stacked piezoelectric actuator can be realized. To this end, it is necessary to consider the factors that affect the accuracy of the output voltage u _out of the operational amplifier. These factors mainly include the following three aspects:

1) The stacked piezoelectric actuator is not an ideal insulator, and its insulation resistance (which is in a parallel relationship with the equivalent capacitance of the piezoelectric actuator) is not infinite, and leakage current will be generated under the action of voltage, which will also cause An operational amplifier produces an output voltage;

2) The piezoelectric ceramic material has dielectric absorption properties, which will generate electric charge on the surface of the stacked piezoelectric actuator wafer, and this electric charge will also cause the operational amplifier to generate an output voltage;

3) The operational amplifier has a _bias current i _BIAS , which also causes the operational amplifier to generate an output voltage.

Considering the above three factors, the output voltage u _out of the operational amplifier can be expressed as:

The last three terms on the right side of the equation (5) are the output voltage of the operational amplifier caused by the leakage current of the stacked piezoelectric actuator, the dielectric absorption charge on the wafer surface, and the bias current of the operational amplifier. Among them, R _P is the insulation resistance of the stacked piezoelectric actuator, Q _DA is the dielectric absorption charge of the stacked piezoelectric actuator wafer, and i _BIAS is the bias current of the operational amplifier.

According to formula (5), the self-perceived expression of the output force of the stacked piezoelectric actuator can be obtained as:

In the formula, F _est is the self-sensing force of the stacked piezoelectric actuator.

It can be seen from equation (6) that as long as α, R _P , Q _DA , and i _BIAS are identified, the self-sensing of the output force of the stacked piezoelectric actuator can be realized. The identification process of α, R _P , Q _DA , and i _BIAS is as follows.

1) Identification of the bias current i _BIAS of the operational amplifier Since the bias current of the operational amplifier is related to the operational amplifier itself, and has nothing to do with the driving voltage u of the stacked piezoelectric actuator, the bias current i _BIAS of the operational amplifier is identified. When , the output voltage u _out of the operational amplifier is collected under the condition that no driving voltage is applied to the stacked piezoelectric actuator (ie, u=0). Since the driving voltage of the stacked piezoelectric actuator is zero, its output force F, leakage current u/R _P , and dielectric absorption charge Q _DA are all zero, and then according to equation (5), the output voltage u of the operational amplifier is _out can be expressed as:

Taking the derivative of both sides of equation (7) at the same time, we can get:

It can be known from (8) that i _BIAS can be identified as long as the output voltage u _out of the operational amplifier under no driving voltage is collected. Since i _BIAS is the slope of u _out , the identification result of i _BIAS is accurate, and u _out needs to be collected continuously for several tens of seconds.

2) Identification of piezoelectric actuator insulation resistance R _P

When identifying the insulation resistance R _P of the stacked piezoelectric actuator, a constant driving voltage u is applied to the stacked piezoelectric actuator under no-load (that is, the piezoelectric actuator is not constrained, F=0). After the driving voltage is applied for several hundred seconds (to eliminate the drift of the output voltage u _out of the operational amplifier), the output voltage u _out of the operational amplifier is collected. Since the dielectric absorption of the dielectric is only related to the instantaneous charging and discharging process, Q _DA is zero at this time, and then according to equation (5), the output voltage u _out of the operational amplifier can be expressed as:

Taking the derivative of both sides of equation (9) at the same time, since the output force F of the stacked piezoelectric actuator is a constant value, its derivative is zero, so it can be obtained:

Furthermore, the insulation resistance of the stacked piezoelectric actuator can be obtained as:

Since the bias current i _BIAS of the operational amplifier has been identified, the insulation resistance R _P of the stacked piezoelectric actuator can be identified by equation (11). It can be seen that as long as the output voltage u _out of the operational amplifier under a constant driving voltage is collected, the insulation resistance R _P of the stacked piezoelectric actuator can be identified.

3) Identification of charge-force coefficient α It can be known from equation (1) that the charge-force coefficient α is the ratio of the chip surface charge of the stacked piezoelectric actuator to the force under the action of the external force F, while the stacked piezoelectric actuator The charge on the wafer surface of the integrator is the same as the charge Q _C (ie Cu _out ) on the integrating capacitor C in the integrator, and then according to equation (4), the charge-force coefficient α can be expressed as:

Therefore, when identifying the charge-force coefficient α, in the case of u=0 (that is, no driving voltage is applied to the piezoelectric actuator), a dynamic standard force is applied to the stacked piezoelectric actuator (such as applying a step by weights). Jump force or apply sine wave force through the exciter. The reason why the dynamic force is applied is because the piezoelectric ceramic has leakage resistance, and its surface charge will quickly leak out under static conditions; according to the size of the force and the reaction force are equal , in the opposite direction, at this time the piezoelectric actuator acts on the external force, that is, the output force of the piezoelectric actuator is equal to the step force generated by the weight to the piezoelectric actuator or the exciter exerts the piezoelectric actuator. The sine wave force generated by the device is F), and the output voltage u _out of the operational amplifier is collected at the same time, and then according to the formula (12), the charge-force coefficient α can be identified. In Equation (12), u _out and F only need to take their respective amplitudes.

4) Identification of the dielectric absorption charge Q _DA on the wafer surface

It can be known from formula (3) that:

Q _C = Q (13)

According to formula (6), QC in _formula (13) can be obtained as:

Q _C = αF _est (14)

In the formula, F _est can be calculated according to the identified parameters.

And Q in formula (13) is the sum of the wafer surface charge (ie αF) and the dielectric absorption charge Q _DA of the stacked piezoelectric actuator under the action of external force, namely:

Q=αF+ _QDA (15)

And thus get:

Q _DA = α(F _est -F) = αΔF _est (16)

The dielectric absorption Q _DA of the dielectric can be represented by the first-order transfer function between αΔF _est and u in magnitude, namely:

where k is the static sensitivity and τ is the time constant.

Equation (17) can be further expressed as:

In the formula, Q ^* _DA (s) = Q _DA (s)/α, k ^* = k/α, where s is a complex variable, Q _DA (s) is the pull-type transformation of the dielectric absorption charge Q _DA , ΔF _est (s) is the pull transform of ΔF _est , u(s) is the pull transform of u, k is the static sensitivity, and τ is the time constant.

It can be known from equation (18) that as long as k ^* and τ are identified, Q ^* _DA (s) can be identified, and then Q _DA in the time domain can be identified. When identifying k ^* and τ, in the case of u=0 (that is, no driving voltage is applied to the stacked piezoelectric actuator), a step force is applied to the stacked piezoelectric actuator through weights, and the operation is collected at the same time. Calculate the output voltage u _out of the amplifier, obtain F _est according to the identified parameters, and then obtain the difference ΔF _est between F _est and F, and draw the curve of ΔF _est changing with time (that is, the response curve of ΔF _est under the action of weights ), the ratio of the steady state value of ΔF _est to the steady state value of the force generated by the weight is k ^* , and the time corresponding to ΔF _est reaching 63.2% of the steady state value is τ. After identifying Q ^* _DA (s), perform inverse Laplace transform on it, and then the time domain response Q ^* _DA of Q ^* _DA (s) can be obtained, and then Q _DA can be obtained.

The self-sensing method of the output force of the stacked piezoelectric actuator under the simultaneous action of external force and voltage is given above, and the self-sensing method of the output displacement of the stacked piezoelectric actuator under the simultaneous action of external force and voltage is given below. It can be seen from equation (2) that the output displacement of the stacked piezoelectric actuator is the displacement generated by only the external force (u=0) (that is, the first term on the right side of the equation (2)) and only the voltage (F=0) The resulting displacement (ie, the second term on the right side of the equation (2)) is the sum. In the first term on the right side of the equation (2), the external force F has been obtained by the self-sensing method (ie, F _est in equation (6)), and the stiffness k _p of the stacked piezoelectric actuator can be obtained by u=0 ( That is, when no driving voltage is applied to the stacked piezoelectric actuator), the ratio of the standard force (for example, can be generated by weights) and the displacement of the stacked piezoelectric actuator under the action of the force can be identified, so that the Obtain the output displacement of the piezoelectric actuator when only external force is applied.

The second term on the right side of the equal sign of equation (2) is given below, that is, the self-sensing method of the output displacement of the stacked piezoelectric actuator under the action of voltage at no load. When the external force acting on the stacked piezoelectric actuator is zero, equations (1) and (2) can be expressed as:

Q=C _p u (19)

δ=λu (20)

According to (19) and (20), the relationship between Q and δ can be obtained as:

Q=βδ (21)

In the formula, β=C _p /λ, and β is the charge-displacement coefficient.

It can be seen from equation (20) that when the stacked piezoelectric actuator is only under the action of voltage, the surface charge of its wafer contains the information of its no-load output displacement, as long as the wafer surface of the stacked piezoelectric actuator is obtained. Charge, the no-load output displacement of the stacked piezoelectric actuator can be obtained.

Similar to the acquisition of the wafer surface charge in the self-sensing force, when the self-sensing stacked piezoelectric actuator has no-load output displacement, the wafer surface charge Q is also acquired by the integrator (as shown in Figure 3). In Figure 3, when the stacked piezoelectric actuator is only under the action of voltage, the output voltage u _out of the operational amplifier A can be expressed as:

Substituting equation (20) into equation (21), we can get:

Considering the leakage resistance, dielectric absorption, and bias current of the stacked piezoelectric actuator, the output voltage u _out of the operational amplifier in Figure 3 can be Expressed as:

Furthermore, the self-sensing expression of the output displacement of the stacked piezoelectric actuator under the action of voltage at no-load can be obtained as:

It can be seen from equation (24) that as long as β, R _P , Q _DA , and i _BIAS are identified, the self-sensing of the output displacement of the stacked piezoelectric actuator under the action of voltage at no-load can be realized. Among them, i _BIAS , R _P , and Q _DA have been identified during self-awareness. The identification process of β is given below.

It can be known from equation (22) that the charge-displacement coefficient β is the ratio of the charge Q _C (ie Cu _out ) on the integrating capacitor C in the integrator to the output displacement δ of the stacked piezoelectric actuator, namely:

Therefore, when identifying the charge-displacement coefficient β, in the case of F=0 (that is, no external force is applied to the stacked piezoelectric actuator), a step or sine wave voltage is applied to the stacked piezoelectric actuator, and the The precision displacement sensor measures its output displacement δ (the precision displacement sensor is only used when identifying parameters, it is not necessary for self-sensing), and at the same time collects the output voltage u _out of the operational amplifier, and then according to formula (25), the charge- Displacement coefficient β. In Equation (25), u _out and δ can take their respective amplitudes.

In addition, Q _DA can also be identified by the measured no-load displacement and self-perceived no-load displacement. This identification method is given below. Among them, Δδ _{fee_est} (s) is the pull transformation of Δδ _{fee_est} , Δδ _{fee_est} is the difference between δ _{fee_est} and δ, and δ _{fee_est} is the self-perceived displacement of the piezoelectric actuator.

According to formula (24), QC in _formula (13) can be obtained as:

Q _C = βδ _{fee_est} (27)

In the formula, δ _{fee_est} can be calculated according to the identified parameters.

And Q in Equation (13) is the sum of the charge (ie βδ) and the dielectric absorption charge Q _DA that make the stacked piezoelectric actuator produce no-load output displacement, namely:

Q=βδ+ _QDA (28)

And thus get:

Q _DA = β(δ _{fee_est} -δ) = βΔδ _{fee_est} (29)

The dielectric absorption Q _DA of the dielectric can be represented by the first-order transfer function between αΔδ _{fee_est} and u in magnitude, namely:

where k is the static sensitivity and τ is the time constant.

Equation (29) can be further expressed as:

In the formula, Q ^* _DA (s)= _QDA /α, k ^* =k/α.

It can be known from equation (30) that as long as k ^* and τ are identified, Q ^* _DA (s) can be identified, and then Q _DA can be identified. When identifying k ^* and τ, a step voltage is applied to the stacked piezoelectric actuator, the output displacement δ of the stacked piezoelectric actuator is measured by a precision displacement sensor, and δ _{fee_est} is obtained according to the identified parameters, and then Calculate the difference between the two, Δδ _{fee_est} , and draw the curve of Δδ _{fee_est changing} with time (that is, the response curve of Δδ _{fee_est} under the action of step voltage u), the ratio of the steady-state value of Δδ _{fee_est} to the steady-state value of u is k ^* , the time corresponding to Δδ _{fee_est} reaching 63.2% of the steady state value is τ. After identifying Q ^* _DA (s), perform inverse Laplace transform on it, and then the time domain response Q ^* _DA of Q ^* _DA (s) can be obtained, and then Q _DA can be obtained.

After obtaining the self-perceived displacement δ _{fee_est} of the stacked piezoelectric actuator under the action of voltage at no-load, the self-perceived displacement δ _est of the stacked piezoelectric actuator under the action of external force and voltage can be expressed as:

In this way, the self-perception of the output displacement and output force of the stacked piezoelectric actuator is realized. The above equations (6) and (31) are the self-perceived expressions of the output displacement and output force of the stacked piezoelectric actuator, respectively. .

The second embodiment, as shown in FIG. 2 and FIG. 5 , is similar to the first embodiment, except that the piezoelectric actuator is a bimorph piezoelectric actuator.

The preferred embodiment of the present invention has been described, and various changes or modifications can be made by those skilled in the art without departing from the scope of the present invention.

Claims (4)

1. A piezoelectric actuator output displacement and output force self-perception method, including the integrator used for obtaining the surface charge of the piezoelectric actuator wafer, the integrator includes operational amplifier and integral capacitor, the positive pole of the piezoelectric actuator connects the positive pole of the power, the negative pole of the power is grounded, the negative pole of the piezoelectric actuator connects the inverting terminal of the operational amplifier, the homodromous terminal of the operational amplifier is grounded, one end of the integral capacitor connects the inverting terminal of the operational amplifier, another end connects the carry-out terminal of the operational amplifier, its characteristic is: the self-perception expression of the output force F of the piezoelectric actuator is as follows:

The self-perception expression of the output displacement delta of the piezoelectric actuator under the action of external force and voltage is as follows:

wherein, F_estIs the self-sensing force of a piezoelectric actuator, delta_estIs the self-sensing displacement of the piezoelectric actuator; c is an integrating capacitor in the integrator; α is the charge-force coefficient; u. of_outIs the output voltage of an operational amplifier in the integrator; c_pIs the capacitance of the piezoelectric actuator; u is the piezoelectric actuator driving voltage; r_PIs the insulation resistance of the piezoelectric actuator; q_DADielectric absorption of charge Q for piezoelectric actuators_DA；i_BIASIs the bias current of the operational amplifier; delta_{fee_est}The piezoelectric actuator senses displacement under the action of voltage when the piezoelectric actuator is in no load; k is a radical of_pIs the stiffness of the piezoelectric actuator; value of C, C_pThe values of (a) and (b) are known;

i_BIASthe value of (d) is obtained by first acquiring the output voltage u of the operational amplifier without the driving voltage_outThen by the arithmetic expression

Obtaining;

R_Pis to apply a constant drive voltage u to the piezoelectric actuator under no load while acquiring the output voltage u of the operational amplifier_outFurther passing through the operation formula

Obtaining;

the value of alpha is that when u is 0, a dynamic standard force is applied to the piezoelectric actuator, according to the relation that the acting force and the reacting force are equal in magnitude and opposite in direction, the output force of the piezoelectric actuator is equal to the dynamic standard force and is F, and the dynamic standard force is acquired and calculated at the same time Output voltage u of amplifier_outBy means of an arithmetic expression

Obtaining;

u_outthe value of (1) is to collect the output voltage u of the operational amplifier without applying the driving voltage u to the piezoelectric actuator to 0_outThen by means of an arithmetic expression

Obtaining;

Q_DAis a pass operation formula

And Q^* _DA(s)＝Q_DA(s)/α、k^*K/α, where s is a complex variable, Q_DA(s) is a dielectrically absorbed charge Q_DAPull-type transformation of delta_est(s) is Δ δ_estU(s) is a pull-type transformation of u, k is a static sensitivity, and τ is a time constant; in the identification of k^*And tau, under the condition that u is 0, applying step force to the piezoelectric actuator through the weight, wherein the output force of the piezoelectric actuator is equal to the step force generated by the weight to the piezoelectric actuator and is F according to the relation that the acting force and the reacting force are equal in magnitude and opposite in direction, and simultaneously collecting the output voltage u of the operational amplifier_outDetermining F from the identified parameters_estFurther, F is obtained_estDifference Δ F from F_estPlotting Δ F_estCurve over time, Δ F_estThe ratio of the steady-state value of (a) to the steady-state value of the force generated by the weight is k^*，ΔF_estThe 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 obtained_DA；

k_pWhen u is 0, a dynamic standard force is applied to the piezoelectric actuator and the forceCalculating a ratio of the displacements of the lower piezoelectric actuators;

δ_{fee_est}is a pass operation formula

Determining a value of β as a charge-displacement coefficient, applying a stepped or sinusoidal voltage to the piezoelectric actuator when F is 0, measuring an output displacement δ by a precision displacement sensor, and collecting an output voltage u of the operational amplifier_outFurther based on the operation formula

And (4) obtaining.

2. The method for self-sensing the output displacement and the output force of the piezoelectric actuator as claimed in claim 1, wherein: q_DAThrough the identification of the actual measurement no-load displacement and the self-sensing no-load displacement,

q thereof_DAIs a pass operation formula

And Q^* _DA(s)＝Q_DA/α、k^*K/α is obtained; in the identification of k^*And tau, applying step voltage to the piezoelectric actuator, measuring the output displacement delta of the stacked piezoelectric actuator by the precise displacement sensor, and calculating delta according to the identified parameters_{fee_est}And further find the difference delta between the two_{fee_est}Drawing Delta delta_{fee_est}Curve of variation with time, delta_{fee_est}The ratio of the steady state value of (a) to the steady state value of u is k^*，Δδ_{fee_est}The time corresponding to the steady state value of 63.2% is tau; 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 obtained_DA。

3. A method of self-sensing output displacement and output force of a piezoelectric actuator as claimed in any one of claims 1 or 2, wherein: the piezoelectric actuator is a stacked piezoelectric actuator.

4. A method of self-sensing output displacement and output force of a piezoelectric actuator as claimed in any one of claims 1 or 2, wherein: the piezoelectric actuator is a double-wafer type piezoelectric actuator.

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