An Output Prediction Modeling Method for Piezoelectric Ceramic Force-Electric-Potential Dynamic Hysteresis

Abstract

The present invention belongs to the field of piezoelectric ceramic characteristic measurement, and discloses an output prediction modeling method for the force-electric-potential dynamic hysteresis of piezoelectric ceramics. First, install the data acquisition hardware system of the piezoelectric ceramic actuator, collect the experimental data of the input voltage, output force and output displacement of the piezoelectric ceramic actuator, establish the API-NARX neural network model of the piezoelectric ceramic actuator, use the processed experimental data as the input and output of the neural network model, select the initial parameters to train the neural network model, and call the trained neural network model for application in engineering. This method takes into account factors such as the force-electric coupling and dynamic hysteresis of the piezoelectric ceramic actuator, and is more accurate and effective than the traditional voltage-displacement modeling method. It can more accurately describe the force-electric-potential hysteresis characteristics of piezoelectric ceramics, and then realize the prediction of high-precision output displacement and output force. Moreover, this method has strong adaptability and can be applied to all systems containing piezoelectric ceramic actuators.

Description

Technical Field

[0001] The present invention belongs to the field of measurement of piezoelectric ceramic properties, and relates to an output prediction modeling method for the dynamic hysteresis of piezoelectric ceramic force-electricity-potential. Background Art

[0002] The dynamic stability derivatives are key parameters for the analysis and design of the stability and controllability of aircraft, and have an important impact on the control system design and flight quality of aircraft. With the continuous development of aircraft systems towards high speed and precision, the performance requirements for aircraft design are also continuously increasing. Among them, the dynamic derivatives including damping derivatives, cross derivatives, and cross-coupling derivatives generated by aircraft at ultra-high speeds and large-amplitude maneuvers play a crucial guiding role in the analysis and design of aircraft shapes. For example, the cross-coupling derivatives generated by the longitudinal motion of an aircraft at a large angle of attack significantly affect the stability of the aircraft.

[0003] In traditional forced vibration tests, the effects of pure rotation rate and translational acceleration cannot be separated, and the combined dynamic derivatives are given. Usually, some mathematical models use the combined dynamic derivatives, and the predicted flight characteristics are reasonably consistent with the actual situation. However, this approximation is not applicable in all cases. For example, using rotational forced oscillation data to represent the derivatives generated by pure rotational angular rate can produce non-negligible deviations at large angles of attack.

[0004] The multi-degree-of-freedom dynamic derivative experiment of the multi-dimensional composite excitation mechanism in a high-speed wind tunnel can excellently fit the flight state of an aircraft at ultra-high speeds and large-amplitude maneuvers; it can greatly improve the measurement accuracy of the dynamic derivatives and their coupling effects in the pitch, yaw, and roll directions to improve the prediction effect of the aircraft flight characteristics. The multi-dimensional composite excitation mechanism drive faces the following several difficulties: First, the driving element needs to drive the model to complete multi-dimensional composite excitation motion within a limited space; second, the driving element needs to resist transient multi-dimensional loads in a complex flow field environment and output precise motion; finally, the working conditions for measuring various dynamic derivatives are different. To enhance the adaptability of the test mechanism, the driving element needs to have capabilities such as high load-bearing, high stiffness, and wide-frequency response.

[0005] The stacked piezoelectric ceramic actuator arranges piezoelectric ceramic sheets in series in terms of structure and connects them in parallel in the circuit. It has the characteristics of fast response speed and compact structure. Moreover, piezoelectric ceramics are small in volume, with a large driving force to energy consumption ratio, and can efficiently convert electrical energy into mechanical energy. As an actuator for dynamic derivative test devices, it can achieve good driving effects. However, the physical properties of piezoelectric materials themselves endow them with nonlinear characteristics such as hysteresis and creep. When stressed, the output displacement of piezoelectric ceramics will relatively decrease, showing a stiffness time-varying nonlinear characteristic, which seriously affects the control accuracy of piezoelectric ceramic actuators in practical applications. Currently, there is an urgent need to conduct modeling research on the output displacement characteristics of piezoelectric ceramics under the coupled action of different driving voltages and load states to improve the control accuracy of piezoelectric ceramic actuators in practical applications.

[0006] Neural networks have strong modeling capabilities for nonlinear systems. In theory, neural networks can fully approximate any arbitrarily complex nonlinear system, and neural networks have strong information integration capabilities and can simultaneously process and coordinate various input information relationships. Therefore, applying neural networks can model the output of piezoelectric ceramic actuators under the coupled action of different driving voltages and load states, which can greatly reduce the errors of piezoelectric ceramic actuators and improve the control accuracy of piezoelectric ceramic actuators.

[0007] In the patent "Modeling Method for Dynamic Hysteresis Characteristics of Piezoelectric Ceramics" by Cao Kairui et al., with the patent number CN202310434548.6, a modeling method for the dynamic hysteresis characteristics of piezoelectric ceramics is introduced, which can more accurately describe the dynamic hysteresis characteristics of piezoelectric ceramics and thus achieve high-precision position prediction. However, this method only considers input voltages of different frequencies and the fitted output displacement and cannot be applied to piezoelectric ceramic driver systems with loads and requiring consideration of force-displacement coupling hysteresis.

[0008] In "Hysteresis Modeling of Piezoelectric Actuators Based on RBF Neural Networks" published by Hu Li et al. in the 5th issue of Piezoelectrics & Acoustooptics in 2018, through the modeling method of radial neural networks, a highly accurate fitting of the nonlinear curve between the output displacement and input voltage of piezoelectric actuators is achieved. However, this method only considers the output displacement and input voltage and cannot be applied to piezoelectric ceramic driver systems with loads and requiring the output force of piezoelectric ceramics.

[0009] According to a piezoelectric ceramic force-position output characteristic test device introduced in the patent with the patent number 202311023647.1, the output displacement and output force of piezoelectric ceramic actuators under different driving voltages and different stress states are measured and collected.

[0010] Based on the problems existing in the above technologies, it is necessary to propose a modeling method for high-precision position prediction. Summary of the Invention

[0011] In order to overcome the deficiencies of the prior art, the present invention proposes an output prediction modeling method for the piezoelectric ceramic force-electricity-potential dynamic hysteresis, so as to more accurately describe the force-electricity-potential hysteresis characteristics of the piezoelectric ceramic and then achieve high-precision position prediction. This method first installs a data acquisition hardware system for the piezoelectric ceramic actuator, collects the experimental data of the input voltage, output force and output displacement of the piezoelectric ceramic actuator, establishes an API-NARX neural network model for the piezoelectric ceramic actuator, uses the processed experimental data as the input and output of the neural network model, selects appropriate initial parameters to train the neural network model of the system, and finally can call the trained neural network model in engineering for application. The neural network model is used to indirectly realize the prediction of the output force and the prediction of the output displacement, avoiding the problem that the force sensor cannot be installed due to its too large structure in the actual system and thus the output force value of the piezoelectric ceramic actuator cannot be obtained in real time. At the same time, factors such as the force-electricity coupling and dynamic hysteresis of the piezoelectric ceramic actuator are considered, which is more accurate and effective compared with the traditional voltage-displacement modeling method. Moreover, this method has strong adaptability and can be applied to all systems containing piezoelectric ceramic actuators.

[0012] The technical solution of the present invention:

[0013] An output prediction modeling method for the piezoelectric ceramic force-electricity-potential dynamic hysteresis, based on a piezoelectric ceramic force-potential output characteristic test system, measures the output displacement of the piezoelectric ceramic under different driving voltages and different stress states;

[0014] The specific steps are as follows:

[0015] The first step: Assemble a piezoelectric ceramic force-potential output characteristic test system and collect the output displacement and output force data of the piezoelectric ceramic actuator

[0016] Realize the measurement and collection of the output displacement and output force of the piezoelectric ceramic actuator under different driving voltages and different stress states;

[0017] The second step: Establish an API-NARX neural network model for the piezoelectric ceramic actuator

[0018] Aiming at the shortcoming that the traditional PI model cannot describe the asymmetric and dynamic hysteresis characteristics, an API-NARX model is established. First, the output force-displacement hysteresis operator and the voltage-displacement hysteresis operator are introduced to establish an API force-electricity-potential model;

[0019] Force-displacement hysteresis operator:

[0020]

[0021] Voltage-displacement hysteresis operator:

[0022]

[0023] API force-electric-potential model:

[0024]

[0025] Among them, y API [F](t) is the displacement output of the piezoelectric ceramic under force-displacement hysteresis, H s,m [F](t) is the force-displacement hysteresis operator, v i is the weight value of the voltage-displacement hysteresis operator; y API [u](t) is the displacement output of the piezoelectric ceramic under voltage-displacement hysteresis, H r,m [u](t) is the voltage-displacement hysteresis operator, w i is the weight value of the force-displacement hysteresis operator; y API [u][F](t) is the API force-electric-potential model;

[0026] Through MATLAB software, a NARX neural network model of the input voltage, output force, and output displacement of the piezoelectric ceramic actuator 2 is established. The NARX neural network model is a model used to describe nonlinear discrete systems and is expressed as:

[0027]

[0028] In the formula: u(t) is the voltage input of the NARX neural network model at time t; F(t) and y(t) are the output force and output displacement of the NARX neural network model at time t, respectively; D u is the maximum order of the time delay of the input voltage; D F , D y is the maximum order of the time delay of the output force and output displacement; Therefore, u(t - D u ), …, u(t - 1) are the historical input voltages relative to time t; F(t - D F ), …, F(t - 1), y(t - D y ), …, y(t - 1) are the historical output force and output displacement relative to time t; f is the nonlinear function obtained by network fitting;

[0029] Taking the predicted output force, output displacement, and system input voltage of the API force-electric-potential model as the input of the NARX neural network model, the API-NARX model is obtained after training;

[0030] Step 3: Train the neural network model and conduct application verification

[0031] Dividing the data collected in the first step into two groups, training and testing the API-NARX model, conducting preset experiments on the piezoelectric ceramic force-position output characteristic test device, predicting the output force and output displacement of the piezoelectric ceramic actuator 2, and verifying the effect of the established piezoelectric ceramic model.

[0032] The established piezoelectric ceramic output prediction model is a superposition coupling model of a voltage-displacement hysteresis model and a force-displacement hysteresis model, including but not limited to a system that uses the superposition coupling model of the voltage-displacement hysteresis model and the force-displacement hysteresis model to predict the output force and output displacement.

[0033] Advantages of the present invention: The piezoelectric ceramic API force-electric-potential model proposed by this method is a superposition coupling model of a voltage-displacement hysteresis model and a force-displacement hysteresis model, which can accurately predict the static output force and static output displacement of a piezoelectric ceramic actuator, solving the problem that the output force value of the piezoelectric ceramic actuator cannot be obtained due to the too large structure of the force sensor and the inability to install it in the actual system. Then, taking the predicted output force, output displacement and system input voltage of the API force-electric-potential model as the inputs of the NARX neural network model, the API-NARX model is obtained, which can solve the problem of too large dynamic hysteresis error. The established piezoelectric ceramic output prediction model is a superposition coupling model of a voltage-displacement hysteresis model and a force-displacement hysteresis model. This modeling method only needs to obtain the experimental data of the input voltage of the piezoelectric ceramic actuator, and can predict the output force and output displacement of the piezoelectric ceramic actuator in real time; moreover, it takes into account the nonlinear characteristics and dynamic hysteresis characteristics of the piezoelectric ceramic actuator, making the control result more accurate and with higher precision; the model establishment and training are convenient and fast, with strong adaptability, and can be applied to all systems containing piezoelectric ceramic actuators. Description of the Drawings

[0034] Figure 1 It is a schematic connection diagram of the force-position output characteristic test system of the piezoelectric ceramic actuator of the present invention;

[0035] Figure 2 It is a flow chart of the force output prediction method of the piezoelectric ceramic actuator of the present invention;

[0036] Figure 3 It is a curve graph of the prediction result of the piezoelectric ceramic actuator API-NARX model in the embodiment. Among them, the X-axis is the input voltage, the Y-axis is the output force, and the Z-axis is the output displacement.

[0037] Figure 4 It is a partial enlarged view of the curve graph of the prediction result of the piezoelectric ceramic actuator API-NARX model in the embodiment. Among them, the X-axis is the input voltage, the Y-axis is the output force, and the Z-axis is the output displacement.

[0038] In the figure: 1 - laser displacement sensor, 2 - piezoelectric ceramic actuator, 3 - main body of the test device, 4 - power amplifier, 5 - real-time controller, 6 - pressure sensor, 7 - data acquisition module, 8 - upper computer. Detailed Embodiments

[0039] The implementation process of the present invention will be described in detail below in combination with the technical solutions and the drawings.

[0040] Figure 1 It is a schematic diagram for data acquisition of the output displacement and output force of a piezoelectric ceramic actuator. The used test device for the force-displacement output characteristics of the piezoelectric ceramic is internally provided with a pressure sensor 6, which can obtain the external force received by the piezoelectric ceramic 2 in real time. The displacement of the piezoelectric ceramic 2 can be measured by a laser displacement sensor 1. The overall test system can ensure synchronous and accurate measurement of force and displacement, and has the characteristics of compact structure and simple control.

[0041] Figure 2 It is a flowchart of the method for predicting the output force and output displacement of a piezoelectric ceramic actuator. The entire prediction modeling method is divided into the following four parts: assembling the test system for the force-displacement output characteristics of the piezoelectric ceramic, data acquisition of the output displacement and output force of the piezoelectric ceramic actuator, establishing an API-NARX neural network model for the piezoelectric ceramic actuator, and training and validating the neural network model of the system.

[0042] The first step: Assembling the test system for the force-displacement output characteristics of the piezoelectric ceramic

[0043] As Figure 1 shown, assemble the test system for the force-displacement output characteristics of the piezoelectric ceramic: Fix the laser displacement sensor 1, the pressure sensor 6 and the piezoelectric ceramic actuator 2 to the main body 3 of the test device, and apply a pre-tightening force to the piezoelectric ceramic 2; The laser displacement sensor 1 and the pressure sensor 6 are respectively connected to the data acquisition module 7; The data acquisition module 7 is sequentially connected to the upper computer 8, the real-time controller 5 and the power amplifier 4; The power amplifier 4 is connected to the piezoelectric ceramic 2;

[0044] The second step: Data acquisition of the output displacement and output force of the piezoelectric ceramic actuator 2

[0045] Conduct a data acquisition experiment, operate the force-displacement output test device to apply a pre-tightening force to the piezoelectric ceramic; Control the test system through the LabVIEW software to output a sinusoidal waveform voltage input signal with variable amplitude and variable frequency; The upper computer 8 transmits the control signal to the real-time controller 5, and then the real-time controller 5 transmits it to the power amplifier 4. The power amplifier 4 converts the control signal into a voltage and inputs it to the piezoelectric ceramic actuator 2 to achieve ceramic displacement and force output; Use the data acquisition module 7 to read the signal changes on the laser displacement sensor 1 and the pressure sensor 6 to realize the acquisition of the output force data and displacement data; Apply different magnitudes of pre-tightening forces and voltage input signals with variable magnitudes and frequencies to the piezoelectric ceramic actuator 2, and the data acquisition module 7 reads and stores the output signals of the laser displacement sensor 1 and the pressure sensor 6 in real time, thereby completing the data acquisition;

[0046] In this embodiment, the LabVIEW software is used to control the test system to input a sinusoidal waveform voltage with gradually increasing amplitude. The formula is as follows:

[0047] U = ξt·sin(ωt) + ξt

[0048] In the formula, the parameters are taken as ω = 3.14 and ξ = 0.01.

[0049] Step 3: Establish the API-NARX neural network model of the piezoelectric ceramic actuator

[0050] First, introduce the output force hysteresis operator and the output displacement hysteresis operator to establish the API force-electric-potential model;

[0051] Force-displacement hysteresis operator:

[0052]

[0053] Voltage-displacement hysteresis operator:

[0054]

[0055] API force-electric-potential model:

[0056]

[0057] Through the MATLAB software, establish the NARX neural network model of the input voltage, output force, and output displacement of the piezoelectric ceramic actuator. In this embodiment, the input layer has 21 nodes, which are the input voltage, output displacement, output force of the piezoelectric ceramic actuator, and the input voltage, output displacement, and output force of the previous 6 cycles; the hidden layer contains 30 nodes, which are divided into two layers; the output layer has two nodes, which are the predicted output displacement and predicted output force of the piezoelectric ceramic actuator. The initial weights and thresholds of each node are set as random numbers between 1 and -1.

[0058] Step 4: Train the neural network model and conduct application verification

[0059] Divide the data measured in the second step into two groups, train and test the API-NARX model, conduct a preset experiment on the piezoelectric ceramic force-position output device, predict the output force and output displacement of the piezoelectric ceramic, and verify the effect of the established piezoelectric ceramic model.

[0060] The output prediction modeling method for the piezoelectric ceramic force-electricity-potential dynamic hysteresis of the present invention. The established piezoelectric ceramic output prediction model is a superimposed coupling model of a voltage-displacement hysteresis model and a force-displacement hysteresis model. This method takes into account factors such as the force-electricity coupling and dynamic hysteresis of the piezoelectric ceramic actuator, and can achieve the prediction of the output displacement and output force of the piezoelectric ceramic under drive voltage signals with variable amplitudes and variable frequencies. It is more accurate and effective compared with the traditional voltage-displacement modeling method. Save the neural network model parameters, and then when using the model, only substitute the trained parameters, without having to repeat the training. It can provide high-precision output data for the application of piezoelectric ceramics, filling the gap in the existing technical field. Moreover, this method has strong adaptability and can be applied to all systems containing piezoelectric ceramic actuators.

Claims

1. A method for output prediction modeling of piezoelectric ceramic force - electricity - potential dynamic hysteresis, characterized in that, The steps are as follows: The first step: Assemble a piezoelectric ceramic force-displacement output characteristic test system and collect the output displacement and output force data of the piezoelectric ceramic actuator Realize the measurement and collection of the output displacement and output force of the piezoelectric ceramic actuator under different driving voltages and different stress states; The second step: Establish an API-NARX neural network model for the piezoelectric ceramic actuator Aiming at the shortcomings that the traditional PI model cannot describe the asymmetric and dynamic hysteresis characteristics, an API-NARX model is established. First, the output force-displacement hysteresis operator and voltage-displacement hysteresis operator are introduced to establish an API force-electricity-displacement model; Output force-displacement hysteresis operator: Voltage-displacement hysteresis operator: API force-electricity-displacement model: where y API [F](t) is the displacement output of the piezoelectric ceramic under force-displacement hysteresis, H s,m [F](t) is the force-displacement hysteresis operator, v i is the weight of the voltage-displacement hysteresis operator; y API [u](t) is the displacement output of the piezoelectric ceramic under voltage-displacement hysteresis, H r,m [u](t) is the voltage-displacement hysteresis operator, w i is the weight of the force-displacement hysteresis operator; y API [u][F](t) is the API force-electric-potential model; Through MATLAB software, establish a NARX neural network model for the input voltage, output force, and output displacement of piezoelectric ceramic actuator 2. The NARX neural network model is a model used to describe nonlinear discrete systems and is expressed as: Where: u(t) is the voltage input of the NARX neural network model at time t; F(t) and y(t) are the output force and output displacement of the NARX neural network model at time t, respectively; D u is the maximum order of the time delay of the input voltage; D F , D y is the maximum order of the time delay of the output force and output displacement; therefore, u(t - D u ), …, u(t - 1) are the historical input voltages relative to time t; F(t - D F ), …, F(t - 1), y(t - D y ), …, y(t - 1) are the historical output forces and output displacements relative to time t; f is the non-linear function obtained by network fitting; Take the predicted output force, output displacement, and system input voltage of the API force-electricity-displacement model as the inputs of the NARX neural network model, and obtain the API-NARX model after training; The third step: Train the neural network model and conduct application verification Divide the data collected in the first step into two groups, train and test the API-NARX model, conduct preset experiments on the piezoelectric ceramic force-displacement output characteristic test device, predict the output force and output displacement of the piezoelectric ceramic actuator, and verify the established piezoelectric ceramic model effect.

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