System identification and control method, device and medium for piezoelectric ceramic displacement stage

Abstract

The application discloses a piezoelectric ceramic displacement table system identification and control method, equipment and medium, the method comprises the following steps: constructing a continuous system model of the piezoelectric ceramic displacement table, and calculating the initial system parameters corresponding to the continuous system model through error analysis; S-K iteration is carried out on the identified initial parameters until the ratio of the first identification iteration parameters obtained through S-K iteration and the adjacent second iteration system parameters meets the iteration condition, so as to determine the system parameters corresponding to the piezoelectric ceramic displacement table; through load nonlinear mapping, an adaptive wave trap related to the system parameters and the load is constructed; the controlled object model and the weighting function of the piezoelectric ceramic displacement table are converted into a state space form to obtain an equivalent controlled object model and a weighting function; and through a robust control method, the control amount of the piezoelectric ceramic displacement table of the equivalent controlled object model is calculated. The application solves the technical problem that the piezoelectric ceramic displacement table in the prior art is unstable when the load changes.

Description

Technical Field

[0001] This application relates to the field of piezoelectric ceramic displacement stage control technology, and in particular to a system identification and control method, equipment and medium for a piezoelectric ceramic displacement stage. Background Technology

[0002] Piezoelectric ceramic displacement stages utilize voltage to control crystal deformation, achieving nanometer-level precision micro-motion platforms through a frictionless elastic structure. As crucial equipment in precision machining, their displacement accuracy directly determines machining precision. Therefore, analyzing the system identification and designing high-performance controllers is essential. In actual working conditions, the characteristics of the piezoelectric ceramic displacement stage vary depending on the mass of the workpiece being processed; this phenomenon is known as the resonant drift of the piezoelectric ceramic displacement stage under different loads.

[0003] Because piezoelectric ceramic displacement stages exhibit resonant drift under varying loads, their system characteristics change, leading to a decrease in machining accuracy. Similarly, if the load mass varies significantly, the controller designed based on nominal conditions may no longer maintain system stability, resulting in system instability and the piezoelectric ceramic displacement stage malfunctioning. Therefore, a high-performance control method for piezoelectric ceramic displacement stage system identification and load variation is urgently needed to prevent system instability under load changes. Summary of the Invention

[0004] This application provides a system identification and control method, device and medium for a piezoelectric ceramic displacement stage, which solves the technical problem of system instability of the piezoelectric ceramic displacement stage when the load changes in the prior art.

[0005] In a first aspect, embodiments of this application provide a system identification and control method for a piezoelectric ceramic displacement stage, characterized in that the method includes: constructing a continuous system model of the piezoelectric ceramic displacement stage, and calculating the initial system parameters corresponding to the continuous system model through error analysis; performing SK iteration on the initial identification parameters until the ratio of the first identification iteration parameter obtained through SK iteration to the adjacent second iteration system parameter satisfies a preset iteration condition, thereby determining the system parameters corresponding to the piezoelectric ceramic displacement stage; obtaining the load of the piezoelectric ceramic displacement stage, and based on the load, constructing an adaptive notch filter related to the system parameters and the load through load nonlinear mapping; according to the adaptive notch filter, transforming the controlled object model and weighting function of the piezoelectric ceramic displacement stage into a state-space form to obtain an equivalent controlled object model and a weighting function corresponding to the closed-loop tracking bandwidth; and through... A robust control method is proposed, which calculates the control quantity of the piezoelectric ceramic displacement stage corresponding to the equivalent controlled object model.

[0006] In one implementation of this application, the initial system parameters corresponding to the continuous system model are calculated through error analysis. Specifically, this includes: converting the time-domain data of the continuous system model into frequency-domain data, and setting a nonlinear first error parameter based on the frequency-domain data; replacing the first error parameter with a preset second error parameter, and calculating the initial system parameters corresponding to the second error parameter using the least squares method.

[0007] In one implementation of this application, the initial identification parameters are subjected to SK iteration until the ratio of the first identification iteration parameter obtained by SK iteration to the adjacent second iteration system parameter satisfies a preset iteration condition, thereby determining the system parameters corresponding to the piezoelectric ceramic displacement stage. Specifically, this includes: calculating the loss function corresponding to the iteration of the initial identification parameters, and performing SK iteration on the initial identification parameters based on the loss function to obtain the first identification iteration parameter and the second system parameter; wherein the iteration number corresponding to the first identification iteration parameter is greater than the iteration number corresponding to the second system parameter; calculating the ratio of the model denominator polynomial corresponding to the first identification iteration parameter and the model denominator polynomial corresponding to the second identification iteration parameter to obtain the iteration judgment coefficient; and, if the iteration judgment coefficient satisfies the preset iteration condition, calculating the minimization parameter corresponding to the loss function to determine the system parameters.

[0008] In one implementation of this application, an adaptive notch filter is constructed based on the load and through load nonlinear mapping. Specifically, this includes: uniformly dividing the numerical range corresponding to the load into several parts to obtain the load grouping of the piezoelectric ceramic displacement stage; dividing the continuous system model into a first system identification model group corresponding to the load grouping, and associating the load variables of the system identification model group to determine the second system identification model group in which the system parameters are associated with the load; and constructing an adaptive notch filter corresponding to the second-order resonance and anti-resonance stages of the second system identification model group.

[0009] In one implementation of this application, based on an adaptive notch filter, the controlled object model and weighting function of the piezoelectric ceramic displacement stage are transformed into state-space form to obtain an equivalent controlled object model and a weighting function corresponding to the closed-loop tracking bandwidth. Specifically, this includes: shaping the adaptive notch filter and integrating the shaped adaptive notch filter with the controlled object model to transform it into an updated equivalent controlled object model; performing state-space transformation on the updated equivalent controlled object model to determine the equivalent controlled object model; constructing the piezoelectric ceramic displacement stage control structure corresponding to the equivalent controlled object model and obtaining the system parameters of the piezoelectric ceramic displacement stage control structure; wherein, the system parameters include: input parameters, control quantity parameters, error parameters, output parameters, and disturbance parameters; calculating the corresponding weighting terms based on the input parameters, error parameters, and output parameters, and performing state-space transformation and function selection on the weighting terms until the sensitivity function and supplementary sensitivity function of the feedback control reach the preset expectation to obtain the weighting function.

[0010] In one implementation of this application, the weighting terms corresponding to the sensitivity function and the complementary sensitivity function are subjected to state-space transformation and function selection to obtain the weighting function. Specifically, this includes: performing state-space transformation on the weighting functions corresponding to the sensitivity function and the complementary sensitivity function to determine the weighting function represented in state space; and performing expected index analysis on the weighting function represented in state space to obtain the weighting function.

[0011] In one implementation of this application, by The robust control method calculates the control quantity of the piezoelectric ceramic displacement stage corresponding to the equivalent controlled object model. Specifically, it includes: calculating the positive definite solution of the equivalent controlled object model through the Riccati equation to obtain the matrix analysis variables corresponding to the feedback controller; calculating the feedback controller corresponding to the equivalent controlled object model based on the matrix analysis variables; and obtaining the control quantity of the piezoelectric ceramic displacement stage based on the feedback controller.

[0012] In one implementation of this application, by means of The robust control method, after calculating the control quantity of the piezoelectric ceramic displacement stage corresponding to the equivalent controlled object model, also includes: verifying the stability of the piezoelectric ceramic displacement stage control quantity until the piezoelectric ceramic displacement stage control quantity meets the preset simulation parameter requirements.

[0013] Secondly, embodiments of this application also provide a system identification and control device for a piezoelectric ceramic displacement stage, characterized in that the device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to implement a system identification and control method for a piezoelectric ceramic displacement stage.

[0014] Thirdly, embodiments of this application also provide a non-volatile computer storage medium for system identification and control of a piezoelectric ceramic displacement stage, storing computer-executable instructions, characterized in that the computer-executable instructions, when executed, can realize a system identification and control method for a piezoelectric ceramic displacement stage.

[0015] This application provides a system identification and control method, device, and medium for a piezoelectric ceramic displacement stage. By identifying the system related to the load mass in the s-domain of the piezoelectric ceramic displacement stage, system parameters associated with the control accuracy of the piezoelectric ceramic displacement stage are obtained. Based on the system parameters and the design of an adaptive notch filter based on the load mass, a piezoelectric ceramic displacement stage control system related to the load mass is constructed. This solves the technical problem of system instability of the piezoelectric ceramic displacement stage when the load changes in the prior art, realizes accurate control of the piezoelectric ceramic displacement stage when the load changes, and improves the stability of the piezoelectric ceramic displacement stage system when the load mass changes significantly. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 A flowchart illustrating a system identification and control method for a piezoelectric ceramic displacement stage provided in this application embodiment; Figure 2 A schematic diagram illustrating the resonant drift phenomenon of a piezoelectric ceramic displacement stage under different loads, provided in an embodiment of this application; Figure 3 A structural diagram of an adaptive notch filter based on load quality is provided for an embodiment of this application; Figure 4 A schematic diagram of the overall control structure of a piezoelectric ceramic displacement stage system provided in this application embodiment; Figure 5 A schematic diagram of a linear fractional transform (LFT) provided in an embodiment of this application; Figure 6 This is a schematic diagram of the internal structure of a system identification and control device for a piezoelectric ceramic displacement stage provided in an embodiment of this application. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0018] This application provides a system identification and control method, device, and medium for a piezoelectric ceramic displacement stage. By identifying the system related to the load mass in the s-domain of the piezoelectric ceramic displacement stage, system parameters associated with the control accuracy of the piezoelectric ceramic displacement stage are obtained. Based on the system parameters and the design of an adaptive notch filter based on the load mass, a piezoelectric ceramic displacement stage control system related to the load mass is constructed. This solves the technical problem of system instability of the piezoelectric ceramic displacement stage when the load changes in the prior art, realizes accurate control of the piezoelectric ceramic displacement stage when the load changes, and improves the stability of the piezoelectric ceramic displacement stage system when the load mass changes significantly.

[0019] The technical solutions proposed in the embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0020] Figure 1 A flowchart illustrating a system identification and control method for a piezoelectric ceramic displacement stage provided in an embodiment of this application. Figure 1 As shown in the embodiment of this application, a system identification and control method for a piezoelectric ceramic displacement stage specifically includes the following steps: Step 101: Construct a continuous system model of the piezoelectric ceramic displacement stage, and calculate the initial system parameters corresponding to the continuous system model through error analysis.

[0021] For example, Figure 1 A flowchart illustrating a system identification and control method for a piezoelectric ceramic displacement stage provided in this application embodiment.

[0022] As shown in the figure, the piezoelectric ceramic displacement stage is an important part of precision machining, and its displacement accuracy directly determines the machining accuracy. In actual working conditions, due to the different masses of the workpieces being machined, the characteristics of the piezoelectric ceramic displacement stage will also be different. This phenomenon is the resonance drift phenomenon of the piezoelectric ceramic displacement stage under different loads.

[0023] The occurrence of resonance drift can lead to the following problems during the operation of piezoelectric ceramic displacement stages: First, changes in the characteristics of the piezoelectric ceramic displacement stage system lead to reduced displacement accuracy and decreased machining precision. Second, significant variations in the load mass render the controller designed under nominal conditions unable to maintain system stability, causing system instability and preventing continued normal operation. Considering the controlled object model as a linear continuous system, this application constructs a continuous system model of the piezoelectric ceramic displacement stage and calculates the corresponding initial system parameters through error analysis. This achieves precision processing of the piezoelectric ceramic displacement stage identification system, improving the accuracy and stability of subsequent control of the piezoelectric ceramic displacement stage.

[0024] Specifically, through error analysis, the initial system parameters corresponding to the continuous system model are calculated, including: converting the time-domain data of the continuous system model into frequency-domain data, and setting a nonlinear first error parameter based on the frequency-domain data; replacing the first error parameter with a preset second error parameter, and calculating the initial system parameters corresponding to the second error parameter using the least squares method.

[0025] In one embodiment, since the controlled object model is a linear continuous system, the mathematical representation of the piezoelectric ceramic displacement stage model is as follows: (1) in, , For Lagrange operators; The transfer function for the controlled object model. for The molecular polynomial; The order of the numerator polynomial. for The denominator polynomial, Let be the order of the denominator polynomial.

[0026] Since the method used in this application is expanded in the s-domain, the input and output in the time domain first need to be numerically solved to obtain the frequency domain data (e.g., FFT).

[0027] definition For the first The frequency of each point, , The number of frequency points For the system at frequency The response is given below, and the first error parameter is defined as follows: .

[0028] In the system identification process, this application aims to obtain the most suitable parameters. This makes the error Minimum, that is: (2) The above formula is a nonlinear least squares problem because the unknowns exist in both the numerator and denominator. To transform the nonlinear least squares problem into a least squares problem, a new error is defined, namely the second error parameter: The corresponding least squares problem is: (3) For this least squares problem, the second error parameter It can be expressed by the following formula: (4) Step 102: Perform SK iteration on the initial identification parameters until the ratio of the first identification iteration parameter obtained by SK iteration to the adjacent second iteration system parameter satisfies the preset iteration condition, so as to determine the system parameters corresponding to the piezoelectric ceramic displacement stage.

[0029] For example, the above problem can be solved using the general linear least squares method. Solving the formula using the linear least squares method can yield a relatively accurate system model. However, the above... The corresponding problem is not entirely equivalent to The corresponding problem is that it involves implicit weighting. Make It cannot minimize the error .

[0030] Specifically, the initial identification parameters are subjected to SK iteration until the ratio of the first identification iteration parameter obtained by SK iteration to the adjacent second iteration system parameter satisfies a preset iteration condition, thereby determining the system parameters corresponding to the piezoelectric ceramic displacement stage. This includes: calculating the loss function corresponding to the iteration of the initial identification parameters, and performing SK iteration on the initial identification parameters based on the loss function to obtain the first identification iteration parameter and the second system parameter; wherein the iteration number corresponding to the first identification iteration parameter is greater than the iteration number corresponding to the second system parameter; calculating the ratio of the model denominator polynomial corresponding to the first identification iteration parameter and the model denominator polynomial corresponding to the second identification iteration parameter to obtain the iteration judgment coefficient; and, if the iteration judgment coefficient satisfies the preset iteration condition, calculating the minimization parameter corresponding to the loss function to determine the system parameters.

[0031] In one embodiment, when determining Given approximate values, an SK iteration approach can be used for optimization to find the desired result. parameters Let the initialization parameters obtained using the above identification method be . , No. The parameters for the next iteration are .

[0032] First, it is necessary to Calculation The value is used to define a new loss function. The following formula will be used to explain this.

[0033] (5) Based on the above loss function, when the following conditions are met... hour, and The corresponding questions are completely equivalent.

[0034] However, since the truth cannot be known... Value, so it can be assumed that when the first Before and after the next iteration D ( jω k , )and D ( jω k , When the preset conditions are met, it can be considered that End the iteration, with the following preset conditions: (6) in, It is a very small real number.

[0035] Finally, the solution needs to be found such that... Minimize parameters ,Right now: (7) Step 103: Obtain the load of the piezoelectric ceramic displacement stage, and based on the load, construct an adaptive notch filter whose system parameters are related to the load through load nonlinear mapping.

[0036] For example, since the characteristics of the piezoelectric ceramic displacement stage are related to the load, a relationship between mass and the system model can be established. This application constructs an adaptive notch filter that correlates system parameters with the load through load nonlinear mapping, providing a model basis for a load-based piezoelectric ceramic displacement stage control system.

[0037] Specifically, based on the load, an adaptive notch filter is constructed by nonlinearly mapping the load to determine the load grouping of the piezoelectric ceramic displacement stage. This includes: uniformly dividing the numerical range corresponding to the load into several parts to obtain the load grouping of the piezoelectric ceramic displacement stage; dividing the continuous system model into a first system identification model group corresponding to the load grouping, and performing load variable correlation on the system identification model group to determine the second system identification model group that correlates the system parameters with the load; and constructing the adaptive notch filter corresponding to the second resonance and anti-resonance stages of the second system identification model group.

[0038] Figure 3 This is a structural diagram of an adaptive notch filter based on load quality, provided in an embodiment of this application.

[0039] In one embodiment, the mass carried by the piezoelectric ceramic displacement stage is defined as... , ;in The maximum load capacity of the system can be represented by the following model: If it is known that the system is in any The model at that location can be obtained by... The resonant part is inverted to achieve more accurate zero-pole cancellation, but in practice, establishing an accurate and continuous [resonance] is more challenging. It is almost impossible, therefore it is possible Divided into 10 parts, namely .

[0040] Let the piezoelectric ceramic system models under the above 10 load conditions be as follows: The identification method for these 10 models is the same as the identification method described above.

[0041] The second-order resonance and anti-resonance elements in the above 10 models are extracted, and their parameters are mapped to the load quality information using a nonlinear function. The results are explained by the following formula.

[0042] (8) in, For gain, The ellipsis represents the time constant, and the ellipsis indicates that similar parts (i.e., polynomials related to s) are omitted and multiplied.

[0043] The notch filter for the second-order resonant and anti-resonant circuits is represented as follows: (9) Among them, parameters , , and These are variables related to load quality. When constructing a nonlinear mapping model, it is recommended to include the input features... higher-order terms (such as) , , ) as the input basis of the model.

[0044] Step 104: Based on the adaptive notch filter, the controlled object model and weighting function of the piezoelectric ceramic displacement stage are transformed into state-space form to obtain the equivalent controlled object model and the weighting function corresponding to the closed-loop tracking bandwidth.

[0045] For example, traditional hybrid sensitivity robust controllers, based on adaptive notch filters, require the design of weighting functions during optimization. Typically, at least two to three weighting functions need to be designed, and no quantitative design method is provided, which is inconvenient in engineering applications. This application transforms the controlled object model and weighting functions of the piezoelectric ceramic displacement stage into state-space form, obtaining an equivalent controlled object model and the weighting functions corresponding to the closed-loop tracking bandwidth. This achieves the construction of the equivalent controlled object model and the weighting functions corresponding to the closed-loop tracking bandwidth, eliminating the need for separate weighting function design and improving the convenience of piezoelectric ceramic displacement stages in engineering applications.

[0046] Specifically, based on the adaptive notch filter, the controlled object model and weighting function of the piezoelectric ceramic displacement stage are transformed into state-space form to obtain the equivalent controlled object model and the weighting function corresponding to the closed-loop tracking bandwidth. This includes: shaping the adaptive notch filter and integrating the shaped adaptive notch filter with the controlled object model to transform it into an updated equivalent controlled object model; performing state-space transformation on the updated equivalent controlled object model to determine the equivalent controlled object model; constructing the piezoelectric ceramic displacement stage control structure corresponding to the equivalent controlled object model and obtaining the system parameters of the piezoelectric ceramic displacement stage control structure; wherein, the system parameters include: input parameters, control quantity parameters, error parameters, output parameters, and disturbance parameters; based on the input parameters, error parameters, and output parameters, calculating the corresponding weighting terms, and performing state-space transformation and function selection on the weighting terms until the sensitivity function and supplementary sensitivity function of the feedback control reach the preset expectation to obtain the weighting function.

[0047] Furthermore, state-space transformation and function selection are performed on the weighting terms corresponding to the sensitivity function and the complementary sensitivity function to obtain the weighting function. Specifically, this includes: performing state-space transformation on the weighting functions corresponding to the sensitivity function and the complementary sensitivity function to determine the weighting function in state-space representation; and performing expected index analysis on the weighting function in state-space representation to obtain the weighting function.

[0048] Figure 4 A schematic diagram of the overall control structure of a piezoelectric ceramic displacement stage system provided in this application embodiment; In one embodiment, such as Figure 4 As shown, in the overall control structure of a piezoelectric ceramic displacement stage system, For input, To control the quantity, For error, For output, For disturbance, For noise, and Sensitivity function Complementary sensitivity function Weighted output, , , It is a feedback controller.

[0049] , , Constructing the sensitivity function Complementary sensitivity function The process can be represented as , , , and It can be represented as: (10) After adaptive notch filter shaping, the new equivalent controlled object is For error The weighting function is For output The weighting function is Its state space is represented as: (11) To address the complexity of weighting function selection, this application provides a method for selecting weighting functions, which can be implemented in practice using the following format: (12) in, The desired system closed-loop tracking bandwidth, in units of .

[0050] Step 105, through A robust control method is proposed, which calculates the control quantity of the piezoelectric ceramic displacement stage corresponding to the equivalent controlled object model.

[0051] For example, this application sets the ideal expected bandwidth, ideal expected settling time, and expected overshoot as quantitative indicators, eliminating the need for separate weighting function design. The optimization of the robust control method can yield a more ideal feedback controller, which solves the technical problem of system instability of the piezoelectric ceramic displacement stage when the load changes in the existing technology, realizes accurate control of the piezoelectric ceramic displacement stage when the load changes, and improves the stability of the piezoelectric ceramic displacement stage system when the load mass changes significantly.

[0052] Specifically, through The robust control method calculates the control quantity of the piezoelectric ceramic displacement stage corresponding to the equivalent controlled object model, including: calculating the positive definite solution of the equivalent controlled object model through the Riccati equation to obtain the matrix analysis variables corresponding to the feedback controller; calculating the feedback controller corresponding to the equivalent controlled object model based on the matrix analysis variables; and obtaining the control quantity of the piezoelectric ceramic displacement stage based on the feedback controller.

[0053] Furthermore, through The robust control method, after calculating the control quantity of the piezoelectric ceramic displacement stage corresponding to the equivalent controlled object model, also includes: verifying the stability of the piezoelectric ceramic displacement stage control quantity until the piezoelectric ceramic displacement stage control quantity meets the preset simulation parameter requirements.

[0054] Figure 5This is a schematic diagram of a linear fractional transform (LFT) provided in an embodiment of this application.

[0055] In one embodiment, for the linear fractional transform (LFT) , ,in, ; .

[0056] Robust controller (i.e., feedback controller) It can be calculated using the above formula: (13) in, ; ; .

[0057] and These are the positive definite solutions to the following Riccati equations: (14) The above are embodiments of the method proposed in this application. Based on the same inventive concept, embodiments of this application also provide a system identification and control device for a piezoelectric ceramic displacement stage, the structure of which is as follows: Figure 6 As shown.

[0058] Figure 6 This is a schematic diagram of the internal structure of a system identification and control device for a piezoelectric ceramic displacement stage, provided as an embodiment of this application. Figure 6 As shown, the device includes: At least one processor 601; And a memory 602 that is communicatively connected to at least one processor; The memory 602 stores instructions that can be executed by at least one processor. The instructions are executed by at least one processor 601 to enable at least one processor 601 to implement a system identification and control method such as a piezoelectric ceramic displacement stage.

[0059] Some embodiments of this application provide corresponding to Figure 1 A non-volatile computer storage medium for system identification and control of a piezoelectric ceramic displacement stage is provided, which stores computer-executable instructions. When the computer-executable instructions are executed, they can realize a system identification and control method for a piezoelectric ceramic displacement stage.

[0060] The various embodiments in this application are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the embodiments for IoT devices and media are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0061] The systems, media, and methods provided in this application are one-to-one correspondences. Therefore, the systems and media also have similar beneficial technical effects as their corresponding methods. Since the beneficial technical effects of the methods have been described in detail above, the beneficial technical effects of the systems and media will not be repeated here.

[0062] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0063] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0064] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0065] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0066] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0067] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0068] Computer-readable media include both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0069] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0070] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A system identification and control method for a piezoelectric ceramic displacement stage, characterized in that, The method includes: A continuous system model of a piezoelectric ceramic displacement stage is constructed, and the initial system parameters corresponding to the continuous system model are calculated through error analysis. The initial identification parameters are subjected to SK iteration until the ratio of the first identification iteration parameter obtained by the SK iteration to the adjacent second iteration system parameter satisfies the preset iteration condition, so as to determine the system parameters corresponding to the piezoelectric ceramic displacement stage. The load of the piezoelectric ceramic displacement stage is obtained, and based on the load, an adaptive notch filter related to the load is constructed through load nonlinear mapping; Based on the adaptive notch filter, the controlled object model and weighting function of the piezoelectric ceramic displacement stage are transformed into state-space form to obtain the equivalent controlled object model and the weighting function corresponding to the closed-loop tracking bandwidth. pass A robust control method is used to calculate the control quantity of the piezoelectric ceramic displacement stage corresponding to the equivalent controlled object model.

2. The system identification and control method for a piezoelectric ceramic displacement stage according to claim 1, characterized in that, Error analysis is used to calculate the initial system parameters corresponding to the continuous system model, specifically including: The time-domain data of the continuous system model is converted into frequency-domain data, and a nonlinear first error parameter is set based on the frequency-domain data. The first error parameter is replaced with a preset second error parameter, and the initial system parameters corresponding to the second error parameter are calculated using the least squares method.

3. The system identification and control method for a piezoelectric ceramic displacement stage according to claim 1, characterized in that, The initial identification parameters are subjected to SK iteration until the ratio of the first identification iteration parameter obtained by the SK iteration to the adjacent second iteration system parameter satisfies a preset iteration condition, thereby determining the system parameters corresponding to the piezoelectric ceramic displacement stage, specifically including: Calculate the loss function for the iteration corresponding to the initial identification parameters, and perform the SK iteration on the initial identification parameters based on the loss function to obtain the first identification iteration parameters and the second system parameters; wherein the number of iterations corresponding to the first identification iteration parameters is greater than the number of iterations corresponding to the second system parameters; Calculate the ratio of the model denominator polynomial corresponding to the first identification iteration parameter to the model denominator polynomial corresponding to the second identification iteration parameter to obtain the iteration judgment coefficient; If the iterative judgment coefficients satisfy the preset iterative conditions, the minimization parameters corresponding to the loss function are calculated to determine the system parameters.

4. The system identification and control method for a piezoelectric ceramic displacement stage according to claim 1, characterized in that, Based on the load, an adaptive notch filter whose system parameters are related to the load is constructed through load nonlinear mapping, specifically including: The numerical range corresponding to the load is evenly divided into several parts to obtain the load grouping of the piezoelectric ceramic displacement stage; The continuous system model is divided into a first system identification model group corresponding to the load group, and the load variables are associated with the system identification model group to determine a second system identification model group that associates the system parameters with the load. Construct adaptive notch filters corresponding to the second-order resonance and anti-resonance stages of the second system identification model group.

5. The system identification and control method for a piezoelectric ceramic displacement stage according to claim 1, characterized in that, Based on the adaptive notch filter, the controlled object model and weighting function of the piezoelectric ceramic displacement stage are transformed into state-space form, resulting in an equivalent controlled object model and a weighting function corresponding to the closed-loop tracking bandwidth, specifically including: The adaptive notch filter is shaped, and the shaped adaptive notch filter is integrated with the controlled object model to transform it into an updated equivalent controlled object model. The updated equivalent controlled object model is subjected to state-space transformation to determine the equivalent controlled object model; Construct a piezoelectric ceramic displacement stage control structure corresponding to the equivalent controlled object model, and obtain the system parameters of the piezoelectric ceramic displacement stage control structure; wherein, the system parameters include: input parameters, control quantity parameters, error parameters, output parameters, and disturbance parameters; Based on the input parameters, error parameters, and output parameters, the corresponding weighting terms are calculated, and state-space transformation and function selection are performed on the weighting terms until the sensitivity function and supplementary sensitivity function of the feedback control reach the preset expectation, so as to obtain the weighting function.

6. The system identification and control method for a piezoelectric ceramic displacement stage according to claim 5, characterized in that, The weighting terms corresponding to the sensitivity function and the complementary sensitivity function are subjected to state-space transformation and function selection to obtain the weighting function, specifically including: The weighting functions corresponding to the sensitivity function and the complementary sensitivity function are subjected to state-space transformation to determine the weighting functions in state-space representation; The weighting function of the state space representation is subjected to expected index analysis to obtain the weighting function.

7. The system identification and control method for a piezoelectric ceramic displacement stage according to claim 1, characterized in that, pass The robust control method calculates the control quantity of the piezoelectric ceramic displacement stage corresponding to the equivalent controlled object model, specifically including: The positive definite solution of the equivalent controlled object model is calculated using the Riccati equation, and the matrix analysis variables corresponding to the feedback controller are obtained. Based on the matrix analysis variables, the feedback controller corresponding to the equivalent controlled object model is calculated, and based on the feedback controller, the control quantity of the piezoelectric ceramic displacement stage is obtained.

8. The system identification and control method for a piezoelectric ceramic displacement stage according to claim 1, characterized in that, In passing The robust control method, after calculating the control quantity of the piezoelectric ceramic displacement stage corresponding to the equivalent controlled object model, further includes: The stability of the control quantity of the piezoelectric ceramic displacement stage is verified until the control quantity of the piezoelectric ceramic displacement stage meets the preset simulation parameter requirements.

9. A system identification and control device for a piezoelectric ceramic displacement stage, characterized in that, The device includes: At least one processor; And, a memory communicatively connected to the at least one processor; The memory stores instructions that can be executed by the at least one processor, which are executed by the at least one processor to enable the at least one processor to implement a system identification and control method for a piezoelectric ceramic displacement stage as described in any one of claims 1-8.

10. A non-volatile computer storage medium for system identification and control of a piezoelectric ceramic displacement stage, storing computer-executable instructions, characterized in that, When the computer-executable instructions are executed, they can realize the system identification and control method of a piezoelectric ceramic displacement stage as described in any one of claims 1-8.

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