A hysteresis and creep characteristic fusion modeling method for inchworm piezoelectric motor

Abstract

The application provides a hysteresis and creep characteristic fusion modeling method for inchworm piezoelectric motor, and belongs to the field of ultra-precision motion control. The method aims to solve the problems of unclear modeling mechanism of piezoelectric material nonlinear characteristics and poor control accuracy. The method comprises data collection, segmented node determination, model structure determination based on step function model and model parameter identification. Based on the step function model, the overall nonlinear model is constructed to realize accurate modeling of the nonlinear motion table. The model establishes the intuitive relationship between the motor input voltage and the output displacement under the segmented condition, improves the segmented nonlinear compensation accuracy, effectively improves the positioning accuracy of the inchworm piezoelectric motor, is suitable for the fields of ultra-precision motion control and semiconductor manufacturing, and has important engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of ultra-precision motion control, and in particular relates to a method for fusing hysteresis and creep characteristics modeling of inchworm piezoelectric motors. Background Technology

[0002] Piezoelectric motors, characterized by high resonant frequency, small size, and high precision, are widely used in fields such as micro-vibration control and isolation, high-precision positioning, and semiconductor manufacturing. However, the inherent hysteresis and creep characteristics of piezoelectric materials significantly limit the application accuracy of these motors, resulting in severe nonlinear characteristics between their input voltage and output displacement. Therefore, to improve the positioning accuracy of piezoelectric motors, it is necessary to model and study the hysteresis and creep effects.

[0003] The motion modes of inchworm-type piezoelectric motors are divided into linear and stepping modes. In linear mode, the creep of the piezoelectric material generates creep nonlinear errors that must be considered. This results in a strong nonlinear relationship between the input voltage of the motion stage actuator and the motor displacement in linear motion mode, which is a key factor affecting the positioning accuracy of the motion stage and severely restricts its positioning precision. Therefore, a fusion modeling method for hysteresis and creep characteristics of inchworm-type piezoelectric motors is proposed, which can comprehensively describe the nonlinear characteristics existing in piezoelectric motors. The establishment of this model is of great significance for improving the positioning accuracy of ultra-precision motion systems driven by this type of actuator.

[0004] Patent document CN202310298699.3 describes a fractional-order coupled model for nonlinearity. This model constructs a nonlinear model by cascading a fractional-order hysteresis model and a creep model. It is a further optimization of the traditional approach of compensating for creep as an error, essentially converging with the previous approach, except that the compensation accuracy is improved through fractional-order modeling. In the model construction, the hysteresis and creep caused by the material properties of the piezoelectric motor are incorporated into the same model. Compared with the fractional-order method of patent CN202310298699.3, this avoids the control accuracy problems caused by directly compensating for creep as an error by handling it separately. Summary of the Invention

[0005] To address the problems existing in the background technology, the present invention provides a method for fusion modeling of hysteresis and creep characteristics for inchworm-type piezoelectric motors, which solves the problems of unclear modeling mechanism of nonlinear characteristics of piezoelectric materials and poor control accuracy, and solves the problem of insufficient control accuracy caused by separate treatment of hysteresis and creep and inclusion of them into the system in the form of error compensation in the prior art.

[0006] The technical solution adopted by this invention to solve its technical problem is: a method for fusing hysteresis and creep characteristics modeling of inchworm-type piezoelectric motors, comprising the following steps:

[0007] Step 1: Collect data. The data is the displacement of the electronic motive after applying voltage to the shearing part of the piezoelectric motor.

[0008] Step 2: Determine the segmented nodes and partition the input voltage to obtain the step model;

[0009] Step 3: Determine the model structure based on the step function model;

[0010] Step 4: Identify model parameters.

[0011] Based on the step function model, the nonlinearity of the motion table is accurately modeled by constructing an overall nonlinear model.

[0012] The relationship of the data collected in step one corresponds to: ,in Input voltage, For displacement, Indicates the time.

[0013] Step 1: Collect hysteresis and creep data. Apply a high-frequency AC voltage to the piezoelectric motor and collect the input voltage curve and motor output displacement data, which are the hysteresis data. Apply a step voltage to the piezoelectric motor and collect the input voltage curve and motor output displacement data, which are the creep data.

[0014] In step two, the time it takes for the signal from the shear pin to reach a rate of change of 0 when the voltage in the clamping section remains unchanged is used as the boundary for distinguishing input stability. The derivative of the input voltage in the linear motion mode is taken as 0 as a constraint and judgment condition. Let the first point in the input cycle that satisfies this condition be... ,Right now:

[0015] (1)

[0016] in For the aforementioned input voltage, As voltage segmentation nodes, they are used to construct and segment the step model in the time dimension.

[0017] In step three, we take the step function:

[0018] (2)

[0019] in For step piecewise functions, This is the mathematical representation of the step function. For the voltage piecewise nodes of the step function, the overall nonlinear model is expressed as:

[0020] (3)

[0021] or:

[0022] (4)

[0023] In the formula This represents the overall nonlinear characteristics of the system. For creep nonlinear models, It is a hysteretic nonlinear model.

[0024] In step three In the overall nonlinear model, based on the existing logarithmic relationship between voltage and time for creep, the creep nonlinear model is nonlinearly fitted and modeled. The existing logarithmic relationship between voltage and time for creep is:

[0025] (6)

[0026] In the formula This refers to the output displacement of a piezoelectric motor when the input voltage remains constant. yes The output displacement of the piezoelectric actuator at any given moment. is the creep coefficient for logarithmic response.

[0027] Based on the division of the voltage variation range, a logarithmic time model is used to express the creep nonlinear model, as follows:

[0028] (7)

[0029] In the formula As the coefficient, equation (4) can be written as:

[0030] (8).

[0031] The parameters identified in step four include those of the hysteresis nonlinear model and the creep nonlinear model. and .

[0032] The beneficial effects of this invention are as follows: This model can establish an intuitive relationship between the motor input voltage and output displacement under segmented conditions, and perform nonlinear compensation according to the segmented conditions. The model takes creep as a part of the process into the system, which will effectively improve the accuracy of segmented compensation, thereby improving the positioning accuracy of the motor.

[0033] The advantage of this method is that it can integrate the influence of the main nonlinear factors in the material deformation process in the model, and take into account the deformation characteristics of creep and hysteresis at different energization stages, which is of great significance for the control of the motion table.

[0034] This method breaks through the traditional separate modeling approach and innovatively integrates hysteresis and creep characteristics into the same model through step partitioning, taking into account the deformation characteristics of both at different energization stages, and intuitively depicting the overall nonlinear relationship of the system. Attached Figure Description

[0035] In the attached diagram:

[0036] Figure 1 This is a flowchart and a schematic diagram of the model structure of the hysteresis and creep characteristics fusion modeling method of the inchworm-type piezoelectric motor based on the step function model of the present invention. Detailed Implementation

[0037] The present invention will now be described in further detail with reference to the accompanying drawings. The drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0038] A method for fusing hysteresis and creep characteristics of inchworm-type piezoelectric motors includes the following steps:

[0039] Step 1: Collect data. The data is the displacement of the electronic motive after applying voltage to the shearing part of the piezoelectric motor.

[0040] Step 2: Determine the segmented nodes and partition the input voltage to obtain the step model;

[0041] Step 3: Determine the model structure based on the step function model;

[0042] Step 4: Identify model parameters.

[0043] The relationship of the data collected in step one corresponds to: ,in Input voltage, For displacement, Indicates the time.

[0044] Step 1 involves collecting hysteresis and creep data, including:

[0045] Acquisition of hysteresis data: A high-frequency AC voltage excitation is applied to the piezoelectric motor, and the input voltage curve and motor output displacement data are collected. Under this excitation, the creep is ignored because of its reversibility, but the hysteresis characteristic still exists. Therefore, the collected data can be approximated as pure hysteresis data for parameter fitting.

[0046] Creep data acquisition: A step voltage excitation is applied to the piezoelectric motor, and the input voltage curve and motor output displacement data are collected. Under this excitation, since the voltage change rate is extremely low, the hysteresis can be ignored and only the creep characteristics are retained. Therefore, the collected data can be approximated as pure creep data for parameter fitting.

[0047] In the linear operating mode of this piezoelectric motor, the shearing part will go through two stages from voltage change to voltage stability, namely the voltage change stage and the voltage stability stage. The nonlinearity in the voltage change stage is mainly hysteresis nonlinearity, while the voltage stability stage is mainly creep nonlinearity. Therefore, the definition of voltage stability becomes the main criterion for interval division.

[0048] In step two, the time when the signal of the shear pin alone reaches a rate of change of 0 when the voltage of the clamping part does not change is used as the dividing line for distinguishing input stability. Before the dividing line, i.e. the voltage change stage, the nonlinear characteristics are mainly hysteresis nonlinearity, and after the dividing line, i.e. the voltage stability stage, the nonlinear characteristics are mainly creep nonlinearity.

[0049] Because in the microscopic mechanism, creep will produce a large creep amount at the moment when the voltage tends to stabilize, while there is no condition to produce a large creep during the voltage change stage, the creep time model has defined this dividing point.

[0050] Taking the zero derivative of the input voltage in the linear motion mode as a constraint and judgment condition, let the first point in the input cycle that satisfies this condition be... ,Right now:

[0051] (1)

[0052] In the formula, For the aforementioned input voltage, As voltage segmentation nodes, they are used to construct and segment the step model in the time dimension.

[0053] In step three, we take the step function:

[0054] (2)

[0055] in For step piecewise functions, This is the mathematical representation of the step function. For the voltage piecewise nodes of the step function, the overall nonlinear model is expressed as:

[0056] (3)

[0057] or:

[0058] (4)

[0059] In the formula This represents the overall nonlinear characteristics of the system. For creep nonlinear models, For a hysteresis nonlinear model, in The system exhibits hysteresis during voltage changes. The voltage constant-time system is dominated by creep.

[0060] In equation (4), considering the hysteresis and the accuracy of the model, a hysteresis nonlinear model is added to the constant model dominated by creep.

[0061] For hysteresis nonlinear models There are several existing phenomenological modeling methods for describing hysteresis. Among them, the PI model, as an invertible model, can provide more convenient conditions for controller design. There are no specific methodological requirements for this part of the modeling work. If an invertible model is used for hysteresis modeling in this part, it can further facilitate controller design. For example, if described using an existing improved DUHEM model, the hysteresis can be mathematically characterized based on the following equations:

[0062] (5)

[0063] In the formula, To output the actual displacement components; To output the linear component of the displacement; The hysteresis nonlinear model represents the hysteresis component of the output displacement; Input voltage; and They are and The derivative with respect to time; and These are the model parameters. This model has a good characterization effect on asymmetry and a stronger resistance to oscillation errors at points where the derivative of the input curve approaches 0. Therefore, this model can be used for hysteresis compensation and parameter identification.

[0064] In step three The overall nonlinear model is mainly a time-dependent creep nonlinear model. Based on the hysteresis and model accuracy, a hysteresis nonlinear model is superimposed on the creep nonlinear model to ensure the accuracy of the nonlinear description.

[0065] exist In the overall nonlinear model, based on the existing logarithmic relationship between creep and voltage and time, nonlinear fitting and modeling of creep nonlinearity are performed. The existing logarithmic relationship between creep and time is:

[0066] (6)

[0067] In the formula This refers to the output displacement of a piezoelectric motor when the input voltage remains constant. yes The output displacement of the piezoelectric actuator at any given moment. is the creep coefficient for logarithmic response.

[0068] Based on the division of the voltage variation range, a logarithmic time model is used to express the creep nonlinear model, as follows:

[0069] (7)

[0070] In the formula As the adjustment coefficient, equation (4) can be written as:

[0071] (8).

[0072] As an adjustment coefficient When these are constants, their product yields the result in the logarithmic creep time model. Based on the division of different time stages, the voltage stages can be further subdivided. To perform identification and assignment.

[0073] The parameters identified in step four include those of the hysteresis nonlinear model and the creep nonlinear model. and The parameters that need to be identified in the hysteresis nonlinear model include and .

[0074] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for fusing hysteresis and creep characteristics modeling of inchworm-type piezoelectric motors, characterized in that: Includes the following steps: Step 1: Collect data. The data is the displacement of the electronic motive after applying voltage to the shearing part of the piezoelectric motor. Step 2: Determine the segmented nodes and partition the input voltage to obtain the step model; Step 3: Determine the model structure based on the step function model; Step 4: Identify model parameters.

2. The method for fusing hysteresis and creep characteristics modeling of a inchworm-type piezoelectric motor according to claim 1, characterized in that: The relationship of the data collected in step one corresponds to: ,in Input voltage, For displacement, Indicates the time.

3. The method for fusing hysteresis and creep characteristics modeling of a inchworm-type piezoelectric motor according to claim 2, characterized in that: Step 1: Collect hysteresis and creep data. Apply a high-frequency AC voltage to the piezoelectric motor and collect the input voltage curve and motor output displacement data, which are the hysteresis data. Apply a step voltage to the piezoelectric motor and collect the input voltage curve and motor output displacement data, which are the creep data.

4. The method for fusing hysteresis and creep characteristics modeling of a inchworm-type piezoelectric motor according to claim 3, characterized in that: In step two, the time it takes for the signal from the shear pin to reach a rate of change of 0 when the voltage in the clamping section remains unchanged is used as the boundary for distinguishing input stability. The derivative of the input voltage in the linear motion mode is taken as 0 as a constraint and judgment condition. Let the first point in the input cycle that satisfies this condition be... ,Right now: （1） in For the aforementioned input voltage, As voltage segmentation nodes, they are used to construct and segment the step model in the time dimension.

5. The method for fusing hysteresis and creep characteristics modeling of a inchworm-type piezoelectric motor according to claim 4, characterized in that: In step three, we take the step function: （2） in For step piecewise functions, This is the mathematical representation of the step function. For the voltage piecewise nodes of the step function, the overall nonlinear model is expressed as: （3） or: （4） In the formula This represents the overall nonlinear characteristics of the system. For creep nonlinear models, It is a hysteretic nonlinear model.

6. The method for fusing hysteresis and creep characteristics modeling of a inchworm-type piezoelectric motor according to claim 5, characterized in that: In step three In the overall nonlinear model, based on the existing logarithmic relationship between voltage and time for creep, the creep nonlinear model is nonlinearly fitted and modeled. The existing logarithmic relationship between voltage and time for creep is: （6） In the formula This refers to the output displacement of a piezoelectric motor when the input voltage remains constant. yes The output displacement of the piezoelectric actuator at any given moment. The creep coefficient is the logarithmic response. Based on the division of the voltage variation range, a logarithmic time model is used to express the creep nonlinear model, as follows: （7） In the formula As the coefficient, equation (4) can be written as: （8）。 7. The method for fusing hysteresis and creep characteristics modeling of a inchworm-type piezoelectric motor according to claim 6, characterized in that: The parameters identified in step four include those of the hysteresis nonlinear model and the creep nonlinear model. and .

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