A compensation control method and device based on piezoelectric element hysteresis nonlinearity

Abstract

The application provides a compensation control method and device based on piezoelectric element hysteresis nonlinearity, comprising: collecting piezoelectric hysteresis characteristic data of a piezoelectric actuator, the piezoelectric hysteresis characteristic data describing a mapping relationship between a control voltage applied to the piezoelectric actuator and an actual displacement of the piezoelectric actuator; using the piezoelectric hysteresis characteristic data and a plurality of preset hysteresis operators to build a positive operator model for describing a mapping relationship between an input voltage and an actual displacement of the piezoelectric actuator; performing model reverse deduction according to model parameters of the positive operator model to obtain an inverse operator model; using the inverse operator model to receive an expected displacement of the piezoelectric actuator output by a controller, and outputting a pre-distortion driving voltage signal to the piezoelectric actuator to make the piezoelectric actuator output the expected displacement. The application builds the inverse operator model and uses the inverse operator model to compensate the hysteresis nonlinearity of the piezoelectric actuator, improves the displacement control precision of the piezoelectric actuator, and further improves the damping performance.

Description

Technical Field

[0001] This application relates to the field of vibration isolation technology, and in particular to a compensation control method and device based on the hysteresis nonlinearity of piezoelectric elements. Background Technology

[0002] Piezoelectric actuators (such as piezoelectric ceramics) utilize piezoelectric materials that inherently possess hysteresis characteristics. Specifically, this means that the rising piezoelectric response displacement curve obtained by continuously applying a rising excitation voltage to the piezoelectric element does not coincide with the falling piezoelectric response displacement curve obtained by continuously applying a falling excitation voltage. This hysteresis error means that, under the same input signal (voltage drive signal), the displacement values ​​on the rising and falling piezoelectric response curves will have a significant difference. Typically, the displacement obtained on the falling piezoelectric response curve is smaller, and this displacement difference changes with the voltage range; generally, the smaller the drive voltage, the smaller the displacement difference. Therefore, the hysteresis characteristic of piezoelectric materials causes a certain degree of distortion in the control error of a parallel piezoelectric ceramic vibration damping system during reciprocating vibration, thereby reducing the control accuracy for vibration suppression of the controlled object. Summary of the Invention

[0003] In view of this, the purpose of this application is to provide at least one compensation control method and device based on the hysteresis nonlinearity of piezoelectric elements. By identifying and analyzing the hysteresis characteristics of the piezoelectric actuator, an inverse operator model is built and the inverse operator model is used to compensate for the hysteresis nonlinearity of the piezoelectric actuator, thereby improving the displacement control accuracy of the piezoelectric actuator and thus improving the vibration reduction performance.

[0004] This application mainly includes the following aspects: In a first aspect, embodiments of this application provide a compensation control method based on the hysteresis nonlinearity of piezoelectric elements, applied to a piezoelectric active vibration isolation system. The piezoelectric active vibration isolation system includes a controller and a piezoelectric actuator. The method includes: acquiring piezoelectric hysteresis characteristic data of the piezoelectric actuator, the piezoelectric hysteresis characteristic data describing the mapping relationship between the control voltage applied to the piezoelectric actuator and the actual displacement of the piezoelectric actuator; using the piezoelectric hysteresis characteristic data and multiple preset hysteresis operators, constructing a positive operator model to describe the mapping relationship between the input voltage and the actual displacement of the piezoelectric actuator; performing inverse model derivation based on the model parameters of the positive operator model to obtain an inverse operator model; using the inverse operator model to receive the desired displacement of the piezoelectric actuator output by the controller, and outputting a pre-distorted drive voltage signal to the piezoelectric actuator to make the piezoelectric actuator output the desired displacement.

[0005] In one possible implementation, the piezoelectric hysteresis characteristic data of the piezoelectric actuator is acquired by applying a given AC voltage covering the full range of the piezoelectric actuator; under the given AC voltage, the input voltage and actual displacement of the piezoelectric actuator are acquired and recorded to form piezoelectric hysteresis characteristic data.

[0006] In one possible implementation, the positive operator model is constructed as follows: Multiple preset hysteresis operators with different hysteresis thresholds are set. The input of each preset hysteresis operator is the control voltage applied to the piezoelectric actuator, and the output of each preset hysteresis operator is the transition hysteresis amount obtained based on the corresponding hysteresis threshold. A fitting function for the positive operator model is constructed by weighted superposition of the multiple preset hysteresis operators. The piezoelectric hysteresis characteristic data is substituted into the fitting function, and with the goal of minimizing the displacement error between the piezoelectric actuator's displacement output by the positive operator model and the actual displacement, the fitting function is solved using the least squares method of a second-order polynomial to obtain the weight coefficients corresponding to each hysteresis operator. The weight coefficients corresponding to each hysteresis operator are then substituted back into the fitting function to obtain the positive operator model.

[0007] In one possible implementation, the output expression corresponding to the preset hysteresis operator is:

[0008] In this expression, This indicates that the preset hysteresis operator is at time [time]. The output signal below, Indicates at time The input signal of the preset hysteresis operator, This represents the hysteresis threshold corresponding to the preset hysteresis operator. This indicates that the preset hysteresis operator is at time [time]. The output signal of the preset hysteresis operator follows the change in the input voltage of the piezoelectric actuator when the change in the input voltage of the piezoelectric actuator exceeds the hysteresis threshold corresponding to the preset hysteresis operator.

[0009] In one possible implementation, the expression corresponding to the positive operator model is:

[0010] in, Indicates the positive operator model at time... The predicted displacement of the piezoelectric actuator outputting the current. This indicates the number of preset hysteresis operators. Indicates the first The weight coefficients corresponding to the preset hysteresis operators Indicates the hysteresis threshold is The A hysteresis operator The control voltage applied to the piezoelectric actuator at time t The transition hysteresis is obtained by processing.

[0011] Secondly, embodiments of this application also provide a compensation control device based on the hysteresis nonlinearity of piezoelectric elements. The device is applied to a piezoelectric active vibration isolation system, which includes a controller and a piezoelectric actuator. The device includes: a data acquisition module for acquiring piezoelectric hysteresis characteristic data of the piezoelectric actuator, which describes the mapping relationship between the control voltage applied to the piezoelectric actuator and the actual displacement of the piezoelectric actuator; a forward operator model building module for building a forward operator model describing the mapping relationship between the input voltage and the actual displacement of the piezoelectric actuator using the piezoelectric hysteresis characteristic data and multiple preset hysteresis operators; an inverse operator model building module for performing inverse model derivation based on the model parameters of the forward operator model to obtain an inverse operator model; and a compensation control module for receiving the desired displacement of the piezoelectric actuator output by the controller using the inverse operator model, and outputting a pre-distorted drive voltage signal to the piezoelectric actuator to make the piezoelectric actuator output the desired displacement.

[0012] In one possible implementation, the data acquisition module is further configured to: apply a given AC voltage covering the full range of the piezoelectric actuator; and under the given AC voltage, acquire and record the input voltage and actual displacement of the piezoelectric actuator to form piezoelectric hysteresis characteristic data.

[0013] In one possible implementation, the positive operator model building module is further configured to: set multiple preset hysteresis operators with different hysteresis thresholds, wherein the input of the preset hysteresis operator is the control voltage applied to the piezoelectric actuator, and the output of the preset hysteresis operator is the transition hysteresis amount obtained based on the corresponding hysteresis threshold; construct a fitting function for the positive operator model by weighted superposition of multiple preset hysteresis operators; substitute the piezoelectric hysteresis characteristic data into the fitting function, and with the goal of minimizing the displacement error between the displacement of the piezoelectric actuator output by the positive operator model and the actual displacement, solve the fitting function using the least squares method of second-order polynomials to obtain the weight coefficients corresponding to each hysteresis operator; and substitute the weight coefficients corresponding to each hysteresis operator back into the fitting function to obtain the positive operator model.

[0014] Thirdly, embodiments of this application also provide an electronic device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor and the memory communicate via the bus. The machine-readable instructions are executed by the processor to perform the steps of the compensation control method based on piezoelectric element hysteresis nonlinearity in the first aspect or any possible implementation of the first aspect.

[0015] Fourthly, embodiments of this application also provide a computer-readable storage medium storing a computer program, which, when run by a processor, executes the steps of the compensation control method based on piezoelectric element hysteresis nonlinearity in the first aspect or any possible implementation of the first aspect.

[0016] This application provides a compensation control method and apparatus based on the hysteresis nonlinearity of piezoelectric elements, comprising: acquiring piezoelectric hysteresis characteristic data of a piezoelectric actuator, wherein the piezoelectric hysteresis characteristic data describes the mapping relationship between the control voltage applied to the piezoelectric actuator and the actual displacement of the piezoelectric actuator; constructing a positive operator model describing the mapping relationship between the input voltage and the actual displacement of the piezoelectric actuator using the piezoelectric hysteresis characteristic data and multiple preset hysteresis operators; performing inverse derivation of the model based on the model parameters of the positive operator model to obtain an inverse operator model; and receiving the desired displacement of the piezoelectric actuator output by the controller using the inverse operator model, and outputting a pre-distorted drive voltage signal to the piezoelectric actuator to make the piezoelectric actuator output the desired displacement. By identifying and analyzing the hysteresis characteristics of the piezoelectric actuator, constructing a corresponding positive operator model and deriving the inverse operator model in reverse, and compensating for the nonlinear hysteresis generated by the piezoelectric actuator based on the inverse operator model, the displacement control accuracy of the piezoelectric actuator is improved, thereby improving vibration reduction performance.

[0017] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A simplified dynamic diagram of a juxtaposed piezoelectric ceramic vibration damping system provided in an embodiment of this application is shown. Figure 2 A flowchart illustrating the steps of a stiffness compensation method based on a juxtaposed piezoelectric ceramic vibration damping system provided in an embodiment of this application is shown. Figure 3 This diagram illustrates an active vibration isolation control block diagram provided by the prior art; Figure 4 This paper shows one of the stiffness compensation control block diagrams of a juxtaposed piezoelectric ceramic vibration damping system provided in an embodiment of this application; Figure 5A flowchart of a method for determining a given stiffness compensation coefficient provided in an embodiment of this application is shown; Figure 6 A flowchart of a compensation control method based on piezoelectric element hysteresis nonlinearity provided in an embodiment of this application is shown; Figure 7 This paper shows a second block diagram of stiffness compensation control for a juxtaposed piezoelectric ceramic vibration damping system provided in an embodiment of this application. Figure 8 A flowchart illustrating the steps of a positive operator model construction method provided in an embodiment of this application is shown. Figure 9 A functional block diagram of a compensation control device based on the hysteresis nonlinearity of piezoelectric elements provided in an embodiment of this application is shown. Figure 10 A schematic diagram of the structure of an electronic device provided in an embodiment of this application is shown. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. It should be understood that the drawings in this application are for illustrative and descriptive purposes only and are not intended to limit the scope of protection of this application. Furthermore, it should be understood that the schematic drawings are not drawn to scale. The flowcharts used in this application illustrate operations implemented according to some embodiments of this application. It should be understood that the operations in the flowcharts may not be implemented in sequence, and steps without logical contextual relationships may be reversed or implemented simultaneously. In addition, those skilled in the art, guided by the content of this application, may add one or more other operations to the flowcharts, or remove one or more operations from the flowcharts.

[0021] Furthermore, the described embodiments are merely some, not all, of the embodiments of this application. The components of the embodiments of this application described and illustrated herein can typically be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0022] Precision optical systems are extremely sensitive to vibration, shock, and noise interference in their working environment. Even minor vibration disturbances can easily cause modal shifts in optical mechanisms, decreased imaging accuracy, and reduced system stability. Therefore, efficient and high-precision vibration isolation and suppression technologies are crucial for ensuring the stable operation of precision optical systems. Currently, the most widely used traditional vibration isolation technologies rely on passive vibration isolation structures such as springs and dampers. While these structures can absorb some vibration energy and achieve basic vibration attenuation through their structural characteristics, they are still passive vibration reduction mechanisms. They cannot actively adjust vibration reduction parameters according to real-time vibration conditions and lack dynamic vibration suppression and adaptive adjustment capabilities, making it difficult to meet the stringent vibration isolation requirements of high-precision optical systems.

[0023] Therefore, existing technology also provides a piezoelectric active vibration isolation system. As an advanced active vibration isolation technology, the piezoelectric active vibration isolation system can suppress the transmission of vibration, impact, and noise to precision equipment and structures through active control strategies, effectively overcoming the shortcomings of traditional passive vibration isolation technologies. Specifically, a piezoelectric active vibration isolation system generally includes a piezoelectric sensor, a controller, and a piezoelectric actuator (exemplarily using piezoelectric ceramics). These three components work together to sense the vibration state of the controlled object in real time and achieve precise dynamic vibration control through closed-loop feedback. It has the advantages of fast response speed and high control accuracy, effectively suppressing multimodal vibration interference faced by the controlled object and significantly improving the vibration suppression performance and overall working accuracy of the controlled object.

[0024] Piezoelectric ceramics, as actuators, possess both direct and inverse piezoelectric effects, which can be utilized simultaneously. This means piezoelectric ceramics can function as both actuators and sensors. When a piezoelectric active vibration isolation system uses piezoelectric ceramics as actuators, the system exhibits a first-order inherent resonance peak (low frequency). Near this first-order resonance, a first-order anti-resonance valley is generated, corresponding to the anti-resonance of the first-order mode. This is primarily due to the dual function of the piezoelectric ceramic, creating two signal paths within the system: a direct electro-mechanical coupling path and a structural mechanical vibration propagation path. Under the influence of these two paths, the driving voltage output by the controller to the piezoelectric ceramic is directly coupled to the sensing signal through the piezoelectric capacitor (i.e., electrical crosstalk). The superposition of these two paths creates the anti-resonance characteristic. The smaller the amplitude of the anti-resonance frequency corresponding to the first-order resonance mode, the higher the corresponding sensitivity. This leads to decreased system stability and stiffness, ultimately affecting the system's ability to suppress the vibration of the controlled object.

[0025] Especially in piezoelectric active vibration isolation systems supported by multiple piezoelectric ceramic combinations, three sets of piezoelectric ceramic systems are usually used to support the controlled object such as the optical system, so as to achieve multi-dimensional vibration control of the controlled object. However, in the multi-device collaborative working mode, if the stiffness loss caused by the low-frequency anti-resonance effect cannot be effectively compensated, it will further reduce the vibration control accuracy of the controlled object, making it difficult to meet the low-frequency, high-precision active vibration isolation requirements of precision optical systems.

[0026] Based on this, this application provides a stiffness compensation method and apparatus based on a juxtaposed piezoelectric ceramic vibration reduction system. By introducing a stiffness compensation signal at the controller input front end, the first-order low-frequency anti-resonance frequency is reduced, thereby improving the system robustness, as detailed below: Please see Figure 1 , Figure 1 A simplified dynamic diagram of a juxtaposed piezoelectric ceramic vibration damping system provided in an embodiment of this application is shown. Figure 1 As shown, the parallel piezoelectric ceramic vibration damping system A provided in this application is fixed between the controlled object Plant and the system platform to achieve vibration suppression of the controlled object Plant.

[0027] In a preferred embodiment, such as Figure 1 As shown, the parallel piezoelectric ceramic vibration reduction system A provided in this application embodiment includes at least a controller 1, a piezoelectric actuator 2, and a piezoelectric sensor 3. Both the piezoelectric actuator 2 and the piezoelectric sensor 3 are made of piezoelectric ceramic, and the piezoelectric actuator 2 and the piezoelectric sensor 3 are placed in parallel at a given angle (45° for example). Specifically, this application introduces a flexible block structure as a carrier for the piezoelectric ceramic.

[0028] Preferably, Fu represents the top force of the controlled object Plant, Fd represents the bottom force of the parallel piezoelectric ceramic vibration damping system, Mu represents the mass of the controlled object Plant, Md represents the mass of the equivalent rigid body RB corresponding to the parallel piezoelectric ceramic vibration damping system A, Xu represents the displacement of the controlled object Plant, Xd represents the displacement of the equivalent rigid body RB, Ks represents the piezoelectric stiffness of the system, Kp represents the preload stiffness, Kf represents the stiffness of the flexible block, Fs represents the output of the piezoelectric sensor 3, and Xact represents the input of the piezoelectric actuator 2.

[0029] Please see Figure 2 , Figure 2 A flowchart illustrating the steps of a stiffness compensation method based on a juxtaposed piezoelectric ceramic vibration damping system provided in an embodiment of this application is shown. Figure 2 As shown, the method provided in this application specifically includes: S100. Inject a given noise signal at the input terminal of the piezoelectric actuator.

[0030] S200: Uses a piezoelectric sensor to collect measurement signals generated by the vibration of the controlled object.

[0031] S300. Based on the given stiffness compensation coefficient, the input signal of the piezoelectric actuator is subjected to stiffness compensation processing based on first-order low-frequency mode anti-resonance to obtain a stiffness compensation signal.

[0032] S400. Based on the controller's planned input signal, measurement signal, and stiffness compensation signal, determine the controller's target input signal and obtain the controller's target output signal under the target input signal.

[0033] S500: Update the input signal of the piezoelectric actuator based on the target output signal and the given noise signal.

[0034] Please see Figure 3 , Figure 3 A block diagram of an active vibration isolation control method provided by the prior art is shown. For example... Figure 3 As shown, in the active vibration isolation control process provided by the existing technology, the piezoelectric sensor 3 collects the measurement signal y1 generated by the vibration of the controlled object, Plant, and compares it with the planned input signal r0 (generally set to 0) of the controller 1 to determine the feedback error signal e1. Then, the feedback error signal e1 is directly input to the controller 1. The controller 1, combined with its internal algorithm, obtains the control output signal r1 based on the feedback error signal e1. The control output signal r1 is further combined with the feedforward filter signal rr to obtain the input signal r2 corresponding to the piezoelectric actuator 2. The piezoelectric actuator 2 suppresses the vibration of the controlled object, Plant, according to the input signal r2. Figure 3 It is known that the existing technology does not compensate for the stiffness loss caused by the anti-resonance effect in the low-frequency band of the system, which reduces the robustness and stability of the system, that is, reduces the effect of the system on the vibration suppression of the controlled object, the plant.

[0035] Based on this, please refer to Figure 4 , Figure 4 A block diagram illustrating the stiffness compensation control of a juxtaposed piezoelectric ceramic vibration damping system provided in an embodiment of this application is shown. Figure 4 and Figure 5 As shown, in steps S100 to S500 provided in this application, compared with the prior art's control approach of active vibration isolation based solely on the measurement signal y1 output by the piezoelectric sensor 3, this application provides a stiffness compensation link 11 based on suppressing low-frequency anti-resonance phenomena. In the stiffness compensation link 11 provided in this application: In addition to considering the measured electrical signal y1 and the planned input signal r0, a given noise signal S2 is injected into the input of the piezoelectric actuator 2, and a stiffness compensation signal y2, corresponding to the given noise signal S2 and based on the given stiffness compensation coefficient SC, is introduced into the input of the controller 1. The stiffness compensation signal y2 is actually based on the difference between the actual anti-resonance frequency of the first-order low-frequency resonance mode of the system and the inherent anti-resonance frequency of the system. It forms a compensation signal for the controller input based on the system stiffness. After the stiffness compensation signal y2 is applied to the input of the controller 1, it can reduce the anti-resonance frequency of the first-order low-frequency resonance mode and compensate for the increase in system sensitivity caused by the decrease in system stiffness. This effectively reduces the sensitivity near the anti-resonance frequency of the first-order low-frequency resonance mode, thereby improving the control accuracy of the controller for the actuator output command and effectively improving the system robustness.

[0036] In a preferred embodiment provided in this application, such as Figure 4 As shown, step S300 further includes: Calculate the product between the input signal r3 of the piezoelectric actuator and the given stiffness compensation coefficient SC, and determine the product as the stiffness compensation signal y2.

[0037] In one specific embodiment, the stiffness compensation signal y2 is determined by the following formula:

[0038] For further details, please refer to Figure 5 , Figure 5 A flowchart illustrating a method for determining a given stiffness compensation coefficient according to an embodiment of this application is shown. Figure 5 As shown, the methods for determining a given stiffness compensation coefficient include: S3001. Calculate the initial stiffness compensation coefficient based on the system stiffness parameters corresponding to the juxtaposed piezoelectric ceramic vibration reduction system.

[0039] S3002, put the parallel piezoelectric ceramic vibration reduction system into a closed-loop control state with stiffness compensation.

[0040] In this context, closed-loop control refers to introducing the controller's output signal into the input terminal of the piezoelectric actuator.

[0041] S3003, synchronously acquires the given noise signal and the input signal of the piezoelectric actuator.

[0042] S3004. Based on the collected given noise signal and the input signal of the piezoelectric actuator, construct a sensitivity function and plot the corresponding sensitivity change curve.

[0043] S3005. Based on the sensitivity change curve and the given sensitivity limit, adjust the initial stiffness compensation coefficient to obtain the given stiffness compensation coefficient.

[0044] In a specific embodiment, in step S3001, the system stiffness parameters include the system piezoelectric stiffness. Preload stiffness and stiffness of flexible blocks Furthermore, step S3001 includes: Based on the system's piezoelectric stiffness, preload stiffness, and flexible block stiffness, the system's resonance point stiffness is calculated. The product of the system's resonance point stiffness and a given coefficient (e.g., 0.1) is determined as the initial stiffness compensation coefficient.

[0045] In other words, the stiffness compensation coefficient in this application is related to the stiffness of the system resonance point, and its purpose is to achieve subsequent stiffness compensation of the input signal of the controller.

[0046] Preferably, the system resonance point stiffness is calculated using the following formula. :

[0047] like Figure 4 As shown, the output signal r1 of the controller in this application is combined with the feedforward filter signal rr to obtain the control output signal r2. Between the control output signal r2 and the injected given noise signal S1, there is a switching switch SW (not shown in the figure) for the operating state of the parallel piezoelectric ceramic vibration reduction system.

[0048] Specifically, when the switch SW is in the off state, the control output signal r2 is not connected to the piezoelectric actuator 2, and the input signal r3 of the piezoelectric actuator 2 is provided by the given noise injection signal S1. At this time, the piezoelectric ceramic vibration reduction system is in open-loop control state.

[0049] When the switch SW is closed, the control output signal r2 is connected to the piezoelectric actuator 2. The input signal r3 of the piezoelectric actuator 2 is provided by the given noise injection signal S1 and the control output signal r2. At this time, the piezoelectric ceramic vibration reduction system is in closed-loop control.

[0050] Specifically, in step S3002, this application puts the parallel piezoelectric ceramic vibration damping system into a closed-loop control state by closing the switching switch SW.

[0051] In steps S3003-S3004, the sensitivity function Gs is defined as follows:

[0052] Based on the collected given noise signal and the input signal of the piezoelectric actuator Calculate the sensitivity function value Furthermore, a sensitivity variation curve is plotted with the acquisition time on the horizontal axis and the sensitivity function value on the vertical axis.

[0053] Specifically, step S3005 further includes: Analyze the sensitivity change curve to determine the sensitivity amplitude at the peak. Determine whether the sensitivity amplitude at the peak meets the given sensitivity limit. If the sensitivity amplitude at the peak meets the given sensitivity limit, directly determine the initial stiffness compensation coefficient as the given stiffness compensation coefficient. If the sensitivity amplitude at the peak does not meet the given sensitivity limit, adjust the initial stiffness compensation coefficient and, based on the adjusted initial stiffness compensation coefficient, return to step S3004.

[0054] In a specific embodiment, the given sensitivity limit is that the sensitivity amplitude at the peak is between 0 dB and 10 dB.

[0055] Specifically, the sensitivity amplitude at the peak is generally selected from the amplitude at the first peak on the sensitivity change curve. When the sensitivity amplitude at the peak is between 0dB and 10dB, it indicates that the current stiffness compensation coefficient meets the given sensitivity limit. The current stiffness compensation coefficient can be directly used as the given stiffness compensation coefficient to compensate the input signal of the controller 1 in the stiffness compensation loop 11. In this application, the execution logic in the controller 1 is the prior art, which will not be elaborated here. When the sensitivity amplitude at the peak is greater than 10dB, it indicates that the current stiffness compensation coefficient does not meet the given sensitivity limit. The current stiffness compensation coefficient is then adjusted, and the execution step S3004 is returned until the updated stiffness compensation coefficient meets the given sensitivity limit.

[0056] In a preferred embodiment, such as Figure 4 As shown, step S400 further includes: Determine the feedback error signal e1 between the controller planning input signal r0 and the measurement signal y1, and determine the difference between the feedback error signal e1 and the stiffness compensation signal y2 as the target input signal e2 of controller 1.

[0057] Specifically, in step S500, such as Figure 4 As shown, with the built-in operating logic of controller 1 unchanged, the target input signal e2 is a signal that integrates the feedback error signal e1 and the stiffness compensation after completing the anti-resonance effect based on the first-order resonant mode. This can improve the accuracy of the output signal of controller 1, thereby improving the frame suppression effect of the system on the controlled object.

[0058] In specific embodiments, the juxtaposed piezoelectric ceramic vibration reduction system provided in this application corresponds to different transfer functions under different operating states, specifically including the open-loop transfer function under open-loop control state and the closed-loop transfer function under closed-loop control state.

[0059] In a specific embodiment, the open-loop transfer function includes a first open-loop transfer function without the stiffness compensation element 11 and a second open-loop transfer function with the stiffness compensation element 11. The closed-loop transfer function includes a first closed-loop transfer function without the stiffness compensation element 11 and a second closed-loop transfer function with the stiffness compensation element 11.

[0060] Preferred, such as Figure 4 As shown, when the closed-loop feedback signal rr is 0 or close to 0: At this point, for the open-loop transfer function, without introducing stiffness compensation, , The first open-loop transfer function is described as follows:

[0061] in, This represents the value of the first open-loop transfer function. That is to refer to The input signal is the output signal of controller 1.

[0062] With the introduction of stiffness compensation, , The second open-loop transfer function is described as follows:

[0063] This represents the value of the second open-loop transfer function.

[0064] Preferably, the first closed-loop transfer function is described as follows:

[0065] This represents the value of the first closed-loop transfer function.

[0066] Preferably, the second closed-loop transfer function is described as follows:

[0067]

[0068] In this application, for each of the above transfer functions, the juxtaposed piezoelectric ceramic vibration damping system can be switched to the control state corresponding to that transfer function. Then, the relevant signals corresponding to that transfer function are collected to plot the frequency response curve of the juxtaposed piezoelectric ceramic vibration damping system under that transfer function. Furthermore, by comparing the frequency response curves before and after stiffness compensation under the same operating state, this application shows that the frequency corresponding to the anti-resonance point under the first-order resonance mode is significantly lower than before stiffness compensation after introducing the stiffness compensation process provided in this application. This indicates that the solution in this application can effectively improve the robustness of the system and increase the accuracy of subsequent output control of the piezoelectric actuator 2, that is, improve the vibration suppression capability for the controlled object.

[0069] For example, taking the open-loop transfer function as an example, the stiffness compensation link 11 of the piezoelectric ceramic vibration damping system is disconnected and, under the condition of normal injection of S2, the data is collected. And R3, calculate the first open-loop transfer function value and perform Fourier transform to obtain the corresponding first open-loop frequency response curve. Then, activate and set the stiffness compensation link 11 of the piezoelectric ceramic vibration damping system. Under normal injection of S2, collect... Calculate the second open-loop transfer function value and perform a Fourier transform with R3 to obtain the corresponding second open-loop frequency response curve. Analyze the first and second open-loop frequency response curves to determine the anti-resonance point (trough) indicated by the first and second open-loop frequency response curves. Comparing the two anti-resonance points, it can be clearly found that the anti-resonance point indicated by the second open-loop frequency response curve is significantly lower than the anti-resonance point indicated by the first open-loop frequency response curve. The closer the anti-resonance point is to 0, the better the overall robustness of the system.

[0070] In addition, the process of plotting and comparing the frequency response curves of the closed-loop transfer function is similar to that described above, and will not be elaborated further here.

[0071] In this application, the piezoelectric material used in the piezoelectric actuator (such as piezoelectric ceramic) inherently possesses a certain hysteresis characteristic. Specifically, this means that the rising piezoelectric response displacement curve obtained by continuously applying a rising excitation voltage to the piezoelectric element does not coincide with the falling piezoelectric response displacement curve obtained by continuously applying a falling excitation voltage to the piezoelectric element, exhibiting a certain hysteresis error. In other words, under the same input signal (referring to the voltage drive signal), the displacement values ​​on the rising and falling piezoelectric response curves of the piezoelectric actuator will have a significant displacement difference. Typically, the displacement obtained on the falling piezoelectric response curve is smaller, and this displacement difference changes with the voltage variation range; generally, the smaller the drive voltage, the smaller the displacement difference. Therefore, the hysteresis characteristic of the piezoelectric material causes a certain degree of distortion in the control error of the parallel piezoelectric ceramic vibration damping system during reciprocating vibration, thereby reducing the control accuracy for vibration suppression of the controlled object.

[0072] Based on this, this application also provides a compensation control method and device based on the hysteresis nonlinearity of piezoelectric elements. By identifying and analyzing the hysteresis characteristics of piezoelectric ceramics, a corresponding positive operator model is built and an inverse operator model is derived in reverse. The nonlinear hysteresis generated by the piezoelectric ceramics is compensated based on the inverse operator model, thereby improving the displacement control accuracy of the piezoelectric ceramics and thus improving the vibration reduction performance. The details are as follows: Please see Figure 6 , Figure 6 A flowchart illustrating a compensation control method based on piezoelectric element hysteresis nonlinearity provided in an embodiment of this application is shown. Please refer to... Figure 7 , Figure 7 This illustration shows a second block diagram of the stiffness compensation control of a juxtaposed piezoelectric ceramic vibration damping system provided in an embodiment of this application. (See diagram below.) Figure 6 and Figure 7 As shown, the compensation control method based on the hysteresis nonlinearity of piezoelectric elements provided in this application embodiment, applied to the above-mentioned juxtaposed piezoelectric ceramic vibration reduction system, specifically includes the following steps: S700: Collects piezoelectric hysteresis characteristic data of piezoelectric actuators.

[0073] Among them, the piezoelectric hysteresis characteristic data describes the mapping relationship between the control voltage applied to the piezoelectric actuator and the actual displacement of the piezoelectric actuator.

[0074] S710. Using piezoelectric hysteresis characteristic data and multiple preset hysteresis operators, a positive operator model is built to describe the mapping relationship between the input voltage and actual displacement of the piezoelectric actuator.

[0075] S720. Based on the model parameters of the positive operator model, perform reverse derivation of the model to obtain the inverse operator model.

[0076] S730 uses the inverse operator model to receive the desired displacement of the piezoelectric actuator from the controller, and outputs a pre-distorted drive voltage signal to the piezoelectric actuator so that the piezoelectric actuator outputs the desired displacement.

[0077] like Figure 7 As shown, in addition to introducing the stiffness compensation link 11, this application determines the expected displacement of the corresponding piezoelectric actuator 2 based on the expected input signal r3 of the piezoelectric actuator obtained by the controller 1 based on the aforementioned stiffness compensation link 11, and inputs the expected displacement into the inverse operator model provided in this application, and outputs the pre-distortion drive voltage signal after calibration by the inverse operator model to the piezoelectric actuator 2, so that the piezoelectric actuator 2 outputs the expected displacement and suppresses the vibration of the controlled object.

[0078] Based on the inherent hysteresis nonlinearity of piezoelectric ceramics, this application proposes to introduce an inverse operator model between the piezoelectric actuator 2 and the controller 1 to compensate for the hysteresis nonlinearity generated by the material of the piezoelectric actuator 2 itself. In fact, the role of the inverse operator model is to clarify the mapping relationship between the actual displacement of the piezoelectric actuator 2 and its input control voltage, so as to output a pre-distorted drive voltage signal that enables the piezoelectric actuator 2 to output the desired displacement based on the desired displacement of the piezoelectric actuator 2. Moreover, when the inverse operator model is sufficiently accurate, the nonlinearity generated by the inverse operator model can just cancel the nonlinearity of the piezoelectric actuator, so that the overall system behaves linearly, that is, the input command is proportional to the output displacement of the piezoelectric actuator 2.

[0079] In a preferred embodiment, step S700 includes: Apply a given AC voltage covering the full range of the piezoelectric actuator 2. Under the given AC voltage, collect and record the input voltage (i.e. the control voltage applied to the piezoelectric actuator) and the actual displacement of the piezoelectric actuator 2 to form piezoelectric hysteresis characteristic data.

[0080] In this application, different controlled objects are introduced in advance into the parallel piezoelectric ceramic vibration reduction system. The above-mentioned piezoelectric hysteresis characteristic data acquisition process is performed under different controlled objects, and the collected abnormal data is cleaned up. This application combines the pre-processed piezoelectric hysteresis characteristic data of the piezoelectric actuator 2 under different controlled objects to build the inverse operator model to prevent data distortion.

[0081] In specific implementations, given an AC voltage that is either a triangular wave or a sine wave, the actual displacement of the piezoelectric actuator can be acquired, for example, by using a laser displacement sensor.

[0082] In a preferred embodiment, please refer to Figure 8 , Figure 8 A flowchart illustrating the steps of a positive operator model construction method provided in an embodiment of this application is shown. Figure 8 As shown, step S710 provided in this application further includes: S7110, Set multiple preset hysteresis operators with different hysteresis thresholds.

[0083] The input to the preset hysteresis operator is the control voltage applied to the piezoelectric actuator, and the output of the preset hysteresis operator is the transition hysteresis amount obtained based on the corresponding hysteresis threshold.

[0084] S7120. By weighting and superimposing multiple preset hysteresis operators, a fitting function for the positive operator model is constructed.

[0085] S7130. Substitute the piezoelectric hysteresis characteristic data into the fitting function, and with the goal of minimizing the displacement error between the piezoelectric ceramic displacement output by the positive operator model and the actual displacement, solve the fitting function using the least squares method of second-order polynomials to obtain the weight coefficients corresponding to each hysteresis operator.

[0086] S7140. Substitute the weight coefficients corresponding to each hysteresis operator back into the fitting function to obtain the positive operator model.

[0087] In step S7110, the positive operator model of this application is formed by the weighted superposition of multiple preset hysteresis operators. The preset hysteresis operator is the play operator. Specifically, the input signal of the preset hysteresis operator is the control voltage applied by the controller 1 to the piezoelectric actuator 2. =r3, the preset output signal of the hysteresis operator is the corresponding input signal. Below, the transition hysteresis amount is obtained based on the corresponding hysteresis threshold. In this application, the preset hysteresis operator can be understood as follows: when the change in the input voltage of the piezoelectric actuator 2 exceeds the hysteresis threshold r corresponding to the preset hysteresis operator, the output signal of the preset hysteresis operator follows the change in the input voltage of the piezoelectric actuator 2.

[0088] In a specific embodiment, the output expression corresponding to the preset hysteresis operator is:

[0089] In this expression, This indicates that the preset hysteresis operator is at time [time]. The output signal below.

[0090] Indicates at time The input signal of the preset hysteresis operator, This represents the hysteresis threshold corresponding to the preset hysteresis operator. This indicates that the preset hysteresis operator is at time [time]. The output signal below.

[0091] Specifically, when Rise above When the preset hysteresis operator's output signal rises following the input signal, when Decline below When the preset hysteresis operator's output signal decreases following the input signal, when The change is in and The output signal remains unchanged during this period.

[0092] In a preferred embodiment, the expression corresponding to the positive operator model is:

[0093] in, Indicates the positive operator model at time... The predicted displacement of the piezoelectric actuator outputting downwards. This indicates the number of preset hysteresis operators. Indicates the first The weight coefficients corresponding to the preset hysteresis operators Indicates the hysteresis threshold is The A hysteresis operator The control voltage applied to the piezoelectric actuator at time t The resulting transition hysteresis, i.e., the first... The output signal of a preset hysteresis operator.

[0094] In step S7130, during the process of solving for the weight coefficients corresponding to the preset hysteresis operator, the fitting objective of the least squares method based on the second-order polynomial is: to make the positive operator model calculate the The displacement error between the measured displacement and the actual displacement is minimized.

[0095] In step S720, the mathematical characteristics of the operator model are utilized to directly derive the model inversely based on the model parameters of the positive operator model (including the weight coefficient and hysteresis threshold of each preset hysteresis operator) to obtain the inverse operator model. In this application, the function of the inverse operator model is to calculate the pre-distortion drive voltage signal applied to the piezoelectric actuator 2 based on the expected displacement of the controller 1.

[0096] In step S730, the input of the inverse operator model is the desired displacement corresponding to the input signal r3 of the actuator (determined by the output of the controller 1) after passing through the stiffness compensation link 11, and the output is the pre-distortion drive voltage signal that guides the piezoelectric actuator 2 to output the desired displacement.

[0097] Based on the same application concept, this application also provides a piezoelectric element hysteresis nonlinearity compensation control device corresponding to the piezoelectric element hysteresis nonlinearity compensation control method provided in the above embodiments. Since the principle of the device in this application is similar to the piezoelectric element hysteresis nonlinearity compensation control method in the above embodiments of this application, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be described again.

[0098] Please see Figure 9 , Figure 9 This diagram illustrates a functional block diagram of a compensation control device based on the hysteresis nonlinearity of piezoelectric elements, according to an embodiment of this application. Figure 9 As shown, the device includes: The data acquisition module 500 is used to acquire the piezoelectric hysteresis characteristic data of the piezoelectric actuator. The piezoelectric hysteresis characteristic data describes the mapping relationship between the control voltage applied to the piezoelectric actuator and the actual displacement of the piezoelectric actuator. The positive operator model building module 510 is used to build a positive operator model that describes the mapping relationship between the input voltage and the actual displacement of a piezoelectric actuator by utilizing piezoelectric hysteresis characteristic data and multiple preset hysteresis operators. The inverse operator model building module 520 is used to perform inverse model derivation based on the model parameters of the forward operator model to obtain the inverse operator model; The compensation control module 530 is used to receive the desired displacement of the piezoelectric actuator from the controller using the inverse operator model, and output a pre-distorted drive voltage signal to the piezoelectric actuator so that the piezoelectric actuator outputs the desired displacement.

[0099] Preferably, the data acquisition module 500 is further configured to: apply a given AC voltage covering the full range of the piezoelectric actuator to the piezoelectric actuator; and under the given AC voltage, acquire and record the input voltage and actual displacement of the piezoelectric actuator to form piezoelectric hysteresis characteristic data.

[0100] Preferably, the positive operator model building module 510 is further configured to: set multiple preset hysteresis operators with different hysteresis thresholds, wherein the input of the preset hysteresis operator is the control voltage applied to the piezoelectric actuator, and the output of the preset hysteresis operator is the transition hysteresis amount obtained based on the corresponding hysteresis threshold; build a fitting function for the positive operator model by weighted superposition of multiple preset hysteresis operators; substitute the piezoelectric hysteresis characteristic data into the fitting function, and with the goal of minimizing the displacement error between the displacement of the piezoelectric actuator output by the positive operator model and the actual displacement, solve the fitting function using the least squares method of second-order polynomials to obtain the weight coefficients corresponding to each hysteresis operator; and substitute the weight coefficients corresponding to each hysteresis operator back into the fitting function to obtain the positive operator model.

[0101] Based on the same application concept, please refer to Figure 10 , Figure 10 A schematic diagram of the structure of an electronic device provided in an embodiment of this application is shown. Figure 10 As shown, the electronic device 80 includes a processor 801, a memory 802, and a bus 803. The memory 802 stores machine-readable instructions that can be executed by the processor 801. When the electronic device 80 is running, the processor 801 and the memory 802 communicate through the bus 803. The machine-readable instructions are executed by the processor 801 to perform the steps of the compensation control method based on the hysteresis nonlinearity of piezoelectric elements and the stiffness compensation method based on the juxtaposed piezoelectric ceramic vibration reduction system provided in any of the above embodiments.

[0102] Based on the same concept, this application also provides a computer-readable storage medium storing a computer program. When the computer program is run by a processor, it executes the steps of the compensation control method based on piezoelectric element hysteresis nonlinearity and the stiffness compensation method based on juxtaposed piezoelectric ceramic vibration reduction system provided in the above embodiments.

[0103] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and devices described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. In the several embodiments provided in this application, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division; in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Another point is that the displayed or discussed mutual coupling or direct coupling or communication connection may be through some communication interfaces; the indirect coupling or communication connection of devices or units may be electrical, mechanical, or other forms.

[0104] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0105] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0106] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0107] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A compensation control method based on the hysteresis nonlinearity of piezoelectric elements, characterized in that, This technology is applied to a juxtaposed piezoelectric ceramic vibration damping system, which includes a controller and a piezoelectric actuator. The method includes: Collect piezoelectric hysteresis characteristic data of the piezoelectric actuator, which describes the mapping relationship between the control voltage applied to the piezoelectric actuator and the actual displacement of the piezoelectric actuator; Using the piezoelectric hysteresis characteristic data and multiple preset hysteresis operators, a positive operator model is built to describe the mapping relationship between the input voltage and the actual displacement of the piezoelectric actuator; Based on the model parameters of the positive operator model, the model is derived in reverse to obtain the inverse operator model; The inverse operator model is used to receive the desired displacement of the piezoelectric actuator output by the controller, and a pre-distorted drive voltage signal is output to the piezoelectric ceramic to make the piezoelectric actuator output the desired displacement.

2. The method according to claim 1, characterized in that, The piezoelectric hysteresis characteristic data of the piezoelectric actuator were collected using the following method: Apply a given AC voltage covering the full range of the piezoelectric actuator to the piezoelectric actuator; Under the given AC voltage, the input voltage and actual displacement of the piezoelectric actuator are collected and recorded to form the piezoelectric hysteresis characteristic data.

3. The method according to claim 1, characterized in that, The positive operator model is constructed using the following method: Multiple preset hysteresis operators with different hysteresis thresholds are set. The input of the preset hysteresis operator is the control voltage applied to the piezoelectric actuator, and the output of the preset hysteresis operator is the transition hysteresis amount obtained based on the corresponding hysteresis threshold. By weighting and superimposing multiple preset hysteresis operators, a fitting function for the positive operator model is constructed; The piezoelectric hysteresis characteristic data are substituted into the fitting function, and the goal is to minimize the displacement error between the displacement of the piezoelectric actuator output by the positive operator model and the actual displacement. The fitting function is solved by the least squares method of the second-order polynomial to obtain the weight coefficients corresponding to each hysteresis operator. The weight coefficients corresponding to each hysteresis operator are then substituted back into the fitting function to obtain the positive operator model.

4. The method according to claim 3, characterized in that, The output expression corresponding to the preset hysteresis operator is: In this expression, This indicates that the preset hysteresis operator is at time [time]. The output signal below, Indicates at time The input signal of the preset hysteresis operator, This represents the hysteresis threshold corresponding to the preset hysteresis operator. This indicates that the preset hysteresis operator is at time [time]. The output signal below; When the change in the input voltage of the piezoelectric actuator exceeds the hysteresis threshold corresponding to the preset hysteresis operator, the output signal of the preset hysteresis operator follows the change in the input voltage of the piezoelectric actuator.

5. The method according to claim 1, characterized in that, The expression corresponding to the positive operator model is: in, Indicates the positive operator model at time... The predicted displacement of the piezoelectric actuator output below, This indicates the number of preset hysteresis operators. Indicates the first The weight coefficients corresponding to the preset hysteresis operators Indicates the hysteresis threshold is The A hysteresis operator The control voltage applied to the piezoelectric actuator at time t The transition hysteresis is obtained by processing.

6. A compensation control device based on the hysteresis nonlinearity of piezoelectric elements, characterized in that, The device is used in a piezoelectric active vibration isolation system, which includes a controller and a piezoelectric actuator. The device includes: The data acquisition module is used to acquire the piezoelectric hysteresis characteristic data of the piezoelectric actuator, wherein the piezoelectric hysteresis characteristic data describes the mapping relationship between the control voltage applied to the piezoelectric actuator and the actual displacement of the piezoelectric actuator; The positive operator model building module is used to build a positive operator model that describes the mapping relationship between the input voltage and the actual displacement of the piezoelectric actuator by using the piezoelectric hysteresis characteristic data and multiple preset hysteresis operators. The inverse operator model building module is used to perform inverse model derivation based on the model parameters of the positive operator model to obtain the inverse operator model; The compensation control module is used to receive the desired displacement of the piezoelectric actuator output by the controller using the inverse operator model, and output a pre-distortion drive voltage signal to the piezoelectric actuator so that the piezoelectric actuator outputs the desired displacement.

7. The apparatus according to claim 6, characterized in that, The data acquisition module is also used for: Apply a given AC voltage covering the full range of the piezoelectric actuator to the piezoelectric actuator; Under the given AC voltage, the input voltage and actual displacement of the piezoelectric actuator are collected and recorded to form the piezoelectric hysteresis characteristic data.

8. The apparatus according to claim 6, characterized in that, The positive operator model building module is also used for: Multiple preset hysteresis operators with different hysteresis thresholds are set. The input of the preset hysteresis operator is the control voltage applied to the piezoelectric actuator, and the output of the preset hysteresis operator is the transition hysteresis amount obtained based on the corresponding hysteresis threshold. By weighting and superimposing multiple preset hysteresis operators, a fitting function for the positive operator model is constructed; The piezoelectric hysteresis characteristic data are substituted into the fitting function, and the goal is to minimize the displacement error between the displacement of the piezoelectric actuator output by the positive operator model and the actual displacement. The fitting function is solved by the least squares method of the second-order polynomial to obtain the weight coefficients corresponding to each hysteresis operator. The weight coefficients corresponding to each hysteresis operator are then substituted back into the fitting function to obtain the positive operator model.

9. An electronic device, characterized in that, include: The device includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory via the bus. The machine-readable instructions are executed by the processor to perform the steps of the compensation control method based on piezoelectric element hysteresis nonlinearity as described in any one of claims 1 to 5.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the compensation control method based on piezoelectric element hysteresis nonlinearity as described in any one of claims 1 to 5.

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