CN113179044B - Hysteresis compensation method and system of piezoelectric ceramic driver and positioning equipment - Google Patents
Hysteresis compensation method and system of piezoelectric ceramic driver and positioning equipment Download PDFInfo
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Abstract
The application discloses hysteresis compensation method, device and positioning equipment of a piezoelectric ceramic driver, wherein the method comprises the following steps: obtaining a first state variable corresponding to an inverse hysteresis model at a first time, wherein the inverse hysteresis model is configured on the piezoelectric ceramic driver and is used for processing expected displacement and outputting an input voltage obtained by processing to the piezoelectric ceramic driver; obtaining a second state variable corresponding to the inverse hysteresis model at a second moment according to at least the first state variable, wherein the second moment is a next moment of the first moment; and updating the second state variable at least according to the output displacement of the piezoelectric ceramic driver at the second moment to obtain a third state variable, so that the inverse hysteresis model outputs the compensated input voltage to the piezoelectric ceramic driver at least by using the third state variable.
Description
Technical Field
The present disclosure relates to the field of hysteresis compensation technologies, and in particular, to a hysteresis compensation method and system for a piezoelectric ceramic driver, and a positioning device.
Background
The piezoelectric ceramic driver has the characteristics of high motion resolution and quick response, can detect displacement and convert the displacement into an electric signal of the displacement for output, and therefore, can be widely applied to scenes such as nanometer positioning, cell manipulation and the like.
However, the hysteresis of the piezo-ceramic driver may cause the displacement of the output to have a large error, resulting in a low accuracy of the positioning of the piezo-ceramic driver.
Disclosure of Invention
In view of this, the present application provides a hysteresis compensation method, device and positioning apparatus for a piezoelectric ceramic driver, so as to solve the technical problem in the prior art that the positioning accuracy of the piezoelectric ceramic driver is low.
The application provides a hysteresis compensation method of a piezoelectric ceramic driver, which comprises the following steps:
obtaining a first state variable corresponding to an inverse hysteresis model at a first time, wherein the inverse hysteresis model is configured on the piezoelectric ceramic driver and is used for processing expected displacement and outputting an input voltage obtained by processing to the piezoelectric ceramic driver;
obtaining a second state variable corresponding to the inverse hysteresis model at a second moment according to at least the first state variable, wherein the second moment is a next moment of the first moment;
and updating the second state variable at least according to the output displacement of the piezoelectric ceramic driver at the second moment to obtain a third state variable, so that the inverse hysteresis model outputs the compensated input voltage to the piezoelectric ceramic driver at least by using the third state variable.
Preferably, the method for updating the second state variable according to at least the output displacement of the piezoceramic driver at the second time to obtain a third state variable includes:
obtaining the corresponding output deviation of the inverse hysteresis model at the second moment according to the output displacement of the piezoelectric ceramic driver at the second moment;
updating the second state variable by using a parameter vector according to the corresponding output deviation of the inverse hysteresis model at the second moment so as to obtain a third state variable;
and obtaining the parameter vector at least according to the covariance matrix of the corresponding state variable of the inverse hysteresis model at the second moment.
In the above method, preferably, the parameter vector is obtained by:
and processing the threshold vector of the inverse hysteresis model at least according to the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second moment to obtain a parameter vector.
Preferably, the above method, processing a threshold vector of the inverse hysteresis model at least according to a covariance matrix of a state variable corresponding to the inverse hysteresis model at the second time to obtain a parameter vector, includes:
obtaining a covariance matrix of the corresponding measurement noise at the second moment;
and processing the threshold vector of the inverse hysteresis model according to the covariance matrix of the measurement noise corresponding to the second moment and the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second moment to obtain a parameter vector.
In the above method, preferably, the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second time is obtained by:
obtaining a covariance matrix of a state variable corresponding to the inverse lag model at the first time;
and obtaining a covariance matrix of the state variable corresponding to the inverse lag model at the second moment at least according to the covariance matrix of the process noise corresponding to the inverse lag model at the second moment and the covariance matrix of the state variable corresponding to the inverse lag model at the first moment.
The above method, preferably, after obtaining the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second time, further includes:
updating the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second moment according to the parameter vector by using a preset forgetting factor to obtain a covariance matrix of a new state variable corresponding to the inverse hysteresis model at the second moment, wherein the covariance matrix of the new state variable corresponding to the inverse hysteresis model at the second moment is used for obtaining the covariance matrix of the state variable corresponding to the inverse hysteresis model at the next moment of the second moment;
wherein the forgetting factor is greater than or equal to a preset threshold.
Preferably, the method for obtaining the corresponding output deviation of the inverse hysteresis model at the second time according to the output displacement of the piezoelectric ceramic driver at the second time includes:
obtaining a corresponding displacement deviation of the piezoelectric ceramic driver at the second moment according to the expected displacement corresponding to the inverse hysteresis model at the second moment and the output displacement of the piezoelectric ceramic driver at the second moment;
and obtaining the corresponding output deviation of the inverse hysteresis model at the second moment according to the displacement deviation.
Preferably, the method for obtaining the output deviation of the inverse hysteresis model at the second time according to the displacement deviation includes:
processing the displacement deviation by using the control proportion of the piezoelectric ceramic driver to obtain the corresponding output deviation of the inverse hysteresis model at the second moment;
the control proportion is the ratio of the maximum control input voltage of the piezoelectric ceramic driver to the maximum control output displacement of the piezoelectric ceramic driver.
The present application further provides a hysteresis compensation device of a piezoelectric ceramic driver, including:
the inverse hysteresis model is configured on the piezoelectric ceramic driver and used for processing the expected displacement and outputting the input voltage obtained by processing to the piezoelectric ceramic driver;
the variable updating module is used for obtaining a first state variable corresponding to the inverse hysteresis model at a first moment; obtaining a second state variable corresponding to the inverse hysteresis model at a second moment according to at least the first state variable, wherein the second moment is a next moment of the first moment; and updating the second state variable at least according to the output displacement of the piezoelectric ceramic driver at the second moment to obtain a third state variable, so that the inverse hysteresis model outputs the compensated input voltage to the piezoelectric ceramic driver at least by using the third state variable.
The present application further provides a positioning apparatus, including:
a piezoelectric ceramic driver;
the hysteresis compensation processor is connected with the piezoelectric ceramic driver;
the hysteresis compensation processor is used for configuring an inverse hysteresis model for the piezoelectric ceramic driver, so that the inverse hysteresis model processes expected displacement and outputs the processed input voltage to the piezoelectric ceramic driver;
the hysteresis compensation processor is further configured to: obtaining a first state variable corresponding to the inverse lag model at a first time; obtaining a second state variable corresponding to the inverse hysteresis model at a second moment according to at least the first state variable, wherein the second moment is a next moment of the first moment; and updating the second state variable at least according to the output displacement of the piezoelectric ceramic driver at the second moment to obtain a third state variable, so that the inverse hysteresis model outputs the compensated input voltage to the piezoelectric ceramic driver at least by using the third state variable.
According to the technical scheme, the hysteresis compensation method, the hysteresis compensation system and the positioning device of the piezoelectric ceramic driver disclosed by the application are realized through the inverse hysteresis model when the piezoelectric ceramic driver is subjected to hysteresis compensation, and meanwhile, the inverse hysteresis model is used for predicting and updating the state variable of the hysteresis compensation in the inverse hysteresis model, so that the inverse hysteresis model outputs the compensated input voltage to the piezoelectric ceramic driver by utilizing the updated state variable, thereby realizing the hysteresis compensation of the piezoelectric ceramic driver, reducing the error of the output displacement of the piezoelectric ceramic driver and achieving the aim of improving the accuracy of positioning of the piezoelectric ceramic driver.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
Fig. 1 is a flowchart of a hysteresis compensation method for a piezoelectric ceramic driver according to an embodiment of the present disclosure;
fig. 2-4 are schematic diagrams illustrating a logic architecture for hysteresis compensation of a piezoelectric ceramic driver according to an embodiment of the present invention;
fig. 5 is a partial flowchart of a hysteresis compensation method for a piezoelectric ceramic driver according to an embodiment of the present disclosure;
fig. 6 is a schematic structural diagram of a hysteresis compensation apparatus of a piezoelectric ceramic driver according to a second embodiment of the present application;
fig. 7 is a schematic structural diagram of a positioning apparatus according to a third embodiment of the present application;
FIG. 8 is a diagram illustrating error comparison of AKF combined with DIM in the present embodiment.
Detailed Description
The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Referring to fig. 1, an implementation flowchart of a hysteresis compensation method for a piezoelectric ceramic driver according to an embodiment of the present disclosure is provided, where the method may be applied to a positioning device that has a piezoelectric ceramic driver and is capable of performing data processing, such as a piezoelectric ultrasonic injector or an atomic Force microscope (afm) (atomic Force microscope), and the positioning device performs positioning through the piezoelectric ceramic driver. The technical scheme of the embodiment is mainly used for improving the accuracy of positioning of the piezoelectric ceramic driver in the positioning equipment.
Specifically, the method in this embodiment may include the following steps:
step 101: and obtaining a corresponding first state variable of the inverse hysteresis model at a first time.
Wherein the inverse hysteresis model is a model configured on the piezoelectric ceramic driver, and is used for expectingProcessing the displacement and outputting the input voltage obtained by the processing to the piezoelectric ceramic driver, processing the input voltage by the piezoelectric ceramic driver based on the processing to obtain the output displacement, wherein the input voltage output to the piezoelectric ceramic driver by the inverse hysteresis model is expressed by u, the output displacement of the piezoelectric ceramic driver is expressed by y, and the expected displacement of the piezoelectric ceramic driver is expressed by ydAnd (4) showing.
It should be noted that, since the controlled object is unchangeable, a good hysteresis compensation effect can be achieved only by obtaining an inverse hysteresis model and connecting the inverse hysteresis model in series to a feed-forward channel of the piezoelectric ceramic driver, the inverse hysteresis model in this embodiment may specifically be an inverse PI (Prandtl-Ishlinskii) model, in the inverse hysteresis model, the desired displacement is processed through a state variable and a threshold vector to obtain an input voltage, and thus the piezoelectric ceramic driver is subjected to hysteresis compensation through the input voltage, wherein the threshold vector may also be referred to as a gap operator vector, the threshold vector is a preset vector related to the desired displacement, and the preset is manually set, and H may be used for Hr(yd) And (4) showing. Referring to fig. 2, an input/output relationship between the piezoelectric ceramic driver and the inverse hysteresis model is shown, where the inverse hysteresis model is configured on a feed-forward channel of the piezoelectric ceramic driver to perform hysteresis compensation on the piezoelectric ceramic driver. In this embodiment, in order to improve the accuracy of positioning of the piezoelectric ceramic driver, the state variable of the inverse hysteresis model is updated, and the accuracy of performing hysteresis compensation on the piezoelectric ceramic driver by the inverse hysteresis model is improved by improving the accuracy of the state variable of the inverse hysteresis model, so that the accuracy of positioning of the piezoelectric ceramic driver is improved. As shown in FIG. 3, a variable update module is provided before the inverse lag model to update the state variables of the inverse lag model.
Based on this, in this embodiment, a first state variable corresponding to the inverse hysteresis model at the first time is obtained, and the state variable of the inverse hysteresis model is updated through subsequent processing.
Specifically, in this embodiment, a first state variable corresponding to the inverse hysteresis model at the first time may be obtained by building a data connection interface with the inverse hysteresis model, or in this embodiment, the state variable in the model parameter of the inverse hysteresis model may be directly read, so as to obtain the first state variable corresponding to the inverse hysteresis model at the first time.
Step 102: and obtaining a second state variable corresponding to the inverse hysteresis model at a second moment according to at least the first state variable.
And the second moment is the next moment of the first moment. Taking the second time as the current time k as an example, the first time is the previous time k-1 of the current time, and based on this, the corresponding first state variable at the first time is
That is, k-1 is a first time, and a corresponding second state variable at a second time
Indicating that k is the second time.
In this embodiment, the first state variable may be processed, and then the second state variable corresponding to the inverse hysteresis model at the second time may be predicted based on the first state variable. That is, the state variable of the inverse hysteresis model at the current time is predicted based on the state variable of the inverse hysteresis model at the previous time in the present embodiment.
Specifically, F may be used in the present embodimentkAnd BkFor the first state variable
Performing calculation to obtain a second state variable
The following formula (1):
wherein, BkCharacterizing an inverse hysteresis modelThe relation between the state variable and the desired displacement as input to the inverse hysteresis model, e.g. BkCharacterizing a second state variable corresponding to the inverse lag model at a second time and an expected displacement y corresponding to the inverse lag model at the second timedkIn the present embodiment, BkCan be set to 0 or other values, at BkSet to 0, a second state variable characterizing the inverse lag model at the second time corresponds to a desired displacement y of the inverse lag model at the second timedkIs irrelevant. FkThe correspondence between state variables characterizing the inverse hysteresis model at adjacent instants, e.g. FkCharacterizing a corresponding second state variable of the inverse lag model at a second time
A first state variable corresponding to the inverse lag model at a first time
The state vector transformation relation between them, in the present embodiment, FkCan be set to 1 or other values at FkSet to 1, characterizing a corresponding second state variable of the inverse lag model at a second time instant
A first state variable corresponding to the inverse lag model at a first time
The inverse lag model is a single mapping relation between the first state variable and the second state variable, and the first state variable and the second state variable can be directly mapped from the inverse lag model in the first correspondence
Obtaining a corresponding second state variable of the inverse lag model at a second moment
Step 103: and updating the second state variable at least according to the output displacement of the piezoelectric ceramic driver at the second moment to obtain a third state variable, so that the inverse hysteresis model outputs the compensated input voltage to the piezoelectric ceramic driver at least by using the third state variable.
In this embodiment, the output position y of the piezoceramic driver at the second time can be measuredkTo the second state variable
Processing to obtain updated third state variable
And (4) showing.
That is to say, in this embodiment, the output displacement of the piezoelectric ceramic driver is fed back to the inverse hysteresis model, and the state variable used for obtaining the input voltage in the inverse hysteresis model is updated, so that the accuracy of the input voltage output to the piezoelectric ceramic driver is improved by improving the accuracy of the state variable of the inverse hysteresis model, and thus the accuracy of the output displacement of the piezoelectric ceramic driver is improved, and the accuracy of the positioning performed by the piezoelectric ceramic driver in the positioning device is improved.
Specifically, in this embodiment, the characteristics of the adaptive kalman filter, such as simple form, fast response, and suitability for a high-frequency fast response system, may be utilized, and the adaptive kalman filter akf (adaptive kalman filter) is used to achieve the obtaining and updating of the state variable of the inverse hysteresis model, as shown in fig. 4, the adaptive kalman filter updates the state variable in the inverse hysteresis model, so as to replace the obtained third state variable into the inverse hysteresis model, thereby enabling the inverse hysteresis model to output the compensated input voltage to the piezoceramic driver by using at least the third state variable.
In the inverse hysteresis model, the third state variable may be transposed first, and then the transposed third state variable is transposed
Vector multiplication is carried out on the threshold vector corresponding to the inverse lag model at the second moment, and the threshold vector corresponding to the inverse lag model at the second moment is represented by Hr(ydk) Indicating that the compensated input voltage at the second time is obtained in ukAnd then, outputting the compensated input voltage to the piezoelectric ceramic driver, and obtaining output displacement by the piezoelectric ceramic driver according to the compensated input voltage to realize positioning.
It can be seen from the foregoing technical solutions that, in the hysteresis compensation method for a piezoelectric ceramic driver provided in the embodiment of the present application, when performing hysteresis compensation on the piezoelectric ceramic driver, the hysteresis compensation is implemented by using an inverse hysteresis model, and meanwhile, in this embodiment, the inverse hysteresis model is used for predicting and updating a state variable for implementing hysteresis compensation in the inverse hysteresis model, so that the inverse hysteresis model outputs a compensated input voltage to the piezoelectric ceramic driver by using the updated state variable, thereby implementing hysteresis compensation on the piezoelectric ceramic driver, reducing an error of an output displacement of the piezoelectric ceramic driver, and achieving an improvement in accuracy of positioning of the piezoelectric ceramic driver.
It should be noted that the third state variable obtained in the present embodiment
And the hysteresis compensation of the piezoelectric ceramic driver at the next moment of the second moment can be further used. For example, after the hysteresis compensation of the piezoelectric ceramic driver at the second time is completed, a third state variable corresponding to the inverse hysteresis model at the second time is obtained
Then according to
Obtaining a corresponding second state variable of the inverse lag model at a time next to the second time, wherein the second state variable can be used
Show thatThen, according to the output position pair of the piezoelectric ceramic driver at the next moment of the second moment
Updating to obtain a third state variable corresponding to the next time of the second time, wherein the third state variable can be used
In this way, the inverse hysteresis model outputs the compensated input voltage to the piezoelectric ceramic driver using at least the third state variable corresponding to the next time of the second time, thereby performing hysteresis compensation on the piezoelectric ceramic driver at the next time of the second time.
That is to say, the hysteresis compensation scheme described in this embodiment is not only applicable to performing hysteresis compensation on the input voltage for positioning the piezoelectric ceramic driver at the second time, but also applicable to performing hysteresis compensation on the piezoelectric ceramic driver at each time, and performing hysteresis compensation on the piezoelectric ceramic driver at each time depends on the state variable updated by the inverse hysteresis model in the hysteresis compensation process at the previous time. For example, when the piezoelectric ceramic driver is subjected to hysteresis compensation for the first time, that is, the first time, the obtained first state variable is an initial preset state variable, the preset state variable is used for predicting a second state variable corresponding to the first time, and after the second state variable is updated, the obtained third state variable is used for the inverse hysteresis model to perform hysteresis compensation on the piezoelectric ceramic driver at the first time; then, when the piezoelectric ceramic driver is subjected to hysteresis compensation at the next moment, namely the second moment, the third state variable updated at the previous moment, namely the first moment, is adopted as a new first state variable and is used for predicting a corresponding new second state variable at the second moment, and after the new second state variable is updated, the obtained new third state variable is used for the inverse hysteresis model to perform hysteresis compensation on the piezoelectric ceramic driver at the second moment; then, when the piezoelectric ceramic driver is subjected to hysteresis compensation at the next moment, namely the third moment, adopting a third state variable updated at the previous time, namely the second time as a new first state variable for predicting a corresponding new second state variable at the third time, after the new second state variable is updated, the obtained new third state variable is used for the inverse hysteresis model to perform hysteresis compensation on the piezoelectric ceramic driver at the third moment, and so on, the state variable of the inverse hysteresis model at each moment is gradually optimized, thereby improving the accuracy of the input voltage output to the piezoelectric ceramic driver by improving the accuracy of the state variable of the inverse hysteresis model, therefore, the accuracy of the output displacement of the piezoelectric ceramic driver is improved, and the accuracy of the positioning of the piezoelectric ceramic driver in the positioning equipment is further improved.
In one implementation, when the second state variable is updated according to at least the output displacement of the piezoceramic driver at the second time, step 103 may be implemented by the following steps, as shown in fig. 5:
step 501: and obtaining the corresponding output deviation of the inverse hysteresis model at the second moment according to the output displacement of the piezoelectric ceramic driver at the second moment.
The actual output of the inverse hysteresis model at the second time, i.e. the input voltage actually output to the piezoceramic driver, cannot be measured directly, i.e. ukTherefore, in the present embodiment, the output deviation of the inverse hysteresis model at the second time is obtained by using the correspondence relationship between the output deviation of the piezoelectric ceramic driver and the output deviation of the inverse hysteresis model, and the output deviation may also be referred to as information entropy. Wherein the desired output of the inverse lag model at the second time instant
And (4) showing. Therefore, in this embodiment, the output deviation of the piezoelectric ceramic actuator at the second time is obtained according to the output displacement of the piezoelectric ceramic actuator at the second time, and the output deviation of the inverse hysteresis model at the second time, that is, the output deviation of the inverse hysteresis model at the second time is obtained according to the corresponding relationship
Specifically, step 501 may be implemented by:
firstly, obtaining the corresponding displacement deviation of the piezoelectric ceramic driver at the second moment according to the expected displacement of the inverse hysteresis model at the second moment and the output displacement of the piezoelectric ceramic driver at the second moment, and then obtaining the corresponding output deviation of the inverse hysteresis model at the second moment according to the displacement deviation.
The expected displacement of the inverse hysteresis model at the second moment is a preset value, and the expected displacement of the inverse hysteresis model at the second moment can be obtained by reading a storage area storing the expected displacement and the like. Based on this, in the present embodiment, the output displacement y of the piezoceramic driver at the second time can be obtainedkSubtracting the expected displacement y corresponding to the inverse lag model at the second timedkThe corresponding displacement deviation of the piezoceramic actuator at the second time is obtained in yk-ydkIs denoted by e for shortk. And then, calculating the corresponding displacement deviation of the piezoelectric ceramic driver at the second moment according to the corresponding relation between the input deviation of the piezoelectric ceramic driver at the second moment or the corresponding output deviation of the inverse hysteresis model at the second moment, and further obtaining the corresponding output deviation of the inverse hysteresis model at the second moment.
Specifically, in this embodiment, the control ratio of the piezoelectric ceramic driver may be used to process the displacement deviation corresponding to the piezoelectric ceramic driver at the second time, so as to obtain the output deviation corresponding to the inverse hysteresis model at the second time. The control proportion is the ratio of the maximum control input voltage of the piezoelectric ceramic driver to the maximum control output displacement of the piezoelectric ceramic driver, and based on the ratio, the corresponding displacement deviation of the piezoelectric ceramic driver at the second moment is multiplied by the control proportion of the piezoelectric ceramic driver to obtain the corresponding output deviation of the inverse hysteresis model at the second moment.
Wherein, the piezoelectric ceramicsThe control ratio of the porcelain actuator may be 1 or other values, which may be represented by η. That is, the control ratio η is multiplied by the corresponding displacement deviation e of the piezoceramic actuator at the second timekThe resulting value i.e.. eta. (y)k-ydk) Representing the corresponding output deviation of the inverse hysteresis model at the second time
Step 502: and updating the second state variable by using the parameter vector according to the corresponding output deviation of the inverse hysteresis model at the second moment so as to obtain a third state variable.
And obtaining the parameter vector at least according to the covariance matrix of the corresponding state variable of the inverse lag model at the second moment. The covariance matrix of the state variable corresponding to the inverse lag model at the second time may be understood as the covariance matrix formed by the state variable of the inverse lag model changing, and may be PkAnd (4) showing.
That is, the covariance matrix P of the state variables corresponding to the second time instant using the inverse hysteresis model in the present embodimentkAnd acquiring a parameter vector for updating the second state variable, and further processing the acquired parameter vector and the second state variable by using the corresponding output deviation of the inverse hysteresis model at the second moment to acquire an updated third state variable.
In a specific implementation, the parameter vector is represented by K, in this embodiment, the second state variable may be updated by using a kalman filter, and the parameter vector K may be a kalman gain vector in the kalman filter. Based on this, the covariance matrix P of the state variables corresponding to the second time instant using the inverse lag model in the present embodimentkAfter updating the kalman gain vector K of the kalman filter, the updated kalman gain K 'and the second state variable are processed by using the corresponding output deviation of the inverse lag model at the second time, for example, the updated kalman gain K' is inverted and then multiplied by the inverse lag model at the second timeThen vector-summing with the second state variable, thereby updating the second state variable and obtaining a third state variable, as shown in equation (2):
in one implementation, the parameter vector is obtained by:
and processing the threshold vector of the inverse hysteresis model at least according to the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second moment to obtain a parameter vector.
In a specific implementation, in this embodiment, the covariance matrix P of the state variable corresponding to the inverse lag model at the second time may be usedkThreshold vector H corresponding to inverse lag model at second time instantr(ydk) Multiplying to obtain a first intermediate vector, and calculating a threshold vector H corresponding to the inverse lag model at a second timer(ydk) After the inversion, the inverse lag model is sequentially multiplied by the covariance matrix P of the state variables corresponding to the inverse lag model at the second momentkThreshold vector H corresponding to inverse lag model at second timer(ydk) And obtaining a second intermediate vector, and dividing the first intermediate vector and the second intermediate vector based on the second intermediate vector to obtain a parameter vector, wherein the parameter vector is obtained according to the following formula (3):
K′＝PkHr(ydk)/(Hr(ydk)TPkHr(ydk)) (3)
further, in the process of updating the second state variable by using the adaptive kalman filter in this embodiment, the adaptive kalman filter may have measurement noise, and in order to improve accuracy, when updating the parameter vector in this embodiment, the following method may be implemented:
first, a covariance matrix of the corresponding measurement noise at the second time is obtained, specifically, the covariance matrix may be obtained by observing an adaptive kalman filter, and may be obtained by using RkRepresents;
then, according to the covariance matrix R of the corresponding measurement noise at the second momentkCovariance matrix P of state variables corresponding to the inverse lag model at the second timekAnd processing the threshold vector of the inverse hysteresis model to obtain a parameter vector.
In a specific implementation, in this embodiment, the covariance matrix P of the state variable corresponding to the inverse lag model at the second time may be usedkThreshold vector H corresponding to inverse lag model at second time instantr(ydk) Multiplying to obtain a first intermediate vector, and calculating a threshold vector H corresponding to the inverse lag model at a second timer(ydk) After the inversion, the inverse lag model is sequentially multiplied by the covariance matrix P of the state variables corresponding to the inverse lag model at the second momentkThreshold vector H corresponding to inverse lag model at second timer(ydk) Finally, the covariance matrix R of the corresponding measured noise at the second moment is addedkAnd obtaining a second intermediate vector, and dividing the first intermediate vector and the second intermediate vector based on the second intermediate vector to obtain a parameter vector, wherein the parameter vector is obtained according to the following formula (4):
K′＝PkHr(ydk)/(Hr(ydk)TPkHr(ydk)+Rk) (4)
in addition, after the parameter vector is updated and the covariance matrix of the state variable corresponding to the inverse lag model at the second time is obtained in the embodiment, the covariance matrix P of the state variable corresponding to the inverse lag model at the second time may be obtainedkUpdating P to be updatedkCovariance matrix P for the corresponding state variable of the inverse lag model at the next time k +1k+1Making a prediction, further, the predicted Pk+1For the next acquisition of the parameter vector.
Specifically, in this embodiment, a preset forgetting factor may be used, and the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second time is updated according to the updated parameter vector, so as to obtain the covariance matrix of the new state variable corresponding to the inverse hysteresis model at the second time, where the covariance matrix of the new state variable corresponding to the inverse hysteresis model at the second time is used to obtain the covariance matrix of the state variable corresponding to the inverse hysteresis model at the next time of the second time.
Wherein the forgetting factor is greater than or equal to a preset threshold. The preset threshold value may be obtained by experimental data. In a specific implementation, in order to improve the stability of updating in this embodiment and avoid sensitivity to noise and interference, the forgetting factor is set to 0.9999 in this embodiment.
Specifically, in this embodiment, the manner of obtaining the covariance matrix of the state variable corresponding to the inverse lag model at the second time may refer to formula (5):
where K' is the parameter vector updated as in equation (4). Based on this, updated Pk' covariance matrix P for the corresponding state variable of the inverse lag model at the next time k +1k+1Making a prediction, further, the predicted Pk+1For updating the next parameter vector, and so on, after the next parameter vector is updated, the covariance matrix P of the corresponding state variable at the time k +1 is updated againk+1To obtain the covariance matrix P of the corresponding new state variable at the time k +1k+1′。
In one implementation, the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second time instant is obtained by:
firstly, obtaining a covariance matrix of a state variable corresponding to the inverse lag model at a first time, and taking P as the covariance matrixk-1Represents;
and then, obtaining the covariance matrix of the state variable corresponding to the inverse lag model at the second moment at least according to the covariance matrix of the process noise corresponding to the inverse lag model at the second moment and the covariance matrix of the state variable corresponding to the inverse lag model at the first moment.
The covariance matrix of the process noise corresponding to the inverse lag model at the second time may be a covariance matrix of noise existing in the process of performing the lag compensation processing on the inverse lag model, and may also be understood as a covariance matrix of state transitionkAnd (4) showing.
Based on this, the present embodiment can use F firstkSequentially multiplying by the covariance matrix P of the state variables corresponding to the inverse lag model at the first timek-1And FkThen adding the covariance matrix Q of the process noise corresponding to the inverse lag model at the second momentkThereby obtaining a covariance matrix P of the state variable corresponding to the inverse lag model at the second timek. As shown in the following equation (6):
at FkSet to 1, characterizing a corresponding second state variable of the inverse lag model at a second time instant
A first state variable corresponding to the inverse lag model at a first time
There is a single mapping relationship between them, at this time, Pk＝Pk-1+Qk。
Referring to fig. 6, a schematic structural diagram of a hysteresis compensation apparatus for a piezoelectric ceramic driver according to a second embodiment of the present disclosure is provided, where the hysteresis compensation apparatus may be configured in a positioning device, such as a piezoelectric ultrasonic injector or an AFM, and the positioning device is capable of performing data processing, and the positioning device is positioned by the piezoelectric ceramic driver. The technical scheme of the embodiment is mainly used for improving the accuracy of positioning of the piezoelectric ceramic driver in the positioning equipment.
Specifically, the apparatus in this embodiment may include the following structural units:
the inverse hysteresis model 601 is configured on the piezoelectric ceramic driver, and the inverse hysteresis model 601 is used for processing the expected displacement and outputting the processed input voltage to the piezoelectric ceramic driver;
a variable updating module 602, configured to obtain a first state variable corresponding to the inverse hysteresis model 601 at a first time; obtaining a second state variable corresponding to the inverse hysteresis model 601 at a second moment according to at least the first state variable, wherein the second moment is a next moment of the first moment; and updating the second state variable at least according to the output displacement of the piezoelectric ceramic driver at the second moment to obtain a third state variable, so that the inverse hysteresis model 601 outputs the compensated input voltage to the piezoelectric ceramic driver at least by using the third state variable.
Specifically, the variable update module 602 may be implemented by using an adaptive kalman filter.
It can be seen from the foregoing technical solutions that, in the hysteresis compensation device for a piezoelectric ceramic driver provided in the second embodiment of the present application, when performing hysteresis compensation on the piezoelectric ceramic driver, the hysteresis compensation is implemented by using an inverse hysteresis model, and meanwhile, in this embodiment, the inverse hysteresis model is used for predicting and updating a state variable for implementing hysteresis compensation in the inverse hysteresis model, so that the inverse hysteresis model outputs a compensated input voltage to the piezoelectric ceramic driver by using the updated state variable, thereby implementing hysteresis compensation on the piezoelectric ceramic driver, reducing an error of an output displacement of the piezoelectric ceramic driver, and achieving an improvement in accuracy of positioning of the piezoelectric ceramic driver.
In one implementation, the variable update module 602 obtains the third state variable by:
obtaining the corresponding output deviation of the inverse hysteresis model at the second moment according to the output displacement of the piezoelectric ceramic driver at the second moment; updating the second state variable by using a parameter vector according to the corresponding output deviation of the inverse hysteresis model at the second moment so as to obtain a third state variable;
and obtaining the parameter vector at least according to the covariance matrix of the corresponding state variable of the inverse hysteresis model at the second moment.
Specifically, the parameter vector is obtained by:
and processing the threshold vector of the inverse hysteresis model at least according to the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second moment to obtain a parameter vector. For example, a covariance matrix of the corresponding measurement noise at the second time is obtained; and processing the threshold vector of the inverse hysteresis model according to the covariance matrix of the measurement noise corresponding to the second moment and the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second moment to obtain a parameter vector.
In one implementation, the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second time instant is obtained by:
obtaining a covariance matrix of a state variable corresponding to the inverse lag model at the first time; and obtaining a covariance matrix of the state variable corresponding to the inverse lag model at the second moment at least according to the covariance matrix of the process noise corresponding to the inverse lag model at the second moment and the covariance matrix of the state variable corresponding to the inverse lag model at the first moment. For example, by using a preset forgetting factor, performing matrix calculation on a covariance matrix of process noise corresponding to the inverse hysteresis model at the second time and a covariance matrix of a state variable corresponding to the inverse hysteresis model at the first time to obtain a covariance matrix of the state variable corresponding to the inverse hysteresis model at the second time; the forgetting factor is a numerical value larger than or equal to a preset threshold value.
In one implementation, the variable update module 602 may obtain the corresponding output deviation of the inverse hysteresis model at the second time by:
obtaining a corresponding displacement deviation of the piezoelectric ceramic driver at the second moment according to the expected displacement corresponding to the inverse hysteresis model at the second moment and the output displacement of the piezoelectric ceramic driver at the second moment; and obtaining the corresponding output deviation of the inverse hysteresis model at the second moment according to the displacement deviation. For example, the displacement deviation is processed by using a control proportion of the piezoelectric ceramic driver to obtain an output deviation corresponding to the inverse hysteresis model at the second time; the control proportion is the ratio of the maximum control input voltage of the piezoelectric ceramic driver to the maximum control output displacement of the piezoelectric ceramic driver.
It should be noted that, in the present embodiment, reference may be made to the corresponding contents in the foregoing for specific implementations of the inverse lag model and the variable update module, and details are not described here.
Referring to fig. 7, a schematic structural diagram of a positioning apparatus provided in the third embodiment of the present application is shown, where the positioning apparatus may be a positioning apparatus that includes a piezoelectric ceramic driver and is capable of performing data processing, such as a piezoelectric ultrasonic injector or an AFM, and the positioning apparatus is positioned by the piezoelectric ceramic driver. The technical scheme of the embodiment is mainly used for improving the accuracy of positioning of the piezoelectric ceramic driver in the positioning equipment.
Specifically, the positioning device in this embodiment may include the following components or assemblies:
a piezoelectric ceramic driver 701;
a hysteresis compensation processor 702, wherein the hysteresis compensation processor 702 is connected with the piezoelectric ceramic driver 701;
the hysteresis compensation processor 702 is configured to configure an inverse hysteresis model for the piezoelectric ceramic driver 701, so that the inverse hysteresis model processes an expected displacement and outputs a processed input voltage to the piezoelectric ceramic driver;
the hysteresis compensation processor 702 is further configured to: obtaining a first state variable corresponding to the inverse lag model at a first time; obtaining a second state variable corresponding to the inverse hysteresis model at a second moment according to at least the first state variable, wherein the second moment is a next moment of the first moment; and updating the second state variable at least according to the output displacement of the piezoelectric ceramic driver at the second moment to obtain a third state variable, so that the inverse hysteresis model outputs the compensated input voltage to the piezoelectric ceramic driver at least by using the third state variable.
The hysteresis compensation processor 702 may obtain the first state variable of the inverse hysteresis model, predict the second state variable, and update the second state variable through an adaptive kalman filter, so that the inverse hysteresis model outputs the compensated input voltage to the piezoceramic driver by using at least the third state variable.
According to the above scheme, in the positioning device provided by the third embodiment of the present application, when performing hysteresis compensation on the piezoelectric ceramic driver, the hysteresis compensation is performed through the inverse hysteresis model, and meanwhile, the inverse hysteresis model is used for predicting and updating the state variable of the hysteresis compensation in the inverse hysteresis model, so that the inverse hysteresis model outputs the compensated input voltage to the piezoelectric ceramic driver by using the updated state variable, thereby implementing the hysteresis compensation on the piezoelectric ceramic driver, reducing the error of the output displacement of the piezoelectric ceramic driver, and achieving the purpose of improving the accuracy of positioning performed by the piezoelectric ceramic driver.
Based on the technical solutions in the above embodiments, the following describes in detail the implementation of the direct inverse hysteresis compensation for the piezoelectric ceramic driver in the present application:
first, the inventors of the present application, when studying the hysteresis phenomenon of the piezoelectric ceramic actuator, found that: model-inversion (MI) methods are widely used in model-based hysteresis compensation, where an inverse hysteresis model can be used as a hysteresis compensator. In the model-inversion approach, the PI model is attractive because the inverse PI model is also a PI model of the same order but with different thresholds and state variables. The identification is typically done offline to obtain a hysteresis model and an inverse hysteresis model. With the integration of nonlinear control algorithms, many advanced hysteresis compensation methods have emerged, and kalman filters are also used to estimate the state of nonlinear systems. The basic idea is that using these measurements over time, a more accurate estimate can be made than from a single measurement. This function can accurately estimate the state of the nonlinear system. Kalman filter based methods are used in atomic force microscopy to improve efficiency and image quality. Another improved version of the kalman filter is the Adaptive Kalman Filter (AKF), widely used for object tracking and localization.
The adaptive kalman filter specifically uses measurement data for filtering, and continuously determines whether the dynamics of the system have changed due to the filter itself. By estimating and correcting model parameters and noise statistics, filter design can be improved and errors reduced. Therefore, the effectiveness of the nonlinear control method is verified, and how to apply the nonlinear algorithm to hysteresis compensation, combining the adaptive algorithm and the hysteresis compensation, has become an important issue in hysteresis compensation.
In view of this, the inventor of the present application proposes a direct Inverse lag compensation scheme based on an adaptive kalman filter, in which a PI model is used as a lag compensator, the equation is simple and easy to understand, and meanwhile, a direct Inverse model method DIM (direct Inverse modeling) is used to directly obtain an Inverse PI model without performing Inverse model calculation, and finally, AKF is integrated into DIM so as to dynamically update state variables of the Inverse PI model.
The specific scheme is divided into the following parts:
1. designing an adaptive Kalman filter system based on a direct inverse model method:
the idea of hysteresis compensation is simplified by the direct inverse model method (DIM), because the controlled object is unchangeable, a good hysteresis compensation effect can be realized only by obtaining the inverse hysteresis model and connecting the inverse hysteresis model in series to a feedforward channel of the system, and the DIM omits the calculation process of the inverse hysteresis model. As shown in fig. 4, the state variables
Sum gap operator vector Hr(yd) The product of (a) constitutes an inverse PI model, i.e. an inverse hysteresis model, whereas the gap operator vector has been previously set manually, so the updating of the state variables is particularly critical.
In the scheme, the DIM and the adaptive Kalman filter are combined to be used as the hysteresis compensation. Wherein an adaptive kalman filter is used to estimate the state variables of the inverse PI model. The adaptive Kalman filter has simple form and quick response, and is very suitable for high-frequency quick response systems such as piezoelectric ceramic drivers.
Since the state variable value is estimated using AKF, the state variable is taken
This is substituted into the adaptive kalman filter's equations, which are described as shown in (1) and (6), i.e., the adaptive kalman filter first predicts the state variable of the inverse lag model at the current time from the state variable of the inverse lag model at the previous time.
For dynamic PI models, the dynamic state variables fluctuate over a small fraction of the static state variables, which means that the dynamic state variables can be treated as constant vectors plus dynamic uncertainties. To simplify the prediction process, the dynamic uncertainty is ignored, and a single mapping is employed, i.e., F can be setkAnd BkSet equal to 1 and 0, respectively. In this case, the current state is observed
Can directly change the state at the previous momentMeasurement of
Thus obtaining the product.
During the updating of the state variables of the second step of the adaptive Kalman filter, the optimal state variables are predicted from the predicted state variables
Sum covariance matrix PkAnd (6) updating. The output of the inverse PI model is ukThe gap operator vector Hr(ydk) Is used as the translation vector. The update rule representation is thus as shown in equation (4), equation (5), and equation (7) below.
Wherein,
is the best estimate within time interval k.
2. Adjusting deviation based on information entropy:
in the updating process of the self-adaptive Kalman filter, the model parameters are output by the actual ukAnd the estimated value
The deviation between them is updated and this deviation is called the information entropy. For the DIM method, an accurate inverse hysteresis model, i.e., u, cannot be obtained in advancekAnd cannot be measured directly. However, the displacement y of the piezo ceramic actuator can be measured. Therefore, the deviation between the desired displacement and the measured displacement is used as the information entropy, and the state variable update rule in equation (7) is modified as shown in equation (2).
Wherein, ydkAnd ykRespectively the expected and measured displacements, ek＝ydk-ykIs a tracking error, and the ratio, i.e. the control ratio eta, is umax/ymaxIs the maximum control input umaxAnd maximum displacement ymaxThe ratio of.
It should be noted that the ratio η is used to map the error in the output to the error in the input, which is important if the input and output are of different orders of magnitude. For the piezoceramic drivers used in this application, umax＝10V，ymaxSince 12.11 μm, η is 0.826V/μm.
Therefore, η is set to 1 in the present application to simplify the calculation because the input (unit: V) and the output (unit: μm) of the piezoelectric ceramic driver are in the same order of magnitude. If the best estimate, i.e., the updated state variable, is obtained, the input voltage of the piezoceramic driver is generated using equation (8) below:
3. the tracking performance under the high-frequency track is realized:
in order to verify the effectiveness of DIM combined with AKF proposed in the present application, other hysteresis compensation schemes can be used to perform comparative experiment tests with the hysteresis compensation scheme in the present application, during the test process, the control parameters in these schemes can be adjusted at low frequency until a satisfactory result is obtained, and the fixed parameters can test the dynamic robustness at higher frequencies.
Based on this, taking several hysteresis compensation schemes as examples for applying hysteresis compensation to the piezoelectric ceramic driver on a 200Hz triangular wave, the generated positioning error is as shown in fig. 8, and for DIM + AKF, the closed-loop system can well follow the expected trajectory; while for other hysteresis compensation schemes the tracking performance will be significantly degraded and the output of the piezo-ceramic driver will be greatly distorted or there will be an observable phase lag and distortion at the piezo-ceramic driver output.
In conclusion, the AKF is integrated into the DIM in the application, so that the state variable of the inverse PI model can be dynamically updated, the proposed DIM and the AKF controller improve the robustness aiming at the saturation and the rate correlation, realize better hysteresis compensation performance, and the DIM + AKF completely eliminates the off-line identification and the field adjustment of control parameters.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in Random Access Memory (RAM), memory, Read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (10)
1. A hysteresis compensation method for a piezoelectric ceramic driver, wherein an inverse hysteresis model is directly obtained by using a direct inverse model method, and an adaptive kalman filter is integrated into the direct inverse model method, the adaptive kalman filter being used to estimate a state variable of the inverse hysteresis model, the method comprising:
obtaining a first state variable corresponding to an inverse hysteresis model at a first time, wherein the inverse hysteresis model is configured on the piezoelectric ceramic driver and is used for processing expected displacement and outputting an input voltage obtained by processing to the piezoelectric ceramic driver;
according to at least the first state variable, the adaptive Kalman filter predicts a corresponding second state variable at a second moment according to the first state variable of the inverse lag model at the first moment, wherein the second moment is the next moment of the first moment;
and the adaptive Kalman filter updates the second state variable at least according to the measured output displacement of the piezoelectric ceramic driver at the second moment to obtain a third state variable, and the third state variable is replaced into the inverse hysteresis model, so that the inverse hysteresis model outputs the compensated input voltage to the piezoelectric ceramic driver at least by using the third state variable.
2. The method of claim 1, wherein updating the second state variable based at least on the output displacement of the piezo ceramic driver at the second time to obtain a third state variable comprises:
obtaining the corresponding output deviation of the inverse hysteresis model at the second moment according to the output displacement of the piezoelectric ceramic driver at the second moment;
updating the second state variable by using a parameter vector according to the corresponding output deviation of the inverse hysteresis model at the second moment so as to obtain a third state variable;
and obtaining the parameter vector at least according to the covariance matrix of the corresponding state variable of the inverse hysteresis model at the second moment.
3. The method of claim 2, wherein the parameter vector is obtained by:
and processing the threshold vector of the inverse hysteresis model at least according to the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second moment to obtain a parameter vector.
4. The method of claim 3, wherein processing the threshold vector of the inverse hysteresis model to obtain a parameter vector at least according to the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second time comprises:
obtaining a covariance matrix of the corresponding measurement noise at the second moment;
and processing the threshold vector of the inverse hysteresis model according to the covariance matrix of the measurement noise corresponding to the second moment and the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second moment to obtain a parameter vector.
5. The method according to claim 2 or 3, wherein the covariance matrix of the corresponding state variable of the inverse hysteresis model at the second time instant is obtained by:
obtaining a covariance matrix of a state variable corresponding to the inverse lag model at the first time;
and obtaining a covariance matrix of the state variable corresponding to the inverse lag model at the second moment at least according to the covariance matrix of the process noise corresponding to the inverse lag model at the second moment and the covariance matrix of the state variable corresponding to the inverse lag model at the first moment.
6. The method of claim 5, wherein after obtaining the covariance matrix of the state variables corresponding to the inverse lag model at the second time, the method further comprises:
updating the covariance matrix of the state variable corresponding to the inverse hysteresis model at the second moment according to the parameter vector by using a preset forgetting factor to obtain a covariance matrix of a new state variable corresponding to the inverse hysteresis model at the second moment, wherein the covariance matrix of the new state variable corresponding to the inverse hysteresis model at the second moment is used for obtaining the covariance matrix of the state variable corresponding to the inverse hysteresis model at the next moment of the second moment;
wherein the forgetting factor is greater than or equal to a preset threshold.
7. The method of claim 2, wherein obtaining the corresponding output deviation of the inverse hysteresis model at the second time according to the output displacement of the piezoceramic driver at the second time comprises:
obtaining a corresponding displacement deviation of the piezoelectric ceramic driver at the second moment according to the expected displacement corresponding to the inverse hysteresis model at the second moment and the output displacement of the piezoelectric ceramic driver at the second moment;
and obtaining the corresponding output deviation of the inverse hysteresis model at the second moment according to the displacement deviation.
8. The method of claim 7, wherein obtaining the corresponding output bias of the inverse hysteresis model at the second time according to the displacement bias comprises:
processing the displacement deviation by using the control proportion of the piezoelectric ceramic driver to obtain the corresponding output deviation of the inverse hysteresis model at the second moment;
the control proportion is the ratio of the maximum control input voltage of the piezoelectric ceramic driver to the maximum control output displacement of the piezoelectric ceramic driver.
9. A hysteresis compensation device of a piezoelectric ceramic driver is characterized in that an inverse hysteresis model is directly obtained by adopting a direct inverse model method, an adaptive Kalman filter is integrated into the direct inverse model method, and the adaptive Kalman filter is used for estimating a state variable of the inverse hysteresis model, and comprises the following steps:
the inverse hysteresis model is configured on the piezoelectric ceramic driver and used for processing the expected displacement and outputting the input voltage obtained by processing to the piezoelectric ceramic driver;
the variable updating module is used for obtaining a first state variable corresponding to the inverse hysteresis model at a first moment; according to at least the first state variable, the adaptive Kalman filter predicts a corresponding second state variable at a second moment according to the first state variable of the inverse lag model at the first moment, wherein the second moment is the next moment of the first moment; and the adaptive Kalman filter updates the second state variable at least according to the measured output displacement of the piezoelectric ceramic driver at the second moment to obtain a third state variable, and the third state variable is replaced into the inverse hysteresis model, so that the inverse hysteresis model outputs the compensated input voltage to the piezoelectric ceramic driver at least by using the third state variable.
10. A positioning apparatus, wherein an inverse hysteresis model is directly obtained using a direct inverse model method, and an adaptive kalman filter is integrated into the direct inverse model method, the adaptive kalman filter being used to estimate state variables of the inverse hysteresis model, comprising:
a piezoelectric ceramic driver;
the hysteresis compensation processor is connected with the piezoelectric ceramic driver;
the hysteresis compensation processor is used for configuring an inverse hysteresis model for the piezoelectric ceramic driver, so that the inverse hysteresis model processes expected displacement and outputs the processed input voltage to the piezoelectric ceramic driver;
the hysteresis compensation processor is further configured to: obtaining a first state variable corresponding to the inverse lag model at a first time; according to at least the first state variable, the adaptive Kalman filter predicts a corresponding second state variable at a second moment according to the first state variable of the inverse lag model at the first moment, wherein the second moment is the next moment of the first moment; and the adaptive Kalman filter updates the second state variable at least according to the measured output displacement of the piezoelectric ceramic driver at the second moment to obtain a third state variable, and the third state variable is replaced into the inverse hysteresis model, so that the inverse hysteresis model outputs the compensated input voltage to the piezoelectric ceramic driver at least by using the third state variable.
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