CN111222248B - Method and device for determining hysteresis phenomenon of piezoelectric ceramic actuators - Google Patents

Abstract

The application relates to a hysteresis determining method and a device of a piezoelectric ceramic actuator, belonging to the technical field of piezoelectric ceramics, wherein the method comprises the following steps: acquiring an input voltage of a piezoelectric ceramic actuator; determining a first derivative and a second derivative of the input voltage; inputting the first derivative and the second derivative of the input voltage into a preset hysteresis model to obtain a hysteresis result of the pressure point ceramic actuator; the method comprises the steps that a preset hysteresis model comprises a first derivative of a hysteresis component of input displacement, the first derivative of the hysteresis component comprises a shape control function, the shape control function is a parameter taking the first derivative and the second derivative of input voltage as variables, and the first derivative and the second derivative of the input voltage enable the value of the shape control function to be in non-central symmetrical change along with time; the problem that the error between the theoretical output displacement and the actual output displacement of the existing hysteresis model established based on the Bouc-Wen model is larger can be solved; and the modeling precision of the hysteresis model is improved.

Description

Method and device for determining hysteresis phenomenon of piezoelectric ceramic actuators

Technical field

The present application relates to a method and device for determining the hysteresis phenomenon of a piezoelectric ceramic actuator, which belongs to the technical field of piezoelectric ceramics.

Background technique

The piezoelectric ceramic actuator is an ideal driving element for micro-motion systems, but it suffers from hysteresis. This brings difficulties to the modeling and control of piezoelectric ceramic micro-displacement systems. The hysteresis nonlinearity of piezoelectric ceramics belongs to the non-local storage type hysteresis nonlinearity, which is an inherent characteristic of piezoelectric ceramics. Its main feature is that the output of the system at the next moment not only depends on the input and output at the current moment, but also depends on the historical state of the input.

Existing modeling devices for piezoelectric ceramic actuators include: modeling based on the Bouc-Wen model. Among them, the Bouc-Wen model is expressed by the following formula:

Among them, y(t) is the function of the output displacement changing with time; x(t) is the function of the linear component of the output displacement changing with time; h(t) is the function of the hysteresis component of the output displacement changing with time; u(t) ) is a function of the input voltage changing with time; "." represents the first derivative of the corresponding function; k, A, β, and γ are model parameters, and n is a preset constant, such as: n=1.

However, the error between the theoretical output displacement and the actual output displacement output by the hysteresis model based on the Bouc-Wen model is still large.

Contents of the invention

This application provides a method and device for determining the hysteresis phenomenon of a piezoelectric ceramic actuator, which can solve the error between the theoretical output displacement and the actual output displacement of the existing hysteresis model based on the Bouc-Wen model. Bigger question. This application provides the following technical solutions:

In a first aspect, a method for determining the hysteresis phenomenon of a piezoelectric ceramic actuator is provided, and the method includes:

Obtain the input voltage of the piezoelectric ceramic actuator;

determining the first-order derivative and the second-order derivative of the input voltage;

Input the first-order derivative and the second-order derivative of the input voltage into the preset hysteresis model to obtain the hysteresis result of the piezoelectric ceramic actuator;

Wherein, the preset hysteresis model is obtained by improving the Bouc-Wen model. The preset hysteresis model includes the first-order derivative of the hysteresis component of the input displacement, and the first-order derivative of the hysteresis component includes the shape control function, so The shape control function is a parameter with the first-order derivative and the second-order derivative of the input voltage as variables. The first-order derivative and the second-order derivative of the input voltage make the value of the shape control function non-centrally symmetrical over time. Variety.

Optionally, the shape control function includes a component with a first-order derivative of the input voltage as a parameter, a component with a second-order derivative of the input voltage as a parameter, and a component with the first-order derivative of the input voltage multiplied by two. Derivatives are components of parameters.

Optionally, the preset hysteresis model is expressed by the following formula:

Among them, y(t) is the function of the output displacement changing with time; x(t) is the function of the linear component of the output displacement changing with time; h(t) is the function of the hysteresis component of the output displacement changing with time; u

(t) is the function of the input voltage changing with time; "." represents the first-order derivative of the corresponding function; ".." represents the second-order derivative of the corresponding function k, A, β ₁ , β ₂ , β ₃ , β ₄ , β ₅ , β ₆ , and γ are model parameters, and n is a preset constant.

In a second aspect, a device for determining the hysteresis phenomenon of a piezoelectric ceramic actuator is provided, and the device includes:

A voltage acquisition module, used to acquire the input voltage of the piezoelectric ceramic actuator;

A derivative determination module, used to determine the first-order derivative and the second-order derivative of the input voltage;

A hysteresis determination module, configured to input the first-order derivative and the second-order derivative of the input voltage into a preset hysteresis model to obtain the hysteresis result of the piezoelectric ceramic actuator;

Wherein, the preset hysteresis model is obtained by improving the Bouc-Wen model. The preset hysteresis model includes the first-order derivative of the hysteresis component of the input displacement, and the first-order derivative of the hysteresis component includes the shape control function, so The shape control function is a parameter with the first-order derivative and the second-order derivative of the input voltage as variables. The first-order derivative and the second-order derivative of the input voltage make the value of the shape control function non-centrally symmetrical over time. Variety.

Optionally, the shape control function includes a component with a first-order derivative of the input voltage as a parameter, a component with a second-order derivative of the input voltage as a parameter, and a component with the first-order derivative of the input voltage multiplied by two. Derivatives are components of parameters.

Optionally, the preset hysteresis model is expressed by the following formula:

Among them, y(t) is the function of the output displacement changing with time; x(t) is the function of the linear component of the output displacement changing with time; h(t) is the function of the hysteresis component of the output displacement changing with time; u(t) ) is a function of the input voltage changing with time; "." represents the first-order derivative of the corresponding function; ".." represents the second-order derivative of the corresponding function k, A, β ₁ , β ₂ , β ₃ , β ₄ , β ₅ , β ₆ , and γ are model parameters, and n is a preset constant.

The beneficial effects of this application are: by obtaining the input voltage of the piezoelectric ceramic actuator; determining the first-order derivative and second-order derivative of the input voltage; inputting the first-order derivative and second-order derivative of the input voltage into the preset hysteresis model to obtain the voltage Hysteresis results of electroceramic actuators; it can solve the existing hysteresis model based on the Bouc-Wen model, which has a large error between the theoretical output displacement and the actual output displacement; because the preset hysteresis model is Obtained by improving the Bouc-Wen model, the preset hysteresis model includes the first-order derivative of the hysteresis component of the input displacement. The first-order derivative of the hysteresis component includes the shape control function. The shape control function is the first-order derivative of the input voltage and the second-order The derivative is the parameter of the variable. The first-order derivative and the second-order derivative of the input voltage cause the value of the shape control function to change non-centrosymmetrically with time. Therefore, it is more consistent with the actual changes of the shape control function, thereby improving the modeling of the hysteresis model. Accuracy.

The above description is only an overview of the technical solutions of the present application. In order to have a clearer understanding of the technical means of the present application and implement them according to the contents of the specification, the preferred embodiments of the present application are described in detail below with reference to the accompanying drawings.

Description of the drawings

Figure 1 is a flow chart of a method for determining the hysteresis phenomenon of a piezoelectric ceramic actuator provided by an embodiment of the present application;

Figure 2 is a schematic diagram of the error curve of the Bouc-Wen model and the preset hysteresis model as a function of time provided by an embodiment of the present application;

FIG. 3 is a block diagram of a device for determining the hysteresis phenomenon of a piezoelectric ceramic actuator provided by an embodiment of the present application.

Detailed ways

Specific implementations of the present application will be described in further detail below with reference to the accompanying drawings and examples. The following examples are used to illustrate the present application but are not intended to limit the scope of the present application.

Optionally, this application uses an example in which the execution subject of each embodiment is an electronic device. The electronic device includes but is not limited to: a computer, a mobile phone, a tablet, or a server. This embodiment does not limit the type of electronic device.

Figure 1 is a flow chart of a method for determining the hysteresis phenomenon of a piezoelectric ceramic actuator provided by an embodiment of the present application. This method includes at least the following steps:

Step 101, obtain the input voltage of the piezoelectric ceramic actuator;

Step 102, determine the first-order derivative and second-order derivative of the input voltage;

Step 103, input the first-order derivative and the second-order derivative of the input voltage into the preset hysteresis model to obtain the hysteresis result of the piezoelectric ceramic actuator; wherein, the preset hysteresis model is obtained by improving the Bouc-Wen model, and the preset hysteresis model is The hysteresis model includes the first-order derivative of the hysteresis component of the input displacement. The first-order derivative of the hysteresis component includes the shape control function. The shape control function is a parameter with the first-order derivative and the second-order derivative of the input voltage as variables. The first-order derivative of the input voltage and second-order derivatives make the value of the shape control function change non-centrosymmetrically with time.

Among them, the hysteresis result of the piezoelectric ceramic actuator is used to indicate the input displacement of the piezoelectric ceramic actuator changing with time.

For the existing Bouc-Wen model, it can be expressed as follows:

in the above formula The equivalent is written as follows:

Among them, y(t) is the function of the output displacement changing with time; x(t) is the function of the linear component of the output displacement changing with time; h(t) is the function of the hysteresis component of the output displacement changing with time; u(t) ) is a function of the input voltage changing with time; "." represents the first derivative of the corresponding function; k, A, β, and γ are model parameters, and n is a preset constant, such as: n=1.

Shape control functions in the Bouc-Wen model The function value changes centrally symmetrically with time. However, in actual implementation, the function value of the shape control function changes non-centrosymmetrically with time. Based on this, the preset hysteresis model provided by this application introduces the second-order derivative of the input voltage on the basis of the existing Bouc-Wen model, so that the function value of the shape control function changes non-centrosymmetrically with time, which is more consistent with The actual changes of the shape control function improve the modeling accuracy of the hysteresis model.

Optionally, the shape control function includes a component with a first-order derivative of the input voltage as a parameter, a component with a second-order derivative of the input voltage as a parameter, and a component with the first-order derivative multiplied by the second-order derivative of the input voltage as a parameter.

Optional, the preset hysteresis model is expressed by:

Among them, y(t) is the function of the output displacement changing with time; x(t) is the function of the linear component of the output displacement changing with time; h(t) is the function of the hysteresis component of the output displacement changing with time; u(t) ) is a function of the input voltage changing with time; "." represents the first-order derivative of the corresponding function; ".." represents the second-order derivative of the corresponding function k, A, β ₁ , β ₂ , β ₃ , β ₄ , β ₅ , β ₆ , and γ are model parameters, and n is a preset constant.

Referring to the time-varying error curves of the Bouc-Wen model and the preset hysteresis model shown in Figure 2, it can be seen from Figure 2 that the hysteresis error of the preset hysteresis model is lower than that of the Bouc-Wen model.

In summary, this embodiment provides a method for determining the hysteresis phenomenon of a piezoelectric ceramic actuator by obtaining the input voltage of the piezoelectric ceramic actuator; determining the first-order derivative and second-order derivative of the input voltage; The first-order derivative and the second-order derivative are input into the preset hysteresis model to obtain the hysteresis result of the piezoelectric ceramic actuator; it can solve the existing hysteresis model based on the Bouc-Wen model. The theoretical output displacement output by this model is different from the actual output displacement. The problem of large errors between the two; because the preset hysteresis model is an improvement of the Bouc-Wen model, the preset hysteresis model includes the first-order derivative of the hysteresis component of the input displacement, and the first-order derivative of the hysteresis component includes the shape control function , the shape control function is a parameter with the first-order derivative and the second-order derivative of the input voltage as variables. The first-order derivative and the second-order derivative of the input voltage cause the value of the shape control function to change non-centrosymmetrically with time. Therefore, it is more consistent with The shape control function actually changes, thereby improving the modeling accuracy of the hysteresis model.

FIG. 3 is a block diagram of a device for determining the hysteresis phenomenon of a piezoelectric ceramic actuator provided by an embodiment of the present application. The device includes at least the following modules: voltage acquisition module 310, derivative determination module 320 and hysteresis determination module 330.

Voltage acquisition module 310, used to acquire the input voltage of the piezoelectric ceramic actuator;

The derivative determination module 320 is used to determine the first-order derivative and the second-order derivative of the input voltage;

The hysteresis determination module 330 is used to input the first-order derivative and the second-order derivative of the input voltage into a preset hysteresis model to obtain the hysteresis result of the piezoelectric ceramic actuator;

Wherein, the preset hysteresis model is obtained by improving the Bouc-Wen model. The preset hysteresis model includes the first-order derivative of the hysteresis component of the input displacement, and the first-order derivative of the hysteresis component includes the shape control function, so The shape control function is a parameter with the first-order derivative and the second-order derivative of the input voltage as variables. The first-order derivative and the second-order derivative of the input voltage make the value of the shape control function non-centrally symmetrical over time. Variety.

Optionally, the shape control function includes a component with a first-order derivative of the input voltage as a parameter, a component with a second-order derivative of the input voltage as a parameter, and a component with the first-order derivative of the input voltage multiplied by two. Derivatives are components of parameters.

Optionally, the preset hysteresis model is expressed by the following formula:

Among them, y(t) is the function of the output displacement changing with time; x(t) is the function of the linear component of the output displacement changing with time; h(t) is the function of the hysteresis component of the output displacement changing with time; u

(t) is the function of the input voltage changing with time; "." represents the first-order derivative of the corresponding function; ".." represents the second-order derivative of the corresponding function k, A, β ₁ , β ₂ , β ₃ , β ₄ , β ₅ , β ₆ , and γ are model parameters, and n is a preset constant.

For relevant details, refer to the above device embodiments.

It should be noted that when the device for determining the hysteresis phenomenon of the piezoelectric ceramic actuator provided in the above embodiments determines the hysteresis phenomenon of the piezoelectric ceramic actuator, the division of the above functional modules is only used as an example. In practical applications, , the above function allocation can be completed by different functional modules as needed, that is, the internal structure of the device for determining the hysteresis phenomenon of the piezoelectric ceramic actuator is divided into different functional modules to complete all or part of the functions described above. In addition, the device for determining the hysteresis phenomenon of the piezoelectric ceramic actuator provided in the above embodiments and the embodiment of the method for determining the hysteresis phenomenon of the piezoelectric ceramic actuator belong to the same concept. The specific implementation process can be found in the device embodiment for details, and will not be described again here. .

Optionally, this application also provides a computer-readable storage medium in which a program is stored, and the program is loaded and executed by a processor to implement the piezoelectric ceramic actuator of the above device embodiment. Hysteresis phenomenon determination device.

Optionally, this application also provides a computer product. The computer product includes a computer-readable storage medium. A program is stored in the computer-readable storage medium. The program is loaded and executed by a processor to implement the above device embodiments. Device for determining the hysteresis phenomenon of piezoelectric ceramic actuators.

The technical features of the above-described embodiments can be combined in any way. To simplify the description, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, All should be considered to be within the scope of this manual.

The above-described embodiments only express several implementation modes of the present application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that, for those of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all fall within the protection scope of the present application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims (6)

1. A method for determining the hysteresis phenomenon of a piezoelectric ceramic actuator, characterized in that the method includes: Obtain the input voltage of the piezoelectric ceramic actuator; determining the first-order derivative and the second-order derivative of the input voltage; Input the first-order derivative and the second-order derivative of the input voltage into the preset hysteresis model to obtain the hysteresis result of the piezoelectric ceramic actuator; Wherein, the preset hysteresis model is obtained by improving the Bouc-Wen model. The preset hysteresis model includes the first-order derivative of the hysteresis component of the input displacement, and the first-order derivative of the hysteresis component includes the shape control function, so The shape control function is a parameter with the first-order derivative and the second-order derivative of the input voltage as variables. The first-order derivative and the second-order derivative of the input voltage make the value of the shape control function non-centrally symmetrical over time. Variety. 2. The method of claim 1, wherein the shape control function includes a component with a first-order derivative of the input voltage as a parameter, a component with a second-order derivative of the input voltage as a parameter, and a component with the second-order derivative of the input voltage as a parameter. The first derivative of the input voltage multiplied by the second derivative is a component of the parameter. 3. The method according to claim 1, characterized in that the preset hysteresis model is expressed by the following formula: Among them, y(t) is the function of the output displacement changing with time; x(t) is the function of the linear component of the output displacement changing with time; h(t) is the function of the hysteresis component of the output displacement changing with time; u(t) ) is a function of the input voltage changing with time; "." represents the first-order derivative of the corresponding function; ".." represents the second-order derivative of the corresponding function k, A, β ₁ , β ₂ , β ₃ , β ₄ , β ₅ , β ₆ , and γ are model parameters, and n is a preset constant. 4. A device for determining the hysteresis phenomenon of a piezoelectric ceramic actuator, characterized in that the device includes: A voltage acquisition module, used to acquire the input voltage of the piezoelectric ceramic actuator; A derivative determination module, used to determine the first-order derivative and the second-order derivative of the input voltage; A hysteresis determination module, configured to input the first-order derivative and the second-order derivative of the input voltage into a preset hysteresis model to obtain the hysteresis result of the piezoelectric ceramic actuator; Wherein, the preset hysteresis model is obtained by improving the Bouc-Wen model. The preset hysteresis model includes the first-order derivative of the hysteresis component of the input displacement, and the first-order derivative of the hysteresis component includes the shape control function, so The shape control function is a parameter with the first-order derivative and the second-order derivative of the input voltage as variables. The first-order derivative and the second-order derivative of the input voltage make the value of the shape control function non-centrally symmetrical over time. Variety. 5. The device of claim 4, wherein the shape control function includes a component with a first-order derivative of the input voltage as a parameter, a component with a second-order derivative of the input voltage as a parameter, and a component with the second-order derivative of the input voltage as a parameter. The first derivative of the input voltage multiplied by the second derivative is a component of the parameter. 6. The device according to claim 4, characterized in that the preset hysteresis model is expressed by the following formula: Among them, y(t) is the function of the output displacement changing with time; x(t) is the function of the linear component of the output displacement changing with time; h(t) is the function of the hysteresis component of the output displacement changing with time; u(t) ) is a function of the input voltage changing with time; "." represents the first-order derivative of the corresponding function; ".." represents the second-order derivative of the corresponding function k, A, β ₁ , β ₂ , β ₃ , β ₄ , β ₅ , β ₆ , and γ are model parameters, and n is a preset constant.